Patent Publication Number: US-11658733-B2

Title: Base station and communication scheme executed by a base station

Description:
TECHNICAL FIELD 
     This application is based on applications (1) No. 2011-093539, (2) No. 2011-102099, (3) No. 2011-118453, (4) No. 2011-140747, and (5) No. 2011-192123 filed in Japan, the contents of which are hereby incorporated by reference. 
     The present invention relates to a precoding scheme, a precoding device, a transmission scheme, a transmission device, a reception scheme, and a reception device that in particular perform communication using a multi-antenna. 
     BACKGROUND ART 
     Multiple-Input Multiple-Output (MIMO) is a conventional example of a communication scheme using a multi-antenna. In multi-antenna communication, of which MIMO is representative, multiple transmission signals are each modulated, and each modulated signal is transmitted from a different antenna simultaneously in order to increase the transmission speed of data. 
       FIG.  28    shows an example of the structure of a transmission and reception device when the number of transmit antennas is two, the number of receive antennas is two, and the number of modulated signals for transmission (transmission streams) is two. In the transmission device, encoded data is interleaved, the interleaved data is modulated, and frequency conversion and the like is performed to generate transmission signals, and the transmission signals are transmitted from antennas. In this case, the scheme for simultaneously transmitting different modulated signals from different transmit antennas at the same time and at the same frequency is a spatial multiplexing MIMO system. 
     In this context, it has been suggested in Patent Literature 1 to use a transmission device provided with a different interleave pattern for each transmit antenna. In other words, the transmission device in  FIG.  28    would have two different interleave patterns with respective interleaves (πa, πb). As shown in Non-Patent Literature 1 and Non-Patent Literature 2, reception quality is improved in the reception device by iterative performance of a detection scheme that uses soft values (the MIMO detector in  FIG.  28   ). 
     Models of actual propagation environments in wireless communications include non-line of sight (NLOS), of which a Rayleigh fading environment is representative, and line of sight (LOS), of which a Rician fading environment is representative. When the transmission device transmits a single modulated signal, and the reception device performs maximal ratio combining on the signals received by a plurality of antennas and then demodulates and decodes the signal resulting from maximal ratio combining, excellent reception quality can be achieved in an LOS environment, in particular in an environment where the Rician factor is large, which indicates the ratio of the received power of direct waves versus the received power of scattered waves. However, depending on the transmission system (for example, spatial multiplexing MIMO system), a problem occurs in that the reception quality deteriorates as the Rician factor increases (see Non-Patent Literature 3). 
       FIGS.  29 A and  29 B  show an example of simulation results of the Bit Error Rate (BER) characteristics (vertical axis: BER, horizontal axis: signal-to-noise power ratio (SNR)) for data encoded with low-density parity-check (LDPC) code and transmitted over a 2×2 (two transmit antennas, two receive antennas) spatial multiplexing MIMO system in a Rayleigh fading environment and in a Rician fading environment with Rician factors of K=3, 10, and 16 dB.  FIG.  29 A  shows the BER characteristics of Max-log A Posteriori Probability (APP) without iterative detection (see Non-Patent Literature 1 and Non-Patent Literature 2), and  FIG.  29 B  shows the BER characteristics of Max-log-APP with iterative detection (see Non-Patent Literature 1 and Non-Patent Literature 2) (number of iterations: five). As is clear from  FIGS.  29 A and  29 B , regardless of whether iterative detection is performed, reception quality degrades in the spatial multiplexing MIMO system as the Rician factor increases. It is thus clear that the unique problem of “degradation of reception quality upon stabilization of the propagation environment in the spatial multiplexing MIMO system”, which does not exist in a conventional single modulation signal transmission system, occurs in the spatial multiplexing MIMO system. 
     Broadcast or multicast communication is a service directed towards line-of-sight users. The radio wave propagation environment between the broadcasting station and the reception devices belonging to the users is often an LOS environment. When using a spatial multiplexing MIMO system having the above problem for broadcast or multicast communication, a situation may occur in which the received electric field strength is high at the reception device, but degradation in reception quality makes it impossible to receive the service. In other words, in order to use a spatial multiplexing MIMO system in broadcast or multicast communication in both an NLOS environment and an LOS environment, there is a desire for development of a MIMO system that offers a certain degree of reception quality. 
     Non-Patent Literature 8 describes a scheme to select a codebook used in precoding (i.e. a precoding matrix, also referred to as a precoding weight matrix) based on feedback information from a communication partner. Non-Patent Literature 8 does not at all disclose, however, a scheme for precoding in an environment in which feedback information cannot be acquired from the communication partner, such as in the above broadcast or multicast communication. 
     On the other hand, Non-Patent Literature 4 discloses a scheme for hopping the precoding matrix over time. This scheme can be applied even when no feedback information is available. Non-Patent Literature 4 discloses using a unitary matrix as the matrix for precoding and hopping the unitary matrix at random but does not at all disclose a scheme applicable to degradation of reception quality in the above-described LOS environment. Non-Patent Literature 4 simply recites hopping between precoding matrices at random. Obviously, Non-Patent Literature 4 makes no mention whatsoever of a precoding scheme, or a structure of a precoding matrix, for remedying degradation of reception quality in an LOS environment. 
     CITATION LIST 
     Patent Literature 
     
         
         Patent Literature 1: WO 2005/050885 
       
    
     Non-Patent Literature 
     
         
         Non-Patent Literature 1: “Achieving near-capacity on a multiple-antenna channel”, IEEE Transaction on Communications, vol. 51, no. 3, pp. 389-399, March 2003. 
         Non-Patent Literature 2: “Performance analysis and design optimization of LDPC-coded MIMO OFDM systems”, IEEE Trans. Signal Processing, vol. 52, no. 2, pp. 348-361, February 2004. 
         Non-Patent Literature 3: “BER performance evaluation in 2×2 MIMO spatial multiplexing systems under Rician fading channels”, IEICE Trans. Fundamentals, vol. E91-A, no. 10, pp. 2798-2807, October 2008. 
         Non-Patent Literature 4: “Turbo space-time codes with time varying linear transformations”, IEEE Trans. Wireless communications, vol. 6, no. 2, pp. 486-493, February 2007. 
         Non-Patent Literature 5: “Likelihood function for QR-MLD suitable for soft-decision turbo decoding and its performance”, IEICE Trans. Commun., vol. E88-B, no. 1, pp. 47-57, January 2004. 
         Non-Patent Literature 6: “A tutorial on ‘parallel concatenated (Turbo) coding’, ‘Turbo (iterative) decoding’ and related topics”, The Institute of Electronics, Information, and Communication Engineers, Technical Report IT 98-51. 
         Non-Patent Literature 7: “Advanced signal processing for PLCs: Wavelet-OFDM”, Proc. of IEEE International symposium on ISPLC 2008, pp. 187-192, 2008. 
         Non-Patent Literature 8: D. J. Love, and R. W. Heath, Jr., “Limited feedback unitary precoding for spatial multiplexing systems”, IEEE Trans. Inf. Theory, vol. 51, no. 8, pp. 2967-2976, August 2005. 
         Non-Patent Literature 9: DVB Document A122, Framing structure, channel coding and modulation for a second generation digital terrestrial television broadcasting system, (DVB-T2), June 2008. 
         Non-Patent Literature 10: L. Vangelista, N. Benvenuto, and S. Tomasin, “Key technologies for next-generation terrestrial digital television standard DVB-T2”, IEEE Commun. Magazine, vol. 47, no. 10, pp. 146-153, October 2009. 
         Non-Patent Literature 11: T. Ohgane, T. Nishimura, and Y. Ogawa, “Application of space division multiplexing and those performance in a MIMO channel”, IEICE Trans. Commun., vol. E88-B, no. 5, pp. 1843-1851, May 2005. 
         Non-Patent Literature 12: R. G. Gallager, “Low-density parity-check codes”, IRE Trans. Inform. Theory, IT-8, pp. 21-28, 1962. 
         Non-Patent Literature 13: D. J. C. Mackay, “Good error-correcting codes based on very sparse matrices”, IEEE Trans. Inform. Theory, vol. 45, no. 2, pp. 399-431, March 1999. 
         Non-Patent Literature 14: ETSI EN 302 307, “Second generation framing structure, channel coding and modulation systems for broadcasting, interactive services, news gathering and other broadband satellite applications”, v. 1.1.2, June 2006. 
         Non-Patent Literature 15: Y.-L. Ueng, and C.-C. Cheng, “A fast-convergence decoding method and memory-efficient VLSI decoder architecture for irregular LDPC codes in the IEEE 802.16e standards”, IEEE VTC-2007 Fall, pp. 1255-1259. 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     It is an object of the present invention to provide a MIMO system that improves reception quality in an LOS environment. 
     Solution to Problem 
     To solve the above problem, the present invention provides a precoding method for generating, from a plurality of signals which are based on a selected modulation scheme and represented by in-phase components and quadrature components, a plurality of precoded signals that are transmitted in the same frequency band at the same time and transmitting the generated precoded signals, the precoding method comprising: selecting one precoding weight matrix from among a plurality of precoding weight matrices by regularly hopping between the matrices; and generating the plurality of precoded signals by multiplying the selected precoding weight matrix by the plurality of signals which are based on the selected modulation scheme, the plurality of precoding weight matrices being nine matrices expressed, using a positive real number a, as Equations 339 through 347 (details are described below). 
     According to each aspect of the above invention, precoded signals, which are generated by precoding signals by using one precoding weight matrix selected from among a plurality of precoding weight matrices by regularly hopping between the matrices, are transmitted and received. Thus the precoding weight matrix used in the precoding is any of a plurality of precoding weight matrices that have been predetermined. This makes it possible to improve the reception quality in an LOS environment based on the design of the plurality of precoding weight matrices. 
     Advantageous Effects of Invention 
     With the above structure, the present invention provides a precoding method, a precoding device, a transmission method, a reception method, a transmission device, and a reception device that remedy degradation of reception quality in an LOS environment, thereby providing high-quality service to LOS users during broadcast or multicast communication. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is an example of the structure of a transmission device and a reception device in a spatial multiplexing MIMO system. 
         FIG.  2    is an example of a frame structure. 
         FIG.  3    is an example of the structure of a transmission device when adopting a scheme of hopping between precoding weights. 
         FIG.  4    is an example of the structure of a transmission device when adopting a scheme of hopping between precoding weights. 
         FIG.  5    is an example of a frame structure. 
         FIG.  6    is an example of a scheme of hopping between precoding weights. 
         FIG.  7    is an example of the structure of a reception device. 
         FIG.  8    is an example of the structure of a signal processing unit in a reception device. 
         FIG.  9    is an example of the structure of a signal processing unit in a reception device. 
         FIG.  10    shows a decoding processing scheme. 
         FIG.  11    is an example of reception conditions. 
         FIGS.  12 A and  12 B  are examples of BER characteristics. 
         FIG.  13    is an example of the structure of a transmission device when adopting a scheme of hopping between precoding weights. 
         FIG.  14    is an example of the structure of a transmission device when adopting a scheme of hopping between precoding weights. 
         FIGS.  15 A and  15 B  are examples of a frame structure. 
         FIGS.  16 A and  16 B  are examples of a frame structure. 
         FIGS.  17 A and  17 B  are examples of a frame structure. 
         FIGS.  18 A and  18 B  are examples of a frame structure. 
         FIGS.  19 A and  19 B  are examples of a frame structure. 
         FIG.  20    shows positions of poor reception quality points. 
         FIG.  21    shows positions of poor reception quality points. 
         FIG.  22    is an example of a frame structure. 
         FIG.  23    is an example of a frame structure. 
         FIGS.  24 A and  24 B  are examples of mapping schemes. 
         FIGS.  25 A and  25 B  are examples of mapping schemes. 
         FIG.  26    is an example of the structure of a weighting unit. 
         FIG.  27    is an example of a scheme for reordering symbols. 
         FIG.  28    is an example of the structure of a transmission device and a reception device in a spatial multiplexing MIMO system. 
         FIGS.  29 A and  29 B  are examples of BER characteristics. 
         FIG.  30    is an example of a 2×2 MIMO spatial multiplexing MIMO system. 
         FIGS.  31 A and  31 B  show positions of poor reception points. 
         FIG.  32    shows positions of poor reception points. 
         FIGS.  33 A and  33 B  show positions of poor reception points. 
         FIG.  34    shows positions of poor reception points. 
         FIGS.  35 A and  35 B  show positions of poor reception points. 
         FIG.  36    shows an example of minimum distance characteristics of poor reception points in an imaginary plane. 
         FIG.  37    shows an example of minimum distance characteristics of poor reception points in an imaginary plane. 
         FIGS.  38 A and  38 B  show positions of poor reception points. 
         FIGS.  39 A and  39 B  show positions of poor reception points. 
         FIG.  40    is an example of the structure of a transmission device in Embodiment 7. 
         FIG.  41    is an example of the frame structure of a modulated signal transmitted by the transmission device. 
         FIGS.  42 A and  42 B  show positions of poor reception points. 
         FIGS.  43 A and  43 B  show positions of poor reception points. 
         FIGS.  44 A and  44 B  show positions of poor reception points. 
         FIGS.  45 A and  45 B  show positions of poor reception points. 
         FIGS.  46 A and  46 B  show positions of poor reception points. 
         FIGS.  47 A and  47 B  are examples of a frame structure in the time and frequency domains. 
         FIGS.  48 A and  48 B  are examples of a frame structure in the time and frequency domains. 
         FIG.  49    shows a signal processing scheme. 
         FIG.  50    shows the structure of modulated signals when using space-time block coding. 
         FIG.  51    is a detailed example of a frame structure in the time and frequency domains. 
         FIG.  52    is an example of the structure of a transmission device. 
         FIG.  53    is an example of a structure of the modulated signal generating units # 1 -#M in  FIG.  52   . 
         FIG.  54    shows the structure of the OFDM related processors ( 5207 _ 1  and  5207 _ 2 ) in  FIG.  52   . 
         FIGS.  55 A and  55 B  are detailed examples of a frame structure in the time and frequency domains. 
         FIG.  56    is an example of the structure of a reception device. 
         FIG.  57    shows the structure of the OFDM related processors ( 5600 _X and  5600 _Y) in  FIG.  56   . 
         FIGS.  58 A and  58 B  are detailed examples of a frame structure in the time and frequency domains. 
         FIG.  59    is an example of a broadcasting system. 
         FIGS.  60 A and  60 B  show positions of poor reception points. 
         FIG.  61    is an example of the frame structure. 
         FIG.  62    is an example of a frame structure in the time and frequency domain. 
         FIG.  63    is an example of a structure of a transmission device. 
         FIG.  64    is an example of a frame structure in the frequency and time domain. 
         FIG.  65    is an example of the frame structure. 
         FIG.  66    is an example of symbol arrangement scheme. 
         FIG.  67    is an example of symbol arrangement scheme. 
         FIG.  68    is an example of symbol arrangement scheme. 
         FIG.  69    is an example of the frame structure. 
         FIG.  70    shows a frame structure in the time and frequency domain. 
         FIG.  71    is an example of a frame structure in the time and frequency domain. 
         FIG.  72    is an example of a structure of a transmission device. 
         FIG.  73    is an example of a structure of a reception device. 
         FIG.  74    is an example of a structure of a reception device. 
         FIG.  75    is an example of a structure of a reception device. 
         FIGS.  76 A and  76 B  show examples of a frame structure in a frequency-time domain. 
         FIGS.  77 A and  77 B  show examples of a frame structure in a frequency-time domain. 
         FIGS.  78 A and  78 B  show a result of allocating precoding matrices. 
         FIGS.  79 A and  79 B  show a result of allocating precoding matrices. 
         FIGS.  80 A and  80 B  show a result of allocating precoding matrices. 
         FIG.  81    is an example of the structure of a signal processing unit. 
         FIG.  82    is an example of the structure of a signal processing unit. 
         FIG.  83    is an example of the structure of the transmission device. 
         FIG.  84    shows the overall structure of a digital broadcasting system. 
         FIG.  85    is a block diagram showing an example of the structure of a reception device. 
         FIG.  86    shows the structure of multiplexed data. 
         FIG.  87    schematically shows how each stream is multiplexed in the multiplexed data. 
         FIG.  88    shows in more detail how a video stream is stored in a sequence of PES packets. 
         FIG.  89    shows the structure of a TS packet and a source packet in multiplexed data. 
         FIG.  90    shows the data structure of a PMT. 
         FIG.  91    shows the internal structure of multiplexed data information. 
         FIG.  92    shows the internal structure of stream attribute information. 
         FIG.  93    is a structural diagram of a video display and an audio output device. 
         FIG.  94    is an example of signal point layout for 16QAM. 
         FIG.  95    is an example of signal point layout for QPSK. 
         FIG.  96    shows a baseband signal hopping unit. 
         FIG.  97    shows the number of symbols and the number of slots. 
         FIG.  98    shows the number of symbols and the number of slots. 
         FIGS.  99 A and  99 B  each show a structure of a frame structure. 
         FIG.  100    shows the number of slots. 
         FIG.  101    shows the number of shots. 
         FIG.  102    shows a PLP in the time and frequency domain. 
         FIG.  103    shows a structure of the PLP. 
         FIG.  104    shows a PLP in the time and frequency domain. 
         FIG.  105    schematically shows absolute values of a log-likelihood ratio obtained by the reception device. 
         FIG.  106    schematically shows absolute values of a log-likelihood ratio obtained by the reception device. 
         FIG.  107    is an example of a structure of a signal processing unit pertaining to a weighting combination unit. 
         FIG.  108    is an example of a structure of the signal processing unit pertaining to the weighting combination unit. 
         FIG.  109    is an example of signal point layout in the I-Q plane for 64QAM. 
         FIG.  110    shows a chart pertaining to the precoding matrices. 
         FIG.  111    shows a chart pertaining to the precoding matrices. 
         FIG.  112    is an example of a structure of the signal processing unit pertaining to the weighting combination unit. 
         FIG.  113    is an example of a structure of the signal processing unit pertaining to the weighting combination unit. 
         FIG.  114    shows a chart pertaining to the precoding matrices. 
         FIG.  115    shows a chart pertaining to the precoding matrices. 
         FIG.  116    is an example of a structure of the signal processing unit pertaining to the weighting combination unit. 
         FIG.  117    is an example of signal point layout. 
         FIG.  118    shows a relationship of positions of signal points. 
         FIG.  119    shows a structure of a weighting unit (precoding unit) and its surroundings. 
         FIG.  120    is an example of signal point layout. 
         FIG.  121    shows a structure of a weighting unit (precoding unit) and its surroundings. 
         FIG.  122    is an example of signal point layout. 
         FIG.  123    is an example of signal point layout. 
         FIG.  124    is an example of signal point layout. 
         FIG.  125    shows a structure of a weighting unit (precoding unit) and its surroundings. 
         FIG.  126    is an example of signal point layout. 
         FIG.  127    shows a structure of a weighting unit (precoding unit) and its surroundings. 
         FIG.  128    is an example of signal point layout. 
         FIG.  129    is an example of signal point layout. 
         FIG.  130    is an example of signal point layout. 
         FIG.  131    is an example of signal point layout. 
         FIG.  132    is an example of signal point layout. 
         FIG.  133    is an example of signal point layout. 
         FIG.  134    is an example of a structure of a signal generating unit. 
         FIG.  135    shows in-phase components and quadrature components of baseband signals. 
         FIG.  136    is an example of a structure of the signal generating unit. 
         FIG.  137    is an example of a structure of the signal generating unit. 
         FIG.  138    shows in-phase components and quadrature components of baseband signals. 
         FIG.  139    is an example of a structure of the signal generating unit. 
         FIG.  140    is an example of a structure of the signal generating unit. 
         FIG.  141    shows the outline of a reception system. 
         FIG.  142    shows the structure of a reception system. 
         FIG.  143    shows the structure of a reception system. 
         FIG.  144    shows the structure of a reception system. 
         FIG.  145    shows the structure of a television. 
         FIG.  146    shows the structure of a reception system. 
         FIG.  147    shows a conceptual diagram of broadcast waves of terrestrial digital television broadcast in portion (a), and shows a conceptual diagram of broadcast waves of BS broadcast in portion (b). 
         FIG.  148    shows a conceptual diagram of received signals before filtering in portion (a), and shows elimination of a received signal having a frequency band at which a plurality of modulated signals have been transmitted from a broadcast station by a plurality of antennas in portion (b). 
         FIG.  149    shows a conceptual diagram of received signals before frequency conversion in portion (a), and shows frequency conversion of received signals having a frequency band at which a plurality of modulated signals have been transmitted from a broadcast station by a plurality of antennas in portion (b). 
         FIG.  150    shows a conceptual diagram of received signals before frequency conversion in portion (a), and shows frequency conversion of received signals having a frequency band at which a plurality of modulated signals have been transmitted from a broadcast station by a plurality of antennas in portion (b). 
         FIG.  151    shows frequency arrangement for leading signals to houses via a single signal line in the case shown in  FIG.  149   . 
         FIG.  152    shows frequency arrangement for leading signals to houses via a single signal line in the case shown in  FIG.  150   . 
         FIG.  153    shows an example of settings of a relay device for community reception in an apartment building in portion (a), shows an example of settings of a relay device for an individual house in portion (b), and shows an example of settings of a relay device for a cable television system operator in portion (c). 
         FIG.  154    shows a conceptual diagram of the data structure of a received television broadcast. 
         FIG.  155    shows an example of the structure of a relay device for a cable television system operator. 
         FIG.  156    shows an example of the structure of a signal processing unit. 
         FIG.  157    shows an example of the structure of a distribution data generating unit. 
         FIG.  158    shows an example of signals before combining. 
         FIG.  159    shows an example of signals after combining. 
         FIG.  160    shows an example of the structure of a television reception device. 
         FIG.  161    shows an example of the structure of a relay device for a cable television system operator. 
         FIG.  162    shows an example of multicast communication in portion (a), shows an example of unicast communication with feedback in portion (b), and shows an example of unicast communication without feedback in portion (c). 
         FIG.  163    shows an example of the structure of a transmission device. 
         FIG.  164    shows an example of the structure of a reception device having a feedback function. 
         FIG.  165    shows an example of the frame structure of CSI. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     The following describes embodiments of the present invention with reference to the drawings. 
     Embodiment 1 
     The following describes the transmission scheme, transmission device, reception scheme, and reception device of the present embodiment. 
     Prior to describing the present embodiment, an overview is provided of a transmission scheme and decoding scheme in a conventional spatial multiplexing MIMO system. 
       FIG.  1    shows the structure of an N t ×N r  spatial multiplexing MIMO system. An information vector z is encoded and interleaved. As output of the interleaving, an encoded bit vector u=(u 1 , . . . , u Nt ) is acquired. Note that u i =(u i1 , . . . , u iM ) (where M is the number of transmission bits per symbol). Letting the transmission vector s=(s 1 , . . . , s Nt ) T  and the transmission signal from transmit antenna # 1  be represented as s i =map(u i ), the normalized transmission energy is represented as E{|s i | 2 }=Es/Nt (E s  being the total energy per channel). Furthermore, letting the received vector be y=(y 1 , . . . , y Nr ) T , the received vector is represented as in Equation 1. 
     
       
         
           
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     In this Equation, H NtNr  is the channel matrix, n=(n 1 , . . . , n Nr ) T  is the noise vector, and n i  is the i.i.d. complex Gaussian random noise with an average value 0 and variance σ 2 . From the relationship between transmission symbols and reception symbols that is induced at the reception device, the probability for the received vector may be provided as a multi-dimensional Gaussian distribution, as in Equation 2. 
     
       
         
           
             
               
                 
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     Here, a reception device that performs iterative decoding composed of an outer soft-in/soft-out decoder and a MIMO detector, as in  FIG.  1   , is considered. The vector of a log-likelihood ratio (L-value) in  FIG.  1    is represented as in Equations 3-5. 
                   Math   ⁢         3                        L   ⁡   (   u   )     =       (       L   ⁡   (     u   1     )     ,   …         ,     L   ⁡   (     u     N   t       )       )     T             Equation   ⁢         3                           Math   ⁢         4                        L   ⁡   (     u   i     )     =     (       L   ⁡   (     u     i   ⁢   1       )     ,   …         ,     L   ⁡   (     u   iM     )       )               Equation   ⁢         4                             Math   ⁢         5                        L   ⁡   (     u   ij     )     =     ln   ⁢       P   ⁡   (       u   ij     =     +   1       )       P   ⁡   (       u   ij     =     -   1       )                 Equation   ⁢         5               
&lt;Iterative Detection Scheme&gt;
 
     The following describes iterative detection of MIMO signals in the N t ×N r  spatial multiplexing MIMO system. 
     The log-likelihood ratio of u mn  is defined as in Equation 6. 
     
       
         
           
             
               
                 
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                             ❘ 
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                           ) 
                         
                         = 
                           
                         
                           ln 
                           ⁢ 
                           
                             
                               
                                 p 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     y 
                                     ❘ 
                                     
                                       u 
                                       mn 
                                     
                                   
                                   = 
                                   
                                     + 
                                     1 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 P 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     u 
                                     mn 
                                   
                                   = 
                                   
                                     + 
                                     1 
                                   
                                 
                                 ) 
                               
                               / 
                               
                                 p 
                                 ⁡ 
                                 ( 
                                 y 
                                 ) 
                               
                             
                             
                               
                                 p 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     y 
                                     ❘ 
                                     
                                       u 
                                       mn 
                                     
                                   
                                   = 
                                   
                                     - 
                                     1 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 P 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     u 
                                     mn 
                                   
                                   = 
                                   
                                     - 
                                     1 
                                   
                                 
                                 ) 
                               
                               / 
                               
                                 p 
                                 ⁡ 
                                 ( 
                                 y 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         
                           
                             ln 
                             ⁢ 
                             
                               
                                 P 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     u 
                                     mn 
                                   
                                   = 
                                   
                                     + 
                                     1 
                                   
                                 
                                 ) 
                               
                               
                                 P 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     u 
                                     mn 
                                   
                                   = 
                                   
                                     - 
                                     1 
                                   
                                 
                                 ) 
                               
                             
                           
                           + 
                           
                             ln 
                             ⁢ 
                             
                               
                                 p 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     y 
                                     ❘ 
                                     
                                       u 
                                       mn 
                                     
                                   
                                   = 
                                   
                                     + 
                                     1 
                                   
                                 
                                 ) 
                               
                               
                                 p 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     y 
                                     ❘ 
                                     
                                       u 
                                       mn 
                                     
                                   
                                   = 
                                   
                                     - 
                                     1 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         
                           
                             ln 
                             ⁢ 
                             
                               
                                 P 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     u 
                                     mn 
                                   
                                   = 
                                   
                                     + 
                                     1 
                                   
                                 
                                 ) 
                               
                               
                                 P 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     u 
                                     mn 
                                   
                                   = 
                                   
                                     - 
                                     1 
                                   
                                 
                                 ) 
                               
                             
                           
                           + 
                           
                             ln 
                             ⁢ 
                             
                               
                                 
                                   ∑ 
                                   
                                     U 
                                     
                                       mn 
                                       , 
                                       
                                         + 
                                         1 
                                       
                                     
                                   
                                 
                                 
                                   
                                     p 
                                     ⁡ 
                                     ( 
                                     
                                       y 
                                       ❘ 
                                       u 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     p 
                                     ⁡ 
                                     ( 
                                     
                                       u 
                                       ❘ 
                                       
                                         u 
                                         mn 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               
                                 
                                   ∑ 
                                   
                                     U 
                                     
                                       mn 
                                       , 
                                       
                                         - 
                                         1 
                                       
                                     
                                   
                                 
                                 
                                   
                                     p 
                                     ⁡ 
                                     ( 
                                     
                                       y 
                                       ❘ 
                                       u 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     p 
                                     ⁡ 
                                     ( 
                                     
                                       u 
                                       ❘ 
                                       
                                         u 
                                         mn 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   7 
                 
               
             
           
         
       
     
     Let U mn,±1 ={u|u mn =±1}. When approximating ln Σa j ˜max ln a j , an approximation of Equation 7 can be sought as Equation 8. Note that the above symbol “˜” indicates approximation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   8 
                 
               
               
                  
               
             
             
               
                 
                   
                     L 
                     ⁡ 
                     ( 
                     
                       
                         u 
                         mn 
                       
                       ❘ 
                       y 
                     
                     ) 
                   
                   ≈ 
                   
                     
                       ln 
                       ⁢ 
                       
                         
                           P 
                           ⁡ 
                           ( 
                           
                             
                               u 
                               mn 
                             
                             = 
                             
                               + 
                               1 
                             
                           
                           ) 
                         
                         
                           P 
                           ⁡ 
                           ( 
                           
                             
                               u 
                               mn 
                             
                             = 
                             
                               - 
                               1 
                             
                           
                           ) 
                         
                       
                     
                     + 
                     
                       
                         max 
                         
                           U 
                           
                             mn 
                             , 
                             
                               + 
                               1 
                             
                           
                         
                       
                          
                       
                         { 
                         
                           
                             ln 
                             ⁢ 
                             
                               p 
                               ⁡ 
                               ( 
                               
                                 y 
                                 ❘ 
                                 u 
                               
                               ) 
                             
                           
                           + 
                           
                             p 
                             ⁡ 
                             ( 
                             
                               u 
                               ❘ 
                               
                                 u 
                                 mn 
                               
                             
                             ) 
                           
                         
                         } 
                       
                     
                     - 
                     
                       
                         max 
                         
                           U 
                           
                             mn 
                             , 
                             
                               - 
                               1 
                             
                           
                         
                       
                          
                       
                         { 
                         
                           
                             ln 
                             ⁢ 
                             
                               p 
                               ⁡ 
                               ( 
                               
                                 y 
                                 ❘ 
                                 u 
                               
                               ) 
                             
                           
                           + 
                           
                             p 
                             ⁡ 
                             ( 
                             
                               u 
                               ❘ 
                               
                                 u 
                                 mn 
                               
                             
                             ) 
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   8 
                 
               
             
           
         
       
     
     P(u|u mn ) and ln P(u|u mn ) in Equation 8 are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   9 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         
                           P 
                           ⁡ 
                           ( 
                           
                             u 
                             ❘ 
                             
                               u 
                               mn 
                             
                           
                           ) 
                         
                         = 
                           
                         
                           
                             ∏ 
                             
                               
                                 ( 
                                 ij 
                                 ) 
                               
                               ≠ 
                               
                                 ( 
                                 mn 
                                 ) 
                               
                             
                           
                           
                             P 
                             ⁡ 
                             ( 
                             
                               u 
                               ij 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         
                           
                             ∏ 
                             
                               
                                 ( 
                                 ij 
                                 ) 
                               
                               ≠ 
                               
                                 ( 
                                 mn 
                                 ) 
                               
                             
                           
                           
                             
                               exp 
                               ⁡ 
                               ( 
                               
                                 
                                   
                                     u 
                                     ij 
                                   
                                   ⁢ 
                                   
                                     L 
                                     ⁡ 
                                     ( 
                                     
                                       u 
                                       ij 
                                     
                                     ) 
                                   
                                 
                                 2 
                               
                               ) 
                             
                             
                               
                                 exp 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     L 
                                     ⁡ 
                                     ( 
                                     
                                       u 
                                       ij 
                                     
                                     ) 
                                   
                                   2 
                                 
                                 ) 
                               
                               + 
                               
                                 exp 
                                 ⁡ 
                                 ( 
                                 
                                   - 
                                   
                                     
                                       L 
                                       ⁡ 
                                       ( 
                                       
                                         u 
                                         ij 
                                       
                                       ) 
                                     
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   9 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   10 
                 
               
               
                  
               
             
             
               
                 
                   
                     ln 
                     ⁢ 
                     
                       P 
                       ⁡ 
                       ( 
                       
                         u 
                         ❘ 
                         
                           u 
                           mn 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           ∑ 
                           ij 
                         
                         
                           ln 
                           ⁢ 
                           
                             P 
                             ⁡ 
                             ( 
                             
                               u 
                               ij 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                     - 
                     
                       ln 
                       ⁢ 
                       
                         P 
                         ⁡ 
                         ( 
                         
                           u 
                           mn 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   10 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   11 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         
                           ln 
                           ⁢ 
                           
                             P 
                             ⁡ 
                             ( 
                             
                               u 
                               ij 
                             
                             ) 
                           
                         
                         = 
                           
                         
                           
                             
                               1 
                               2 
                             
                             ⁢ 
                             
                               u 
                               ij 
                             
                             ⁢ 
                             
                               P 
                               ⁡ 
                               ( 
                               
                                 u 
                                 ij 
                               
                               ) 
                             
                           
                           - 
                           
                             ln 
                             ⁡ 
                             ( 
                             
                               
                                 exp 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     L 
                                     ⁡ 
                                     ( 
                                     
                                       u 
                                       ij 
                                     
                                     ) 
                                   
                                   2 
                                 
                                 ) 
                               
                               + 
                               
                                 exp 
                                 ⁡ 
                                 ( 
                                 
                                   - 
                                   
                                     
                                       L 
                                       ⁡ 
                                       ( 
                                       
                                         u 
                                         ij 
                                       
                                       ) 
                                     
                                     2 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         ≈ 
                           
                         
                           
                             
                               1 
                               2 
                             
                             ⁢ 
                             
                               u 
                               ij 
                             
                             ⁢ 
                             
                               L 
                               ⁡ 
                               ( 
                               
                                 u 
                                 ij 
                               
                               ) 
                             
                           
                           - 
                           
                             
                               1 
                               2 
                             
                             ⁢ 
                             
                               
                                 ❘ 
                                 &#34;\[LeftBracketingBar]&#34; 
                               
                               
                                 L 
                                 ⁡ 
                                 ( 
                                 
                                   u 
                                   ij 
                                 
                                 ) 
                               
                               
                                 ❘ 
                                 &#34;\[RightBracketingBar]&#34; 
                               
                             
                             ⁢ 
                                 
                             for 
                             ⁢ 
                                 
                             
                               
                                 ❘ 
                                 &#34;\[LeftBracketingBar]&#34; 
                               
                               
                                 L 
                                 ⁡ 
                                 ( 
                                 
                                   u 
                                   ij 
                                 
                                 ) 
                               
                               
                                 ❘ 
                                 &#34;\[RightBracketingBar]&#34; 
                               
                             
                           
                         
                         &gt; 
                         2 
                       
                     
                   
                   
                     
                       
                         = 
                           
                         
                           
                             
                               ❘ 
                               &#34;\[LeftBracketingBar]&#34; 
                             
                             
                               
                                 L 
                                 ⁡ 
                                 ( 
                                 
                                   u 
                                   ij 
                                 
                                 ) 
                               
                               2 
                             
                             
                               ❘ 
                               &#34;\[RightBracketingBar]&#34; 
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   u 
                                   ij 
                                 
                                 ⁢ 
                                 sign 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     L 
                                     ⁡ 
                                     ( 
                                     
                                       u 
                                       ij 
                                     
                                     ) 
                                   
                                   ) 
                                 
                               
                               - 
                               1 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   11 
                 
               
             
           
         
       
     
     Incidentally, the logarithmic probability of the equation defined in Equation 2 is represented in Equation 12. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   12 
                 
               
               
                  
               
             
             
               
                 
                   
                     ln 
                     ⁢ 
                     
                       P 
                       ⁡ 
                       ( 
                       
                         y 
                         ❘ 
                         u 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         - 
                         
                           
                             N 
                             r 
                           
                           2 
                         
                       
                       ⁢ 
                       
                         ln 
                         ⁡ 
                         ( 
                         
                           2 
                           ⁢ 
                           π 
                           ⁢ 
                           
                             σ 
                             2 
                           
                         
                         ) 
                       
                     
                     - 
                     
                       
                         1 
                         
                           2 
                           ⁢ 
                           
                             σ 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         
                            
                           
                             y 
                             - 
                             
                               Hs 
                               ⁡ 
                               ( 
                               u 
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   12 
                 
               
             
           
         
       
     
     Accordingly, from Equations 7 and 13, in MAP or A Posteriori Probability (APP), the a posteriori L-value is represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   13 
                 
               
               
                  
               
             
             
               
                 
                   
                     L 
                     ⁡ 
                     ( 
                     
                       
                         u 
                         mn 
                       
                       ❘ 
                       y 
                     
                     ) 
                   
                   = 
                   
                     ln 
                     ⁢ 
                     
                       
                         
                           ∑ 
                           
                             U 
                             
                               mn 
                               , 
                               
                                 + 
                                 1 
                               
                             
                           
                         
                         
                           exp 
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   - 
                                   
                                     1 
                                     
                                       2 
                                       ⁢ 
                                       
                                         σ 
                                         2 
                                       
                                     
                                   
                                 
                                 ⁢ 
                                 
                                   
                                      
                                     
                                       y 
                                       - 
                                       
                                         Hs 
                                         ⁡ 
                                         ( 
                                         u 
                                         ) 
                                       
                                     
                                      
                                   
                                   2 
                                 
                               
                               + 
                               
                                 
                                   ∑ 
                                   ij 
                                 
                                 
                                   ln 
                                   ⁢ 
                                   
                                     P 
                                     ⁡ 
                                     ( 
                                     
                                       u 
                                       ij 
                                     
                                     ) 
                                   
                                 
                               
                             
                             } 
                           
                         
                       
                       
                         
                           ∑ 
                           
                             U 
                             
                               mn 
                               , 
                               
                                 - 
                                 1 
                               
                             
                           
                         
                         
                           exp 
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   - 
                                   
                                     1 
                                     
                                       2 
                                       ⁢ 
                                       
                                         σ 
                                         2 
                                       
                                     
                                   
                                 
                                 ⁢ 
                                 
                                   
                                      
                                     
                                       y 
                                       - 
                                       
                                         Hs 
                                         ⁡ 
                                         ( 
                                         u 
                                         ) 
                                       
                                     
                                      
                                   
                                   2 
                                 
                               
                               + 
                               
                                 
                                   ∑ 
                                   ij 
                                 
                                 
                                   ln 
                                   ⁢ 
                                   
                                     P 
                                     ⁡ 
                                     ( 
                                     
                                       u 
                                       ij 
                                     
                                     ) 
                                   
                                 
                               
                             
                             } 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   13 
                 
               
             
           
         
       
     
     Hereinafter, this is referred to as iterative APP decoding. From Equations 8 and 12, in the log-likelihood ratio utilizing Max-Log approximation (Max-Log APP), the a posteriori L-value is represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   14 
                 
               
               
                  
               
             
             
               
                 
                   
                     L 
                     ⁡ 
                     ( 
                     
                       
                         u 
                         mn 
                       
                       ❘ 
                       y 
                     
                     ) 
                   
                   ≈ 
                   
                     
                       
                         max 
                         
                           Umn 
                           , 
                           
                             + 
                             1 
                           
                         
                       
                          
                       
                         { 
                         
                           Ψ 
                           ⁡ 
                           ( 
                           
                             u 
                             , 
                             y 
                             , 
                             
                               L 
                               ⁡ 
                               ( 
                               u 
                               ) 
                             
                           
                           ) 
                         
                         } 
                       
                     
                     - 
                     
                       
                         max 
                         
                           Umn 
                           , 
                           
                             - 
                             1 
                           
                         
                       
                          
                       
                         { 
                         
                           Ψ 
                           ⁡ 
                           ( 
                           
                             u 
                             , 
                             y 
                             , 
                             
                               L 
                               ⁡ 
                               ( 
                               u 
                               ) 
                             
                           
                           ) 
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   14 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   15 
                 
               
               
                  
               
             
             
               
                 
                   
                     Ψ 
                     ⁡ 
                     ( 
                     
                       u 
                       , 
                       y 
                       , 
                       
                         L 
                         ⁡ 
                         ( 
                         u 
                         ) 
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         - 
                         
                           1 
                           
                             2 
                             ⁢ 
                             
                               σ 
                               2 
                             
                           
                         
                       
                       ⁢ 
                       
                         
                            
                           
                             y 
                             - 
                             
                               Hs 
                               ⁡ 
                               ( 
                               u 
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                     + 
                     
                       
                         ∑ 
                         ij 
                       
                       
                         ln 
                         ⁢ 
                         
                           P 
                           ⁡ 
                           ( 
                           
                             u 
                             ij 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   15 
                 
               
             
           
         
       
     
     Hereinafter, this is referred to as iterative Max-log APP decoding. The extrinsic information required in an iterative decoding system can be sought by subtracting prior inputs from Equations 13 and 14. 
     &lt;System Model&gt; 
       FIG.  28    shows the basic structure of the system that is related to the subsequent description. This system is a 2×2 spatial multiplexing MIMO system. There is an outer encoder for each of streams A and B. The two outer encoders are identical LDPC encoders. (Here, a structure using LDPC encoders as the outer encoders is described as an example, but the error correction coding used by the outer encoder is not limited to LDPC coding. The present invention may similarly be embodied using other error correction coding such as turbo coding, convolutional coding, LDPC convolutional coding, and the like. Furthermore, each outer encoder is described as having a transmit antenna, but the outer encoders are not limited to this structure. A plurality of transmit antennas may be used, and the number of outer encoders may be one. Also, a greater number of outer encoders may be used than the number of transmit antennas.) The streams A and B respectively have interleavers (π a , πb). Here, the modulation scheme is 2 h -QAM (with h bits transmitted in one symbol). 
     The reception device performs iterative detection on the above MIMO signals (iterative APP (or iterative Max-log APP) decoding). Decoding of LDPC codes is performed by, for example, sum-product decoding. 
       FIG.  2    shows a frame structure and lists the order of symbols after interleaving. In this case, (i a , j a ), (i b , j b ) are represented by the following Equations.
 
Math 16
 
( i   a   ,j   a )=π a (Ω ia,ja   a )  Equation 16
 
Math 17
 
( i   b   ,j   b )=π b (Ω ib,jb   a )  Equation 17
 
     In this case, i a , i b  indicate the order of symbols after interleaving, j a , j b  indicate the bit positions (j a , j b =1, . . . , h) in the modulation scheme, π a , π b  indicate the interleavers for the streams A and B, and Ω a   ia,ja , Q b   ib,jb  indicate the order of data in streams A and B before interleaving. Note that  FIG.  2    shows the frame structure for i a =i b . 
     &lt;Iterative Decoding&gt; 
     The following is a detailed description of the algorithms for sum-product decoding used in decoding of LDPC codes and for iterative detection of MIMO signals in the reception device. 
     Sum-Product Decoding 
     Let a two-dimensional M×N matrix H={H mn } be the check matrix for LDPC codes that are targeted for decoding. Subsets A(m), B(n) of the set [1, N]={1, 2, . . . , N} are defined by the following Equations.
 
Math 18
 
 A ( m )≡{ n:H   mn =1}  Equation 18
 
Math 19
 
 B ( n )≡{ m:H   mn =1}  Equation 19
 
     In these Equations, A(m) represents the set of column indices of 1&#39;s in the m th  column of the check matrix H, and B(n) represents the set of row indices of 1&#39;s in the n th  row of the check matrix H. The algorithm for sum-product decoding is as follows. 
     Step A⋅1 (initialization): let a priori value log-likelihood ratio β mn =0 for all combinations (m, n) satisfying H mn =1. Assume that the loop variable (the number of iterations) l sum =1 and the maximum number of loops is set to l sum,max . 
     Step A⋅2 (row processing): the extrinsic value log-likelihood ratio α mn  is updated for all combinations (m, n) satisfying H mn =1 in the order of m=1, 2, . . . , M, using the following updating Equations. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   20 
                 
               
               
                  
               
             
             
               
                 
                   
                     α 
                     mn 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           ∏ 
                           
                             
                               n 
                               ′ 
                             
                             ∈ 
                             
                               
                                 A 
                                 ⁡ 
                                 ( 
                                 m 
                                 ) 
                               
                               ⁢ 
                               \ 
                               ⁢ 
                               n 
                                 
                             
                           
                         
                           
                         
                           sign 
                           ⁢ 
                           
                             ( 
                             
                               
                                 λ 
                                 
                                   n 
                                   ′ 
                                 
                               
                               + 
                               
                                 β 
                                 
                                   mn 
                                   ′ 
                                 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                     ⨯ 
                     
                       f 
                       ⁡ 
                       ( 
                       
                         
                           ∑ 
                           
                             
                               n 
                               ′ 
                             
                             ∈ 
                             
                               
                                 A 
                                 ⁡ 
                                 ( 
                                 m 
                                 ) 
                               
                               ⁢ 
                               \ 
                               ⁢ 
                               n 
                             
                           
                         
                         
                           f 
                           ⁡ 
                           ( 
                           
                             
                               λ 
                               
                                 n 
                                 ′ 
                               
                             
                             + 
                             
                               β 
                               
                                 mn 
                                 ′ 
                               
                             
                           
                           ) 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   20 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   21 
                 
               
               
                   
               
             
             
               
                 
                   
                     sign 
                     ⁢ 
                     
                       ( 
                       x 
                       ) 
                     
                   
                   ≡ 
                   
                     { 
                     
                       
                         
                           1 
                         
                         
                           
                             x 
                             ≥ 
                             0 
                           
                         
                       
                       
                         
                           
                             - 
                             1 
                           
                         
                         
                           
                             x 
                             &lt; 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   21 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   22 
                 
               
               
                  
               
             
             
               
                 
                   
                     f 
                     ⁡ 
                     ( 
                     x 
                     ) 
                   
                   ≡ 
                   
                     ln 
                     ⁢ 
                     
                       
                         
                           exp 
                           ⁡ 
                           ( 
                           x 
                           ) 
                         
                         + 
                         1 
                       
                       
                         
                           exp 
                           ⁡ 
                           ( 
                           x 
                           ) 
                         
                         - 
                         1 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   22 
                 
               
             
           
         
       
     
     In these Equations, f represents a Gallager function. Furthermore, the scheme of seeking λ n  is described in detail later. 
     Step A⋅3 (column processing): the extrinsic value log-likelihood ratio β mn  is updated for all combinations (m, n) satisfying H mn =1 in the order of n=1, 2, . . . , N, using the following updating Equation. 
                   Math   ⁢         23                        β   mn     =       ∑       m   ′     ∈       B   ⁡   (   n   )     ⁢   \   ⁢   m           α       m   ′     ⁢   n                 Equation   ⁢         23               
Step A⋅4 (calculating a log-likelihood ratio): the log-likelihood ratio L n  is sought for n∈[1, N] by the following Equation.
 
                   Math   ⁢         24                        L   n     =         ∑       m   ′     ∈       B   ⁡   (   n   )     ⁢   \   ⁢   m           α       m   ′     ⁢   n         +     λ   n               Equation   ⁢         24               
Step A⋅5 (count of the number of iterations): if l sum &lt;l sum,max , then l sum  is incremented, and processing returns to step A⋅2. If l sum =l sum,max , the sum-product decoding in this round is finished.
 
     The operations in one sum-product decoding have been described. Subsequently, iterative MIMO signal detection is performed. In the variables m, n, α mn , β mn , λ n , and L n , used in the above description of the operations of sum-product decoding, the variables in stream A are m a , n a , α a   mana , β a   mana , λ na , and L na , and the variables in stream B are m b , n b , α b   mbnb , β b   mbnb , λ nb , and L nb . 
     &lt;Iterative MIMO Signal Detection&gt; 
     The following describes the scheme of seeking λ n  in iterative MIMO signal detection in detail. 
     The following Equation holds from Equation 1. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   25 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         
                           y 
                           ⁡ 
                           ( 
                           t 
                           ) 
                         
                         = 
                           
                         
                           
                             ( 
                             
                               
                                 
                                   y 
                                   1 
                                 
                                 ( 
                                 t 
                                 ) 
                               
                               , 
                               
                                 
                                   y 
                                   2 
                                 
                                 ( 
                                 t 
                                 ) 
                               
                             
                             ) 
                           
                           T 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         
                           
                             
                               
                                 H 
                                 22 
                               
                               ( 
                               t 
                               ) 
                             
                             ⁢ 
                             
                               s 
                               ⁡ 
                               ( 
                               t 
                               ) 
                             
                           
                           + 
                           
                             n 
                             ⁡ 
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   25 
                 
               
             
           
         
       
     
     The following Equations are defined from the frame structures of  FIG.  2    and from Equations 16 and 17.
 
Math 26
 
 n   a =Ω ia,ja   a   Equation 26
 
Math 27
 
 n   b =Ω ib,jb   b   Equation 27
 
     In this case, n a ,n b ∈[1, N]. Hereinafter, λ na , L na , λ nb , and L nb , where the number of iterations of iterative MIMO signal detection is k, are represented as λ k,na , L k,na , λ k,nb , and L k,nb . 
     Step B⋅1 (initial detection; k=0): λ 0,na  and λ 0,nb  are sought as follows in the case of initial detection. 
     In iterative APP decoding: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   28 
                 
               
               
                  
               
             
             
               
                 
                   
                     λ 
                     
                       0 
                       , 
                       
                         n 
                         X 
                       
                     
                   
                   = 
                   
                     ln 
                     ⁢ 
                     
                       
                         
                           ∑ 
                           
                             U 
                             
                               0 
                               , 
                               
                                 n 
                                 X 
                               
                               , 
                               
                                 + 
                                 1 
                               
                             
                           
                         
                         
                           exp 
                           ⁢ 
                           
                             { 
                             
                               
                                 - 
                                 
                                   1 
                                   
                                     2 
                                     ⁢ 
                                     
                                       σ 
                                       2 
                                     
                                   
                                 
                               
                               ⁢ 
                               
                                 
                                    
                                   
                                     
                                       y 
                                       ⁡ 
                                       ( 
                                       
                                         i 
                                         X 
                                       
                                       ) 
                                     
                                     - 
                                     
                                       
                                         
                                           H 
                                           22 
                                         
                                         ( 
                                         
                                           i 
                                           X 
                                         
                                         ) 
                                       
                                       ⁢ 
                                       
                                         s 
                                         ⁡ 
                                         ( 
                                         
                                           u 
                                           ⁡ 
                                           ( 
                                           
                                             i 
                                             X 
                                           
                                           ) 
                                         
                                         ) 
                                       
                                     
                                   
                                    
                                 
                                 2 
                               
                             
                             } 
                           
                         
                       
                       
                         
                           ∑ 
                           
                             U 
                             
                               0 
                               , 
                               
                                 n 
                                 X 
                               
                               , 
                               
                                 - 
                                 1 
                               
                             
                           
                         
                         
                           exp 
                           ⁢ 
                           
                             { 
                             
                               
                                 - 
                                 
                                   1 
                                   
                                     2 
                                     ⁢ 
                                     
                                       σ 
                                       2 
                                     
                                   
                                 
                               
                               ⁢ 
                               
                                 
                                    
                                   
                                     
                                       y 
                                       ⁡ 
                                       ( 
                                       
                                         i 
                                         X 
                                       
                                       ) 
                                     
                                     - 
                                     
                                       
                                         
                                           H 
                                           22 
                                         
                                         ( 
                                         
                                           i 
                                           X 
                                         
                                         ) 
                                       
                                       ⁢ 
                                       
                                         s 
                                         ⁡ 
                                         ( 
                                         
                                           u 
                                           ⁡ 
                                           ( 
                                           
                                             i 
                                             X 
                                           
                                           ) 
                                         
                                         ) 
                                       
                                     
                                   
                                    
                                 
                                 2 
                               
                             
                             } 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   28 
                 
               
             
           
         
       
     
     In iterative Max-log APP decoding: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   29 
                 
               
               
                  
               
             
             
               
                 
                   
                     λ 
                     
                       0 
                       , 
                       
                         n 
                         X 
                       
                     
                   
                   = 
                   
                     
                       
                         max 
                         
                           U 
                           
                             0 
                             , 
                             
                               n 
                               X 
                             
                             , 
                             
                               + 
                               1 
                             
                           
                         
                       
                         
                       
                         { 
                         
                           Ψ 
                           ⁡ 
                           ( 
                           
                             
                               u 
                               ⁡ 
                               ( 
                               
                                 i 
                                 X 
                               
                               ) 
                             
                             , 
                             
                               y 
                               ⁡ 
                               ( 
                               
                                 i 
                                 X 
                               
                               ) 
                             
                           
                           ) 
                         
                         } 
                       
                     
                     - 
                     
                       
                         max 
                         
                           U 
                           
                             0 
                             , 
                             
                               n 
                               X 
                             
                             , 
                             
                               - 
                               1 
                             
                           
                         
                       
                         
                       
                         { 
                         
                           Ψ 
                           ⁡ 
                           ( 
                           
                             
                               u 
                               ⁡ 
                               ( 
                               
                                 i 
                                 X 
                               
                               ) 
                             
                             , 
                             
                               y 
                               ⁡ 
                               ( 
                               
                                 i 
                                 X 
                               
                               ) 
                             
                           
                           ) 
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     29 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   30 
                 
               
               
                  
               
             
             
               
                 
                   
                     Ψ 
                     ⁡ 
                     ( 
                     
                       
                         u 
                         ⁡ 
                         ( 
                         
                           i 
                           X 
                         
                         ) 
                       
                       , 
                       
                         y 
                         ⁡ 
                         ( 
                         
                           i 
                           X 
                         
                         ) 
                       
                     
                     ) 
                   
                   = 
                   
                     
                       - 
                       
                         1 
                         
                           2 
                           ⁢ 
                           
                             σ 
                             2 
                           
                         
                       
                     
                     ⁢ 
                     
                       
                          
                         
                           
                             y 
                             ⁡ 
                             ( 
                             
                               i 
                               X 
                             
                             ) 
                           
                           - 
                           
                             
                               
                                 H 
                                 22 
                               
                               ( 
                               
                                 i 
                                 X 
                               
                               ) 
                             
                             ⁢ 
                             
                               s 
                               ⁡ 
                               ( 
                               
                                 u 
                                 ⁡ 
                                 ( 
                                 
                                   i 
                                   X 
                                 
                                 ) 
                               
                               ) 
                             
                           
                         
                          
                       
                       2 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   30 
                 
               
             
           
         
       
     
     Here, let X=a, b. Then, assume that the number of iterations of iterative MIMO signal detection is l mimo =0 and the maximum number of iterations is set to l mimo,max . 
     Step B⋅2 (iterative detection; the number of iterations k): λ k,na  and λ k,nb , where the number of iterations is k, are represented as in Equations 31-34, from Equations 11,13-15,16, and 17. Let (X, Y)=(a, b)(b, a). 
     In Iterative APP Decoding: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   31 
                 
               
               
                  
               
             
             
               
                 
                   
                     λ 
                     
                       k 
                       , 
                       
                         n 
                         X 
                       
                     
                   
                   = 
                   
                     
                       
                         L 
                         
                           
                             k 
                             - 
                             1 
                           
                           , 
                           
                             Ω 
                             
                               iX 
                               , 
                               jX 
                             
                             X 
                           
                         
                       
                       ( 
                       
                         u 
                         
                           Ω 
                           
                             iX 
                             , 
                             jX 
                           
                           X 
                         
                       
                       ) 
                     
                     + 
                     
                       ln 
                       ⁢ 
                       
                         
                           
                             
                               
                                 
                                   ∑ 
                                   
                                     
                                       U 
                                       
                                         k 
                                         , 
                                         nX 
                                       
                                     
                                     , 
                                     
                                       + 
                                       1 
                                     
                                   
                                 
                                 exp 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     { 
                                     
                                       
                                         
                                           - 
                                           
                                             1 
                                             
                                               2 
                                               ⁢ 
                                               
                                                 σ 
                                                 2 
                                               
                                             
                                           
                                         
                                         ⁢ 
                                         
                                           
                                              
                                             
                                               
                                                 y 
                                                 ⁡ 
                                                 ( 
                                                 
                                                   i 
                                                   X 
                                                 
                                                 ) 
                                               
                                               - 
                                               
                                                 
                                                   
                                                     H 
                                                     22 
                                                   
                                                   ( 
                                                   
                                                     i 
                                                     X 
                                                   
                                                   ) 
                                                 
                                                 ⁢ 
                                                 
                                                   s 
                                                   ⁡ 
                                                   ( 
                                                   
                                                     u 
                                                     ⁡ 
                                                     ( 
                                                     
                                                       i 
                                                       X 
                                                     
                                                     ) 
                                                   
                                                   ) 
                                                 
                                               
                                             
                                              
                                           
                                           2 
                                         
                                       
                                       + 
                                       
                                         ρ 
                                         ( 
                                         
                                           u 
                                           
                                             Ω 
                                             
                                               iX 
                                               , 
                                               jX 
                                             
                                             X 
                                           
                                         
                                       
                                     
                                   
                                   ) 
                                 
                                 } 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   ∑ 
                                   
                                     
                                       U 
                                       
                                         k 
                                         , 
                                         nX 
                                       
                                     
                                     , 
                                     
                                       - 
                                       1 
                                     
                                   
                                 
                                 exp 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     { 
                                     
                                       
                                         
                                           - 
                                           
                                             1 
                                             
                                               2 
                                               ⁢ 
                                               
                                                 σ 
                                                 2 
                                               
                                             
                                           
                                         
                                         ⁢ 
                                         
                                           
                                              
                                             
                                               
                                                 y 
                                                 ⁡ 
                                                 ( 
                                                 
                                                   i 
                                                   X 
                                                 
                                                 ) 
                                               
                                               - 
                                               
                                                 
                                                   
                                                     H 
                                                     22 
                                                   
                                                   ( 
                                                   
                                                     i 
                                                     X 
                                                   
                                                   ) 
                                                 
                                                 ⁢ 
                                                 
                                                   s 
                                                   ⁡ 
                                                   ( 
                                                   
                                                     u 
                                                     ⁡ 
                                                     ( 
                                                     
                                                       i 
                                                       X 
                                                     
                                                     ) 
                                                   
                                                   ) 
                                                 
                                               
                                             
                                              
                                           
                                           2 
                                         
                                       
                                       + 
                                       
                                         ρ 
                                         ( 
                                         
                                           u 
                                           
                                             Ω 
                                             
                                               iX 
                                               , 
                                               jX 
                                             
                                             X 
                                           
                                         
                                       
                                     
                                   
                                   ) 
                                 
                                 } 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   31 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   32 
                 
               
               
                  
               
             
             
               
                 
                   
                     ρ 
                     ( 
                     
                       u 
                       
                         Ω 
                         
                           iX 
                           , 
                           jX 
                         
                         X 
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         
                           ∑ 
                           
                             
                               
                                 
                                   γ 
                                   = 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   γ 
                                   ≠ 
                                   jX 
                                 
                               
                             
                           
                         
                         h 
                       
                       
                         
                           
                             ❘ 
                             &#34;\[LeftBracketingBar]&#34; 
                           
                           
                             
                               
                                 L 
                                 
                                   
                                     k 
                                     - 
                                     1 
                                   
                                   , 
                                   
                                     Ω 
                                     
                                       iX 
                                       , 
                                       γ 
                                     
                                     X 
                                   
                                 
                               
                               ( 
                               
                                 u 
                                 
                                   Ω 
                                   
                                     iX 
                                     , 
                                     γ 
                                   
                                   X 
                                 
                               
                               ) 
                             
                             2 
                           
                           
                             ❘ 
                             &#34;\[RightBracketingBar]&#34; 
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 u 
                                 
                                   Ω 
                                   
                                     iX 
                                     , 
                                     γ 
                                   
                                   X 
                                 
                               
                               ⁢ 
                               
                                 sign 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     L 
                                     
                                       
                                         k 
                                         - 
                                         1 
                                       
                                       , 
                                       
                                         Ω 
                                         
                                           iX 
                                           , 
                                           γ 
                                         
                                         X 
                                       
                                     
                                   
                                   ( 
                                   
                                     u 
                                     
                                       Ω 
                                       
                                         iX 
                                         , 
                                         γ 
                                       
                                       X 
                                     
                                   
                                   ) 
                                 
                                 ) 
                               
                             
                             - 
                             1 
                           
                           ) 
                         
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           γ 
                           = 
                           1 
                         
                         h 
                       
                         
                       
                         
                           
                             ❘ 
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                                 L 
                                 
                                   
                                     k 
                                     - 
                                     1 
                                   
                                   , 
                                   
                                     Ω 
                                     
                                       iX 
                                       , 
                                       γ 
                                     
                                     X 
                                   
                                 
                               
                               ( 
                               
                                 u 
                                 
                                   Ω 
                                   
                                     iX 
                                     , 
                                     γ 
                                   
                                   X 
                                 
                               
                               ) 
                             
                             2 
                           
                           
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                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 u 
                                 
                                   Ω 
                                   
                                     iX 
                                     , 
                                     γ 
                                   
                                   X 
                                 
                               
                               ⁢ 
                               
                                 sign 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     L 
                                     
                                       
                                         k 
                                         - 
                                         1 
                                       
                                       , 
                                       
                                         Ω 
                                         
                                           iX 
                                           , 
                                           γ 
                                         
                                         X 
                                       
                                     
                                   
                                   ( 
                                   
                                     u 
                                     
                                       Ω 
                                       
                                         iX 
                                         , 
                                         γ 
                                       
                                       X 
                                     
                                   
                                   ) 
                                 
                                 ) 
                               
                             
                             - 
                             1 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   32 
                 
               
             
           
         
       
     
     In Iterative Max-Log APP Decoding: 
             Math   ⁢         33                       λ     k   ,     n   X         =         L       k   -   1     ,     Ω     iX   ,   jX     X         (     u     Ω     iX   ,   jX     X       )     +       max     U     k   ,     n   X     ,     +   1                 {     Ψ   (       u   ⁡   (     i   X     )     ,     y   ⁡   (     i   X     )     ,     ρ   (         u     Ω     iX   ,   jX     X       )         }       -       max     U     k   ,     n   X     ,     -   1                 {     Ψ   (       u   ⁡   (     i   X     )     ,     y   ⁡   (     i   X     )     ,     ρ   (         u     Ω     iX   ,   jX     X       )         }                 Equation   ⁢         33                     Math   ⁢         34                       Ψ   ⁢     (       u   ⁢     (     i   X     )       ,     y   ⁡   (     i   X     )     ,     ρ   (         u     Ω     iX   ,   jX     X       )       )       =         -     1     2   ⁢     σ   2           ⁢              y   ⁡   (     i   X     )     -         H   22     (     i   X     )     ⁢     s   ⁡   (     u   ⁡   (     i   X     )     )              2       +     ρ   ⁢     (     u     Ω     iX   ,   jX     X       )                 Equation   ⁢         34               
Step B⋅3 (counting the number of iterations and estimating a codeword): increment l mimo  if l mimo &lt;l mimo,max , and return to step B⋅2. Assuming that l mimo =l mimo ,max, the estimated codeword is sought as in the following Equation.
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   35 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       u 
                       ^ 
                     
                     
                       n 
                       X 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           1 
                         
                         
                           
                             
                               L 
                               
                                 
                                   l 
                                   mimo 
                                 
                                 , 
                                 
                                   n 
                                   X 
                                 
                               
                             
                             ≥ 
                             0 
                           
                         
                       
                       
                         
                           
                             - 
                             1 
                           
                         
                         
                           
                             
                               L 
                               
                                 
                                   l 
                                   mimo 
                                 
                                 , 
                                 
                                   n 
                                   X 
                                 
                               
                             
                             &lt; 
                             0 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   35 
                 
               
             
           
         
       
     
     Here, let X=a, b. 
       FIG.  3    is an example of the structure of a transmission device  300  in the present embodiment. An encoder  302 A receives information (data)  301 A and a frame structure signal  313  as inputs and, in accordance with the frame structure signal  313 , performs error correction coding such as convolutional coding, LDPC coding, turbo coding, or the like, outputting encoded data  303 A. (The frame structure signal  313  includes information such as the error correction scheme used for error correction coding of data, the coding rate, the block length, and the like. The encoder  302 A uses the error correction scheme indicated by the frame structure signal  313 . Furthermore, the error correction scheme may be hopped.) 
     An interleaver  304 A receives the encoded data  303 A and the frame structure signal  313  as inputs and performs interleaving, i.e. changing the order of the data, to output interleaved data  305 A. (The scheme of interleaving may be hopped based on the frame structure signal  313 .) 
     A mapping unit  306 A receives the interleaved data  305 A and the frame structure signal  313  as inputs, performs modulation such as Quadrature Phase Shift Keying (QPSK), 16 Quadrature Amplitude Modulation (16QAM), 64 Quadrature Amplitude Modulation (64QAM), or the like, and outputs a resulting baseband signal  307 A. (The modulation scheme may be hopped based on the frame structure signal  313 .) 
       FIGS.  24 A and  24 B  are an example of a mapping scheme over an I-Q plane, having an in-phase component I and a quadrature component Q, to form a baseband signal in QPSK modulation. For example, as shown in  FIG.  24 A , if the input data is “00”, the output is I=1.0, Q=1.0. Similarly, for input data of “01”, the output is I=−1.0, Q=1.0, and so forth.  FIG.  24 B  is an example of a different scheme of mapping in an I-Q plane for QPSK modulation than  FIG.  24 A . The difference between  FIG.  24 B  and  FIG.  24 A  is that the signal points in  FIG.  24 A  have been rotated around the origin to yield the signal points of  FIG.  24 B . Non-Patent Literature 9 and Non-Patent Literature 10 describe such a constellation rotation scheme, and the Cyclic Q Delay described in Non-Patent Literature 9 and Non-Patent Literature 10 may also be adopted. As another example apart from  FIGS.  24 A and  24 B ,  FIGS.  25 A and  25 B  show signal point layout in the I-Q plane for 16QAM. The example corresponding to  FIG.  24 A  is shown in  FIG.  25 A , and the example corresponding to  FIG.  24 B  is shown in  FIG.  25 B . 
     An encoder  302 B receives information (data)  301 B and the frame structure signal  313  as inputs and, in accordance with the frame structure signal  313 , performs error correction coding such as convolutional coding, LDPC coding, turbo coding, or the like, outputting encoded data  303 B. (The frame structure signal  313  includes information such as the error correction scheme used, the coding rate, the block length, and the like. The error correction scheme indicated by the frame structure signal  313  is used. Furthermore, the error correction scheme may be hopped.) 
     An interleaver  304 B receives the encoded data  303 B and the frame structure signal  313  as inputs and performs interleaving, i.e. changing the order of the data, to output interleaved data  305 B. (The scheme of interleaving may be hopped based on the frame structure signal  313 .) 
     A mapping unit  306 B receives the interleaved data  305 B and the frame structure signal  313  as inputs, performs modulation such as Quadrature Phase Shift Keying (QPSK), 16 Quadrature Amplitude Modulation (16QAM), 64 Quadrature Amplitude Modulation (64QAM), or the like, and outputs a resulting baseband signal  307 B. (The modulation scheme may be hopped based on the frame structure signal  313 .) 
     A weighting information generating unit  314  receives the frame structure signal  313  as an input and outputs information  315  regarding a weighting scheme based on the frame structure signal  313 . The weighting scheme is characterized by regular hopping between weights. 
     A weighting unit  308 A receives the baseband signal  307 A, the baseband signal  307 B, and the information  315  regarding the weighting scheme, and based on the information  315  regarding the weighting scheme, performs weighting on the baseband signal  307 A and the baseband signal  307 B and outputs a signal  309 A resulting from the weighting. Details on the weighting scheme are provided later. 
     A wireless unit  310 A receives the signal  309 A resulting from the weighting as an input and performs processing such as orthogonal modulation, band limiting, frequency conversion, amplification, and the like, outputting a transmission signal  311 A. A transmission signal  511 A is output as a radio wave from an antenna  312 A. 
     A weighting unit  308 B receives the baseband signal  307 A, the baseband signal  307 B, and the information  315  regarding the weighting scheme, and based on the information  315  regarding the weighting scheme, performs weighting on the baseband signal  307 A and the baseband signal  307 B and outputs a signal  309 B resulting from the weighting. 
       FIG.  26    shows the structure of a weighting unit. The baseband signal  307 A is multiplied by w 11 ( t ), yielding w 11 ( t )s 1 ( t ), and is multiplied by w 21 ( t ), yielding w 21 ( t )s 1 ( t ). Similarly, the baseband signal  307 B is multiplied by w 12 ( t ) to generate w 12 ( t )s 2 ( t ) and is multiplied by w 22 ( t ) to generate w 22 ( t )s 2 ( t ). Next, z 1 ( t )=w 11 ( t )s 1 ( t )+w 12 ( t )s 2 ( t ) and z 2 ( t )=w 21 ( t )s 1 ( t )+w 22 ( t )s 2 ( t ) are obtained. 
     Details on the weighting scheme are provided later. 
     A wireless unit  310 B receives the signal  309 B resulting from the weighting as an input and performs processing such as orthogonal modulation, band limiting, frequency conversion, amplification, and the like, outputting a transmission signal  311 B. The transmission signal  311 B is output as a radio wave from an antenna  312 B. 
       FIG.  4    shows an example of the structure of a transmission device  400  that differs from  FIG.  3   . The differences in  FIG.  4    from  FIG.  3    are described. 
     An encoder  402  receives information (data)  401  and the frame structure signal  313  as inputs and, in accordance with the frame structure signal  313 , performs error correction coding and outputs encoded data  403 . 
     A distribution unit  404  receives the encoded data  403  as an input, distributes the data  403 , and outputs data  405 A and data  405 B. Note that in  FIG.  4   , one encoder is shown, but the number of encoders is not limited in this way. The present invention may similarly be embodied when the number of encoders is m (where m is an integer greater than or equal to one) and the distribution unit divides encoded data generated by each encoder into two parts and outputs the divided data. 
       FIG.  5    shows an example of a frame structure in the time domain for a transmission device according to the present embodiment. A symbol  500 _ 1  is a symbol for notifying the reception device of the transmission scheme. For example, the symbol  500 _ 1  conveys information such as the error correction scheme used for transmitting data symbols, the coding rate, and the modulation scheme used for transmitting data symbols. 
     The symbol  501 _ 1  is for estimating channel fluctuation for the modulated signal z 1 ( t ) (where t is time) transmitted by the transmission device. The symbol  502 _ 1  is the data symbol transmitted as symbol number u (in the time domain) by the modulated signal z 1 ( t ), and the symbol  503 _ 1  is the data symbol transmitted as symbol number u+1 by the modulated signal z 1 ( t ). 
     The symbol  501 _ 2  is for estimating channel fluctuation for the modulated signal z 2 ( t ) (where t is time) transmitted by the transmission device. The symbol  502 _ 2  is the data symbol transmitted as symbol number u by the modulated signal z 2 ( t ), and the symbol  503 _ 2  is the data symbol transmitted as symbol number u+1 by the modulated signal z 2 ( t ). 
     The following describes the relationships between the modulated signals z 1 ( t ) and z 2 ( t ) transmitted by the transmission device and the received signals r 1 ( t ) and r 2 ( t ) received by the reception device. 
     In  FIGS.  5 ,  504   # 1  and  504 # 2  indicate transmit antennas in the transmission device, and  505 # 1  and  505 # 2  indicate receive antennas in the reception device. The transmission device transmits the modulated signal z 1 ( t ) from transmit antenna  504 # 1  and transmits the modulated signal z 2 ( t ) from transmit antenna  504 # 2 . In this case, the modulated signal z 1 ( t ) and the modulated signal z 2 ( t ) are assumed to occupy the same (a shared/common) frequency (band). Letting the channel fluctuation for the transmit antennas of the transmission device and the antennas of the reception device be h 11 (t), h 12 (t), h 21 (t), and h 22 (t), the signal received by the receive antenna  505 # 1  of the reception device be r 1 ( t ), and the signal received by the receive antenna  505 # 2  of the reception device be r 2 ( t ), the following relationship holds. 
     
       
         
           
             
               
                 
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       FIG.  6    relates to the weighting scheme (precoding scheme) in the present embodiment. A weighting unit  600  integrates the weighting units  308 A and  308 B in  FIG.  3   . As shown in  FIG.  6   , a stream s 1 ( t ) and a stream s 2 ( t ) correspond to the baseband signals  307 A and  307 B in  FIG.  3   . In other words, the streams s 1 ( t ) and s 2 ( t ) are the baseband signal in-phase components I and quadrature components Q when mapped according to a modulation scheme such as QPSK, 16QAM, 64QAM, or the like. As indicated by the frame structure of  FIG.  6   , the stream s 1 ( t ) is represented as s 1 ( u ) at symbol number u, as s 1 ( u +1) at symbol number u+1, and so forth. Similarly, the stream s 2 ( t ) is represented as s 2 ( u ) at symbol number u, as s 2 ( u +1) at symbol number u+1, and so forth. The weighting unit  600  receives the baseband signals  307 A (s 1 ( t )) and  307 B (s 2 ( t )) and the information  315  regarding weighting information in  FIG.  3    as inputs, performs weighting in accordance with the information  315  regarding weighting, and outputs the signals  309 A (z 1 ( t )) and  309 B (z 2 ( t )) after weighting in  FIG.  3   . In this case, z 1 ( t ) and z 2 ( t ) are represented as follows. 
     For symbol number 4i (where i is an integer greater than or equal to zero): 
                   Math   ⁢         37                        (           z   ⁢   1   ⁢     (     4   ⁢   i     )                 z   ⁢   2   ⁢     (     4   ⁢   i     )             )     =       1     2       ⁢     (           e     j   ⁢   0             e     j   ⁢   0                 e     j   ⁢   0             e     j   ⁢     3   4     ⁢   π             )     ⁢     (           s   ⁢   1   ⁢     (     4   ⁢   i     )                 s   ⁢   2   ⁢     (     4   ⁢   i     )             )               Equation   ⁢         37               
Here, j is an imaginary unit.
 
For symbol number 4i+1:
 
                   Math   ⁢         38                        (           z   ⁢   1   ⁢     (       4   ⁢   i     +   1     )                 z   ⁢   2   ⁢     (       4   ⁢   i     +   1     )             )     =       1     2       ⁢     (           e     j   ⁢   0             e     j   ⁢   0                 e     j   ⁢     3   4     ⁢   π             e     j   ⁢   0             )     ⁢     (           s   ⁢   1   ⁢     (       4   ⁢   i     +   1     )                 s   ⁢   2   ⁢     (       4   ⁢   i     +   1     )             )               Equation   ⁢         38               
For symbol number 4i+2:
 
                   Math   ⁢         39                        (           z   ⁢   1   ⁢     (       4   ⁢   i     +   2     )                 z   ⁢   2   ⁢     (       4   ⁢   i     +   2     )             )     =       1     2       ⁢     (           e     j   ⁢   0             e     j   ⁢     3   4     ⁢   π                 e     j   ⁢   0             e     j   ⁢   0             )     ⁢     (           s   ⁢   1   ⁢     (       4   ⁢   i     +   2     )                 s   ⁢   2   ⁢     (       4   ⁢   i     +   2     )             )               Equation   ⁢         39               
For symbol number 4i+3:
 
     
       
         
           
             
               
                 
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     In this way, the weighting unit in  FIG.  6    regularly hops between precoding weights over a four-slot period (cycle). (While precoding weights have been described as being hopped between regularly over four slots, the number of slots for regular hopping is not limited to four.) 
     Incidentally, Non-Patent Literature 4 describes hopping the precoding weights for each slot. This hopping of precoding weights is characterized by being random. On the other hand, in the present embodiment, a certain period (cycle) is provided, and the precoding weights are hopped between regularly. Furthermore, in each 2×2 precoding weight matrix composed of four precoding weights, the absolute value of each of the four precoding weights is equivalent to (1/sqrt(2)), and hopping is regularly performed between precoding weight matrices having this characteristic. 
     In an LOS environment, if a special precoding matrix is used, reception quality may greatly improve, yet the special precoding matrix differs depending on the conditions of direct waves. In an LOS environment, however, a certain tendency exists, and if precoding matrices are hopped between regularly in accordance with this tendency, the reception quality of data greatly improves. On the other hand, when precoding matrices are hopped between at random, a precoding matrix other than the above-described special precoding matrix may exist, and the possibility of performing precoding only with biased precoding matrices that are not suitable for the LOS environment also exists. Therefore, in an LOS environment, excellent reception quality may not always be obtained. Accordingly, there is a need for a precoding hopping scheme suitable for an LOS environment. The present invention proposes such a precoding scheme. 
       FIG.  7    is an example of the structure of a reception device  700  in the present embodiment. A wireless unit  703 _X receives, as an input, a received signal  702 _X received by an antenna  701 _X, performs processing such as frequency conversion, quadrature demodulation, and the like, and outputs a baseband signal  704 _X. 
     A channel fluctuation estimating unit  705 _ 1  for the modulated signal z 1  transmitted by the transmission device receives the baseband signal  704 _X as an input, extracts a reference symbol  501 _ 1  for channel estimation as in  FIG.  5   , estimates a value corresponding to h 11  in Equation 36, and outputs a channel estimation signal  706 _ 1 . 
     A channel fluctuation estimating unit  705 _ 2  for the modulated signal z 2  transmitted by the transmission device receives the baseband signal  704 _X as an input, extracts a reference symbol  501 _ 2  for channel estimation as in  FIG.  5   , estimates a value corresponding to h 12  in Equation 36, and outputs a channel estimation signal  706 _ 2 . 
     A wireless unit  703 _Y receives, as input, a received signal  702 _Y received by an antenna  701 _Y, performs processing such as frequency conversion, quadrature demodulation, and the like, and outputs a baseband signal  704 _Y. 
     A channel fluctuation estimating unit  707 _ 1  for the modulated signal z 1  transmitted by the transmission device receives the baseband signal  704 _Y as an input, extracts a reference symbol  501 _ 1  for channel estimation as in  FIG.  5   , estimates a value corresponding to h 21  in Equation 36, and outputs a channel estimation signal  708 _ 1 . 
     A channel fluctuation estimating unit  707 _ 2  for the modulated signal z 2  transmitted by the transmission device receives the baseband signal  704 _Y as an input, extracts a reference symbol  501 _ 2  for channel estimation as in  FIG.  5   , estimates a value corresponding to h 22  in Equation 36, and outputs a channel estimation signal  708 _ 2 . 
     A control information decoding unit  709  receives the baseband signal  704 _X and the baseband signal  704 _Y as inputs, detects the symbol  500 _ 1  that indicates the transmission scheme as in  FIG.  5   , and outputs a signal  710  regarding information on the transmission scheme indicated by the transmission device. 
     A signal processing unit  711  receives, as inputs, the baseband signals  704 _X and  704 _Y, the channel estimation signals  706 _ 1 ,  706 _ 2 ,  708 _ 1 , and  708 _ 2 , and the signal  710  regarding information on the transmission scheme indicated by the transmission device, performs detection and decoding, and outputs received data  712 _ 1  and  712 _ 2 . 
     Next, operations by the signal processing unit  711  in  FIG.  7    are described in detail.  FIG.  8    is an example of the structure of the signal processing unit  711  in the present embodiment.  FIG.  8    shows an INNER MIMO detector, a soft-in/soft-out decoder, and a weighting coefficient generating unit as the main elements. Non-Patent Literature 2 and Non-Patent Literature 3 describe the scheme of iterative decoding with this structure. The MIMO system described in Non-Patent Literature 2 and Non-Patent Literature 3 is a spatial multiplexing MIMO system, whereas the present embodiment differs from Non-Patent Literature 2 and Non-Patent Literature 3 by describing a MIMO system that changes precoding weights with time. Letting the (channel) matrix in Equation 36 be H(t), the precoding weight matrix in  FIG.  6    be W(t) (where the precoding weight matrix changes over t), the received vector be R(t)=(r 1 ( t ),r 2 ( t ) T , and the stream vector be S(t)=(s 1 ( t ),s 2 ( t ) T , the following Equation holds.
 
Math 41
 
 R ( t )= H ( t ) W ( t ) S ( t )  Equation 41
 
     In this case, the reception device can apply the decoding scheme in Non-Patent Literature 2 and Non-Patent Literature 3 to the received vector R(t) by considering H(t)W(t) as the channel matrix. 
     Therefore, a weighting coefficient generating unit  819  in  FIG.  8    receives, as input, a signal  818  regarding information on the transmission scheme indicated by the transmission device (corresponding to  710  in  FIG.  7   ) and outputs a signal  820  regarding information on weighting coefficients. 
     An INNER MIMO detector  803  receives the signal  820  regarding information on weighting coefficients as input and, using the signal  820 , performs the calculation in Equation 41. Iterative detection and decoding is thus performed. The following describes operations thereof. 
     In the signal processing unit in  FIG.  8   , a processing scheme such as that shown in  FIG.  10    is necessary for iterative decoding (iterative detection). First, one codeword (or one frame) of the modulated signal (stream) s 1  and one codeword (or one frame) of the modulated signal (stream) s 2  are decoded. As a result, the Log-Likelihood Ratio (LLR) of each bit of the one codeword (or one frame) of the modulated signal (stream) s 1  and of the one codeword (or one frame) of the modulated signal (stream) s 2  is obtained from the soft-in/soft-out decoder. Detection and decoding is performed again using the LLR. These operations are performed multiple times (these operations being referred to as iterative decoding (iterative detection)). Hereinafter, description focuses on the scheme of generating the log-likelihood ratio (LLR) of a symbol at a particular time in one frame. 
     In  FIG.  8   , a storage unit  815  receives, as inputs, a baseband signal  801 X (corresponding to the baseband signal  704 _X in  FIG.  7   ), a channel estimation signal group  802 X (corresponding to the channel estimation signals  706 _ 1  and  706 _ 2  in  FIG.  7   ), a baseband signal  801 Y (corresponding to the baseband signal  704 _Y in  FIG.  7   ), and a channel estimation signal group  802 Y (corresponding to the channel estimation signals  708 _ 1  and  708 _ 2  in  FIG.  7   ). In order to achieve iterative decoding (iterative detection), the storage unit  815  calculates H(t)W(t) in Equation 41 and stores the calculated matrix as a transformed channel signal group. The storage unit  815  outputs the above signals when necessary as a baseband signal  816 X, a transformed channel estimation signal group  817 X, a baseband signal  816 Y, and a transformed channel estimation signal group  817 Y. 
     Subsequent operations are described separately for initial detection and for iterative decoding (iterative detection). 
     &lt;Initial Detection&gt; 
     The INNER MIMO detector  803  receives, as inputs, the baseband signal  801 X, the channel estimation signal group  802 X, the baseband signal  801 Y, and the channel estimation signal group  802 Y. Here, the modulation scheme for the modulated signal (stream) s 1  and the modulated signal (stream) s 2  is described as 16QAM. 
     The INNER MIMO detector  803  first calculates H(t)W(t) from the channel estimation signal group  802 X and the channel estimation signal group  802 Y to seek candidate signal points corresponding to the baseband signal  801 X.  FIG.  11    shows such calculation. In  FIG.  11   , each black dot (●) is a candidate signal point in the I-Q plane. Since the modulation scheme is 16QAM, there are 256 candidate signal points. (Since  FIG.  11    is only for illustration, not all 256 candidate signal points are shown.) Here, letting the four bits transferred by modulated signal s 1  be b 0 , b 1 , b 2 , and b 3 , and the four bits transferred by modulated signal s 2  be b 4 , b 5 , b 6 , and b 7 , candidate signal points corresponding to (b 0 , b 1 , b 2 , b 3 , b 4 , b 5 , b 6 , b 7 ) in  FIG.  11    exist. The squared Euclidian distance is sought between a received signal point  1101  (corresponding to the baseband signal  801 X) and each candidate signal point. Each squared Euclidian distance is divided by the noise variance σ 2 . Accordingly, Ex(b 0 , b 1 , b 2 , b 3 , b 4 , b 5 , b 6 , b 7 ), i.e. the value of the squared Euclidian distance between a candidate signal point corresponding to (b 0 , b 1 , b 2 , b 3 , b 4 , b 5 , b 6 , b 7 ) and a received signal point, divided by the noise variance, is sought. Note that the baseband signals and the modulated signals s 1  and s 2  are each complex signals. 
     Similarly, H(t)W(t) is calculated from the channel estimation signal group  802 X and the channel estimation signal group  802 Y, candidate signal points corresponding to the baseband signal  801 Y are sought, the squared Euclidian distance for the received signal point (corresponding to the baseband signal  801 Y) is sought, and the squared Euclidian distance is divided by the noise variance σ 2 . Accordingly, E Y (b 0 , b 1 , b 2 , b 3 , b 4 , b 5 , b 6 , b 7 ), i.e. the value of the squared Euclidian distance between a candidate signal point corresponding to (b 0 , b 1 , b 2 , b 3 , b 4 , b 5 , b 6 , b 7 ) and a received signal point, divided by the noise variance, is sought. 
     Then Ex(b 0 , b 1 , b 2 , b 3 , b 4 , b 5 , b 6 , b 7 )+E Y (b 0 , b 1 , b 2 , b 3 , b 4 , b 5 , b 6 , b 7 )=E(b 0 , b 1 , b 2 , b 3 , b 4 , b 5 , b 6 , b 7 ) is sought. 
     The INNER MIMO detector  803  outputs E(b 0 , b 1 , b 2 , b 3 , b 4 , b 5 , b 6 , b 7 ) as a signal  804 . 
     A log-likelihood calculating unit  805 A receives the signal  804  as input, calculates the log likelihood for bits b 0 , b 1 , b 2 , and b 3 , and outputs a log-likelihood signal  806 A. Note that during calculation of the log likelihood, the log likelihood for “1” and the log likelihood for “0” are calculated. The calculation scheme is as shown in Equations 28, 29, and 30. Details can be found in Non-Patent Literature 2 and Non-Patent Literature 3. 
     Similarly, a log-likelihood calculating unit  805 B receives the signal  804  as input, calculates the log likelihood for bits b 4 , b 5 , b 6 , and b 7 , and outputs a log-likelihood signal  806 B. 
     A deinterleaver ( 807 A) receives the log-likelihood signal  806 A as an input, performs deinterleaving corresponding to the interleaver (the interleaver ( 304 A) in  FIG.  3   ), and outputs a deinterleaved log-likelihood signal  808 A. 
     Similarly, a deinterleaver ( 807 B) receives the log-likelihood signal  806 B as an input, performs deinterleaving corresponding to the interleaver (the interleaver ( 304 B) in  FIG.  3   ), and outputs a deinterleaved log-likelihood signal  808 B. 
     A log-likelihood ratio calculating unit  809 A receives the interleaved log-likelihood signal  808 A as an input, calculates the log-likelihood ratio (LLR) of the bits encoded by the encoder  302 A in  FIG.  3   , and outputs a log-likelihood ratio signal  810 A. 
     Similarly, a log-likelihood ratio calculating unit  809 B receives the interleaved log-likelihood signal  808 B as an input, calculates the log-likelihood ratio (LLR) of the bits encoded by the encoder  302 B in  FIG.  3   , and outputs a log-likelihood ratio signal  810 B. 
     A soft-in/soft-out decoder  811 A receives the log-likelihood ratio signal  810 A as an input, performs decoding, and outputs a decoded log-likelihood ratio  812 A. 
     Similarly, a soft-in/soft-out decoder  811 B receives the log-likelihood ratio signal  810 B as an input, performs decoding, and outputs a decoded log-likelihood ratio  812 B. 
     &lt;Iterative Decoding (Iterative Detection), Number of Iterations k&gt; 
     An interleaver ( 813 A) receives the log-likelihood ratio  812 A decoded by the soft-in/soft-out decoder in the (k−1) th  iteration as an input, performs interleaving, and outputs an interleaved log-likelihood ratio  814 A. The interleaving pattern in the interleaver ( 813 A) is similar to the interleaving pattern in the interleaver ( 304 A) in  FIG.  3   . 
     An interleaver ( 813 B) receives the log-likelihood ratio  812 B decoded by the soft-in/soft-out decoder in the (k−1) th  iteration as an input, performs interleaving, and outputs an interleaved log-likelihood ratio  814 B. The interleaving pattern in the interleaver ( 813 B) is similar to the interleaving pattern in the interleaver ( 304 B) in  FIG.  3   . 
     The INNER MIMO detector  803  receives, as inputs, the baseband signal  816 X, the transformed channel estimation signal group  817 X, the baseband signal  816 Y, the transformed channel estimation signal group  817 Y, the interleaved log-likelihood ratio  814 A, and the interleaved log-likelihood ratio  814 B. The reason for using the baseband signal  816 X, the transformed channel estimation signal group  817 X, the baseband signal  816 Y, and the transformed channel estimation signal group  817 Y instead of the baseband signal  801 X, the channel estimation signal group  802 X, the baseband signal  801 Y, and the channel estimation signal group  802 Y is because a delay occurs due to iterative decoding. 
     The difference between operations by the INNER MIMO detector  803  for iterative decoding and for initial detection is the use of the interleaved log-likelihood ratio  814 A and the interleaved log-likelihood ratio  814 B during signal processing. The INNER MIMO detector  803  first seeks E(b 0 , b 1 , b 2 , b 3 , b 4 , b 5 , b 6 , b 7 ), as during initial detection. Additionally, coefficients corresponding to Equations 11 and 32 are sought from the interleaved log-likelihood ratio  814 A and the interleaved log-likelihood ratio  914 B. The value E(b 0 , b 1 , b 2 , b 3 , b 4 , b 5 , b 6 , b 7 ) is adjusted using the sought coefficients, and the resulting value E′(b 0 , b 1 , b 2 , b 3 , b 4 , b 5 , b 6 , b 7 ) is output as the signal  804 . 
     The log-likelihood calculating unit  805 A receives the signal  804  as input, calculates the log likelihood for bits b 0 , b 1 , b 2 , and b 3 , and outputs the log-likelihood signal  806 A. Note that during calculation of the log likelihood, the log likelihood for “1” and the log likelihood for “0” are calculated. The calculation scheme is as shown in Equations 31, 32, 33, 34, and 35. Details can be found in Non-Patent Literature 2 and Non-Patent Literature 3. 
     Similarly, the log-likelihood calculating unit  805 B receives the signal  804  as input, calculates the log likelihood for bits b 4 , b 5 , b 6 , and b 7 , and outputs the log-likelihood signal  806 B. Operations by the deinterleaver onwards are similar to initial detection. 
     Note that while  FIG.  8    shows the structure of the signal processing unit when performing iterative detection, iterative detection is not always essential for obtaining excellent reception quality, and a structure not including the interleavers  813 A and  813 B, which are necessary only for iterative detection, is possible. In such a case, the INNER MIMO detector  803  does not perform iterative detection. 
     The main part of the present embodiment is calculation of H(t)W(t). Note that as shown in Non-Patent Literature 5 and the like, QR decomposition may be used to perform initial detection and iterative detection. 
     Furthermore, as shown in Non-Patent Literature 11, based on H(t)W(t), linear operation of the Minimum Mean Squared Error (MMSE) and Zero Forcing (ZF) may be performed in order to perform initial detection. 
       FIG.  9    is the structure of a different signal processing unit than  FIG.  8    and is for the modulated signal transmitted by the transmission device in  FIG.  4   . The difference with  FIG.  8    is the number of soft-in/soft-out decoders. A soft-in/soft-out decoder  901  receives, as inputs, the log-likelihood ratio signals  810 A and  810 B, performs decoding, and outputs a decoded log-likelihood ratio  902 . A distribution unit  903  receives the decoded log-likelihood ratio  902  as an input and distributes the log-likelihood ratio  902 . Other operations are similar to  FIG.  8   . 
       FIGS.  12 A and  12 B  show BER characteristics for a transmission scheme using the precoding weights of the present embodiment under similar conditions to  FIGS.  29 A and  29 B .  FIG.  12 A  shows the BER characteristics of Max-log A Posteriori Probability (APP) without iterative detection (see Non-Patent Literature 1 and Non-Patent Literature 2), and  FIG.  12 B  shows the BER characteristics of Max-log-APP with iterative detection (see Non-Patent Literature 1 and Non-Patent Literature 2) (number of iterations: five). Comparing  FIGS.  12 A,  12 B,  29 A, and  29 B  shows how if the transmission scheme of the present embodiment is used, the BER characteristics when the Rician factor is large greatly improve over the BER characteristics when using spatial multiplexing MIMO system, thereby confirming the usefulness of the scheme in the present embodiment. 
     As described above, when a transmission device transmits a plurality of modulated signals from a plurality of antennas in a MIMO system, the advantageous effect of improved transmission quality, as compared to conventional spatial multiplexing MIMO system, is achieved in an LOS environment in which direct waves dominate by hopping between precoding weights regularly over time, as in the present embodiment. 
     In the present embodiment, and in particular with regards to the structure of the reception device, operations have been described for a limited number of antennas, but the present invention may be embodied in the same way even if the number of antennas increases. In other words, the number of antennas in the reception device does not affect the operations or advantageous effects of the present embodiment. Furthermore, in the present embodiment, the example of LDPC coding has particularly been explained, but the present invention is not limited to LDPC coding. Furthermore, with regards to the decoding scheme, the soft-in/soft-out decoders are not limited to the example of sum-product decoding. Another soft-in/soft-out decoding scheme may be used, such as a BCJR algorithm, a SOVA algorithm, a Max-log-MAP algorithm, and the like. Details are provided in Non-Patent Literature 6. 
     Additionally, in the present embodiment, the example of a single carrier scheme has been described, but the present invention is not limited in this way and may be similarly embodied for multi-carrier transmission. Accordingly, when using a scheme such as spread spectrum communication, Orthogonal Frequency-Division Multiplexing (OFDM), Single Carrier Frequency Division Multiple Access (SC-FDMA), Single Carrier Orthogonal Frequency-Division Multiplexing (SC-OFDM), or wavelet OFDM as described in Non-Patent Literature 7 and the like, for example, the present invention may be similarly embodied. Furthermore, in the present embodiment, symbols other than data symbols, such as pilot symbols (preamble, unique word, and the like), symbols for transmission of control information, and the like, may be arranged in the frame in any way. 
     The following describes an example of using OFDM as an example of a multi-carrier scheme. 
       FIG.  13    shows the structure of a transmission device when using OFDM. In  FIG.  13   , elements that operate in a similar way to  FIG.  3    bear the same reference signs. 
     An OFDM related processor  1301 A receives, as input, the weighted signal  309 A, performs processing related to OFDM, and outputs a transmission signal  1302 A. Similarly, an OFDM related processor  1301 B receives, as input, the weighted signal  309 B, performs processing related to OFDM, and outputs a transmission signal  1302 B. 
       FIG.  14    shows an example of a structure from the OFDM related processors  1301 A and  1301 B in  FIG.  13    onwards. The part from  1401 A to  1410 A is related to the part from  1301 A to  312 A in  FIG.  13   , and the part from  1401 B to  1410 B is related to the part from  1301 B to  312 B in  FIG.  13   . 
     A serial/parallel converter  1402 A performs serial/parallel conversion on a weighted signal  1401 A (corresponding to the weighted signal  309 A in  FIG.  13   ) and outputs a parallel signal  1403 A. 
     A reordering unit  1404 A receives a parallel signal  1403 A as input, performs reordering, and outputs a reordered signal  1405 A. Reordering is described in detail later. 
     An inverse fast Fourier transformer  1406 A receives the reordered signal  1405 A as an input, performs a fast Fourier transform, and outputs a fast Fourier transformed signal  1407 A. 
     A wireless unit  1408 A receives the fast Fourier transformed signal  1407 A as an input, performs processing such as frequency conversion, amplification, and the like, and outputs a modulated signal  1409 A. The modulated signal  1409 A is output as a radio wave from an antenna  1410 A. 
     A serial/parallel converter  1402 B performs serial/parallel conversion on a weighted signal  1401 B (corresponding to the weighted signal  309 B in  FIG.  13   ) and outputs a parallel signal  1403 B. 
     A reordering unit  1404 B receives a parallel signal  1403 B as input, performs reordering, and outputs a reordered signal  1405 B. Reordering is described in detail later. 
     An inverse fast Fourier transformer  1406 B receives the reordered signal  1405 B as an input, performs a fast Fourier transform, and outputs a fast Fourier transformed signal  1407 B. 
     A wireless unit  1408 B receives the fast Fourier transformed signal  1407 B as an input, performs processing such as frequency conversion, amplification, and the like, and outputs a modulated signal  1409 B. The modulated signal  1409 B is output as a radio wave from an antenna  1410 B. 
     In the transmission device of  FIG.  3   , since the transmission scheme does not use multi-carrier, precoding hops to form a four-slot period (cycle), as shown in  FIG.  6   , and the precoded symbols are arranged in the time domain. When using a multi-carrier transmission scheme as in the OFDM scheme shown in  FIG.  13   , it is of course possible to arrange the precoded symbols in the time domain as in  FIG.  3    for each (sub)carrier. In the case of a multi-carrier transmission scheme, however, it is possible to arrange symbols in the frequency domain, or in both the frequency and time domains. The following describes these arrangements. 
       FIGS.  15 A and  15 B  show an example of a scheme of reordering symbols by reordering units  1404 A and  1404 B in  FIG.  14   , the horizontal axis representing frequency, and the vertical axis representing time. The frequency domain runs from (sub)carrier  0  through (sub)carrier  9 . The modulated signals z 1  and z 2  use the same frequency band at the same time.  FIG.  15 A  shows the reordering scheme for symbols of the modulated signal z 1 , and  FIG.  15 B  shows the reordering scheme for symbols of the modulated signal z 2 . Numbers # 1 , # 2 , # 3 , # 4 , . . . are assigned to in order to the symbols of the weighted signal  1401 A which is input into the serial/parallel converter  1402 A. At this point, symbols are assigned regularly, as shown in  FIG.  15 A . The symbols # 1 , # 2 , # 3 , # 4 , . . . are arranged in order starting from carrier  0 . The symbols # 1  through # 9  are assigned to time $ 1 , and subsequently, the symbols # 10  through # 19  are assigned to time $ 2 . 
     Similarly, numbers # 1 , # 2 , # 3 , # 4 , . . . are assigned in order to the symbols of the weighted signal  1401 B which is input into the serial/parallel converter  1402 B. At this point, symbols are assigned regularly, as shown in  FIG.  15 B . The symbols # 1 , # 2 , # 3 , # 4 , . . . are arranged in order starting from carrier  0 . The symbols # 1  through # 9  are assigned to time $ 1 , and subsequently, the symbols # 10  through # 19  are assigned to time $ 2 . Note that the modulated signals z 1  and z 2  are complex signals. 
     The symbol group  1501  and the symbol group  1502  shown in  FIGS.  15 A and  15 B  are the symbols for one period (cycle) when using the precoding weight hopping scheme shown in  FIG.  6   . Symbol # 0  is the symbol when using the precoding weight of slot 4i in  FIG.  6   . Symbol # 1  is the symbol when using the precoding weight of slot 4i+1 in  FIG.  6   . Symbol # 2  is the symbol when using the precoding weight of slot 4i+2 in  FIG.  6   . Symbol # 3  is the symbol when using the precoding weight of slot 4i+3 in  FIG.  6   . Accordingly, symbol #x is as follows. When x mod 4 is 0, the symbol #x is the symbol when using the precoding weight of slot 4i in  FIG.  6   . When x mod 4 is 1, the symbol #x is the symbol when using the precoding weight of slot 4i+1 in  FIG.  6   . When x mod 4 is 2, the symbol #x is the symbol when using the precoding weight of slot 4i+2 in  FIG.  6   . When x mod 4 is 3, the symbol #x is the symbol when using the precoding weight of slot 4i+3 in  FIG.  6   . 
     In this way, when using a multi-carrier transmission scheme such as OFDM, unlike during single carrier transmission, symbols can be arranged in the frequency domain. Furthermore, the ordering of symbols is not limited to the ordering shown in  FIGS.  15 A and  15 B . Other examples are described with reference to  FIGS.  16 A,  16 B,  17 A, and  17 B . 
       FIGS.  16 A and  16 B  show an example of a scheme of reordering symbols by the reordering units  1404 A and  1404 B in  FIG.  14   , the horizontal axis representing frequency, and the vertical axis representing time, that differs from  FIGS.  15 A and  15 B .  FIG.  16 A  shows the reordering scheme for symbols of the modulated signal z 1 , and  FIG.  16 B  shows the reordering scheme for symbols of the modulated signal z 2 . The difference in  FIGS.  16 A and  16 B  as compared to  FIGS.  15 A and  15 B  is that the reordering scheme of the symbols of the modulated signal z 1  differs from the reordering scheme of the symbols of the modulated signal z 2 . In  FIG.  16 B , symbols # 0  through # 5  are assigned to carriers  4  through  9 , and symbols # 6  through # 9  are assigned to carriers  0  through  3 . Subsequently, symbols # 10  through # 19  are assigned regularly in the same way. At this point, as in  FIGS.  15 A and  15 B , the symbol group  1601  and the symbol group  1602  shown in  FIGS.  16 A and  16 B  are the symbols for one period (cycle) when using the precoding weight hopping scheme shown in  FIG.  6   . 
       FIGS.  17 A and  17 B  show an example of a scheme of reordering symbols by the reordering units  1404 A and  1404 B in  FIG.  14   , the horizontal axis representing frequency, and the vertical axis representing time, that differs from  FIGS.  15 A and  15 B .  FIG.  17 A  shows the reordering scheme for symbols of the modulated signal z 1 , and  FIG.  17 B  shows the reordering scheme for symbols of the modulated signal z 2 . The difference in  FIGS.  17 A and  17 B  as compared to  FIGS.  15 A and  15 B  is that whereas the symbols are arranged in order by carrier in  FIGS.  15 A and  15 B , the symbols are not arranged in order by carrier in  FIGS.  17 A and  17 B . It is obvious that, in  FIGS.  17 A and  17 B , the reordering scheme of the symbols of the modulated signal z 1  may differ from the reordering scheme of the symbols of the modulated signal z 2 , as in  FIGS.  16 A and  16 B . 
       FIGS.  18 A and  18 B  show an example of a scheme of reordering symbols by the reordering units  1404 A and  1404 B in  FIG.  14   , the horizontal axis representing frequency, and the vertical axis representing time, that differs from  FIGS.  15 A through  17 B .  FIG.  18 A  shows the reordering scheme for symbols of the modulated signal z 1 , and  FIG.  18 B  shows the reordering scheme for symbols of the modulated signal z 2 . In  FIGS.  15 A through  17 B , symbols are arranged in the frequency domain, whereas in  FIGS.  18 A and  18 B , symbols are arranged in both the frequency and time domains. 
     In  FIG.  6   , an example has been described of hopping between precoding weights over four slots. Here, however, an example of hopping over eight slots is described. The symbol groups  1801  and  1802  shown in  FIGS.  18 A and  18 B  are the symbols for one period (cycle) when using the precoding weight hopping scheme (and are therefore eight-symbol groups). Symbol # 0  is the symbol when using the precoding weight of slot 8i. Symbol # 1  is the symbol when using the precoding weight of slot 8i+1. Symbol # 2  is the symbol when using the precoding weight of slot 8i+2. Symbol # 3  is the symbol when using the precoding weight of slot 8i+3. Symbol # 4  is the symbol when using the precoding weight of slot 8i+4. Symbol # 5  is the symbol when using the precoding weight of slot 8i+5. Symbol # 6  is the symbol when using the precoding weight of slot 8i+6. Symbol # 7  is the symbol when using the precoding weight of slot 8i+7. Accordingly, symbol #x is as follows. When x mod 8 is 0, the symbol #x is the symbol when using the precoding weight of slot 8i. When x mod 8 is 1, the symbol #x is the symbol when using the precoding weight of slot 8i+1. When x mod 8 is 2, the symbol #x is the symbol when using the precoding weight of slot 8i+2. When x mod 8 is 3, the symbol #x is the symbol when using the precoding weight of slot 8i+3. When x mod 8 is 4, the symbol #x is the symbol when using the precoding weight of slot 8i+4. When x mod 8 is 5, the symbol #x is the symbol when using the precoding weight of slot 8i+5. When x mod 8 is 6, the symbol #x is the symbol when using the precoding weight of slot 8i+6. When x mod 8 is 7, the symbol #x is the symbol when using the precoding weight of slot 8i+7. In the symbol ordering in  FIGS.  18 A and  18 B , four slots in the time domain and two slots in the frequency domain for a total of 4×2=8 slots are used to arrange symbols for one period (cycle). In this case, letting the number of symbols in one period (cycle) be m×n symbols (in other words, m×n precoding weights exist), the number of slots (the number of carriers) in the frequency domain used to arrange symbols in one period (cycle) be n, and the number of slots used in the time domain be m, then m&gt;n should be satisfied. This is because the phase of direct waves fluctuates more slowly in the time domain than in the frequency domain. Therefore, since the precoding weights are changed in the present embodiment to minimize the influence of steady direct waves, it is preferable to reduce the fluctuation in direct waves in the period (cycle) for changing the precoding weights. Accordingly, m&gt;n should be satisfied. Furthermore, considering the above points, rather than reordering symbols only in the frequency domain or only in the time domain, direct waves are more likely to become stable when symbols are reordered in both the frequency and the time domains as in  FIGS.  18 A and  18 B , thereby making it easier to achieve the advantageous effects of the present invention. When symbols are ordered in the frequency domain, however, fluctuations in the frequency domain are abrupt, leading to the possibility of yielding diversity gain. Therefore, reordering in both the frequency and the time domains is not necessarily always the best scheme. 
       FIGS.  19 A and  19 B  show an example of a scheme of reordering symbols by the reordering units  1404 A and  1404 B in  FIG.  14   , the horizontal axis representing frequency, and the vertical axis representing time, that differs from  FIGS.  18 A and  18 B .  FIG.  19 A  shows the reordering scheme for symbols of the modulated signal z 1 , and  FIG.  19 B  shows the reordering scheme for symbols of the modulated signal z 2 . As in  FIGS.  18 A and  18 B ,  FIGS.  19 A and  19 B  show arrangement of symbols using both the frequency and the time axes. The difference as compared to  FIGS.  18 A and  18 B  is that, whereas symbols are arranged first in the frequency domain and then in the time domain in  FIGS.  18 A and  18 B , symbols are arranged first in the time domain and then in the frequency domain in  FIGS.  19 A and  19 B . In  FIGS.  19 A and  19 B , the symbol group  1901  and the symbol group  1902  are the symbols for one period (cycle) when using the precoding hopping scheme. 
     Note that in  FIGS.  18 A,  18 B,  19 A, and  19 B , as in  FIGS.  16 A and  16 B , the present invention may be similarly embodied, and the advantageous effect of high reception quality achieved, with the symbol arranging scheme of the modulated signal z 1  differing from the symbol arranging scheme of the modulated signal z 2 . Furthermore, in  FIGS.  18 A,  18 B,  19 A, and  19 B , as in  FIGS.  17 A and  17 B , the present invention may be similarly embodied, and the advantageous effect of high reception quality achieved, without arranging the symbols in order. 
       FIG.  27    shows an example of a scheme of reordering symbols by the reordering units  1404 A and  1404 B in  FIG.  14   , the horizontal axis representing frequency, and the vertical axis representing time, that differs from the above examples. The case of hopping between precoding matrices regularly over four slots, as in Equations 37-40, is considered. The characteristic feature of  FIG.  27    is that symbols are arranged in order in the frequency domain, but when progressing in the time domain, symbols are cyclically shifted by n symbols (in the example in  FIG.  27   , n=1). In the four symbols shown in the symbol group  2710  in the frequency domain in  FIG.  27   , precoding hops between the precoding matrices of Equations 37-40. 
     In this case, symbol # 0  is precoded using the precoding matrix in Equation 37, symbol # 1  is precoded using the precoding matrix in Equation 38, symbol # 2  is precoded using the precoding matrix in Equation 39, and symbol # 3  is precoded using the precoding matrix in Equation 40. 
     Similarly, for the symbol group  2720  in the frequency domain, symbol # 4  is precoded using the precoding matrix in Equation 37, symbol # 5  is precoded using the precoding matrix in Equation 38, symbol # 6  is precoded using the precoding matrix in Equation 39, and symbol # 7  is precoded using the precoding matrix in Equation 40. 
     For the symbols at time $ 1 , precoding hops between the above precoding matrices, but in the time domain, symbols are cyclically shifted. Therefore, precoding hops between precoding matrices for the symbol groups  2701 ,  2702 ,  2703 , and  2704  as follows. 
     In the symbol group  2701  in the time domain, symbol # 0  is precoded using the precoding matrix in Equation 37, symbol # 9  is precoded using the precoding matrix in Equation 38, symbol # 18  is precoded using the precoding matrix in Equation 39, and symbol # 27  is precoded using the precoding matrix in Equation 40. 
     In the symbol group  2702  in the time domain, symbol # 28  is precoded using the precoding matrix in Equation 37, symbol # 1  is precoded using the precoding matrix in Equation 38, symbol # 10  is precoded using the precoding matrix in Equation 39, and symbol # 19  is precoded using the precoding matrix in Equation 40. 
     In the symbol group  2703  in the time domain, symbol # 20  is precoded using the precoding matrix in Equation 37, symbol # 29  is precoded using the precoding matrix in Equation 38, symbol # 2  is precoded using the precoding matrix in Equation 39, and symbol # 11  is precoded using the precoding matrix in Equation 40. 
     In the symbol group  2704  in the time domain, symbol # 12  is precoded using the precoding matrix in Equation 37, symbol # 21  is precoded using the precoding matrix in Equation 38, symbol # 30  is precoded using the precoding matrix in Equation 39, and symbol # 3  is precoded using the precoding matrix in Equation 40. 
     The characteristic of  FIG.  27    is that, for example focusing on symbol # 11 , the symbols on either side in the frequency domain at the same time (symbols # 10  and # 12 ) are both precoded with a different precoding matrix than symbol # 11 , and the symbols on either side in the time domain in the same carrier (symbols # 2  and # 20 ) are both precoded with a different precoding matrix than symbol # 11 . This is true not only for symbol # 11 . Any symbol having symbols on either side in the frequency domain and the time domain is characterized in the same way as symbol # 11 . As a result, precoding matrices are effectively hopped between, and since the influence on stable conditions of direct waves is reduced, the possibility of improved reception quality of data increases. 
     In  FIG.  27   , the case of n=1 has been described, but n is not limited in this way. The present invention may be similarly embodied with n=3. Furthermore, in  FIG.  27   , when symbols are arranged in the frequency domain and time progresses in the time domain, the above characteristic is achieved by cyclically shifting the number of the arranged symbol, but the above characteristic may also be achieved by randomly (or regularly) arranging the symbols. 
     Embodiment 2 
     In Embodiment 1, regular hopping of the precoding weights as shown in  FIG.  6    has been described. In the present embodiment, a scheme for designing specific precoding weights that differ from the precoding weights in  FIG.  6    is described. 
     In  FIG.  6   , the scheme for hopping between the precoding weights in Equations 37-40 has been described. By generalizing this scheme, the precoding weights may be changed as follows. (The hopping period (cycle) for the precoding weights has four slots, and Equations are listed similarly to Equations 37-40.) For symbol number 4i (where i is an integer greater than or equal to zero): 
                   Math   ⁢         42                        (           z   ⁢   1   ⁢     (     4   ⁢   i     )                 z   ⁢   2   ⁢     (     4   ⁢   i     )             )     =       1     2       ⁢     (           e     j   ⁢       θ   11     (     4   ⁢   i     )               e     j   ⁢     (         θ   11     (     4   ⁢   i     )     +   λ     )                   e     j   ⁢       θ   21     (     4   ⁢   i     )               e     j   ⁢     (         θ   21     (     4   ⁢   i     )     +   λ   +   δ     )               )     ⁢     (           s   ⁢   1   ⁢     (     4   ⁢   i     )                 s   ⁢   2   ⁢     (     4   ⁢   i     )             )               Equation   ⁢         42               
Here, j is an imaginary unit.
 
For symbol number 4i+1:
 
                   Math   ⁢         43                        (           z   ⁢   1   ⁢     (       4   ⁢   i     +   1     )                 z   ⁢   2   ⁢     (       4   ⁢   i     +   1     )             )     =       1     2       ⁢     (           e     j   ⁢       θ   11     (       4   ⁢   i     +   1     )               e     j   ⁢     (         θ   11     (       4   ⁢   i     +   1     )     +   λ     )                   e     j   ⁢       θ   21     (       4   ⁢   i     +   1     )               e     j   ⁢     (         θ   21     (       4   ⁢   i     +   1     )     +   λ   +   δ     )               )     ⁢     (           s   ⁢   1   ⁢     (       4   ⁢   i     +   1     )                 s   ⁢   2   ⁢     (       4   ⁢   i     +   1     )             )               Equation   ⁢         43               
For symbol number 4i+2:
 
                   Math   ⁢         44                        (           z   ⁢   1   ⁢     (       4   ⁢   i     +   2     )                 z   ⁢   2   ⁢     (       4   ⁢   i     +   2     )             )     =       1     2       ⁢     (           e     j   ⁢       θ   11     (       4   ⁢   i     +   2     )               e     j   ⁢     (         θ   11     (       4   ⁢   i     +   2     )     +   λ     )                   e     j   ⁢       θ   21     (       4   ⁢   i     +   2     )               e     j   ⁢     (         θ   21     (       4   ⁢   i     +   2     )     +   λ   +   δ     )               )     ⁢     (           s   ⁢   1   ⁢     (       4   ⁢   i     +   2     )                 s   ⁢   2   ⁢     (       4   ⁢   i     +   2     )             )               Equation   ⁢         44               
For symbol number 4i+3:
 
                   Math   ⁢         45                        (           z   ⁢   1   ⁢     (       4   ⁢   i     +   3     )                 z   ⁢   2   ⁢     (       4   ⁢   i     +   3     )             )     =       1     2       ⁢     (           e     j   ⁢       θ   11     (       4   ⁢   i     +   3     )               e     j   ⁢     (         θ   11     (       4   ⁢   i     +   3     )     +   λ     )                   e     j   ⁢       θ   21     (       4   ⁢   i     +   3     )               e     j   ⁢     (         θ   21     (       4   ⁢   i     +   3     )     +   λ   +   δ     )               )     ⁢     (           s   ⁢   1   ⁢     (       4   ⁢   i     +   3     )                 s   ⁢   2   ⁢     (       4   ⁢   i     +   3     )             )               Equation   ⁢         45               
From Equations 36 and 41, the received vector R(t)=(r 1 ( t ), r 2 ( t )) T  can be represented as follows.
 
For symbol number 4i:
 
                   Math   ⁢         46                        (           r   ⁢   1   ⁢     (     4   ⁢   i     )                 r   ⁢   2   ⁢     (     4   ⁢   i     )             )     =       1     2       ⁢     (             h   11     (     4   ⁢   i     )             h   12     ⁢     (     4   ⁢   i     )                   h   21     ⁢     (     4   ⁢   i     )               h   22     ⁢     (     4   ⁢   i     )             )     ⁢     (           e     j   ⁢       θ   11     (     4   ⁢   i     )               e     j   ⁢     (         θ   11     (     4   ⁢   i     )     +   λ     )                   e     j   ⁢       θ   21     (     4   ⁢   i     )               e     j   ⁢     (         θ   21     (     4   ⁢   i     )     +   λ   +   δ     )               )     ⁢     (           s   ⁢   1   ⁢     (     4   ⁢   i     )                 s   ⁢   2   ⁢     (     4   ⁢   i     )             )                 Equation   ⁢         46                 
For symbol number 4i+1:
 
                   Math   ⁢         47                        (           r   ⁢   1   ⁢     (       4   ⁢   i     +   1     )                 r   ⁢   2   ⁢     (       4   ⁢   i     +   1     )             )     =       1     2       ⁢     (             h   11     (       4   ⁢   i     +   1     )             h   12     (       4   ⁢   i     +   1     )                 h   21     (       4   ⁢   i     +   1     )             h   22     (       4   ⁢   i     +   1     )           )     ⁢     (           e     j   ⁢       θ   11     (       4   ⁢   i     +   1     )               e     j   ⁢     (         θ   11     (       4   ⁢   i     +   1     )     +   λ     )                   e     j   ⁢       θ   21     (       4   ⁢   i     +   1     )               e     j   ⁢     (         θ   21     (       4   ⁢   i     +   1     )     +   λ   +   δ     )               )     ⁢     (           s   ⁢   1   ⁢     (       4   ⁢   i     +   1     )                 s   ⁢   2   ⁢     (       4   ⁢   i     +   1     )             )                 Equation   ⁢         47                 
For symbol number 4i+2:
 
                   Math   ⁢         48                        (           r   ⁢   1   ⁢     (       4   ⁢   i     +   1     )                 r   ⁢   2   ⁢     (       4   ⁢   i     +   1     )             )     =       1     2       ⁢     (             h   11     (       4   ⁢   i     +   2     )             h   12     (       4   ⁢   i     +   2     )                 h   21     (       4   ⁢   i     +   2     )             h   22     (       4   ⁢   i     +   2     )           )     ⁢     (           e     j   ⁢       θ   11     (       4   ⁢   i     +   2     )               e     j   ⁢     (         θ   11     (       4   ⁢   i     +   2     )     +   λ     )                   e     j   ⁢       θ   21     (       4   ⁢   i     +   2     )               e     j   ⁢     (         θ   21     (       4   ⁢   i     +   2     )     +   λ   +   δ     )               )     ⁢     (           s   ⁢   1   ⁢     (       4   ⁢   i     +   2     )                 s   ⁢   2   ⁢     (       4   ⁢   i     +   2     )             )                 Equation   ⁢         48                 
For symbol number 4i+3:
 
     
       
         
           
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                                   + 
                                   3 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       4 
                                       ⁢ 
                                       i 
                                     
                                     + 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         4 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       3 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       4 
                                       ⁢ 
                                       i 
                                     
                                     + 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         4 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       3 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     4 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   3 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     4 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   3 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   49 
                 
               
             
           
         
       
     
     In this case, it is assumed that only components of direct waves exist in the channel elements h 11 (t), h 12 (t), h 21 (t), and h 22 (t), that the amplitude components of the direct waves are all equal, and that fluctuations do not occur over time. With these assumptions, Equations 46-49 can be represented as follows. 
     For symbol number 4i: 
                   Math   ⁢         50                        (           r   ⁢   1   ⁢     (     4   ⁢   i     )                 r   ⁢   2   ⁢     (     4   ⁢   i     )             )     =       1     2       ⁢     (           Ae     j   ⁢   0           q             Ae     j   ⁢   0           q         )     ⁢     (           e     j   ⁢       θ   11     (     4   ⁢   i     )               e     j   ⁢     (         θ   11     (     4   ⁢   i     )     +   λ     )                   e     j   ⁢       θ   21     (     4   ⁢   i     )               e     j   (             θ   21     (     4   ⁢   i     )     +   λ   +   δ     )             )     ⁢     (           s   ⁢   1   ⁢     (     4   ⁢   i     )                 s   ⁢   2   ⁢     (     4   ⁢   i     )             )               Equation   ⁢         50               
For symbol number 4i+1:
 
                   Math   ⁢         51                        (           r   ⁢   1   ⁢     (       4   ⁢   i     +   1     )                 r   ⁢   2   ⁢     (       4   ⁢   i     +   1     )             )     =       1     2       ⁢     (           Ae     j   ⁢   0           q             Ae     j   ⁢   0           q         )     ⁢     (           e     j   ⁢       θ   11     (       4   ⁢   i     +   1     )               e     j   (             θ   11     (       4   ⁢   i     +   1     )     +   λ     )                 e     j   ⁢       θ   21     (       4   ⁢   i     +   1     )               e     j   (             θ   21     (       4   ⁢   i     +   1     )     +   λ   +   δ     )             )     ⁢     (           s   ⁢   1   ⁢     (       4   ⁢   i     +   1     )                 s   ⁢   2   ⁢     (       4   ⁢   i     +   1     )             )                 Equation   ⁢         51                 
For symbol number 4i+2:
 
             Math   ⁢         52                       (           r   ⁢   1   ⁢     (       4   ⁢   i     +   2     )                 r   ⁢   2   ⁢     (       4   ⁢   i     +   2     )             )     =       1     2       ⁢     (           Ae     j   ⁢   0           q             Ae     j   ⁢   0           q         )     ⁢     (           e     j   ⁢       θ   11     (       4   ⁢   i     +   2     )               e     j   ⁢     (         θ   11     (       4   ⁢   i     +   2     )     +   λ     )                   e     j   ⁢       θ   21     (       4   ⁢   i     +   2     )               e     j   ⁢     (         θ   21     (       4   ⁢   i     +   2     )     +   λ   +   δ     )               )     ⁢     (           s   ⁢   1   ⁢     (       4   ⁢   i     +   2     )                 s   ⁢   2   ⁢     (       4   ⁢   i     +   2     )             )               Equation   ⁢         52               
For symbol number 4i+3:
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   53 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   4 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 3 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   4 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 3 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               Ae 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             q 
                           
                         
                         
                           
                             
                               Ae 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       4 
                                       ⁢ 
                                       i 
                                     
                                     + 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         4 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       3 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       4 
                                       ⁢ 
                                       i 
                                     
                                     + 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         4 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       3 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     4 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   3 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     4 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   3 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     53 
                   
                 
               
             
           
         
       
     
     In Equations 50-53, let A be a positive real number and q be a complex number. The values of A and q are determined in accordance with the positional relationship between the transmission device and the reception device. Equations 50-53 can be represented as follows. 
     For symbol number 4i: 
                   Math   ⁢         54                        (           r   ⁢   1   ⁢     (     4   ⁢   i     )                 r   ⁢   2   ⁢     (     4   ⁢   i     )             )     =       1     2       ⁢     (           e     j   ⁢   0                 e     j   ⁢   0             )     ⁢     (           Ae     j   ⁢   0           q         )     ⁢     (           e     j   ⁢       θ   11     (     4   ⁢   i     )               e     j   (             θ   11     (     4   ⁢   i     )     +   λ     )                 e     j   ⁢       θ   21     (     4   ⁢   i     )               e     j   (             θ   21     (     4   ⁢   i     )     +   λ   +   δ     )             )     ⁢     (           s   ⁢   1   ⁢     (     4   ⁢   i     )                 s   ⁢   2   ⁢     (     4   ⁢   i     )             )                 Equation   ⁢         54                 
For symbol number 4i+1:
 
                   Math   ⁢         55                        (           r   ⁢   1   ⁢     (       4   ⁢   i     +   1     )                 r   ⁢   2   ⁢     (       4   ⁢   i     +   2     )             )     =       1     2       ⁢     (           e     j   ⁢   0                 e     j   ⁢   0             )     ⁢     (           Ae     j   ⁢   0           q         )     ⁢     (           e     j   ⁢       θ   11     (       4   ⁢   i     +   1     )               e     j   (             θ   11     (       4   ⁢   i     +   1     )     +   λ     )                 e     j   ⁢       θ   21     (       4   ⁢   i     +   1     )               e     j   (             θ   21     (       4   ⁢   i     +   1     )     +   λ   +   δ     )             )     ⁢     (           s   ⁢   1   ⁢     (       4   ⁢   i     +   1     )                 s   ⁢   2   ⁢     (       4   ⁢   i     +   1     )             )                 Equation   ⁢         55                 
For symbol number 4i+2:
 
             Math   ⁢         56                       (           r   ⁢   1   ⁢     (       4   ⁢   i     +   2     )                 r   ⁢   2   ⁢     (       4   ⁢   i     +   2     )             )     =       1     2       ⁢     (           e     j   ⁢   0                 e     j   ⁢   0             )     ⁢     (           Ae     j   ⁢   0           q         )     ⁢     (           e     j   ⁢       θ   11     (       4   ⁢   i     +   2     )               e     j   ⁡   (         θ   11     (       4   ⁢   i     +   1     )     +   λ     )                 e     j   ⁢       θ   21     (       4   ⁢   i     +   2     )               e     j   ⁡   (         θ   21     (       4   ⁢   i     +   1     )     +   λ   +   δ     )             )     ⁢     (           s   ⁢   1   ⁢     (       4   ⁢   i     +   2     )                 s   ⁢   2   ⁢     (       4   ⁢   i     +   2     )             )               Equation   ⁢         56               
For symbol number 4i+3:
 
     
       
         
           
             Math 
             ⁢ 
                 
             57 
           
         
       
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   4 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 3 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   4 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 3 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               Ae 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       4 
                                       ⁢ 
                                       i 
                                     
                                     + 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         4 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       3 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       4 
                                       ⁢ 
                                       i 
                                     
                                     + 
                                     3 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         4 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       3 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     4 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   3 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     4 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   3 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   57 
                 
               
             
           
         
       
     
     As a result, when q is represented as follows, a signal component based on one of s 1  and s 2  is no longer included in r 1  and r 2 , and therefore one of the signals s 1  and s 2  can no longer be obtained. 
     For symbol number 4i:
 
Math 58
 
 q=−Ae   j(θ     11     (4i)−θ     21     (4i))   ,−Ae   j(θ     11     (4i)−θ     21     (4i)−δ)   Equation 58
 
For symbol number 4i+1:
 
Math 59
 
 q=−Ae   j(θ     11     (4i+1)−θ     21     (4i+1))   ,−Ae   j(θ     11     (4i+1)−θ     21     (4i+1)−δ)   Equation 59
 
For symbol number 4i+2:
 
Math 60
 
 q=−Ae   j(θ     11     (4i+2)−θ     21     (4i+2))   ,−Ae   j(θ     11     (4i+2)−θ     21     (4i+2)−δ)   Equation 60
 
For symbol number 4i+3:
 
Math 61
 
 q=−Ae   j(θ     11     (4i+3)−θ     21     (4i+3))   ,−Ae   j(θ     11     (4i+3)−θ     21     (4i+3)−δ)   Equation 61
 
     In this case, if q has the same solution in symbol numbers 4i, 4i+1, 4i+2, and 4i+3, then the channel elements of the direct waves do not greatly fluctuate. Therefore, a reception device having channel elements in which the value of q is equivalent to the same solution can no longer obtain excellent reception quality for any of the symbol numbers. Therefore, it is difficult to achieve the ability to correct errors, even if error correction codes are introduced. Accordingly, for q not to have the same solution, the following condition is necessary from Equations 58-61 when focusing on one of two solutions of q which does not include δ.
 
Math 62
 
 e   j(θ     11     (4i+x)−θ     21     (4i+x))   ≠e   j(θ     11     (4i+y)−θ     21     (4i+y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2,3)  Condition #1
 
(x is 0, 1, 2, 3; y is 0, 1, 2, 3; and x≠y.)
 
In an example fulfilling Condition #1, values are set as follows:
 
     Example #1 
     (1) θ 11 (4i)=θ 11 (4i+1)=θ 11 (4i+2)=θ 11 (4i+3)=0 radians, 
     (2) θ 21 (4i)=0 radians, 
     (3) θ 21 (4i+1)=π/2 radians, 
     (4) θ 21 (4i+2)=π radians, and 
     (5) θ 21 (4i+3)=3π/2 radians. 
     (The above is an example. It suffices for one each of zero radians, π/2 radians, π radians, and 3π/2 radians to exist for the set (θ 21 (4i), θ 21 (4i+1), θ 21 (4i+2), θ 21 (4i+3)).) In this case, in particular under condition (1), there is no need to perform signal processing (rotation processing) on the baseband signal S 1 ( t ), which therefore offers the advantage of a reduction in circuit size. Another example is to set values as follows. 
     Example #2 
     (6) ƒ 11 (4i)=0 radians, 
     (7) θ 11 (4i+1)=π/2 radians, 
     (8) θ 11 (4i+2)=π radians, 
     (9) θ 11 (4i+3)=3π/2 radians, and 
     (10) θ 21 (4i)=θ 21 (4i+1)=θ 21 (4i+2)=θ 21 (4i+3)=0 radians. 
     (The above is an example. It suffices for one each of zero radians, π/2 radians, π radians, and 3π/2 radians to exist for the set (θ 11 (4i), θ 11 (4i+1), θ 11 (4i+2), θ 11 (4i+3)).) In this case, in particular under condition (6), there is no need to perform signal processing (rotation processing) on the baseband signal S 2 ( t ), which therefore offers the advantage of a reduction in circuit size. Yet another example is as follows. 
     Example #3 
     (11) θ 11 (4i)=θ 11 (4i+1)=θ 11 (4i+2)=θ 11 (4i+3)=0 radians, 
     (12) θ 21 (4i)=0 radians, 
     (13) θ 21 (4i+1)=π/4 radians, 
     (14) θ 21 (4i+2)=π/2 radians, and 
     (15) θ 21 (4i+3)=3π/4 radians. 
     (The above is an example. It suffices for one each of zero radians, π/4 radians, π/2 radians, and 3π/4 radians to exist for the set (θ 21 (4i), θ 21 (4i+1), θ 21 (4i+2), θ 21 (4i+3)).) 
     Example #4 
     (16) θ 11 (4i)=0 radians, 
     (17) θ 11 (4i+1)=π/4 radians, 
     (18) θ 11 (4i+2)=π/2 radians, 
     (19) θ 11 (4i+3)=3π/4 radians, and 
     (20) θ 21 (4i)=θ 21 (4i+1)=θ 21 (4i+2)=θ 21 (4i+3)=0 radians. 
     (The above is an example. It suffices for one each of zero radians, π/4 radians, π/2 radians, and 3π/4 radians to exist for the set (θ 11 (4i), θ 11 (4i+1), θ 11 (4i+2), θ 11 (4i+3)).) 
     While four examples have been shown, the scheme of satisfying Condition #1 is not limited to these examples. 
     Next, design requirements for not only θ 11  and θ 12 , but also for λ and δ are described. It suffices to set λ to a certain value; it is then necessary to establish requirements for δ. The following describes the design scheme for δ when λ is set to zero radians. 
     In this case, by defining δ so that π/2 radians≤|δ|≤π radians, excellent reception quality is achieved, particularly in an LOS environment. 
     Incidentally, for each of the symbol numbers 4i, 4i+1, 4i+2, and 4i+3, two points q exist where reception quality becomes poor. Therefore, a total of 2×4=8 such points exist. In an LOS environment, in order to prevent reception quality from degrading in a specific reception terminal, these eight points should each have a different solution. In this case, in addition to Condition #1, Condition #2 is necessary.
 
Math 63
 
 e   j(θ     11     (4i+x)−θ     21     (4i+x))   ≠e   j(θ     11     (4i+y)−θ     21     (4i+y)−δ)  for ∀ x,∀y  ( x,y= 0,1,2,3) and
 
 e   j(θ     11     (4i+x)−θ     21     (4i+x)−δ)   ≠e   j(θ     11     (4i+y)−θ     21     (4i+y)−δ)  for ∀ x,∀y  ( x≠y;x,y= 0,1,2,3)  Condition #2
 
     Additionally, the phase of these eight points should be evenly distributed (since the phase of a direct wave is considered to have a high probability of even distribution). The following describes the design scheme for δ to satisfy this requirement. 
     In the case of example #1 and example #2, the phase becomes even at the points at which reception quality is poor by setting δ to ±3π/4 radians. For example, letting δ be 3π/4 radians in example #1 (and letting A be a positive real number), then each of the four slots, points at which reception quality becomes poor exist once, as shown in  FIG.  20   . In the case of example #3 and example #4, the phase becomes even at the points at which reception quality is poor by setting δ to ±π radians. For example, letting δ be π radians in example #3, then in each of the four slots, points at which reception quality becomes poor exist once, as shown in  FIG.  21   . (If the element q in the channel matrix H exists at the points shown in  FIGS.  20  and  21   , reception quality degrades.) 
     With the above structure, excellent reception quality is achieved in an LOS environment. Above, an example of changing precoding weights in a four-slot period (cycle) is described, but below, changing precoding weights in an N-slot period (cycle) is described. Making the same considerations as in Embodiment 1 and in the above description, processing represented as below is performed on each symbol number. 
     For symbol number Ni (where i is an integer greater than or equal to zero): 
                   Math   ⁢         64                        (           z   ⁢   1   ⁢     (   Ni   )                 z   ⁢   2   ⁢     (     N   ⁢   i     )             )     =       1     2       ⁢     (           e     j   ⁢       θ   11     (     N   ⁢   i     )               e     j   (             θ   11     (     N   ⁢   i     )     +   λ     )                 e     j   ⁢       θ   21     (     N   ⁢   i     )               e     j   (             θ   21     (     N   ⁢   i     )     +   λ   +   δ     )             )     ⁢     (           s   ⁢   1   ⁢     (   Ni   )                 s   ⁢   2   ⁢     (     N   ⁢   i     )             )               Equation   ⁢         62               
Here, j is an imaginary unit.
 
For symbol number Ni+1:
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   65 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   N 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       N 
                                       ⁢ 
                                       i 
                                     
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         N 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       N 
                                       ⁢ 
                                       i 
                                     
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         N 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     N 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     63 
                   
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number Ni+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             Math 
             ⁢ 
                 
             66 
           
         
       
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         N 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         N 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     N 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   64 
                 
               
             
           
         
       
     
     Furthermore, for symbol number Ni+N−1: 
                   Math   ⁢         67                        (           z   ⁢   1   ⁢     (     Ni   +   N   -   1     )                 z   ⁢   2   ⁢     (       N   ⁢   i     +   N   -   1     )             )     =       1     2       ⁢     (           e     j   ⁢       θ   11     (       N   ⁢   i     +   N   -   1     )               e     j   (             θ   11     (       N   ⁢   i     +   N   -   1     )     +   λ     )                 e     j   ⁢       θ   21     (       N   ⁢   i     +   N   -   1     )               e     j   (             θ   21     (       N   ⁢   i     +   N   -   1     )     +   λ   +   δ     )             )     ⁢     (           s   ⁢   1   ⁢     (     Ni   +   N   -   1     )                 s   ⁢   2   ⁢     (       N   ⁢   i     +   N   -   1     )             )                 Equation   ⁢         65                 
Accordingly, r 1  and r 2  are represented as follows.
 
For symbol number Ni (where i is an integer greater than or equal to zero):
 
                   Math   ⁢         68                        (           r   ⁢   1   ⁢     (   Ni   )                 r   ⁢   2   ⁢     (     N   ⁢   i     )             )     =       1     2       ⁢     (             h   11     (   Ni   )             h   12     ⁢     (   Ni   )                   h   21     ⁢     (   Ni   )               h   22     ⁢     (   Ni   )             )     ⁢     (           e     j   ⁢       θ   11     (     N   ⁢   i     )               e     j   (             θ   11     (     N   ⁢   i     )     +   λ     )                 e     j   ⁢       θ   21     (     N   ⁢   i     )               e     j   (             θ   21     (     N   ⁢   i     )     +   λ   +   δ     )             )     ⁢     (           s   ⁢   1   ⁢     (   Ni   )                 s   ⁢   2   ⁢     (     N   ⁢   i     )             )                 Equation   ⁢         66                 
Here, j is an imaginary unit.
 
For symbol number Ni+1:
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   69 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   N 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 h 
                                 11 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 12 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               
                                 h 
                                 21 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 22 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       N 
                                       ⁢ 
                                       i 
                                     
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         N 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       N 
                                       ⁢ 
                                       i 
                                     
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         N 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     N 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     67 
                   
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number Ni+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   70 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   N 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 h 
                                 11 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 12 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               
                                 h 
                                 21 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 22 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       N 
                                       ⁢ 
                                       i 
                                     
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         N 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       N 
                                       ⁢ 
                                       i 
                                     
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         N 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     N 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     68 
                   
                 
               
             
           
         
       
     
     Furthermore, for symbol number Ni+N−1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   71 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   N 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 h 
                                 11 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 12 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               
                                 h 
                                 21 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 22 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       N 
                                       ⁢ 
                                       i 
                                     
                                     + 
                                     N 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         N 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       N 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       N 
                                       ⁢ 
                                       i 
                                     
                                     + 
                                     N 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         N 
                                         ⁢ 
                                         i 
                                       
                                       + 
                                       N 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     N 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     69 
                   
                 
               
             
           
         
       
     
     In this case, it is assumed that only components of direct waves exist in the channel elements h 11 (t), h 12 (t), h 21 (t), and h 22 (t), that the amplitude components of the direct waves are all equal, and that fluctuations do not occur over time. With these assumptions, Equations 66-69 can be represented as follows. 
     For symbol number Ni (where i is an integer greater than or equal to zero): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                     
                   72 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               Ni 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               Ni 
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                                 
                               
                                 A 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     0 
                                   
                                 
                               
                             
                           
                           
                             q 
                           
                         
                         
                           
                             
                               A 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   Ni 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       Ni 
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   Ni 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       Ni 
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 Ni 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 Ni 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   70 
                 
               
             
           
         
       
     
     Here, j is an imaginary unit. 
     For symbol number Ni+1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   73 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                                 
                               
                                 A 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     0 
                                   
                                 
                               
                             
                           
                           
                             q 
                           
                         
                         
                           
                             
                               A 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     71 
                   
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number Ni+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   74 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                                 
                               
                                 A 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     0 
                                   
                                 
                               
                             
                           
                           
                             q 
                           
                         
                         
                           
                             
                               A 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         k 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         k 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     72 
                   
                 
               
             
           
         
       
     
     Furthermore, for symbol number Ni+N−1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   75 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                                 
                               
                                 A 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     0 
                                   
                                 
                               
                             
                           
                           
                             q 
                           
                         
                         
                           
                             
                               A 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     N 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         N 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     N 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         N 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     73 
                   
                 
               
             
           
         
       
     
     In Equations 70-73, let A be a real number and q be a complex number. The values of A and q are determined in accordance with the positional relationship between the transmission device and the reception device. Equations 70-73 can be represented as follows. 
     For symbol number Ni (where i is an integer greater than or equal to zero): 
                   Math   ⁢         76                        (           r   ⁢   1   ⁢     (   Ni   )                 r   ⁢   2   ⁢     (   Ni   )             )     =       1     2       ⁢     (                 e     j   ⁢   0                         e     j   ⁢   0               )     ⁢     (                 A     e     j   ⁢   0               q         )     ⁢     (           e     j   ⁢       θ   11     (   Ni   )               e     j   ⁢     (         θ   11     (   Ni   )     +   λ     )                   e     j   ⁢       θ   21     (   Ni   )               e     j   ⁢     (         θ   21     (   Ni   )     +   λ   +   δ     )               )     ⁢     (           s   ⁢   1   ⁢     (   Ni   )                 s   ⁢   2   ⁢     (   Ni   )             )                 Equation   ⁢         74                 
Here, j is an imaginary unit.
 
For symbol number Ni+1:
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   77 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                                 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                                 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                                 
                               
                                 A 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     0 
                                   
                                 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     75 
                   
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number Ni+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   78 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                                 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                                 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                                 
                               
                                 A 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     0 
                                   
                                 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         k 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         k 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     76 
                   
                 
               
             
           
         
       
     
     Furthermore, for symbol number Ni+N−1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   79 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                                 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                                 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                                 
                               
                                 A 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     0 
                                   
                                 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     N 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         N 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     N 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         N 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     77 
                   
                 
               
             
           
         
       
     
     As a result, when q is represented as follows, a signal component based on one of s 1  and s 2  is no longer included in r 1  and r 2 , and therefore one of the signals s 1  and s 2  can no longer be obtained. 
     For symbol number Ni (where i is an integer greater than or equal to zero):
 
Math 80
 
 q=−Ae   j(θ     11     (Ni)−θ     21     (Ni))   ,−Ae   j(θ     11     (Ni)−θ     21     (Ni)−δ)   Equation 78
 
For symbol number Ni+1:
 
Math 81
 
 q=−Ae   j(θ     11     (Ni+1)−θ     21     (Ni+1))   ,−Ae   j(θ     11     (Ni+1)−θ     21     (Ni+1)−δ)   Equation 79
 
     When generalized, this equation is as follows. 
     For symbol number Ni+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)):
 
Math 82
 
 q=−Ae   j(θ     11     (Ni+k)−θ     21     (Ni+k))   ,−Ae   j(θ     11     (Ni+k)−θ     21     (Ni+k)−δ)   Equation 80
 
     Furthermore, for symbol number Ni+N−1:
 
Math 83
 
 q=−Ae   j(θ     11     (Ni+N−1)−θ     21     (Ni+N−1))   ,−Ae   j(θ     11     (Ni+N−1)−θ     21     (Ni+N−1)−δ)   Equation 81
 
     In this case, if q has the same solution in symbol numbers Ni through Ni+N−1, then since the channel elements of the direct waves do not greatly fluctuate, a reception device having channel elements in which the value of q is equivalent to this same solution can no longer obtain excellent reception quality for any of the symbol numbers. Therefore, it is difficult to achieve the ability to correct errors, even if error correction codes are introduced. Accordingly, for q not to have the same solution, the following condition is necessary from Equations 78-81 when focusing on one of two solutions of q which does not include δ.
 
Math 84
 
 e   j(θ     11     (Ni+x)−θ     21     (Ni+x))   ≠e   j(θ     11     (Ni+y)−θ     21     (Ni+y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2, . . . , N− 2, N− 1)   Condition #3
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
     Next, design requirements for not only θ 11  and θ 12 , but also for λ and δ are described. It suffices to set λ to a certain value; it is then necessary to establish requirements for δ. The following describes the design scheme for δ when λ is set to zero radians. 
     In this case, similar to the scheme of changing the precoding weights in a four-slot period (cycle), by defining δ so that π/2 radians≤|δ|≤π radians, excellent reception quality is achieved, particularly in an LOS environment. 
     In each symbol number Ni through Ni+N−1, two points labeled q exist where reception quality becomes poor, and therefore 2N such points exist. In an LOS environment, in order to achieve excellent characteristics, these 2N points should each have a different solution. In this case, in addition to Condition #3, Condition #4 is necessary.
 
Math 85
 
 e   j(θ     11     (Ni+x)−θ     21     (Ni+x))   ≠e   j(θ     11     (Ni+y)−θ     21     (Ni+y)−δ)  for ∀ x,∀y  ( x,y= 0,1,2, . . . , N− 2, N− 1) and
 
 e   j(θ     11     (Ni+x)−θ     21     (Ni+x)−δ)   ≠e   j(θ     11     (Ni+y)−θ     21     (Ni+y)−δ)  for ∀ x,∀y  ( x≠y;x,y= 0,1,2, . . . , N− 2, N− 1)  Condition #4
 
     Additionally, the phase of these 2N points should be evenly distributed (since the phase of a direct wave at each reception device is considered to have a high probability of even distribution). 
     As described above, when a transmission device transmits a plurality of modulated signals from a plurality of antennas in a MIMO system, the advantageous effect of improved transmission quality, as compared to conventional spatial multiplexing MIMO system, is achieved in an LOS environment in which direct waves dominate by hopping between precoding weights regularly over time. 
     In the present embodiment, the structure of the reception device is as described in Embodiment 1, and in particular with regards to the structure of the reception device, operations have been described for a limited number of antennas, but the present invention may be embodied in the same way even if the number of antennas increases. In other words, the number of antennas in the reception device does not affect the operations or advantageous effects of the present embodiment. Furthermore, in the present embodiment, similar to Embodiment 1, the error correction codes are not limited. 
     In the present embodiment, in contrast with Embodiment 1, the scheme of changing the precoding weights in the time domain has been described. As described in Embodiment 1, however, the present invention may be similarly embodied by changing the precoding weights by using a multi-carrier transmission scheme and arranging symbols in the frequency domain and the frequency-time domain. Furthermore, in the present embodiment, symbols other than data symbols, such as pilot symbols (preamble, unique word, and the like), symbols for control information, and the like, may be arranged in the frame in any way. 
     Embodiment 3 
     In Embodiment 1 and Embodiment 2, the scheme of regularly hopping between precoding weights has been described for the case where the amplitude of each element in the precoding weight matrix is equivalent. In the present embodiment, however, an example that does not satisfy this condition is described. 
     For the sake of contrast with Embodiment 2, the case of changing precoding weights over an N-slot period (cycle) is described. Making the same considerations as in Embodiment 1 and Embodiment 2, processing represented as below is performed on each symbol number. Let β be a positive real number, and β≠1. For symbol number Ni (where i is an integer greater than or equal to zero): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   86 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               Ni 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               Ni 
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   Ni 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         Ni 
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     Ni 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       Ni 
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 Ni 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 Ni 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     82 
                   
                 
               
             
           
         
       
     
     Here, j is an imaginary unit. 
     For symbol number Ni+1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   87 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         
                                           Ni 
                                           + 
                                           1 
                                         
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     83 
                   
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number Ni+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   88 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         
                                           Ni 
                                           + 
                                           k 
                                         
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         k 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     84 
                   
                 
               
             
           
         
       
     
     Furthermore, for symbol number Ni+N−1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   89 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     N 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         
                                           Ni 
                                           + 
                                           N 
                                           - 
                                           1 
                                         
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       N 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         N 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     85 
                   
                 
               
             
           
         
       
     
     Accordingly, r 1  and r 2  are represented as follows. 
     For symbol number Ni (where i is an integer greater than or equal to zero): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   90 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               Ni 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               Ni 
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 h 
                                 11 
                               
                               ( 
                               Ni 
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 12 
                               
                               ⁢ 
                               
                                 ( 
                                 Ni 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 h 
                                 21 
                               
                               ⁢ 
                               
                                 ( 
                                 Ni 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 h 
                                 22 
                               
                               ⁢ 
                               
                                 ( 
                                 Ni 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   Ni 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         Ni 
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     Ni 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       Ni 
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 Ni 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 Ni 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     86 
                   
                 
               
             
           
         
       
     
     Here, j is an imaginary unit. 
     For symbol number Ni+1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   91 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 h 
                                 11 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 12 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               
                                 h 
                                 21 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 22 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         
                                           Ni 
                                           + 
                                           1 
                                         
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     87 
                   
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number Ni+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                     
                   92 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 h 
                                 11 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 12 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               
                                 h 
                                 21 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 22 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         
                                           Ni 
                                           + 
                                           k 
                                         
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         k 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     88 
                   
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number Ni+N−1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   93 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 h 
                                 11 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 12 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 h 
                                 21 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 h 
                                 22 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     N 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ( 
                                     
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         N 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       N 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       N 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     89 
                   
                 
               
             
           
         
       
     
     In this case, it is assumed that only components of direct waves exist in the channel elements h 11 (t), h 12 (t), h 21 (t), and h 22 (t), that the amplitude components of the direct waves are all equal, and that fluctuations do not occur over time. With these assumptions, Equations 86-89 can be represented as follows. 
     For symbol number Ni (where i is an integer greater than or equal to zero): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   94 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               Ni 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               Ni 
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                   
                                 A 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                         
                           
                             
                               
                                   
                                 A 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   Ni 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ( 
                                     
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       Ni 
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     Ni 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     Ni 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 Ni 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 Ni 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     90 
                   
                 
               
             
           
         
       
     
     Here, j is an imaginary unit. 
     For symbol number Ni+1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   95 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                   
                                 A 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                         
                           
                             
                               
                                   
                                 A 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ( 
                                     
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     91 
                   
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number Ni+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   96 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                   
                                 A 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                         
                           
                             
                               
                                   
                                 A 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ( 
                                     
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         k 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     92 
                   
                 
               
             
           
         
       
     
     Furthermore, for symbol number Ni+N−1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   97 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                   
                                 A 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                         
                           
                             
                               
                                   
                                 A 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     N 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ( 
                                     
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         N 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       N 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       N 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     93 
                   
                 
               
             
           
         
       
     
     In Equations 90-93, let A be a real number and q be a complex number. Equations 90-93 can be represented as follows. 
     For symbol number Ni (where i is an integer greater than or equal to zero): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   98 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               Ni 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               Ni 
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                   
                                 A 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   Ni 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ( 
                                     
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       Ni 
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     Ni 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     Ni 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 Ni 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 Ni 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     94 
                   
                 
               
             
           
         
       
     
     Here, j is an imaginary unit. 
     For symbol number Ni+1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   99 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                   
                                 A 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ( 
                                     
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     95 
                   
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number Ni+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   100 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                   
                                 A 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ( 
                                     
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         k 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     96 
                   
                 
               
             
           
         
       
     
     Furthermore, for symbol number Ni+N−1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   101 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                   
                                 A 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     Ni 
                                     + 
                                     N 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ( 
                                     
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         Ni 
                                         + 
                                         N 
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                   
                                 
                                   β 
                                   × 
                                 
                               
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       N 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       Ni 
                                       + 
                                       N 
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   Ni 
                                   + 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     97 
                   
                 
               
             
           
         
       
     
     As a result, when q is represented as follows, one of the signals s 1  and s 2  can no longer be obtained. 
     For symbol number Ni (where i is an integer greater than or equal to zero): 
                   Math   ⁢         102                        q   =       -     A   β       ⁢     e     j   ⁡   (         θ   11     (   Ni   )     -       θ   21     (   Ni   )       )           ,       -   A     ⁢   β   ⁢     e     j   ⁡   (         θ   11     (   Ni   )     -       θ   21     (   Ni   )     -   δ     )                 Equation   ⁢         98               
For symbol number Ni+1:
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   103 
                 
               
               
                  
               
             
             
               
                 
                   
                     q 
                     = 
                     
                       
                         - 
                         
                           A 
                           β 
                         
                       
                       ⁢ 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   , 
                   
                     
                       - 
                       A 
                     
                     ⁢ 
                     β 
                     ⁢ 
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             
                               Ni 
                               + 
                               1 
                             
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             
                               Ni 
                               + 
                               1 
                             
                             ) 
                           
                           - 
                           δ 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   99 
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number Ni+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   104 
                 
               
               
                  
               
             
             
               
                 
                   
                     q 
                     = 
                     
                       
                         - 
                         
                           A 
                           β 
                         
                       
                       ⁢ 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   , 
                   
                     
                       - 
                       A 
                     
                     ⁢ 
                     β 
                     ⁢ 
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             
                               Ni 
                               + 
                               k 
                             
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             
                               Ni 
                               + 
                               k 
                             
                             ) 
                           
                           - 
                           δ 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   100 
                 
               
             
           
         
       
     
     Furthermore, for symbol number Ni+N−1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   105 
                 
               
               
                  
               
             
             
               
                 
                   
                     q 
                     = 
                     
                       
                         - 
                         
                           A 
                           β 
                         
                       
                       ⁢ 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 Ni 
                                 + 
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   , 
                   
                     
                       - 
                       A 
                     
                     ⁢ 
                     β 
                     ⁢ 
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             
                               Ni 
                               + 
                               N 
                               - 
                               1 
                             
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             
                               Ni 
                               + 
                               N 
                               - 
                               1 
                             
                             ) 
                           
                           - 
                           δ 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   101 
                 
               
             
           
         
       
     
     In this case, if q has the same solution in symbol numbers Ni through Ni+N−1, then since the channel elements of the direct waves do not greatly fluctuate, excellent reception quality can no longer be obtained for any of the symbol numbers. Therefore, it is difficult to achieve the ability to correct errors, even if error correction codes are introduced. Accordingly, for q not to have the same solution, the following condition is necessary from Equations 98-101 when focusing on one of two solutions of q which does not include δ.
 
Math 106
 
 e   j(θ     11     (Ni+x)−θ     21     (Ni+x))   ≠e   j(θ     11     (Ni+y)−θ     21     (Ni+y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2, . . . , N− 2, N− 1)   Condition #5
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
     Next, design requirements for not only θ 11  and θ 12 , but also for λ and δ are described. It suffices to set λ to a certain value; it is then necessary to establish requirements for S. The following describes the design scheme for δ when λ is set to zero radians. 
     In this case, similar to the scheme of changing the precoding weights in a four-slot period (cycle), by defining δ so that π/2 radians≤|δ|≤π radians, excellent reception quality is achieved, particularly in an LOS environment. 
     In each of symbol numbers Ni through Ni+N−1, two points q exist where reception quality becomes poor, and therefore 2N such points exist. In an LOS environment, in order to achieve excellent characteristics, these 2N points should each have a different solution. In this case, in addition to Condition #5, considering that β is a positive real number, and β≠1, Condition #6 is necessary.
 
Math 107
 
 e   j(θ     11     (Ni+x)−θ     21     (Ni+x)−δ)   ≠e   j(θ     11     (Ni+y)−θ     21     (Ni+y)−δ)  for ∀ x,∀y  ( x≠y;x,y= 0,1,2, . . . , N− 2, N− 1)  Condition #6
 
     As described above, when a transmission device transmits a plurality of modulated signals from a plurality of antennas in a MIMO system, the advantageous effect of improved transmission quality, as compared to conventional spatial multiplexing MIMO system, is achieved in an LOS environment in which direct waves dominate by hopping between precoding weights regularly over time. 
     In the present embodiment, the structure of the reception device is as described in Embodiment 1, and in particular with regards to the structure of the reception device, operations have been described for a limited number of antennas, but the present invention may be embodied in the same way even if the number of antennas increases. In other words, the number of antennas in the reception device does not affect the operations or advantageous effects of the present embodiment. Furthermore, in the present embodiment, similar to Embodiment 1, the error correction codes are not limited. 
     In the present embodiment, in contrast with Embodiment 1, the scheme of changing the precoding weights in the time domain has been described. As described in Embodiment 1, however, the present invention may be similarly embodied by changing the precoding weights by using a multi-carrier transmission scheme and arranging symbols in the frequency domain and the frequency-time domain. Furthermore, in the present embodiment, symbols other than data symbols, such as pilot symbols (preamble, unique word, and the like), symbols for control information, and the like, may be arranged in the frame in any way. 
     Embodiment 4 
     In Embodiment 3, the scheme of regularly hopping between precoding weights has been described for the example of two types of amplitudes for each element in the precoding weight matrix, 1 and β. 
     In this case, 
                   1         β   2     +   1               Math   ⁢         108               
is ignored.
 
     Next, the example of changing the value of β by slot is described. For the sake of contrast with Embodiment 3, the case of changing precoding weights over a 2×N-slot period (cycle) is described. 
     Making the same considerations as in Embodiment 1, Embodiment 2, and Embodiment 3, processing represented as below is performed on symbol numbers. Let β be a positive real number, and β≠1. Furthermore, let a be a positive real number, and α≠β. 
     For symbol number 2Ni (where i is an integer greater than or equal to zero): 
                   Math   ⁢         109                        (           z   ⁢   1   ⁢     (     2   ⁢   Ni     )                 z   ⁢   2   ⁢     (     2   ⁢   Ni     )             )     =       1         β   2     +   1         ⁢     (           e     j   ⁢       θ   11     (     2   ⁢   Ni     )                     β     ×     e     j   (             θ   11     (     2   ⁢   Ni     )     +   λ     )                         β     ×     e     j   ⁢       θ   21     (     2   ⁢   Ni     )                 e     j   (             θ   21     (     2   ⁢   Ni     )     +   λ   +   δ     )             )     ⁢     (           s   ⁢   1   ⁢     (     2   ⁢   Ni     )                 s   ⁢   2   ⁢     (     2   ⁢   Ni     )             )                 Equation   ⁢         102                 
Here, j is an imaginary unit.
 
For symbol number 2Ni+1:
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   110 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           Ni 
                                         
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     103 
                   
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number 2Ni+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   111 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           Ni 
                                         
                                         + 
                                         k 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     104 
                   
                 
               
             
           
         
       
     
     Furthermore, for symbol number 2Ni+N−1: 
                   Math   ⁢         112                        (           z   ⁢   1   ⁢     (       2   ⁢   Ni     +   N   -   1     )                 z   ⁢   2   ⁢     (       2   ⁢   Ni     +   N   -   1     )             )     =       1         β   2     +   1         ⁢     (           e     j   ⁢       θ   11     (       2   ⁢   Ni     +   N   -   1     )               β   ×     e     j   ⁡   (         θ   11     (       2   ⁢   Ni     +   N   -   1     )     +   λ     )                   β   ×     e     j   ⁢       θ   21     (       2   ⁢   Ni     +   N   -   1     )                 e     j   ⁡   (         θ   21     (       2   ⁢   Ni     +   N   -   1     )     +   λ   +   δ     )             )     ⁢     (           s   ⁢   1   ⁢     (       2   ⁢   Ni     +   N   -   1     )                 s   ⁢   2   ⁢     (       2   ⁢   Ni     +   N   -   1     )             )                 Equation   ⁢         105                 
For symbol number 2Ni+N (where i is an integer greater than or equal to zero):
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   113 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     N 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           Ni 
                                         
                                         + 
                                         N 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   N 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   N 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     106 
                   
                 
               
             
           
         
       
     
     Here, j is an imaginary unit. 
     For symbol number 2Ni+N+1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   114 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     N 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           Ni 
                                         
                                         + 
                                         N 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   N 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   N 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     107 
                   
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number 2Ni+N+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   115 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     N 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           Ni 
                                         
                                         + 
                                         N 
                                         + 
                                         k 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   N 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   N 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     108 
                   
                 
               
             
           
         
       
     
     Furthermore, for symbol number 2Ni+2N−1: 
     
       
         
           
             Math 
             ⁢ 
                 
             116 
           
         
       
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   N 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     
                                       2 
                                       ⁢ 
                                       N 
                                     
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           
                                             1 
                                             ⁢ 
                                             1 
                                           
                                         
                                         ( 
                                         
                                           
                                             2 
                                             ⁢ 
                                             Ni 
                                           
                                           + 
                                           
                                             2 
                                             ⁢ 
                                             N 
                                           
                                           - 
                                           1 
                                         
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       
                                         2 
                                         ⁢ 
                                         1 
                                       
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       
                                         2 
                                         ⁢ 
                                         N 
                                       
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         
                                           2 
                                           ⁢ 
                                           1 
                                         
                                       
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           Ni 
                                         
                                         + 
                                         
                                           2 
                                           ⁢ 
                                           N 
                                         
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   
                                     2 
                                     ⁢ 
                                     N 
                                   
                                   - 
                                   1 
                                 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     N 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   
                                     2 
                                     ⁢ 
                                     N 
                                   
                                   - 
                                   1 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   109 
                 
               
             
           
         
       
     
     Accordingly, r 1  and r 2  are represented as follows. 
     For symbol number 2Ni (where i is an integer greater than or equal to zero): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   117 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 h 
                                 11 
                               
                               ( 
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 12 
                               
                               ( 
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               
                                 h 
                                 21 
                               
                               ( 
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 22 
                               
                               ( 
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     110 
                   
                 
               
             
           
         
       
     
     Here, j is an imaginary unit. 
     For symbol number 2Ni+1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   118 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 h 
                                 11 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 12 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               
                                 h 
                                 21 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 22 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           Ni 
                                         
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     111 
                   
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number 2Ni+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   119 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 h 
                                 11 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 12 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               
                                 h 
                                 21 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 22 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           Ni 
                                         
                                         + 
                                         k 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     112 
                   
                 
               
             
           
         
       
     
     Furthermore, for symbol number 2Ni+N−1: 
                   Math   ⁢         120                        (           r   ⁢   1   ⁢     (       2   ⁢   Ni     +   N   -   1     )                 r   ⁢   2   ⁢     (       2   ⁢   Ni     +   N   -   1     )             )     =       1         β   2     +   1         ⁢     (             h   11     (       2   ⁢   Ni     +   N   -   1     )             h   12     (       2   ⁢   Ni     +   N   -   1     )                 h   21     (       2   ⁢   Ni     +   N   -   1     )             h   22     (       2   ⁢   Ni     +   N   -   1     )           )     ⁢     (           e     j   ⁢       θ   11     (       2   ⁢   Ni     +   N   -   1     )               β   ×     e     j   ⁡   (         θ   11     (       2   ⁢   Ni     +   N   -   1     )     +   λ     )                   β   ×     e     j   ⁢       θ   21     (       2   ⁢   Ni     +   N   -   1     )                 e     j   ⁡   (         θ   21     (       2   ⁢   Ni     +   N   -   1     )     +   λ   +   δ     )             )     ⁢     (           s   ⁢   1   ⁢     (       2   ⁢   Ni     +   N   -   1     )                 s   ⁢   2   ⁢     (       2   ⁢   Ni     +   N   -   1     )             )                 Equation   ⁢         113                 
For symbol number 2Ni+N (where i is an integer greater than or equal to zero):
 
                   Math   ⁢         121                        (           r   ⁢   1   ⁢     (       2   ⁢   Ni     +   N     )                 r   ⁢   2   ⁢     (       2   ⁢   Ni     +   N     )             )     =       1         α   2     +   1         ⁢     (             h   11     (       2   ⁢   Ni     +   N     )             h   12     (       2   ⁢   Ni     +   N     )                 h   21     (       2   ⁢   Ni     +   N     )             h   22     (       2   ⁢   Ni     +   N     )           )     ⁢     (           e     j   ⁢       θ   11     (       2   ⁢   Ni     +   N     )               α   ×     e     j   ⁡   (         θ   11     (       2   ⁢   Ni     +   N     )     +   λ     )                   α   ×     e     j   ⁢       θ   21     (       2   ⁢   Ni     +   N     )                 e     j   ⁡   (         θ   21     (       2   ⁢   Ni     +   N     )     +   λ   +   δ     )             )     ⁢     (           s   ⁢   1   ⁢     (       2   ⁢   Ni     +   N     )                 s   ⁢   2   ⁢     (       2   ⁢   Ni     +   N     )             )                 Equation   ⁢         114                 
Here, j is an imaginary unit.
 
For symbol number 2Ni+N+1:
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   122 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 h 
                                 11 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 12 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               
                                 h 
                                 21 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 22 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     N 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           Ni 
                                         
                                         + 
                                         N 
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   N 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   N 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     115 
                   
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number 2Ni+N+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   123 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 h 
                                 11 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 12 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               
                                 h 
                                 21 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 22 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     N 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           Ni 
                                         
                                         + 
                                         N 
                                         + 
                                         k 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   N 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   N 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     116 
                   
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number 2Ni+2N−1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   124 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 h 
                                 11 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 12 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               
                                 h 
                                 21 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                           
                             
                               
                                 h 
                                 22 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     
                                       2 
                                       ⁢ 
                                       N 
                                     
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           Ni 
                                         
                                         + 
                                         
                                           2 
                                           ⁢ 
                                           N 
                                         
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       
                                         2 
                                         ⁢ 
                                         N 
                                       
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       
                                         2 
                                         ⁢ 
                                         N 
                                       
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   
                                     2 
                                     ⁢ 
                                     N 
                                   
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   
                                     2 
                                     ⁢ 
                                     N 
                                   
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     117 
                   
                 
               
             
           
         
       
     
     In this case, it is assumed that only components of direct waves exist in the channel elements h 11 (t), h 12 (t), h 21 (t), and h 22 ( t ), that the amplitude components of the direct waves are all equal, and that fluctuations do not occur over time. With these assumptions, Equations 110-117 can be represented as follows. 
     For symbol number 2Ni (where i is an integer greater than or equal to zero): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   125 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               A 
                               ⁢ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                         
                           
                             
                               A 
                               ⁢ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             q 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   118 
                 
               
             
           
         
       
     
     Here, j is an imaginary unit. 
     For symbol number 2Ni+1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   126 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           β 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             ⁢ 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           q 
                         
                       
                       
                         
                           
                             A 
                             ⁢ 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           q 
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             β 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             β 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             s 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             s 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   119 
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number 2Ni+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   127 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           β 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             ⁢ 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           q 
                         
                       
                       
                         
                           
                             A 
                             ⁢ 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           q 
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             β 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             β 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             s 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             s 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   120 
                 
               
             
           
         
       
     
     Furthermore, for symbol number 2Ni+N−1: 
                   Math   ⁢         128                        (           r   ⁢   1   ⁢     (       2   ⁢   Ni     +   N   -   1     )                 r   ⁢   2   ⁢     (       2   ⁢   Ni     +   N   -   1     )             )     ⁢     1         β   2     +   1         ⁢     (           A   ⁢     e     j   ⁢   0             q             A   ⁢     e     j   ⁢   0             q         )     ⁢     (           e     j   ⁢       θ   11     (       2   ⁢   Ni     +   N   -   1     )               β   ×     e     j   ⁡   (         θ   11     (       2   ⁢   Ni     +   N   -   1     )     +   λ     )                   β   ×     e     j   ⁢       θ   21     (       2   ⁢   Ni     +   N   -   1     )                 e     j   ⁢     (         θ   21     (       2   ⁢   Ni     +   N   -   1     )     +   λ   +   δ     )               )     ⁢     (           s   ⁢   1   ⁢     (       2   ⁢   Ni     +   N   -   1     )                 s   ⁢   2   ⁢     (       2   ⁢   Ni     +   N   -   1     )             )             Equation   ⁢          121               
For symbol number 2Ni+N (where i is an integer greater than or equal to zero):
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   129 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           α 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             ⁢ 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           q 
                         
                       
                       
                         
                           
                             A 
                             ⁢ 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           q 
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   N 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     N 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             s 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             s 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   122 
                 
               
             
           
         
       
     
     Here, j is an imaginary unit. 
     For symbol number 2Ni+N+1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   130 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           α 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             ⁢ 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           q 
                         
                       
                       
                         
                           
                             A 
                             ⁢ 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           q 
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   N 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     N 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             s 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             s 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   123 
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number 2Ni+N+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   131 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           α 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             ⁢ 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           q 
                         
                       
                       
                         
                           
                             A 
                             ⁢ 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           q 
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   N 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     N 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             s 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             s 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   124 
                 
               
             
           
         
       
     
     Furthermore, for symbol number 2Ni+2N−1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   132 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           α 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             ⁢ 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           q 
                         
                       
                       
                         
                           
                             A 
                             ⁢ 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           q 
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   
                                     2 
                                     ⁢ 
                                     N 
                                   
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       
                                         2 
                                         ⁢ 
                                         N 
                                       
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     
                                       2 
                                       ⁢ 
                                       N 
                                     
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       
                                         2 
                                         ⁢ 
                                         N 
                                       
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             s 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             s 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   125 
                 
               
             
           
         
       
     
     In Equations 118-125, let A be a real number and q be a complex number. Equations 118-125 can be represented as follows. 
     For symbol number 2Ni (where i is an integer greater than or equal to zero): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   133 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           β 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               0 
                             
                           
                         
                       
                       
                         
                           
                               
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         Ae 
                         
                           j 
                           ⁢ 
                           0 
                         
                       
                       ⁢ 
                            
                       q 
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             β 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             β 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ⁡ 
                               ( 
                               
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   ) 
                                 
                                 + 
                                 λ 
                                 + 
                                 δ 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             s 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             s 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   126 
                 
               
             
           
         
       
     
     Here, j is an imaginary unit. 
     For symbol number 2Ni+1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   134 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           β 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               0 
                             
                           
                         
                       
                       
                         
                           
                               
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         Ae 
                         
                           j 
                           ⁢ 
                           0 
                         
                       
                       ⁢ 
                            
                       q 
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             β 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             β 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ⁡ 
                               ( 
                               
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     1 
                                   
                                   ) 
                                 
                                 + 
                                 λ 
                                 + 
                                 δ 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             s 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             s 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   127 
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number 2Ni+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   135 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           β 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               0 
                             
                           
                         
                       
                       
                         
                           
                               
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         Ae 
                         
                           j 
                           ⁢ 
                           0 
                         
                       
                       ⁢ 
                            
                       q 
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             β 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             β 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ⁡ 
                               ( 
                               
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     k 
                                   
                                   ) 
                                 
                                 + 
                                 λ 
                                 + 
                                 δ 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             s 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             s 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   128 
                 
               
             
           
         
       
     
     Furthermore, for symbol number 2Ni+N−1: 
                   Math   ⁢         136                        (           r   ⁢   1   ⁢     (       2   ⁢   Ni     +   N   -   1     )                 r   ⁢   2   ⁢     (       2   ⁢   Ni     +   N   -   1     )             )     ⁢     1         β   2     +   1         ⁢     (           e     j   ⁢   0                       e     j   ⁢   0               )     ⁢     (       Ae     j   ⁢   0       ⁢          q     )     ⁢     (           e     j   ⁢       θ   11     (       2   ⁢   Ni     +   N   -   1     )               β   ×     e     j   ⁡   (         θ   11     (       2   ⁢   Ni     +   N   -   1     )     +   λ     )                   β   ×     e     j   ⁢       θ   21     (       2   ⁢   Ni     +   N   -   1     )                 e     j   ⁡   (         θ   21     (       2   ⁢   Ni     +   N   -   1     )     +   λ   +   δ     )             )     ⁢     (           s   ⁢   1   ⁢     (       2   ⁢   Ni     +   N   -   1     )                 s   ⁢   2   ⁢     (       2   ⁢   Ni     +   N   -   1     )             )             Equation   ⁢         129               
For symbol number 2Ni+N (where i is an integer greater than or equal to zero):
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   137 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           α 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               0 
                             
                           
                         
                       
                       
                         
                           
                               
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         Ae 
                         
                           j 
                           ⁢ 
                           0 
                         
                       
                       ⁢ 
                            
                       q 
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   N 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     N 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ⁡ 
                               ( 
                               
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     N 
                                   
                                   ) 
                                 
                                 + 
                                 λ 
                                 + 
                                 δ 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             s 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             s 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   130 
                 
               
             
           
         
       
     
     Here, j is an imaginary unit. 
     For symbol number 2Ni+N+1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   138 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           α 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               0 
                             
                           
                         
                       
                       
                         
                           
                               
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         Ae 
                         
                           j 
                           ⁢ 
                           0 
                         
                       
                       ⁢ 
                            
                       q 
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   N 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     N 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ⁡ 
                               ( 
                               
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     N 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                                 + 
                                 λ 
                                 + 
                                 δ 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             s 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             s 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   131 
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number 2Ni+N+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   139 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           α 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               0 
                             
                           
                         
                       
                       
                         
                           
                               
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         Ae 
                         
                           j 
                           ⁢ 
                           0 
                         
                       
                       ⁢ 
                            
                       q 
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   N 
                                   + 
                                   k 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       N 
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     N 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ⁡ 
                               ( 
                               
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     + 
                                     N 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                                 + 
                                 λ 
                                 + 
                                 δ 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             s 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             s 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   132 
                 
               
             
           
         
       
     
     Furthermore, for symbol number 2Ni+2N−1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                   
                        
                        
                   
                   ⁢ 
                   140 
                 
               
               
                   
               
             
           
         
       
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             r 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             r 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                             
                             
                           A 
                         
                         
                           e 
                           q 
                           
                             j 
                             ⁢ 
                             0 
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       Ni 
                                     
                                     - 
                                     
                                       2 
                                       ⁢ 
                                       N 
                                     
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           Ni 
                                         
                                         + 
                                         
                                           2 
                                           ⁢ 
                                           N 
                                         
                                         - 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       
                                         2 
                                         ⁢ 
                                         N 
                                       
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         Ni 
                                       
                                       + 
                                       
                                         2 
                                         ⁢ 
                                         N 
                                       
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   
                                     2 
                                     ⁢ 
                                     N 
                                   
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     Ni 
                                   
                                   + 
                                   
                                     2 
                                     ⁢ 
                                     N 
                                   
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     133 
                   
                 
               
             
           
         
       
     
     As a result, when q is represented as follows, one of the signals s 1  and s 2  can no longer be obtained. 
     For symbol number 2Ni (where i is an integer greater than or equal to zero): 
             Math   ⁢           1   ⁢   41                         q   =       -     A   β       ⁢     e     j   ⁡   (         θ   11     (     2   ⁢   Ni     )     -       θ   21     (     2   ⁢   Ni     )       )           ,   
       -   A     ⁢   β   ⁢     e     j   ⁡   (         θ   11     (     2   ⁢   Ni     )     -       θ   21     (     2   ⁢   Ni     )     -   δ     )                 Equation   ⁢         134               
For symbol number 2Ni+1:
 
     
       
         
           
             Math 
             ⁢ 
                 
             
               1 
               ⁢ 
               42 
             
           
         
       
       
         
           
             
               
                 
                   
                     q 
                     = 
                     
                       
                         - 
                         
                           A 
                           β 
                         
                       
                       ⁢ 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   , 
                   
 
                   
                     
                       - 
                       A 
                     
                     ⁢ 
                     β 
                     ⁢ 
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               + 
                               1 
                             
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               + 
                               1 
                             
                             ) 
                           
                           - 
                           δ 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   135 
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number 2Ni+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             Math 
             ⁢ 
                 
             
               1 
               ⁢ 
               43 
             
           
         
       
       
         
           
             
               
                 
                   
                     q 
                     = 
                     
                       
                         - 
                         
                           A 
                           β 
                         
                       
                       ⁢ 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   , 
                   
 
                   
                     
                       - 
                       A 
                     
                     ⁢ 
                     β 
                     ⁢ 
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               + 
                               k 
                             
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               + 
                               k 
                             
                             ) 
                           
                           - 
                           δ 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   136 
                 
               
             
           
         
       
     
     Furthermore, for symbol number 2Ni+N−1: 
             Math   ⁢         144                       q   =       -     A   β       ⁢     e     j   ⁡   (         θ   11     (       2   ⁢   Ni     +   N   -   1     )     -       θ   21     (       2   ⁢   Ni     +   N   -   1     )       )           ,   
       -   A     ⁢   β   ⁢     e     j   ⁡   (         θ   11     (       2   ⁢   Ni     +   N   -   1     )     -       θ   21     (       2   ⁢   Ni     +   N   -   1     )     -   δ     )                 Equation   ⁢         137               
For symbol number 2Ni+N (where i is an integer greater than or equal to zero):
 
             Math   ⁢           1   ⁢   45                         q   =       -     A   α       ⁢     e     j   ⁡   (         θ   11     (       2   ⁢   Ni     +   N     )     -       θ   21     (       2   ⁢   Ni     +   N     )       )           ,   
       -   A     ⁢   α   ⁢     e     j   ⁡   (         θ   11     (       2   ⁢   Ni     +   N     )     -       θ   21     (       2   ⁢   Ni     +   N     )     -   δ     )                 Equation   ⁢         138               
For symbol number 2Ni+N+1:
 
     
       
         
           
             Math 
             ⁢ 
                 
             
               1 
               ⁢ 
               46 
             
           
         
       
       
         
           
             
               
                 
                   
                     q 
                     = 
                     
                       
                         - 
                         
                           A 
                           α 
                         
                       
                       ⁢ 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   , 
                   
 
                   
                     
                       - 
                       A 
                     
                     ⁢ 
                     α 
                     ⁢ 
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               + 
                               N 
                               + 
                               1 
                             
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               + 
                               N 
                               + 
                               1 
                             
                             ) 
                           
                           - 
                           δ 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   139 
                 
               
             
           
         
       
     
     When generalized, this equation is as follows. 
     For symbol number 2Ni+N+k (k=0, 1, . . . , N−1 (k being an integer in a range of 0 to N−1)): 
     
       
         
           
             Math 
             ⁢ 
                 
             
               1 
               ⁢ 
               47 
             
           
         
       
       
         
           
             
               
                 
                   
                     q 
                     = 
                     
                       
                         - 
                         
                           A 
                           α 
                         
                       
                       ⁢ 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 N 
                                 + 
                                 k 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   , 
                   
 
                   
                     
                       - 
                       A 
                     
                     ⁢ 
                     α 
                     ⁢ 
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               + 
                               N 
                               + 
                               k 
                             
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               + 
                               N 
                               + 
                               k 
                             
                             ) 
                           
                           - 
                           δ 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   140 
                 
               
             
           
         
       
     
     Furthermore, for symbol number 2Ni+2N−1: 
     
       
         
           
             Math 
             ⁢ 
                 
             
               1 
               ⁢ 
               48 
             
           
         
       
       
         
           
             
               
                 
                   
                     q 
                     = 
                     
                       
                         - 
                         
                           A 
                           α 
                         
                       
                       ⁢ 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   Ni 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   N 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   , 
                   
 
                   
                     
                       - 
                       A 
                     
                     ⁢ 
                     α 
                     ⁢ 
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               + 
                               
                                 2 
                                 ⁢ 
                                 N 
                               
                               - 
                               1 
                             
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 Ni 
                               
                               + 
                               
                                 2 
                                 ⁢ 
                                 N 
                               
                               - 
                               1 
                             
                             ) 
                           
                           - 
                           δ 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   141 
                 
               
             
           
         
       
     
     In this case, if q has the same solution in symbol numbers 2Ni through 2Ni+N−1, then since the channel elements of the direct waves do not greatly fluctuate, excellent reception quality can no longer be obtained for any of the symbol numbers. Therefore, it is difficult to achieve the ability to correct errors, even if error correction codes are introduced. Accordingly, for q not to have the same solution, Condition #7 or Condition #8 becomes necessary from Equations 134-141 and from the fact that α≠β when focusing on one of two solutions of q which does not include δ.
 
Math 149
 
 e   j(θ     11     (2Ni+x)−θ     21     (2Ni+x))   ≠e   j(θ     11     (2Ni+y)−θ     21     (2Ni+y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2, . . . , N− 2, N− 1)
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; and x≠y.)
 
and
 
 e   j(θ     11     (2Ni+N+x)−θ     21     (2Ni+N+x))   ≠e   j(θ     11     (2Ni+N+y)−θ     21     (2Ni+N+y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2, . . . , N− 2, N− 1)  Condition #7
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; and x≠y.)
 
Math 150
 
 e   j(θ     11     (2Ni+x)−θ     21     (2Ni+x))   ≠e   j(θ     11     (2Ni+y)−θ     21     (2Ni+y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2, . . . ,2 N− 2, N− 1)  Condition #8
 
     In this case, Condition #8 is similar to the conditions described in Embodiment 1 through Embodiment 3. However, with regards to Condition #7, since α≠β, the solution not including δ among the two solutions of q is a different solution. 
     Next, design requirements for not only θ 11  and θ 12 , but also for λ and δ are described. It suffices to set λ to a certain value; it is then necessary to establish requirements for δ. The following describes the design scheme for δ when λ is set to zero radians. 
     In this case, similar to the scheme of changing the precoding weights in a four-slot period (cycle), by defining δ so that π/2 radians≤|δ|≤π radians, excellent reception quality is achieved, particularly in an LOS environment. 
     In symbol numbers 2Ni through 2Ni+2N−1, two points q exist where reception quality becomes poor, and therefore 4N such points exist. In an LOS environment, in order to achieve excellent characteristics, these 4N points should each have a different solution. In this case, focusing on amplitude, the following condition is necessary for Condition #7 or Condition #8, since α≠β. 
     
       
         
           
             Math 
             ⁢ 
                 
             
               1 
               ⁢ 
               51 
             
           
         
       
       
         
           
             
               
                 
                   α 
                   ≠ 
                   
                     1 
                     β 
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #9 
                 
               
             
           
         
       
     
     As described above, when a transmission device transmits a plurality of modulated signals from a plurality of antennas in a MIMO system, the advantageous effect of improved transmission quality, as compared to conventional spatial multiplexing MIMO system, is achieved in an LOS environment in which direct waves dominate by hopping between precoding weights regularly over time. 
     In the present embodiment, the structure of the reception device is as described in Embodiment 1, and in particular with regards to the structure of the reception device, operations have been described for a limited number of antennas, but the present invention may be embodied in the same way even if the number of antennas increases. In other words, the number of antennas in the reception device does not affect the operations or advantageous effects of the present embodiment. Furthermore, in the present embodiment, similar to Embodiment 1, the error correction codes are not limited. 
     In the present embodiment, in contrast with Embodiment 1, the scheme of changing the precoding weights in the time domain has been described. As described in Embodiment 1, however, the present invention may be similarly embodied by changing the precoding weights by using a multi-carrier transmission scheme and arranging symbols in the frequency domain and the frequency-time domain. Furthermore, in the present embodiment, symbols other than data symbols, such as pilot symbols (preamble, unique word, and the like), symbols for control information, and the like, may be arranged in the frame in any way. 
     Embodiment 5 
     In Embodiment 1 through Embodiment 4, the scheme of regularly hopping between precoding weights has been described. In the present embodiment, a modification of this scheme is described. 
     In Embodiment 1 through Embodiment 4, the scheme of regularly hopping between precoding weights as in  FIG.  6    has been described. In the present embodiment, a scheme of regularly hopping between precoding weights that differs from  FIG.  6    is described. 
     As in  FIG.  6   , this scheme hops between four different precoding weights (matrices).  FIG.  22    shows the hopping scheme that differs from  FIG.  6   . In  FIG.  22   , four different precoding weights (matrices) are represented as W1, W2, W3, and W4. (For example, W1 is the precoding weight (matrix) in Equation 37, W2 is the precoding weight (matrix) in Equation 38, W3 is the precoding weight (matrix) in Equation 39, and W4 is the precoding weight (matrix) in Equation 40.) In  FIG.  3   , elements that operate in a similar way to  FIG.  3    and  FIG.  6    bear the same reference signs. 
     The parts unique to  FIG.  22    are as follows. 
     The first period (cycle)  2201 , the second period (cycle)  2202 , the third period (cycle)  2203 , . . . are all four-slot period (cycle)s. 
     A different precoding weight matrix is used in each of the four slots, i.e. W1, W2, W3, and W4 are each used once. 
     It is not necessary for W1, W2, W3, and W4 to be in the same order in the first period (cycle)  2201 , the second period (cycle)  2202 , the third period (cycle)  2203 , . . . . 
     In order to implement this scheme, a precoding weight generating unit  2200  receives, as an input, a signal regarding a weighting scheme and outputs information  2210  regarding precoding weights in order for each period (cycle). The weighting unit  600  receives, as inputs, this information, s 1 ( t ), and s 2 ( t ), performs weighting, and outputs z 1 ( t ) and z 2 ( t ). 
       FIG.  23    shows a different weighting scheme than  FIG.  22    for the above precoding scheme. In  FIG.  23   , the difference from  FIG.  22    is that a similar scheme to  FIG.  22    is achieved by providing a reordering unit after the weighting unit and by reordering signals. 
     In  FIG.  23   , the precoding weight generating unit  2200  receives, as an input, information  315  regarding a weighting scheme and outputs information  2210  on precoding weights in the order of precoding weights W1, W2, W3, W4, W1, W2, W3, W4, . . . . Accordingly, the weighting unit  600  uses the precoding weights in the order of precoding weights W1, W2, W3, W4, W1, W2, W3, W4, . . . and outputs precoded signals  2300 A and  2300 B. 
     A reordering unit  2300  receives, as inputs, the precoded signals  2300 A and  2300 B, reorders the precoded signals  2300 A and  2300 B in the order of the first period (cycle)  2201 , the second period (cycle)  2202 , and the third period (cycle)  2203  in  FIG.  23   , and outputs z 1 ( t ) and z 2 ( t ). 
     Note that in the above description, the period (cycle) for hopping between precoding weights has been described as having four slots for the sake of comparison with  FIG.  6   . As in Embodiment 1 through Embodiment 4, however, the present invention may be similarly embodied with a period (cycle) having other than four slots. 
     Furthermore, in Embodiment 1 through Embodiment 4, and in the above precoding scheme, within the period (cycle), the value of δ and β has been described as being the same for each slot, but the value of δ and β may change in each slot. 
     As described above, when a transmission device transmits a plurality of modulated signals from a plurality of antennas in a MIMO system, the advantageous effect of improved transmission quality, as compared to conventional spatial multiplexing MIMO system, is achieved in an LOS environment in which direct waves dominate by hopping between precoding weights regularly over time. 
     In the present embodiment, the structure of the reception device is as described in Embodiment 1, and in particular with regards to the structure of the reception device, operations have been described for a limited number of antennas, but the present invention may be embodied in the same way even if the number of antennas increases. In other words, the number of antennas in the reception device does not affect the operations or advantageous effects of the present embodiment. Furthermore, in the present embodiment, similar to Embodiment 1, the error correction codes are not limited. 
     In the present embodiment, in contrast with Embodiment 1, the scheme of changing the precoding weights in the time domain has been described. As described in Embodiment 1, however, the present invention may be similarly embodied by changing the precoding weights by using a multi-carrier transmission scheme and arranging symbols in the frequency domain and the frequency-time domain. Furthermore, in the present embodiment, symbols other than data symbols, such as pilot symbols (preamble, unique word, and the like), symbols for control information, and the like, may be arranged in the frame in any way. 
     Embodiment 6 
     In Embodiments 1-4, a scheme for regularly hopping between precoding weights has been described. In the present embodiment, a scheme for regularly hopping between precoding weights is again described, including the content that has been described in Embodiments 1-4. 
     First, out of consideration of an LOS environment, a scheme of designing a precoding matrix is described for a 2×2 spatial multiplexing MIMO system that adopts precoding in which feedback from a communication partner is not available. 
       FIG.  30    shows a model of a 2×2 spatial multiplexing MIMO system that adopts precoding in which feedback from a communication partner is not available. An information vector z is encoded and interleaved. As output of the interleaving, an encoded bit vector u(p)=(u 1 (p), u 2 (p)) is acquired (where p is the slot time). Let u 1 (p)=(u 11 (p), . . . , u ih (p)) (where h is the number of transmission bits per symbol). Letting a signal after modulation (mapping) be s(p)=(s 1 ( p ), s 2 ( p )) T  and a precoding matrix be F(p), a precoded symbol x(p)=(x 1 (p), x 2 (p)) T  is represented by the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   152 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         
                           x 
                           ⁡ 
                           ( 
                           p 
                           ) 
                         
                         = 
                           
                         
                           
                             ( 
                             
                               
                                 
                                   x 
                                   1 
                                 
                                 ( 
                                 p 
                                 ) 
                               
                               , 
                               
                                 
                                   x 
                                   2 
                                 
                                 ( 
                                 p 
                                 ) 
                               
                             
                             ) 
                           
                           T 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         
                           
                             F 
                             ⁡ 
                             ( 
                             p 
                             ) 
                           
                           ⁢ 
                           
                             s 
                             ⁡ 
                             ( 
                             p 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   142 
                 
               
             
           
         
       
     
     Accordingly, letting a received vector be y(p)=(y 1 (p), y 2 (p)) T , the received vector y(p) is represented by the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   153 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         
                           y 
                           ⁡ 
                           ( 
                           p 
                           ) 
                         
                         = 
                           
                         
                           
                             ( 
                             
                               
                                 
                                   y 
                                   1 
                                 
                                 ( 
                                 p 
                                 ) 
                               
                               , 
                               
                                 
                                   y 
                                   2 
                                 
                                 ( 
                                 p 
                                 ) 
                               
                             
                             ) 
                           
                           T 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         
                           
                             
                               H 
                               ⁡ 
                               ( 
                               p 
                               ) 
                             
                             ⁢ 
                             
                               F 
                               ⁡ 
                               ( 
                               p 
                               ) 
                             
                             ⁢ 
                             
                               s 
                               ⁡ 
                               ( 
                               p 
                               ) 
                             
                           
                           + 
                           
                             n 
                             ⁡ 
                             ( 
                             p 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   143 
                 
               
             
           
         
       
     
     In this Equation, H(p) is the channel matrix, n(p)=(n 1 (p), n 2 (p)) T  is the noise vector, and n i (p) is the i.i.d. complex Gaussian random noise with an average value 0 and variance σ 2 . Letting the Rician factor be K, the above equation can be represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   154 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         
                           y 
                           ⁡ 
                           ( 
                           p 
                           ) 
                         
                         = 
                           
                         
                           
                             ( 
                             
                               
                                 
                                   y 
                                   1 
                                 
                                 ( 
                                 p 
                                 ) 
                               
                               , 
                               
                                 
                                   y 
                                   2 
                                 
                                 ( 
                                 p 
                                 ) 
                               
                             
                             ) 
                           
                           T 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     
                                       K 
                                       
                                         K 
                                         + 
                                         1 
                                       
                                     
                                   
                                   ⁢ 
                                   
                                     
                                       H 
                                       d 
                                     
                                     ( 
                                     p 
                                     ) 
                                   
                                 
                                 + 
                                 
                                   
                                     
                                       1 
                                       
                                         K 
                                         + 
                                         1 
                                       
                                     
                                   
                                   ⁢ 
                                   
                                     
                                       H 
                                       s 
                                     
                                     ( 
                                     p 
                                     ) 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               F 
                               ⁡ 
                               ( 
                               p 
                               ) 
                             
                             ⁢ 
                             
                               s 
                               ⁡ 
                               ( 
                               p 
                               ) 
                             
                           
                           + 
                           
                             n 
                             ⁡ 
                             ( 
                             p 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   144 
                 
               
             
           
         
       
     
     In this equation, H d (p) is the channel matrix for the direct wave components, and H s (p) is the channel matrix for the scattered wave components. Accordingly, the channel matrix H(p) is represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   155 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         
                           H 
                           ⁡ 
                           ( 
                           p 
                           ) 
                         
                         = 
                           
                         
                           
                             
                               
                                 K 
                                 
                                   K 
                                   + 
                                   1 
                                 
                               
                             
                             ⁢ 
                             
                               
                                 H 
                                 d 
                               
                               ( 
                               p 
                               ) 
                             
                           
                           + 
                           
                             
                               
                                 1 
                                 
                                   K 
                                   + 
                                   1 
                                 
                               
                             
                             ⁢ 
                             
                               
                                 H 
                                 s 
                               
                               ( 
                               p 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         
                           ( 
                           
                             
                               
                                 
                                   K 
                                   
                                     K 
                                     + 
                                     1 
                                   
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         h 
                                         
                                           11 
                                           , 
                                           d 
                                         
                                       
                                     
                                     
                                       
                                         h 
                                         
                                           12 
                                           , 
                                           d 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         h 
                                         
                                           21 
                                           , 
                                           d 
                                         
                                       
                                     
                                     
                                       
                                         h 
                                         
                                           22 
                                           , 
                                           d 
                                         
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                             + 
                             
                               
                                 
                                   1 
                                   
                                     K 
                                     + 
                                     1 
                                   
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         
                                           h 
                                           
                                             11 
                                             , 
                                             s 
                                           
                                         
                                         ( 
                                         p 
                                         ) 
                                       
                                     
                                     
                                       
                                         
                                           h 
                                           
                                             12 
                                             , 
                                             s 
                                           
                                         
                                         ( 
                                         p 
                                         ) 
                                       
                                     
                                   
                                   
                                     
                                       
                                         
                                           h 
                                           
                                             21 
                                             , 
                                             s 
                                           
                                         
                                         ( 
                                         p 
                                         ) 
                                       
                                     
                                     
                                       
                                         
                                           h 
                                           
                                             22 
                                             , 
                                             s 
                                           
                                         
                                         ( 
                                         p 
                                         ) 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   145 
                 
               
             
           
         
       
     
     In Equation 145, it is assumed that the direct wave environment is uniquely determined by the positional relationship between transmitters, and that the channel matrix H d (p) for the direct wave components does not fluctuate with time. Furthermore, in the channel matrix H d (p) for the direct wave components, it is assumed that as compared to the interval between transmitting antennas, the probability of an environment with a sufficiently long distance between transmission and reception devices is high, and therefore that the channel matrix for the direct wave components can be treated as a non-singular matrix. Accordingly, the channel matrix H d (p) is represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   156 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         
                           
                             H 
                             d 
                           
                           ( 
                           p 
                           ) 
                         
                         = 
                           
                         
                           ( 
                           
                             
                               
                                 
                                   h 
                                   
                                     11 
                                     , 
                                     d 
                                   
                                 
                               
                               
                                 
                                   h 
                                   
                                     12 
                                     , 
                                     d 
                                   
                                 
                               
                             
                             
                               
                                 
                                   h 
                                   
                                     21 
                                     , 
                                     d 
                                   
                                 
                               
                               
                                 
                                   h 
                                   
                                     22 
                                     , 
                                     d 
                                   
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         
                           ( 
                           
                             
                               
                                 
                                   
                                       
                                       
                                     A 
                                   
                                   
                                     e 
                                       
                                     
                                       j 
                                       ⁢ 
                                       ψ 
                                     
                                   
                                 
                               
                               
                                 q 
                               
                             
                             
                               
                                 
                                   
                                       
                                       
                                     A 
                                   
                                   
                                     e 
                                       
                                     
                                       j 
                                       ⁢ 
                                       ψ 
                                     
                                   
                                 
                               
                               
                                 q 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   146 
                 
               
             
           
         
       
     
     In this equation, let A be a positive real number and q be a complex number. Subsequently, out of consideration of an LOS environment, a scheme of designing a precoding matrix is described for a 2×2 spatial multiplexing MIMO system that adopts precoding in which feedback from a communication partner is not available. 
     From Equations 144 and 145, it is difficult to seek a precoding matrix without appropriate feedback in conditions including scattered waves, since it is difficult to perform analysis under conditions including scattered waves. Additionally, in a NLOS environment, little degradation in reception quality of data occurs as compared to an LOS environment. Therefore, the following describes a scheme of designing precoding matrices without appropriate feedback in an LOS environment (precoding matrices for a precoding scheme that hops between precoding matrices over time). 
     As described above, since it is difficult to perform analysis under conditions including scattered waves, an appropriate precoding matrix for a channel matrix including components of only direct waves is sought from Equations 144 and 145. Therefore, in Equation 144, the case when the channel matrix includes components of only direct waves is considered. It follows that from Equation 146, Equation 144 can be represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   157 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         
                           ( 
                           
                             
                               
                                 
                                   
                                     y 
                                     1 
                                   
                                   ( 
                                   p 
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   
                                     y 
                                     2 
                                   
                                   ( 
                                   p 
                                   ) 
                                 
                               
                             
                           
                           ) 
                         
                         = 
                           
                         
                           
                             
                               
                                 H 
                                 d 
                               
                               ( 
                               p 
                               ) 
                             
                             ⁢ 
                             
                               F 
                               ⁡ 
                               ( 
                               p 
                               ) 
                             
                             ⁢ 
                             
                               s 
                               ⁡ 
                               ( 
                               p 
                               ) 
                             
                           
                           + 
                           
                             n 
                             ⁡ 
                             ( 
                             p 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     
                                       
                                           
                                           
                                         A 
                                       
                                       
                                         e 
                                           
                                         
                                           j 
                                           ⁢ 
                                           ψ 
                                         
                                       
                                     
                                   
                                   
                                     q 
                                   
                                 
                                 
                                   
                                     
                                       
                                           
                                           
                                         A 
                                       
                                       
                                         e 
                                           
                                         
                                           j 
                                           ⁢ 
                                           ψ 
                                         
                                       
                                     
                                   
                                   
                                     q 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               F 
                               ⁡ 
                               ( 
                               p 
                               ) 
                             
                             ⁢ 
                             
                               s 
                               ⁡ 
                               ( 
                               p 
                               ) 
                             
                           
                           + 
                           
                             n 
                             ⁡ 
                             ( 
                             p 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   147 
                 
               
             
           
         
       
     
     In this equation, a unitary matrix is used as the precoding matrix. Accordingly, the precoding matrix is represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   158 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     ⁡ 
                     ( 
                     p 
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   p 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         p 
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     p 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     p 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   148 
                 
               
             
           
         
       
     
     In this equation, λ is a fixed value. Therefore, Equation 147 can be represented as follows. 
     
       
         
           
             
               Math 
               ⁢ 
                   
               159 
             
             ⁢ 
             
 
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             
                               
                                 y 
                                 1 
                               
                               ( 
                               p 
                               ) 
                             
                           
                         
                         
                           
                             
                               
                                 y 
                                 2 
                               
                               ( 
                               p 
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     = 
                     
                       
                         
                           1 
                           
                             
                               
                                 α 
                                 2 
                               
                               + 
                               1 
                             
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 
                                   
                                       
                                       
                                     A 
                                   
                                   
                                     e 
                                       
                                     
                                       j 
                                       ⁢ 
                                       ψ 
                                     
                                   
                                 
                               
                               
                                 q 
                               
                             
                             
                               
                                 
                                   
                                       
                                       
                                     A 
                                   
                                   
                                     e 
                                       
                                     
                                       j 
                                       ⁢ 
                                       ψ 
                                     
                                   
                                 
                               
                               
                                 q 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       p 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   α 
                                   × 
                                   
                                     e 
                                     
                                       j 
                                       ⁢ 
                                       
                                         ( 
                                         
                                           
                                             
                                               θ 
                                               11 
                                             
                                             ( 
                                             p 
                                             ) 
                                           
                                           + 
                                           λ 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   α 
                                   × 
                                   
                                     e 
                                     
                                       j 
                                       ⁢ 
                                       
                                         
                                           θ 
                                           21 
                                         
                                         ( 
                                         p 
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   e 
                                   
                                     j 
                                     ( 
                                       
                                     
                                       
                                         
                                           θ 
                                           21 
                                         
                                         ( 
                                         p 
                                         ) 
                                       
                                       + 
                                       λ 
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 
                                   s 
                                   ⁢ 
                                   1 
                                   ⁢ 
                                   
                                     ( 
                                     p 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   s 
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   
                                     ( 
                                     p 
                                     ) 
                                   
                                 
                               
                             
                           
                           ) 
                         
                       
                       + 
                       
                         n 
                         ⁡ 
                         ( 
                         p 
                         ) 
                       
                     
                   
                 
                 
                   
                     Equation 
                     ⁢ 
                         
                     149 
                   
                 
               
             
           
         
       
     
     As is clear from Equation 149, when the reception device performs linear operation of Zero Forcing (ZF) or the Minimum Mean Squared Error (MMSE), the transmitted bit cannot be determined by s 1 ( p ), s 2 ( p ). Therefore, the iterative APP (or iterative Max-log APP) or APP (or Max-log APP) described in Embodiment 1 is performed (hereafter referred to as Maximum Likelihood (ML) calculation), the log-likelihood ratio of each bit transmitted in s 1 ( p ), s 2 ( p ) is sought, and decoding with error correction codes is performed. Accordingly, the following describes a scheme of designing a precoding matrix without appropriate feedback in an LOS environment for a reception device that performs ML calculation. 
     The precoding in Equation 149 is considered. The right-hand side and left-hand side of the first line are multiplied by e −jΨ , and similarly the right-hand side and left-hand side of the second line are multiplied by e −jΨ . The following equation represents the result. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   160 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               e 
                               
                                 
                                   - 
                                   j 
                                 
                                 ⁢ 
                                 ψ 
                               
                             
                             ⁢ 
                             
                               
                                 y 
                                 1 
                               
                               ( 
                               p 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               e 
                               
                                 
                                   - 
                                   j 
                                 
                                 ⁢ 
                                 ψ 
                               
                             
                             ⁢ 
                             
                               
                                 y 
                                 2 
                               
                               ( 
                               p 
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         e 
                         
                           
                             - 
                             j 
                           
                           ⁢ 
                           ψ 
                         
                       
                       ⁢ 
                       
                         { 
                         
                           
                             
                               1 
                               
                                 
                                   
                                     α 
                                     2 
                                   
                                   + 
                                   1 
                                 
                               
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     
                                       
                                           
                                           
                                         A 
                                       
                                       
                                         e 
                                           
                                         
                                           j 
                                           ⁢ 
                                           ψ 
                                         
                                       
                                     
                                   
                                   
                                     q 
                                   
                                 
                                 
                                   
                                     
                                       
                                           
                                           
                                         A 
                                       
                                       
                                         e 
                                           
                                         
                                           j 
                                           ⁢ 
                                           ψ 
                                         
                                       
                                     
                                   
                                   
                                     q 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     
                                       e 
                                       
                                         j 
                                         ⁢ 
                                         
                                           
                                             θ 
                                             11 
                                           
                                           ( 
                                           p 
                                           ) 
                                         
                                       
                                     
                                   
                                   
                                     
                                       α 
                                       × 
                                       
                                         e 
                                         
                                           j 
                                           ⁢ 
                                           
                                             ( 
                                             
                                               
                                                 
                                                   θ 
                                                   11 
                                                 
                                                 ( 
                                                 p 
                                                 ) 
                                               
                                               + 
                                               λ 
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       α 
                                       × 
                                       
                                         e 
                                         
                                           j 
                                           ⁢ 
                                           
                                             
                                               θ 
                                               21 
                                             
                                             ( 
                                             p 
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                   
                                     
                                       e 
                                       
                                         j 
                                         ( 
                                           
                                         
                                           
                                             
                                               θ 
                                               21 
                                             
                                             ( 
                                             p 
                                             ) 
                                           
                                           + 
                                           λ 
                                           + 
                                           π 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     
                                       s 
                                       ⁢ 
                                       1 
                                       ⁢ 
                                       
                                         ( 
                                         p 
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       s 
                                       ⁢ 
                                       2 
                                       ⁢ 
                                       
                                         ( 
                                         p 
                                         ) 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             n 
                             ⁡ 
                             ( 
                             p 
                             ) 
                           
                         
                         } 
                       
                     
                     = 
                     
                       
                         
                           1 
                           
                             
                               
                                 α 
                                 2 
                               
                               + 
                               1 
                             
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 
                                   
                                       
                                       
                                     A 
                                   
                                   
                                     e 
                                       
                                     
                                       j 
                                       ⁢ 
                                       0 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     e 
                                       
                                     
                                       
                                         - 
                                         j 
                                       
                                       ⁢ 
                                       ψ 
                                     
                                   
                                   ⁢ 
                                   q 
                                 
                               
                             
                             
                               
                                 
                                   
                                       
                                       
                                     A 
                                   
                                   
                                     e 
                                       
                                     j0 
                                   
                                 
                               
                               
                                 
                                   
                                     e 
                                       
                                     
                                       
                                         - 
                                         j 
                                       
                                       ⁢ 
                                       ψ 
                                     
                                   
                                   ⁢ 
                                   q 
                                 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       p 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   α 
                                   × 
                                   
                                     e 
                                     
                                       j 
                                       ⁢ 
                                       
                                         ( 
                                         
                                           
                                             
                                               θ 
                                               11 
                                             
                                             ( 
                                             p 
                                             ) 
                                           
                                           + 
                                           λ 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   α 
                                   × 
                                   
                                     e 
                                     
                                       j 
                                       ⁢ 
                                       
                                         
                                           θ 
                                           21 
                                         
                                         ( 
                                         p 
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   e 
                                   
                                     j 
                                     ( 
                                       
                                     
                                       
                                         
                                           θ 
                                           21 
                                         
                                         ( 
                                         p 
                                         ) 
                                       
                                       + 
                                       λ 
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 
                                   s 
                                   ⁢ 
                                   1 
                                   ⁢ 
                                   
                                     ( 
                                     p 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   s 
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   
                                     ( 
                                     p 
                                     ) 
                                   
                                 
                               
                             
                           
                           ) 
                         
                       
                       + 
                       
                         
                           e 
                             
                           
                             
                               - 
                               j 
                             
                             ⁢ 
                             ψ 
                           
                         
                         ⁢ 
                         
                           n 
                           ⁡ 
                           ( 
                           p 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   150 
                 
               
             
           
         
       
     
     e −jΨ y 1 (p), e −jΨ y 2 (p), and e −jΨ q are respectively redefined as y 1 (p), y 2 (p), and q. Furthermore, since e −jΨ n(p)=(e −jΨ n 1 (p), e −jΨ n 2 (p)) T , and e −jΨ n 1 (p), e −jΨ n 2 (p) are the independent identically distributed (i.i.d.) complex Gaussian random noise with an average value 0 and variance σ 2 , e −jΨ n(p) is redefined as n(p). As a result, generality is not lost by restating Equation 150 as Equation 151. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   161 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                             ( 
                             p 
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                             ( 
                             p 
                             ) 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 
                                     
                                     
                                   A 
                                 
                                 
                                   e 
                                     
                                   
                                     j 
                                     ⁢ 
                                     0 
                                   
                                 
                               
                             
                             
                               q 
                             
                           
                           
                             
                               
                                 
                                     
                                     
                                   A 
                                 
                                 
                                   e 
                                     
                                   
                                     j 
                                     ⁢ 
                                     0 
                                   
                                 
                               
                             
                             
                               q 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     p 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     
                                       ( 
                                       
                                         
                                           
                                             θ 
                                             11 
                                           
                                           ( 
                                           p 
                                           ) 
                                         
                                         + 
                                         λ 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       p 
                                       ) 
                                     
                                   
                                 
                               
                             
                             
                               
                                 e 
                                 
                                   j 
                                   ( 
                                     
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       p 
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 s 
                                 ⁢ 
                                 1 
                                 ⁢ 
                                 
                                   ( 
                                   p 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 s 
                                 ⁢ 
                                 2 
                                 ⁢ 
                                 
                                   ( 
                                   p 
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       n 
                       ⁡ 
                       ( 
                       p 
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   151 
                 
               
             
           
         
       
     
     Next, Equation 151 is transformed into Equation 152 for the sake of clarity. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                     
                   162 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                             ( 
                             p 
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                             ( 
                             p 
                             ) 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 e 
                                   
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                 e 
                                   
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 
                                     
                                     
                                   A 
                                 
                                 
                                   e 
                                     
                                   
                                     j 
                                     ⁢ 
                                     0 
                                   
                                 
                               
                             
                             
                               q 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     p 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     
                                       ( 
                                       
                                         
                                           
                                             θ 
                                             11 
                                           
                                           ( 
                                           p 
                                           ) 
                                         
                                         + 
                                         λ 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       p 
                                       ) 
                                     
                                   
                                 
                               
                             
                             
                               
                                 e 
                                 
                                   j 
                                   ( 
                                     
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       p 
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 s 
                                 ⁢ 
                                 1 
                                 ⁢ 
                                 
                                   ( 
                                   p 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 s 
                                 ⁢ 
                                 2 
                                 ⁢ 
                                 
                                   ( 
                                   p 
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       n 
                       ⁡ 
                       ( 
                       p 
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   152 
                 
               
             
           
         
       
     
     In this case, letting the minimum Euclidian distance between a received signal point and a received candidate signal point be d min   2 , then a poor point has a minimum value of zero for d min   2 , and two values of q exist at which conditions are poor in that all of the bits transmitted by s 1 ( p ) and all of the bits transmitted by s 2 ( p ) being eliminated. 
     In Equation 152, when s 1 ( p ) does not exist. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   163 
                 
               
               
                  
               
             
             
               
                 
                   q 
                   = 
                   
                     
                       - 
                       
                         A 
                         α 
                       
                     
                     ⁢ 
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             p 
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             p 
                             ) 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   153 
                 
               
             
           
         
       
     
     In Equation 152, when s 2 ( p ) does not exist.
 
Math 164
 
 q=−Aαe   j(θ     11     (p)−θ     21     (p)−π)   Equation 154
 
     (Hereinafter, the values of q satisfying Equations 153 and 154 are respectively referred to as “poor reception points for s 1  and s 2 ”). 
     When Equation 153 is satisfied, since all of the bits transmitted by s 1 ( p ) are eliminated, the received log-likelihood ratio cannot be sought for any of the bits transmitted by s 1 ( p ). When Equation 154 is satisfied, since all of the bits transmitted by s 2 ( p ) are eliminated, the received log-likelihood ratio cannot be sought for any of the bits transmitted by s 2 ( p ). 
     A broadcast/multicast transmission system that does not change the precoding matrix is now considered. In this case, a system model is considered in which a base station transmits modulated signals using a precoding scheme that does not hop between precoding matrices, and a plurality of terminals (Γ terminals) receive the modulated signals transmitted by the base station. 
     It is considered that the conditions of direct waves between the base station and the terminals change little over time. Therefore, from Equations 153 and 154, for a terminal that is in a position fitting the conditions of Equation 155 or Equation 156 and that is in an LOS environment where the Rician factor is large, the possibility of degradation in the reception quality of data exists. Accordingly, to resolve this problem, it is necessary to change the precoding matrix over time. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   165 
                 
               
               
                  
               
             
             
               
                 
                   q 
                   ≈ 
                   
                     
                       - 
                       
                         A 
                         α 
                       
                     
                     ⁢ 
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             p 
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             p 
                             ) 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   155 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   166 
                 
               
               
                  
               
             
             
               
                 
                   q 
                   ≈ 
                   
                     
                       - 
                       A 
                     
                     ⁢ 
                     
                       αe 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             p 
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             p 
                             ) 
                           
                           - 
                           π 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   156 
                 
               
             
           
         
       
     
     A scheme of regularly hopping between precoding matrices over a time period (cycle) with N slots (hereinafter referred to as a precoding hopping scheme) is considered. 
     Since there are N slots in the time period (cycle), N varieties of precoding matrices F[i] based on Equation 148 are prepared (i=0, 1, . . . , N−1 (i being an integer in a range of 0 to N−1)). In this case, the precoding matrices F[i] are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   167 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     ⁡ 
                     ( 
                     i 
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   [ 
                                   i 
                                   ] 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         [ 
                                         i 
                                         ] 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     [ 
                                     i 
                                     ] 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     [ 
                                     i 
                                     ] 
                                   
                                   + 
                                   λ 
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   157 
                 
               
             
           
         
       
     
     In this equation, let α not change over time, and let λ also not change over time (though change over time may be allowed). 
     As in Embodiment 1, F[i] is the precoding matrix used to obtain a precoded signal x (p=N×k+i) in Equation 142 for time N×k+i (where k is an integer equal to or greater than 0, and i=0, 1, . . . , N−1 (i being an integer in a range of 0 to N−1)). The same is true below as well. 
     At this point, based on Equations 153 and 154, design conditions such as the following are important for the precoding matrices for precoding hopping. 
     Math 168
 
Condition #10
 
 e   j(θ     11     [x]−θ     21     [x])   ≠e   j(θ     11     [y]−θ   21   [y])   Equation 158
 
for ∀x, ∀y (x≠y; x, y=0,1, . . . , N−1)
 
Math 169
 
Condition #11
 
 e   j(θ     11     [x]−θ     21     [x]−π)≠   e   j(θ     11     [y]−θ   21   [y]−π)   Equation 159
 
for ∀x, ∀y (x≠y; x, y=0, 1, . . . , N−1)
 
     From Condition #10, in all of the Γ terminals, there is one slot or less having poor reception points for s 1  among the N slots in a time period (cycle). Accordingly, the log-likelihood ratio for bits transmitted by s 1 ( p ) can be obtained for at least N−1 slots. Similarly, from Condition #11, in all of the Γ terminals, there is one slot or less having poor reception points for s 2  among the N slots in a time period (cycle). Accordingly, the log-likelihood ratio for bits transmitted by s 2 ( p ) can be obtained for at least N−1 slots. 
     In this way, by providing the precoding matrix design model of Condition #10 and Condition #11, the number of bits for which the log-likelihood ratio is obtained among the bits transmitted by s 1 ( p ), and the number of bits for which the log-likelihood ratio is obtained among the bits transmitted by s 2 ( p ) is guaranteed to be equal to or greater than a fixed number in all of the Γ terminals. Therefore, in all of the Γ terminals, it is considered that degradation of data reception quality is moderated in an LOS environment where the Rician factor is large. 
     The following shows an example of a precoding matrix in the precoding hopping scheme. 
     The probability density distribution of the phase of a direct wave can be considered to be evenly distributed over [0 2π]. Therefore, the probability density distribution of the phase of q in Equations 151 and 152 can also be considered to be evenly distributed over [0 2π]. Accordingly, the following is established as a condition for providing fair data reception quality insofar as possible for Γ terminals in the same LOS environment in which only the phase of q differs. 
     Condition #12 
     When using a precoding hopping scheme with an N-slot time period (cycle), among the N slots in the time period (cycle), the poor reception points for s 1  are arranged to have an even distribution in terms of phase, and the poor reception points for s 2  are arranged to have an even distribution in terms of phase. 
     The following describes an example of a precoding matrix in the precoding hopping scheme based on Condition #10 through Condition #12. Let α=1.0 in the precoding matrix in Equation 157. 
     Example #5 
     Let the number of slots N in the time period (cycle) be 8. In order to satisfy Condition #10 through Condition #12, precoding matrices for a precoding hopping scheme with an N=8 time period (cycle) are provided as in the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   170 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     i 
                                     ⁢ 
                                     π 
                                   
                                   4 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                     + 
                                     n 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   160 
                 
               
             
           
         
       
     
     Here, j is an imaginary unit, and i=0, 1, . . . , 7. Instead of Equation 160, Equation 161 may be provided (where λ and θ 11 [i] do not change over time (though change may be allowed)). 
     
       
         
           
             Math 
             ⁢ 
                 
             171 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   [ 
                                   i 
                                   ] 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     + 
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     + 
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                     + 
                                     λ 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   161 
                 
               
             
           
         
       
     
     Accordingly, the poor reception points for s 1  and s 2  become as in  FIGS.  31 A and  31 B . (In  FIGS.  31 A and  31 B , the horizontal axis is the real axis, and the vertical axis is the imaginary axis.) Instead of Equations 160 and 161, Equations 162 and 163 may be provided (where i=0, 1, . . . , 7, and where λ and θ 11 [i] do not change over time (though change may be allowed)). 
     
       
         
           
             Math 
             ⁢ 
                 
             172 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     - 
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       - 
                                       
                                         
                                           i 
                                           ⁢ 
                                           π 
                                         
                                         4 
                                       
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   162 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             173 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   [ 
                                   i 
                                   ] 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     - 
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     - 
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                     + 
                                     λ 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   163 
                 
               
             
           
         
       
     
     Next, the following is established as a condition, different from Condition #12, for providing fair data reception quality insofar as possible for Γ terminals in the same LOS environment in which only the phase of q differs. 
     Condition #13 
     When using a precoding hopping scheme with an N-slot time period (cycle), in addition to the condition
 
Math 174
 
 e   j(θ     11     [x]−θ     21     [x])   ≠e   j(θ     11     [y]−θ   21   [y]−π)  for ∀ x,∀y  ( x,y= 0,1, . . . , N− 1)  Equation 164
 
the poor reception points for s 1  and the poor reception points for s 2  are arranged to be in an even distribution with respect to phase in the N slots in the time period (cycle).
 
     The following describes an example of a precoding matrix in the precoding hopping scheme based on Condition #10, Condition #11, and Condition #13. Let α=1.0 in the precoding matrix in Equation 157. 
     Example #6 
     Let the number of slots N in the time period (cycle) be 4. Precoding matrices for a precoding hopping scheme with an N=4 time period (cycle) are provided as in the following equation. 
     
       
         
           
             Math 
             ⁢ 
                 
             175 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     i 
                                     ⁢ 
                                     π 
                                   
                                   4 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                                 + 
                                 π 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   165 
                 
               
             
           
         
       
     
     Here, j is an imaginary unit, and i=0, 1, 2, 3. Instead of Equation 165, Equation 166 may be provided (where λ and θ 11 [i] do not change over time (though change may be allowed)). 
     
       
         
           
             Math 
             ⁢ 
                 
             176 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   [ 
                                   i 
                                   ] 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     + 
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     + 
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                     + 
                                     λ 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   166 
                 
               
             
           
         
       
     
     Accordingly, the poor reception points for s 1  and s 2  become as in  FIG.  32   . (In  FIG.  32   , the horizontal axis is the real axis, and the vertical axis is the imaginary axis.) Instead of Equations 165 and 166, Equations 167 and 168 may be provided (where i=0, 1, 2, 3, and where λ and θ 11 [i] do not change over time (though change may be allowed)). 
     
       
         
           
             Math 
             ⁢ 
                 
             177 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     - 
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       - 
                                       
                                         
                                           i 
                                           ⁢ 
                                           π 
                                         
                                         4 
                                       
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   167 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             178 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   [ 
                                   i 
                                   ] 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     - 
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     - 
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                     + 
                                     λ 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   168 
                 
               
             
           
         
       
     
     Next, a precoding hopping scheme using a non-unitary matrix is described. 
     Based on Equation 148, the precoding matrices presently under consideration are represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             179 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     ⁡ 
                     ( 
                     p 
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   p 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         p 
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     p 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       p 
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     169 
                   
                 
               
             
           
         
       
     
     Equations corresponding to Equations 151 and 152 are represented as follows. 
     
       
         
           
                               
             
               Math 
               ⁢ 
                   
               180 
             
           
         
       
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                             ( 
                             p 
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                             ( 
                             p 
                             ) 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 Ae 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                             
                               q 
                             
                           
                           
                             
                               
                                 Ae 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                             
                               q 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     p 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     
                                       ( 
                                       
                                         
                                           
                                             θ 
                                             11 
                                           
                                           ( 
                                           p 
                                           ) 
                                         
                                         + 
                                         λ 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       p 
                                       ) 
                                     
                                   
                                 
                               
                             
                             
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           21 
                                         
                                         ( 
                                         p 
                                         ) 
                                       
                                       + 
                                       λ 
                                       + 
                                       δ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 s 
                                 ⁢ 
                                 1 
                                 ⁢ 
                                 
                                   ( 
                                   p 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 s 
                                 ⁢ 
                                 2 
                                 ⁢ 
                                 
                                   ( 
                                   p 
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       n 
                       ⁡ 
                       ( 
                       p 
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   170 
                 
               
             
           
         
       
       
         
           
                               
             
               Math 
               ⁢ 
                   
               181 
             
           
         
       
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                             ( 
                             p 
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                             ( 
                             p 
                             ) 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 Ae 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                             
                               q 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     p 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     
                                       ( 
                                       
                                         
                                           
                                             θ 
                                             11 
                                           
                                           ( 
                                           p 
                                           ) 
                                         
                                         + 
                                         λ 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       p 
                                       ) 
                                     
                                   
                                 
                               
                             
                             
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           21 
                                         
                                         ( 
                                         p 
                                         ) 
                                       
                                       + 
                                       λ 
                                       + 
                                       δ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 s 
                                 ⁢ 
                                 1 
                                 ⁢ 
                                 
                                   ( 
                                   p 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 s 
                                 ⁢ 
                                 2 
                                 ⁢ 
                                 
                                   ( 
                                   p 
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       n 
                       ⁡ 
                       ( 
                       p 
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   171 
                 
               
             
           
         
       
     
     In this case, there are two q at which the minimum value d min   2  of the Euclidian distance between a received signal point and a received candidate signal point is zero. 
     In Equation 171, when s 1 ( p ) does not exist: 
     
       
         
           
             Math 
             ⁢ 
                 
             182 
           
         
       
       
         
           
             
               
                 
                   q 
                   = 
                   
                     
                       - 
                       
                         A 
                         α 
                       
                     
                     ⁢ 
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             p 
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             p 
                             ) 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     172 
                   
                 
               
             
           
         
       
     
     In Equation 171, when s 2 ( p ) does not exist:
 
Math 183
 
 q=−Aαe   j(θ     11     (p)−θ     21     (p)−δ)   Equation 173
 
     In the precoding hopping scheme for an N-slot time period (cycle), by referring to Equation 169, N varieties of the precoding matrix F[i] are represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             184 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   [ 
                                   i 
                                   ] 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         [ 
                                         i 
                                         ] 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     [ 
                                     i 
                                     ] 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     174 
                   
                 
               
             
           
         
       
     
     In this equation, let α and δ not change over time. At this point, based on Equations 34 and 35, design conditions such as the following are provided for the precoding matrices for precoding hopping. 
     Math 185
 
Condition #14
 
 e   j(θ     11     [x]−θ     21     [x])   ≠e   j(θ     11     [y]−θ   21   [y])   Equation 175
 
for ∀x, ∀y (x≠y; x, y=0, 1, . . . , N−1)
 
Math 186
 
Condition #15
 
 e   j(θ     11     [x]−θ     21     [x]−δ)   ≠e   j(θ     11     [y]−θ   21   [y]−δ)   Equation 176
 
for ∀x, ∀y (x≠y; x, y=0, 1, . . . , N−1)
 
     Example #7 
     Let α=1.0 in the precoding matrix in Equation 174. Let the number of slots N in the time period (cycle) be 16. In order to satisfy Condition #12, Condition #14, and Condition #15, precoding matrices for a precoding hopping scheme with an N=16 time period (cycle) are provided as in the following equations. 
     For i=0, 1, . . . , 7: 
             Math   ⁢         187                       F   [   i   ]     =       1     2       ⁢     (           e     j   ⁢   0             e     j   ⁢   0                 e     j   ⁢       i   ⁢   π     4               e     j   ⁢     (         i   ⁢   π     4     +       7   ⁢   π     8       )               )               Equation   ⁢         177               
For i=8, 9, . . . , 15:
 
     
       
         
           
             Math 
             ⁢ 
                 
             188 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     i 
                                     ⁢ 
                                     π 
                                   
                                   4 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                     + 
                                     
                                       
                                         7 
                                         ⁢ 
                                         π 
                                       
                                       8 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   178 
                 
               
             
           
         
       
     
     Furthermore, a precoding matrix that differs from Equations 177 and 178 can be provided as follows. 
     For i=0, 1, . . . , 7: 
             Math   ⁢         189                       F   [   i   ]     =       1     2       ⁢     (           e     j   ⁢       θ   11     [   i   ]               e     j   ⁢     (         θ   11     [   i   ]     +   λ     )                   e     j   (             θ   11     [   i   ]     +       i   ⁢   π     4       )             e     j   ⁢     (         θ   11     [   i   ]     +       i   ⁢   π     4     +   λ   +       7   ⁢   π     8       )               )               Equation   ⁢         179               
For i=8, 9, . . . , 15:
 
     
       
         
           
             Math 
             ⁢ 
                 
             190 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     [ 
                                     i 
                                     ] 
                                   
                                   + 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                                 ) 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     + 
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                     + 
                                     λ 
                                     + 
                                     
                                       
                                         7 
                                         ⁢ 
                                         π 
                                       
                                       8 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   [ 
                                   i 
                                   ] 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   180 
                 
               
             
           
         
       
     
     Accordingly, the poor reception points for s 1  and s 2  become as in  FIGS.  33 A and  33 B . 
     (In  FIGS.  33 A and  33 B , the horizontal axis is the real axis, and the vertical axis is the imaginary axis.) Instead of Equations 177 and 178, and Equations 179 and 180, precoding matrices may be provided as below. 
     For i=0, 1, . . . , 7: 
             Math   ⁢         191                       F   [   i   ]     =       1     2       ⁢     (           e     j   ⁢   0             e     j   ⁢   0                 e     j   ⁢     (     -       i   ⁢   π     4       )               e     j   ⁢     (       -       i   ⁢   π     4       +       7   ⁢   π     8       )               )               Equation   ⁢         181               
For i=8, 9, . . . , 15:
 
     
       
         
           
             Math 
             ⁢ 
                 
             192 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     - 
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       - 
                                       
                                         
                                           i 
                                           ⁢ 
                                           π 
                                         
                                         4 
                                       
                                     
                                     + 
                                     
                                       
                                         7 
                                         ⁢ 
                                         π 
                                       
                                       8 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   182 
                 
               
             
           
         
       
     
     or 
     For i=0, 1, . . . , 7: 
                   Math   ⁢         193                        F   [   i   ]     =       1     2       ⁢     (           e     j   ⁢       θ   11     [   i   ]               e     j   ⁢     (         θ   11     [   i   ]     +   λ     )                   e     j   ⁢     (         θ   11     [   i   ]     -       i   ⁢   π     4       )               e     j   ⁡   (         θ   11     [   i   ]     -       i   ⁢   π     4     +   λ   +       7   ⁢   π     8       )             )               Equation   ⁢         183               
For i=8, 9, . . . , 15:
 
                   Math   ⁢         194                        F   [   i   ]     =       1     2       ⁢     (           e     j   ⁢     (         θ   11     [   i   ]     -       i   ⁢   π     4       )               e     j   ⁢     (         θ   11     [   i   ]     -       i   ⁢   π     4     +   λ   +       7   ⁢   π     8       )                   e     j   ⁢       θ   11     [   i   ]               e     j   ⁡   (         θ   11     [   i   ]     +   λ     )             )               Equation   ⁢         184               
(In Equations 177-184, 7π/8 may be changed to −7π/8.)
 
     Next, the following is established as a condition, different from Condition #12, for providing fair data reception quality insofar as possible for Γ terminals in the same LOS environment in which only the phase of q differs. 
     Condition #16 
     When using a precoding hopping scheme with an N-slot time period (cycle), the following condition is set:
 
Math 195
 
 e   j(θ     11     [x]−θ     21     [x])   ≠e   j(θ     11     [y]−θ   21   [y]−δ)  for ∀ x,∀y  ( x,y= 0,1, . . . , N− 1)  Equation 185
 
     and the poor reception points for s 1  and the poor reception points for s 2  are arranged to be in an even distribution with respect to phase in the N slots in the time period (cycle). 
     The following describes an example of a precoding matrix in the precoding hopping scheme based on Condition #14, Condition #15, and Condition #16. Let α=1.0 in the precoding matrix in Equation 174. 
     Example #8 
     Let the number of slots N in the time period (cycle) be 8. Precoding matrices for a precoding hopping scheme with an N=8 time period (cycle) are provided as in the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   196 
                 
               
               
                  
               
             
             
               
                 
                       
                   
                     
                       F 
                       [ 
                       i 
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           2 
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                             
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                             
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                     + 
                                     
                                       
                                         7 
                                         ⁢ 
                                         π 
                                       
                                       8 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   186 
                 
               
             
           
         
       
     
     Here, i=0, 1, . . . , 7. 
     Furthermore, a precoding matrix that differs from Equation 186 can be provided as follows (where i=0, 1, . . . , 7, and where λ and θ 11 [i] do not change over time (though change may be allowed)). 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   197 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   [ 
                                   i 
                                   ] 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     + 
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     [ 
                                     i 
                                     ] 
                                   
                                   + 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   λ 
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   187 
                 
               
             
           
         
       
     
     Accordingly, the poor reception points for s 1  and s 2  become as in  FIG.  34   . Instead of Equations 186 and 187, precoding matrices may be provided as follows (where i=0, 1, . . . , 7, and where λ and θ 11 [i] do not change over time (though change may be allowed)). 
                   Math   ⁢         198                                   F   [   i   ]     =       1     2       ⁢     (           e     j   ⁢   0             e     j   ⁢   0                 e     j   ⁡   (     -       i   ⁢   π     4       )             e     j   ⁡   (       -       i   ⁢   π     4       +       7   ⁢   π     8       )             )     ⁢         or               Equation   ⁢         188                           Math   ⁢         199                                  F   [   i   ]     =       1     2       ⁢     (           e     j   ⁢       θ   11     [   i   ]               e     j   ⁢     (         θ   11     [   i   ]     +   λ     )                   e     j   ⁢     (         θ   11     [   i   ]     -       i   ⁢   π     4       )               e     j   ⁡   (         θ   11     [   i   ]     -       i   ⁢   π     4     +   λ   +       7   ⁢   π     8       )             )                 Equation   ⁢       189               
(In Equations 186-189, 7π/8 may be changed to −7π/8.)
 
     Next, in the precoding matrix of Equation 174, a precoding hopping scheme that differs from Example #7 and Example #8 by letting a 1, and by taking into consideration the distance in the complex plane between poor reception points, is examined. 
     In this case, the precoding hopping scheme for an N-slot time period (cycle) of Equation 174 is used, and from Condition #14, in all of the Γ terminals, there is one slot or less having poor reception points for s 1  among the N slots in a time period (cycle). Accordingly, the log-likelihood ratio for bits transmitted by s 1 ( p ) can be obtained for at least N−1 slots. Similarly, from Condition #15, in all of the Γ terminals, there is one slot or less having poor reception points for s 2  among the N slots in a time period (cycle). Accordingly, the log-likelihood ratio for bits transmitted by s 2 ( p ) can be obtained for at least N−1 slots. 
     Therefore, it is clear that a larger value for N in the N-slot time period (cycle) increases the number of slots in which the log-likelihood ratio can be obtained. 
     Incidentally, since the influence of scattered wave components is also present in an actual channel model, it is considered that when the number of slots N in the time period (cycle) is fixed, there is a possibility of improved data reception quality if the minimum distance in the complex plane between poor reception points is as large as possible. Accordingly, in the context of Example #7 and Example #8, precoding hopping schemes in which a 1 and which improve on Example #7 and Example #8 are considered. The precoding scheme that improves on Example #8 is easier to understand and is therefore described first. 
     Example #9 
     From Equation 186, the precoding matrices in an N=8 time period (cycle) precoding hopping scheme that improves on Example #8 are provided in the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   200 
                 
               
               
                  
               
             
             
               
                 
                         
                   
                     
                       F 
                       [ 
                       i 
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     0 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                   
                                 
                               
                             
                             
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                     + 
                                     
                                       
                                         7 
                                         ⁢ 
                                         π 
                                       
                                       8 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   190 
                 
               
             
           
         
       
     
     Here, i=0, 1, . . . , 7. Furthermore, precoding matrices that differ from Equation 190 can be provided as follows (where i=0, 1, . . . , 7, and where λ and θ 11 [i] do not change over time (though change may be allowed)). 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   201 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   [ 
                                   i 
                                   ] 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         [ 
                                         i 
                                         ] 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         [ 
                                         i 
                                         ] 
                                       
                                       + 
                                       
                                         
                                           i 
                                           ⁢ 
                                           π 
                                         
                                         4 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     [ 
                                     i 
                                     ] 
                                   
                                   + 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   λ 
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                         
                     or 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   191 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   202 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       - 
                                       
                                         
                                           i 
                                           ⁢ 
                                           π 
                                         
                                         4 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     - 
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                          
                     or 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   192 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   203 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   [ 
                                   i 
                                   ] 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         [ 
                                         i 
                                         ] 
                                       
                                       - 
                                       
                                         
                                           i 
                                           ⁢ 
                                           π 
                                         
                                         4 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     [ 
                                     i 
                                     ] 
                                   
                                   - 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   λ 
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                         
                     or 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   193 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   204 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   - 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                         
                     or 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   194 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   205 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     0 
                                     11 
                                   
                                   [ 
                                   i 
                                   ] 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         [ 
                                         i 
                                         ] 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         [ 
                                         i 
                                         ] 
                                       
                                       + 
                                       
                                         
                                           i 
                                           ⁢ 
                                           π 
                                         
                                         4 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     [ 
                                     i 
                                     ] 
                                   
                                   + 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   λ 
                                   - 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                         
                     or 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   195 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   206 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       - 
                                       
                                         
                                           i 
                                           ⁢ 
                                           π 
                                         
                                         4 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     - 
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                   
                                   - 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                         
                     or 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   196 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   207 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   [ 
                                   i 
                                   ] 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         [ 
                                         i 
                                         ] 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         [ 
                                         i 
                                         ] 
                                       
                                       - 
                                       
                                         
                                           i 
                                           ⁢ 
                                           π 
                                         
                                         4 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     [ 
                                     i 
                                     ] 
                                   
                                   - 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   λ 
                                   - 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   197 
                 
               
             
           
         
       
     
     Therefore, the poor reception points for s 1  and s 2  are represented as in  FIG.  35 A  when α&lt;1.0 and as in  FIG.  35 B  when α&gt;1.0. 
     (i) When α&lt;1.0 
     When α&lt;1.0, the minimum distance in the complex plane between poor reception points is represented as min{d #1,#2 , d #1,#3 } when focusing on the distance (d #1,#2 ) between poor reception points #1 and #2 and the distance (d #1,#3 ) between poor reception points #1 and #3. In this case, the relationship between α and d #1,#2  and between α and d #1,#3  is shown in  FIG.  36   . The a which makes min{d #1,#2 , d #1,#3 } the largest is as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   208 
                 
               
               
                  
               
             
             
               
                 
                   α 
                   = 
                   
                     
                       1 
                       
                         
                           
                             cos 
                             ⁡ 
                             ( 
                             
                               π 
                               8 
                             
                             ) 
                           
                           + 
                           
                             
                               3 
                             
                             ⁢ 
                             
                               sin 
                               ⁡ 
                               ( 
                               
                                 π 
                                 8 
                               
                               ) 
                             
                           
                         
                       
                     
                     ≈ 
                     0.7938 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   198 
                 
               
             
           
         
       
     
     The min {d #1,#2 , d #1,#3 } in this case is as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   209 
                 
               
               
                  
               
             
             
               
                 
                   
                     min 
                     ⁢ 
                     
                       { 
                       
                         
                           d 
                           
                             #1 
                             , 
                             #2 
                           
                         
                         , 
                         
                           d 
                           
                             #1 
                             , 
                             #3 
                           
                         
                       
                       } 
                     
                   
                   = 
                   
                     
                       
                         2 
                         ⁢ 
                         A 
                         ⁢ 
                         
                           sin 
                           ⁡ 
                           ( 
                           
                             π 
                             8 
                           
                           ) 
                         
                       
                       
                         
                           
                             cos 
                             ⁡ 
                             ( 
                             
                               π 
                               8 
                             
                             ) 
                           
                           + 
                           
                             
                               3 
                             
                             ⁢ 
                             
                               sin 
                               ⁡ 
                               ( 
                               
                                 π 
                                 8 
                               
                               ) 
                             
                           
                         
                       
                     
                     ≈ 
                     
                       0.6076 
                       A 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   199 
                 
               
             
           
         
       
     
     Therefore, the precoding scheme using the value of α in Equation 198 for Equations 190-197 is effective. Setting the value of α as in Equation 198 is one appropriate scheme for obtaining excellent data reception quality. Setting α to be a value near Equation 198, however, may similarly allow for excellent data reception quality. Accordingly, the value to which α is set is not limited to Equation 198. 
     (ii) When α&gt;1.0 
     When α&gt;1.0, the minimum distance in the complex plane between poor reception points is represented as min {d #4,#5 , d #4,#6 } when focusing on the distance (d #4,#5 ) between poor reception points #4 and #5 and the distance (d #4,#6 ) between poor reception points #4 and #6. In this case, the relationship between α and d #4,#5  and between α and d #4,#6  is shown in  FIG.  37   . The a which makes min{d #4,#5 , d #4,#6 } the largest is as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   210 
                 
               
               
                  
               
             
             
               
                 
                   α 
                   = 
                   
                     
                       
                         
                           cos 
                           ⁡ 
                           ( 
                           
                             π 
                             8 
                           
                           ) 
                         
                         + 
                         
                           
                             3 
                           
                           ⁢ 
                           
                             sin 
                             ⁡ 
                             ( 
                             
                               π 
                               8 
                             
                             ) 
                           
                         
                       
                     
                     ≈ 
                     1.2596 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   200 
                 
               
             
           
         
       
     
     The min{d #4,#5 , d #4,#6 } in this case is as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   211 
                 
               
               
                  
               
             
             
               
                 
                   
                     min 
                     ⁢ 
                     
                       { 
                       
                         
                           d 
                           
                             #4 
                             , 
                             #5 
                           
                         
                         , 
                         
                           d 
                           
                             #4 
                             , 
                             #6 
                           
                         
                       
                       } 
                     
                   
                   = 
                   
                     
                       
                         2 
                         ⁢ 
                         A 
                         ⁢ 
                         
                           sin 
                           ⁡ 
                           ( 
                           
                             π 
                             8 
                           
                           ) 
                         
                       
                       
                         
                           
                             cos 
                             ⁡ 
                             ( 
                             
                               π 
                               8 
                             
                             ) 
                           
                           + 
                           
                             
                               3 
                             
                             ⁢ 
                             
                               sin 
                               ⁡ 
                               ( 
                               
                                 π 
                                 8 
                               
                               ) 
                             
                           
                         
                       
                     
                     ≈ 
                     
                       0.6076 
                       A 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   201 
                 
               
             
           
         
       
     
     Therefore, the precoding scheme using the value of a in Equation 200 for Equations 190-197 is effective. Setting the value of a as in Equation 200 is one appropriate scheme for obtaining excellent data reception quality. Setting α to be a value near Equation 200, however, may similarly allow for excellent data reception quality. Accordingly, the value to which α is set is not limited to Equation 200. 
     Example #10 
     Based on consideration of Example #9, the precoding matrices in an N=16 time period (cycle) precoding hopping scheme that improves on Example #7 are provided in the following equations (where λ and θ 11 [i] do not change over time (though change may be allowed)). 
     For i=0, 1, . . . , 7: 
                   Math   ⁢         212                        F   [   i   ]     =       1         α   2     +   1         ⁢     (           e     j   ⁢   0             α   ×     e     j   ⁢   0                   α   ×     e     j   ⁢       i   ⁢   π     4                 e     j   ⁡   (         i   ⁢   π     4     +       7   ⁢   π     8       )             )               Equation   ⁢         202               
For i=8, 9, . . . , 15:
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   213 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   203 
                 
               
             
           
         
       
     
     or 
     For i=0, 1, . . . , 7: 
                   Math   ⁢         214                        F   [   i   ]     =       1         α   2     +   1         ⁢     (           e     j   ⁢       θ   11     [   i   ]               α   ×     e     j   ⁢     (         θ   11     [   i   ]     +   λ     )                     α   ×     e     j   ⁢     (         θ   11     [   i   ]     +       i   ⁢   π     4       )                 e     j   (         θ   11     [   i   ]     +       i   ⁢   π     4     +   λ   +       7   ⁢   π     8                 )               Equation   ⁢         204               
For i=8, 9, . . . , 15:
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   215 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       [ 
                                       i 
                                       ] 
                                     
                                     + 
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     [ 
                                     i 
                                     ] 
                                   
                                   + 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   λ 
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   [ 
                                   i 
                                   ] 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         [ 
                                         i 
                                         ] 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   205 
                 
               
             
           
         
       
     
     or 
     For i=0, 1, . . . , 7: 
                   Math   ⁢         216                        F   [   i   ]     =       1         α   2     +   1         ⁢     (           e     j   ⁢   0             α   ×     e     j   ⁢   0                   α   ×     e     j   ⁡   (     -       i   ⁢   π     4       )               e     j   ⁡   (       -       i   ⁢   π     4       +       7   ⁢   π     8       )             )               Equation   ⁢         206               
For i=8, 9, . . . , 15:
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   217 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       - 
                                       
                                         
                                           i 
                                           ⁢ 
                                           π 
                                         
                                         4 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       - 
                                       
                                         
                                           i 
                                           ⁢ 
                                           π 
                                         
                                         4 
                                       
                                     
                                     + 
                                     
                                       
                                         7 
                                         ⁢ 
                                         π 
                                       
                                       8 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   207 
                 
               
             
           
         
       
     
     or 
     For i=0, 1, . . . , 7: 
                   Math   ⁢         218                        F   [   i   ]     =       1         α   2     +   1         ⁢     (           e     j   ⁢       θ   11     [   i   ]               α   ×     e     j   ⁡   (         θ   11     [   i   ]     +   λ     )                   α   ×     e     j   ⁡   (         θ   11     [   i   ]     -       i   ⁢   π     4       )               e     j   ⁡   (         θ   11     [   i   ]     -       i   ⁢   π     4     +   λ   +       7   ⁢   π     8       )             )               Equation   ⁢         208               
For i=8, 9, . . . , 15:
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   219 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         [ 
                                         i 
                                         ] 
                                       
                                       - 
                                       
                                         
                                           i 
                                           ⁢ 
                                           π 
                                         
                                         4 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     [ 
                                     i 
                                     ] 
                                   
                                   - 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   λ 
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   [ 
                                   i 
                                   ] 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         [ 
                                         i 
                                         ] 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   209 
                 
               
             
           
         
       
     
     or 
     For i=0, 1, . . . , 7: 
                   Math   ⁢         220                        F   [   i   ]     =       1       α   2     +   1       ⁢     (           e     j   ⁢   0             α   ×     e     j   ⁢   0                   α   ×     e     j   ⁢       i   ⁢   π     4                 e     j   ⁡   (         i   ⁢   π     4     -       7   ⁢   π     8       )             )               Equation   ⁢         210               
For i=8, 9, . . . , 15:
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   221 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                     - 
                                     
                                       
                                         7 
                                         ⁢ 
                                         π 
                                       
                                       8 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   211 
                 
               
             
           
         
       
     
     or 
     For i=0, 1, . . . , 7: 
                   Math   ⁢         222                        F   [   i   ]     =       1         α   2     +   1         ⁢     (           e     j   ⁢       θ   11     [   i   ]               α   ×     e     j   ⁡   (         θ   11     [   i   ]     +   λ     )                   α   ×     e     j   ⁡   (         θ   11     [   i   ]     +       i   ⁢   π     4       )               e     j   ⁡   (         θ   11     [   i   ]     +       i   ⁢   π     4     +   λ   -       7   ⁢   π     8       )             )               Equation   ⁢         212               
For i=8, 9, . . . , 15:
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   223 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         [ 
                                         i 
                                         ] 
                                       
                                       + 
                                       
                                         
                                           i 
                                           ⁢ 
                                           π 
                                         
                                         4 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     [ 
                                     i 
                                     ] 
                                   
                                   + 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   λ 
                                   - 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   [ 
                                   i 
                                   ] 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         [ 
                                         i 
                                         ] 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   213 
                 
               
             
           
         
       
     
     or 
     For i=0, 1, . . . , 7: 
                   Math   ⁢         224                        F   [   i   ]     =       1         α   2     +   1         ⁢     (           e     j   ⁢   0             α   ×     e     j   ⁢   0                   α   ×     e     j   ⁡   (     -       i   ⁢   π     4       )               e     j   ⁡   (       -       i   ⁢   π     4       -       7   ⁢   π     8       )             )               Equation   ⁢         214               
For i=8, 9, . . . , 15:
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   225 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     - 
                                       
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       - 
                                       
                                         
                                           i 
                                           ⁢ 
                                           π 
                                         
                                         4 
                                       
                                     
                                     - 
                                     
                                       
                                         7 
                                         ⁢ 
                                         π 
                                       
                                       8 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   215 
                 
               
             
           
         
       
     
     or 
     For i=0, 1, . . . , 7: 
                   Math   ⁢         226                        F   [   i   ]     =       1         α   2     +   1         ⁢     (           e     j   ⁢       θ   11     [   i   ]               α   ×     e     j   ⁡   (         θ   11     [   i   ]     +   λ     )                   α   ×     e     j   ⁡   (         θ   11     [   i   ]     -       i   ⁢   π     4       )               e     j   ⁡   (         θ   11     [   i   ]     -       i   ⁢   π     4     +   λ   -       7   ⁢   π     8       )             )               Equation   ⁢         216               
For i=8, 9, . . . , 15:
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   227 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         [ 
                                         i 
                                         ] 
                                       
                                       - 
                                       
                                         
                                           i 
                                           ⁢ 
                                           π 
                                         
                                         4 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     [ 
                                     i 
                                     ] 
                                   
                                   - 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   λ 
                                   - 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   [ 
                                   i 
                                   ] 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         [ 
                                         i 
                                         ] 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   217 
                 
               
             
           
         
       
     
     The value of α in Equation 198 and in Equation 200 is appropriate for obtaining excellent data reception quality. The poor reception points for s 1  are represented as in  FIGS.  38 A and  38 B  when α&lt;1.0 and as in  FIGS.  39 A and  39 B  when α&gt;1.0. 
     In the present embodiment, the scheme of structuring N different precoding matrices for a precoding hopping scheme with an N-slot time period (cycle) has been described. In this case, as the N different precoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] are prepared. In the present embodiment, an example of a single carrier transmission scheme has been described, and therefore the case of arranging symbols in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1] in the time domain (or the frequency domain) has been described. The present invention is not, however, limited in this way, and the N different precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1] generated in the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaption in this case, precoding weights may be changed by arranging symbols in the frequency domain and in the frequency-time domain. Note that a precoding hopping scheme with an N-slot time period (cycle) has been described, but the same advantageous effects may be obtained by randomly using N different precoding matrices. In other words, the N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Examples #5 through #10 have been shown based on Conditions #10 through #16. However, in order to achieve a precoding matrix hopping scheme with a longer period (cycle), the period (cycle) for hopping between precoding matrices may be lengthened by, for example, selecting a plurality of examples from Examples #5 through #10 and using the precoding matrices indicated in the selected examples. For example, a precoding matrix hopping scheme with a longer period (cycle) may be achieved by using the precoding matrices indicated in Example #7 and the precoding matrices indicated in Example #10. In this case, Conditions #10 through #16 are not necessarily observed. (In Equation 158 of Condition #10, Equation 159 of Condition #11, Equation 164 of Condition #13, Equation 175 of Condition #14, and Equation 176 of Condition #15, it becomes important for providing excellent reception quality for the conditions “all x and all y” to be “existing x and existing y”.) When viewed from a different perspective, in the precoding matrix hopping scheme over an N-slot period (cycle) (where N is a large natural number), the probability of providing excellent reception quality increases when the precoding matrices of one of Examples #5 through #10 are included. 
     Embodiment 7 
     The present embodiment describes the structure of a reception device for receiving modulated signals transmitted by a transmission scheme that regularly hops between precoding matrices as described in Embodiments 1-6. 
     In Embodiment 1, the following scheme has been described. A transmission device that transmits modulated signals, using a transmission scheme that regularly hops between precoding matrices, transmits information regarding the precoding matrices. Based on this information, a reception device obtains information on the regular precoding matrix hopping used in the transmitted frames, decodes the precoding, performs detection, obtains the log-likelihood ratio for the transmitted bits, and subsequently performs error correction decoding. 
     The present embodiment describes the structure of a reception device, and a scheme of hopping between precoding matrices, that differ from the above structure and scheme. 
       FIG.  40    is an example of the structure of a transmission device in the present embodiment. Elements that operate in a similar way to  FIG.  3    bear the same reference signs. An encoder group ( 4002 ) receives transmission bits ( 4001 ) as input. The encoder group ( 4002 ), as described in Embodiment 1, includes a plurality of encoders for error correction coding, and based on the frame structure signal  313 , a certain number of encoders operate, such as one encoder, two encoders, or four encoders. 
     When one encoder operates, the transmission bits ( 4001 ) are encoded to yield encoded transmission bits. The encoded transmission bits are allocated into two parts, and the encoder group ( 4002 ) outputs allocated bits ( 4003 A) and allocated bits ( 4003 B). 
     When two encoders operate, the transmission bits ( 4001 ) are divided in two (referred to as divided bits A and B). The first encoder receives the divided bits A as input, encodes the divided bits A, and outputs the encoded bits as allocated bits ( 4003 A). The second encoder receives the divided bits B as input, encodes the divided bits B, and outputs the encoded bits as allocated bits ( 4003 B). 
     When four encoders operate, the transmission bits ( 4001 ) are divided in four (referred to as divided bits A, B, C, and D). The first encoder receives the divided bits A as input, encodes the divided bits A, and outputs the encoded bits A. The second encoder receives the divided bits B as input, encodes the divided bits B, and outputs the encoded bits B. The third encoder receives the divided bits C as input, encodes the divided bits C, and outputs the encoded bits C. The fourth encoder receives the divided bits D as input, encodes the divided bits D, and outputs the encoded bits D. The encoded bits A, B, C, and D are divided into allocated bits ( 4003 A) and allocated bits ( 4003 B). 
     The transmission device supports a transmission scheme such as, for example, the following Table 1 (Table 1A and Table 1B). 
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 1A 
               
               
                   
               
               
                 Number of 
                   
                   
                   
                   
                   
               
               
                 modulated 
                   
                   
                   
                   
                   
               
               
                 transmission 
                   
                   
                   
                   
                 Prece- 
               
               
                 signals 
                   
                 Number 
                 Error 
                   
                 ding 
               
               
                 (number of 
                   
                 of 
                 correction 
                   
                 matrix 
               
               
                 transmit 
                 Modulation 
                 enco- 
                 coding 
                 Transmission 
                 hopping 
               
               
                 antennas) 
                 scheme 
                 ders 
                 scheme 
                 information 
                 scheme 
               
               
                   
               
             
            
               
                 1 
                 QPSK 
                 1 
                 A 
                 00000000 
                 — 
               
               
                   
                   
                   
                 B 
                 00000001 
                 — 
               
               
                   
                   
                   
                 C 
                 00000010 
                 — 
               
               
                   
                 16QAM 
                 1 
                 A 
                 00000011 
                 — 
               
               
                   
                   
                   
                 B 
                 00000100 
                 — 
               
               
                   
                   
                   
                 C 
                 00000101 
                 — 
               
               
                   
                 64QAM 
                 1 
                 A 
                 00000110 
                 — 
               
               
                   
                   
                   
                 B 
                 00000111 
                 — 
               
               
                   
                   
                   
                 C 
                 00001000 
                 — 
               
               
                   
                 256QAM 
                 1 
                 A 
                 00001001 
                 — 
               
               
                   
                   
                   
                 B 
                 00001010 
                 — 
               
               
                   
                   
                   
                 C 
                 00001011 
                 — 
               
               
                   
                 1024- 
                 1 
                 A 
                 00001100 
                 — 
               
               
                   
                 QAM 
                   
                 B 
                 00001101 
                 — 
               
               
                   
                   
                   
                 C 
                 00001110 
                 — 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 1B 
               
               
                   
               
               
                 Number of 
                   
                   
                   
                   
                   
               
               
                 modulated 
                   
                   
                   
                   
                   
               
               
                 transmission 
                   
                   
                   
                   
                 Prece- 
               
               
                 signals 
                   
                 Number 
                 Error 
                   
                 ding 
               
               
                 (number of 
                   
                 of 
                 correction 
                   
                 matrix 
               
               
                 transmit 
                 Modulation 
                 enco- 
                 coding 
                 Transmission 
                 hopping 
               
               
                 antennas) 
                 scheme 
                 ders 
                 scheme 
                 information 
                 scheme 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 2 
                 #1: QPSK, 
                 1 
                 A 
                 00001111 
                 D 
               
               
                   
                 #2: QPSK 
                   
                 B 
                 00010000 
                 D 
               
               
                   
                   
                   
                 C 
                 00010001 
                 D 
               
               
                   
                   
                 2 
                 A 
                 00010010 
                 E 
               
               
                   
                   
                   
                 B 
                 00010011 
                 E 
               
               
                   
                   
                   
                 C 
                 00010100 
                 E 
               
               
                   
                 #1: QPSK, 
                 1 
                 A 
                 00010101 
                 D 
               
               
                   
                 #2: 
                   
                 B 
                 00010110 
                 D 
               
               
                   
                 16QAM 
                   
                 C 
                 00010111 
                 D 
               
               
                   
                   
                 2 
                 A 
                 00011000 
                 E 
               
               
                   
                   
                   
                 B 
                 00011001 
                 E 
               
               
                   
                   
                   
                 C 
                 00011010 
                 E 
               
               
                   
                 #1: 
                 1 
                 A 
                 00011011 
                 D 
               
               
                   
                 16QAM, 
                   
                 B 
                 00011100 
                 D 
               
               
                   
                 #2: 
                   
                 C 
                 00011101 
                 D 
               
               
                   
                 16QAM 
                 2 
                 A 
                 00011110 
                 E 
               
               
                   
                   
                   
                 B 
                 00011111 
                 E 
               
               
                   
                   
                   
                 C 
                 00100000 
                 E 
               
               
                   
                 #1: 
                 1 
                 A 
                 00100001 
                 D 
               
               
                   
                 16QAM, 
                   
                 B 
                 00100010 
                 D 
               
               
                   
                 #2: 
                   
                 C 
                 00100011 
                 D 
               
               
                   
                 64QAM 
                 2 
                 A 
                 00100100 
                 E 
               
               
                   
                   
                   
                 B 
                 00100101 
                 E 
               
               
                   
                   
                   
                 C 
                 00100110 
                 E 
               
               
                   
                 #1: 
                 1 
                 A 
                 00100111 
                 F 
               
               
                   
                 64QAM, 
                   
                 B 
                 00101000 
                 F 
               
               
                   
                 #2: 
                   
                 C 
                 00101001 
                 F 
               
               
                   
                 64QAM 
                 2 
                 A 
                 00101010 
                 G 
               
               
                   
                   
                   
                 B 
                 00101011 
                 G 
               
               
                   
                   
                   
                 C 
                 00101100 
                 G 
               
               
                   
                 #1: 
                 1 
                 A 
                 00101101 
                 F 
               
               
                   
                 64QAM, 
                   
                 B 
                 00101110 
                 F 
               
               
                   
                 #2: 
                   
                 C 
                 00101111 
                 F 
               
               
                   
                 256QAM 
                 2 
                 A 
                 00110000 
                 G 
               
               
                   
                   
                   
                 B 
                 00110001 
                 G 
               
               
                   
                   
                   
                 C 
                 00110010 
                 G 
               
               
                   
                 #1: 
                 1 
                 A 
                 00110011 
                 F 
               
               
                   
                 256QAM, 
                   
                 B 
                 00110100 
                 F 
               
               
                   
                 #2: 
                   
                 C 
                 00110101 
                 F 
               
               
                   
                 256QAM 
                 2 
                 A 
                 00110110 
                 G 
               
               
                   
                   
                   
                 B 
                 00110111 
                 G 
               
               
                   
                   
                   
                 C 
                 00111000 
                 G 
               
               
                   
                   
                 4 
                 A 
                 00111001 
                 H 
               
               
                   
                   
                   
                 B 
                 00111010 
                 H 
               
               
                   
                   
                   
                 C 
                 00111011 
                 H 
               
               
                   
                 #1: 
                 1 
                 A 
                 00111100 
                 F 
               
               
                   
                 256QAM, 
                   
                 B 
                 00111101 
                 F 
               
               
                   
                 #2: 
                   
                 C 
                 00111110 
                 F 
               
               
                   
                 1024QAM 
                 2 
                 A 
                 00111111 
                 G 
               
               
                   
                   
                   
                 B 
                 01000000 
                 G 
               
               
                   
                   
                   
                 C 
                 01000001 
                 G 
               
               
                   
                   
                 4 
                 A 
                 01000010 
                 H 
               
               
                   
                   
                   
                 B 
                 01000011 
                 H 
               
               
                   
                   
                   
                 C 
                 01000100 
                 H 
               
               
                   
                 #1: 
                 1 
                 A 
                 01000101 
                 F 
               
               
                   
                 1024QAM, 
                   
                 B 
                 01000110 
                 F 
               
               
                   
                 #2: 
                   
                 C 
                 01000111 
                 F 
               
               
                   
                 1024QAM 
                 2 
                 A 
                 01001000 
                 G 
               
               
                   
                   
                   
                 B 
                 01001001 
                 G 
               
               
                   
                   
                   
                 C 
                 01001010 
                 G 
               
               
                   
                   
                 4 
                 A 
                 01001011 
                 H 
               
               
                   
                   
                   
                 B 
                 01001100 
                 H 
               
               
                   
                   
                   
                 C 
                 01001101 
                 H 
               
               
                   
               
            
           
         
       
     
     As shown in Table 1, transmission of a one-stream signal and transmission of a two-stream signal are supported as the number of transmission signals (number of transmit antennas). Furthermore, QPSK, 16QAM, 64QAM, 256QAM, and 1024QAM are supported as the modulation scheme. In particular, when the number of transmission signals is two, it is possible to set separate modulation schemes for stream # 1  and stream # 2 . For example, “# 1 : 256QAM, # 2 : 1024QAM” in Table 1 indicates that “the modulation scheme of stream # 1  is 256QAM, and the modulation scheme of stream # 2  is 1024QAM” (other entries in the table are similarly expressed). Three types of error correction coding schemes, A, B, and C, are supported. In this case, A, B, and C may all be different coding schemes. A, B, and C may also be different coding rates, and A, B, and C may be coding schemes with different block sizes. 
     The pieces of transmission information in Table 1 are allocated to modes that define a “number of transmission signals”, “modulation scheme”, “number of encoders”, and “error correction coding scheme”. Accordingly, in the case of “number of transmission signals: 2”, “modulation scheme: # 1 : 1024QAM, # 2 : 1024QAM”, “number of encoders: 4”, and “error correction coding scheme: C”, for example, the transmission information is set to 010θ1101. In the frame, the transmission device transmits the transmission information and the transmission data. When transmitting the transmission data, in particular when the “number of transmission signals” is two, a “precoding matrix hopping scheme” is used in accordance with Table 1. In Table 1, five types of the “precoding matrix hopping scheme”, D, E, F, G, and H, are prepared. The precoding matrix hopping scheme is set to one of these five types in accordance with Table 1. The following, for example, are ways of implementing the five different types. 
     Prepare five different precoding matrices. 
     Use five different types of period (cycle)s, for example a four-slot period (cycle) for D, an eight-slot period (cycle) for E, . . . . 
     Use both different precoding matrices and different period (cycle)s. 
       FIG.  41    shows an example of a frame structure of a modulated signal transmitted by the transmission device in  FIG.  40   . The transmission device is assumed to support settings for both a mode to transmit two modulated signals, z 1 ( t ) and z 2 ( t ), and for a mode to transmit one modulated signal. 
     In  FIG.  41   , the symbol ( 4100 ) is a symbol for transmitting the “transmission information” shown in Table 1. The symbols ( 4101 _ 1 ) and ( 4101 _ 2 ) are reference (pilot) symbols for channel estimation. The symbols ( 4102 _ 1 ,  4103 _ 1 ) are data transmission symbols for transmitting the modulated signal z 1 ( t ). The symbols ( 4102 _ 2 ,  4103 _ 2 ) are data transmission symbols for transmitting the modulated signal z 2 ( t ). The symbol ( 4102 _ 1 ) and the symbol ( 4102 _ 2 ) are transmitted at the same time along the same (shared/common) frequency, and the symbol ( 4103 _ 1 ) and the symbol ( 4103 _ 2 ) are transmitted at the same time along the same (shared/common) frequency. The symbols ( 4102 _ 1 ,  4103 _ 1 ) and the symbols ( 4102 _ 2 ,  4103 _ 2 ) are the symbols after precoding matrix calculation using the scheme of regularly hopping between precoding matrices described in Embodiments 1-4 and Embodiment 6 (therefore, as described in Embodiment 1, the structure of the streams s 1 ( t ) and s 2 ( t ) is as in  FIG.  6   ). 
     Furthermore, in  FIG.  41   , the symbol ( 4104 ) is a symbol for transmitting the “transmission information” shown in Table 1. The symbol ( 4105 ) is a reference (pilot) symbol for channel estimation. The symbols ( 4106 ,  4107 ) are data transmission symbols for transmitting the modulated signal z 1 ( t ). The data transmission symbols for transmitting the modulated signal z 1 ( t ) are not precoded, since the number of transmission signals is one. 
     Accordingly, the transmission device in  FIG.  40    generates and transmits modulated signals in accordance with Table 1 and the frame structure in  FIG.  41   . In  FIG.  40   , the frame structure signal  313  includes information regarding the “number of transmission signals”, “modulation scheme”, “number of encoders”, and “error correction coding scheme” set based on Table 1. The encoder ( 4002 ), the mapping units  306 A, B, and the weighting units  308 A, B receive the frame structure signal as an input and operate based on the “number of transmission signals”, “modulation scheme”, “number of encoders”, and “error correction coding scheme” that are set based on Table 1. “Transmission information” corresponding to the set “number of transmission signals”, “modulation scheme”, “number of encoders”, and “error correction coding scheme” is also transmitted to the reception device. 
     The structure of the reception device may be represented similarly to  FIG.  7    of Embodiment 1. The difference with Embodiment 1 is as follows: since the transmission device and the reception device store the information in Table 1 in advance, the transmission device does not need to transmit information for regularly hopping between precoding matrices, but rather transmits “transmission information” corresponding to the “number of transmission signals”, “modulation scheme”, “number of encoders”, and “error correction coding scheme”, and the reception device obtains information for regularly hopping between precoding matrices from Table 1 by receiving the “transmission information”. Accordingly, by the control information decoding unit  709  obtaining the “transmission information” transmitted by the transmission device in  FIG.  40   , the reception device in  FIG.  7    obtains, from the information corresponding to Table 1, a signal  710  regarding information on the transmission scheme, as notified by the transmission device, which includes information for regularly hopping between precoding matrices. Therefore, when the number of transmission signals is two, the signal processing unit  711  can perform detection based on a precoding matrix hopping pattern to obtain received log-likelihood ratios. 
     Note that in the above description, “transmission information” is set with respect to the “number of transmission signals”, “modulation scheme”, “number of encoders”, and “error correction coding scheme” as in Table 1, and the precoding matrix hopping scheme is set with respect to the “transmission information”. However, it is not necessary to set the “transmission information” with respect to the “number of transmission signals”, “modulation scheme”, “number of encoders”, and “error correction coding scheme”. For example, as in Table 2, the “transmission information” may be set with respect to the “number of transmission signals” and “modulation scheme”, and the precoding matrix hopping scheme may be set with respect to the “transmission information”. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Number of 
                   
                   
                   
               
               
                 modulated 
                   
                   
                 Preceding 
               
               
                 transmission signals 
                   
                   
                 matrix 
               
               
                 (number of transmit 
                 Modulation 
                 Transmission 
                 hopping 
               
               
                 antennas) 
                 scheme 
                 information 
                 scheme 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 1 
                 QPSK 
                 00000 
                 — 
               
               
                   
                 16QAM 
                 00001 
                 — 
               
               
                   
                 64QAM 
                 00010 
                 — 
               
               
                   
                 256QAM 
                 00011 
                 — 
               
               
                   
                 1024QAM 
                 00100 
                 — 
               
               
                 2 
                 #1: QPSK, 
                 10000 
                 D 
               
               
                   
                 #2: QPSK 
                   
                   
               
               
                   
                 #1: QPSK, 
                 10001 
                 E 
               
               
                   
                 #2: 16QAM 
                   
                   
               
               
                   
                 #1: 16QAM, 
                 10010 
                 E 
               
               
                   
                 #2: 16QAM 
                   
                   
               
               
                   
                 #1: 16QAM, 
                 10011 
                 E 
               
               
                   
                 #2: 64QAM 
                   
                   
               
               
                   
                 #1: 64QAM, 
                 10100 
                 F 
               
               
                   
                 #2: 64QAM 
                   
                   
               
               
                   
                 #1: 64QAM, 
                 10101 
                 F 
               
               
                   
                 #2: 256QAM 
                   
                   
               
               
                   
                 #1: 256QAM, 
                 10110 
                 G 
               
               
                   
                 #2: 256QAM 
                   
                   
               
               
                   
                 #1: 256QAM, 
                 10111 
                 G 
               
               
                   
                 #2: 1024QAM 
                   
                   
               
               
                   
                 #1: 1024QAM, 
                 11000 
                 H 
               
               
                   
                 #2: 1024QAM 
                   
                   
               
               
                   
               
            
           
         
       
     
     In this context, the “transmission information” and the scheme of setting the precoding matrix hopping scheme is not limited to Tables 1 and 2. As long as a rule is determined in advance for hopping the precoding matrix hopping scheme based on transmission parameters, such as the “number of transmission signals”, “modulation scheme”, “number of encoders”, “error correction coding scheme”, or the like (as long as the transmission device and the reception device share a predetermined rule, or in other words, if the precoding matrix hopping scheme is hopped based on any of the transmission parameters (or on any plurality of transmission parameters)), the transmission device does not need to transmit information regarding the precoding matrix hopping scheme. The reception device can identify the precoding matrix hopping scheme used by the transmission device by identifying the information on the transmission parameters and can therefore accurately perform decoding and detection. Note that in Tables 1 and 2, a transmission scheme that regularly hops between precoding matrices is used when the number of modulated transmission signals is two, but a transmission scheme that regularly hops between precoding matrices may be used when the number of modulated transmission signals is two or greater. 
     Accordingly, if the transmission device and reception device share a table regarding transmission patterns that includes information on precoding hopping schemes, the transmission device need not transmit information regarding the precoding hopping scheme, transmitting instead control information that does not include information regarding the precoding hopping scheme, and the reception device can infer the precoding hopping scheme by acquiring this control information. 
     As described above, in the present embodiment, the transmission device does not transmit information directly related to the scheme of regularly hopping between precoding matrices. Rather, a scheme has been described wherein the reception device infers information regarding precoding for the “scheme of regularly hopping between precoding matrices” used by the transmission device. This scheme yields the advantageous effect of improved transmission efficiency of data as a result of the transmission device not transmitting information directly related to the scheme of regularly hopping between precoding matrices. 
     Note that the present embodiment has been described as changing precoding weights in the time domain, but as described in Embodiment 1, the present invention may be similarly embodied when using a multi-carrier transmission scheme such as OFDM or the like. 
     In particular, when the precoding hopping scheme only changes depending on the number of transmission signals, the reception device can learn the precoding hopping scheme by acquiring information, transmitted by the transmission device, on the number of transmission signals. 
     In the present description, it is considered that a communications/broadcasting device such as a broadcast station, a base station, an access point, a terminal, a mobile phone, or the like is provided with the transmission device, and that a communications device such as a television, radio, terminal, personal computer, mobile phone, access point, base station, or the like is provided with the reception device. Additionally, it is considered that the transmission device and the reception device in the present description have a communications function and are capable of being connected via some sort of interface to a device for executing applications for a television, radio, personal computer, mobile phone, or the like. 
     Furthermore, in the present embodiment, symbols other than data symbols, such as pilot symbols (preamble, unique word, postamble, reference symbol, and the like), symbols for control information, and the like may be arranged in the frame in any way. While the terms “pilot symbol” and “symbols for control information” have been used here, any term may be used, since the function itself is what is important. 
     It suffices for a pilot symbol, for example, to be a known symbol modulated with PSK modulation in the transmission and reception devices (or for the reception device to be able to synchronize in order to know the symbol transmitted by the transmission device). The reception device uses this symbol for frequency synchronization, time synchronization, channel estimation (estimation of Channel State Information (CSI) for each modulated signal), detection of signals, and the like. 
     A symbol for control information is for transmitting information other than data (of applications or the like) that needs to be transmitted to the communication partner for achieving communication (for example, the modulation scheme, error correction coding scheme, coding rate of the error correction coding scheme, setting information in the upper layer, and the like). 
     Note that the present invention is not limited to the above Embodiments 1-5 and may be embodied with a variety of modifications. For example, the above embodiments describe communications devices, but the present invention is not limited to these devices and may be implemented as software for the corresponding communications scheme. 
     Furthermore, a precoding hopping scheme used in a scheme of transmitting two modulated signals from two antennas has been described, but the present invention is not limited in this way. The present invention may be also embodied as a precoding hopping scheme for similarly changing precoding weights (matrices) in the context of a scheme whereby four mapped signals are precoded to generate four modulated signals that are transmitted from four antennas, or more generally, whereby N mapped signals are precoded to generate N modulated signals that are transmitted from N antennas. 
     In the description, terms such as “precoding” and “precoding weight” are used, but any other terms may be used. What matters in the present invention is the actual signal processing. 
     Different data may be transmitted in streams s 1 ( t ) and s 2 ( t ), or the same data may be transmitted. 
     Each of the transmit antennas of the transmission device and the receive antennas of the reception device shown in the figures may be formed by a plurality of antennas. 
     Programs for executing the above transmission scheme may, for example, be stored in advance in Read Only Memory (ROM) and be caused to operate by a Central Processing Unit (CPU). 
     Furthermore, the programs for executing the above transmission scheme may be stored in a computer-readable recording medium, the programs stored in the recording medium may be loaded in the Random Access Memory (RAM) of the computer, and the computer may be caused to operate in accordance with the programs. 
     The components in the above embodiments may be typically assembled as a Large Scale Integration (LSI), a type of integrated circuit. Individual components may respectively be made into discrete chips, or part or all of the components in each embodiment may be made into one chip. While an LSI has been referred to, the terms Integrated Circuit (IC), system LSI, super LSI, or ultra LSI may be used depending on the degree of integration. Furthermore, the scheme for assembling integrated circuits is not limited to LSI, and a dedicated circuit or a general-purpose processor may be used. A Field Programmable Gate Array (FPGA), which is programmable after the LSI is manufactured, or a reconfigurable processor, which allows reconfiguration of the connections and settings of circuit cells inside the LSI, may be used. 
     Furthermore, if technology for forming integrated circuits that replaces LSIs emerges, owing to advances in semiconductor technology or to another derivative technology, the integration of functional blocks may naturally be accomplished using such technology. The application of biotechnology or the like is possible. 
     Embodiment 8 
     The present embodiment describes an application of the scheme described in Embodiments 1-4 and Embodiment 6 for regularly hopping between precoding weights. 
       FIG.  6    relates to the weighting scheme (precoding scheme) in the present embodiment. The weighting unit  600  integrates the weighting units  308 A and  308 B in  FIG.  3   . As shown in  FIG.  6   , the stream s 1 ( t ) and the stream s 2 ( t ) correspond to the baseband signals  307 A and  307 B in  FIG.  3   . In other words, the streams s 1 ( t ) and s 2 ( t ) are the baseband signal in-phase components I and quadrature components Q when mapped according to a modulation scheme such as QPSK, 16QAM, 64QAM, or the like. As indicated by the frame structure of  FIG.  6   , the stream s 1 ( t ) is represented as s 1 ( u ) at symbol number u, as s 1 ( u+ 1) at symbol number u+1, and so forth. Similarly, the stream s 2 ( t ) is represented as s 2 ( u ) at symbol number u, as s 2 ( u+ 1) at symbol number u+1, and so forth. The weighting unit  600  receives the baseband signals  307 A (s 1 ( t )) and  307 B (s 2 ( t )) and the information  315  regarding weighting information in  FIG.  3    as inputs, performs weighting in accordance with the information  315  regarding weighting, and outputs the signals  309 A (z 1 ( t )) and  309 B (z 2 ( t )) after weighting in  FIG.  3   . 
     At this point, when for example a precoding matrix hopping scheme with an N=8 period (cycle) as in Example #8 in Embodiment 6 is used, z 1 ( t ) and z 2 ( t ) are represented as follows. 
     For symbol number 8i (where i is an integer greater than or equal to zero): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   228 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 8 
                                 ⁢ 
                                 i 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 8 
                                 ⁢ 
                                 i 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       k 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   218 
                 
               
             
           
         
       
     
     Here, j is an imaginary unit, and k=0. 
     For symbol number 8i+1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   229 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       k 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
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                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
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                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   219 
                 
               
             
           
         
       
     
     Here, k=1. 
     For symbol number 8i+2: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   230 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
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                   = 
                   
                     
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                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   2 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   220 
                 
               
             
           
         
       
     
     Here, k=2. 
     For symbol number 8i+3: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   231 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 3 
                               
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 3 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                 
                                   
                                     
                                       k 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   3 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   3 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   221 
                 
               
             
           
         
       
     
     Here, k=3. 
     For symbol number 8i+4: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   232 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 4 
                               
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 4 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                 
                                   
                                     
                                       k 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   4 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   4 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   222 
                 
               
             
           
         
       
     
     Here, k=4. 
     For symbol number 8i+5: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   233 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 5 
                               
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 5 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                 
                                   
                                     
                                       k 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   5 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   5 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   223 
                 
               
             
           
         
       
     
     Here, k=5. 
     For symbol number 8i+6: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   234 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 6 
                               
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 6 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                 
                                   
                                     
                                       k 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   6 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   6 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   224 
                 
               
             
           
         
       
     
     Here, k=6. 
     For symbol number 8i+7: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   235 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 7 
                               
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 7 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                 
                                   
                                     
                                       k 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   7 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   7 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   225 
                 
               
             
           
         
       
     
     Here, k=7. 
     The symbol numbers shown here can be considered to indicate time. As described in other embodiments, in Equation 225, for example, z 1 (8i+7) and z 2 (8i+7) at time 8i+7 are signals at the same time, and the transmission device transmits z 1  (8i+7) and z 2 (8i+7) over the same (shared/common) frequency. In other words, letting the signals at time T be s 1 (T), s 2 (T), z 1 (T), and z 2 (T), then z 1 (T) and z 2 (T) are sought from some sort of precoding matrices and from s 1 (T) and s 2 (T), and the transmission device transmits z 1 (T) and z 2 (T) over the same (shared/common) frequency (at the same time). Furthermore, in the case of using a multi-carrier transmission scheme such as OFDM or the like, and letting signals corresponding to s 1 , s 2 , z 1 , and z 2  for (sub)carrier L and time T be s 1 (T, L), s 2 (T, L), z 1 (T, L), and z 2 (T, L), then z 1 (T, L) and z 2 (T, L) are sought from some sort of precoding matrices and from s 1 (T, L) and s 2 (T, L), and the transmission device transmits z 1 (T, L) and z 2 (T, L) over the same (shared/common) frequency (at the same time). 
     In this case, the appropriate value of α is given by Equation 198 or Equation 200. 
     The present embodiment describes a precoding hopping scheme that increases period (cycle) size, based on the above-described precoding matrices of Equation 190. 
     Letting the period (cycle) of the precoding hopping scheme be 8M, 8M different precoding matrices are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   236 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       
                         8 
                         × 
                         k 
                       
                       + 
                       i 
                     
                     ] 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           α 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               0 
                             
                           
                         
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                       
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       k 
                                       ⁢ 
                                       π 
                                     
                                     
                                       4 
                                       ⁢ 
                                       M 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ( 
                               
                                 
                                   
                                     i 
                                     ⁢ 
                                     π 
                                   
                                   4 
                                 
                                 + 
                                 
                                   
                                     k 
                                     ⁢ 
                                     π 
                                   
                                   
                                     4 
                                     ⁢ 
                                     M 
                                   
                                 
                                 + 
                                 
                                   
                                     7 
                                     ⁢ 
                                     π 
                                   
                                   8 
                                 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   226 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, 3, 4, 5, 6, 7, and k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     For example, letting M=2 and α&lt;1, the poor reception points for s 1 (◯) and for s 2 (□) at k=0 are represented as in  FIG.  42 A . Similarly, the poor reception points for s 1 (◯) and for s 2 (□) at k=1 are represented as in  FIG.  42 B . In this way, based on the precoding matrices in Equation 190, the poor reception points are as in  FIG.  42 A , and by using, as the precoding matrices, the matrices yielded by multiplying each term in the second line on the right-hand side of Equation 190 by e jX  (see Equation 226), the poor reception points are rotated with respect to  FIG.  42 A  (see  FIG.  42 B ). (Note that the poor reception points in  FIG.  42 A  and  FIG.  42 B  do not overlap. Even when multiplying by e jX , the poor reception points should not overlap, as in this case. Furthermore, the matrices yielded by multiplying each term in the first line on the right-hand side of Equation 190, rather than in the second line on the right-hand side of Equation 190, by e jX  may be used as the precoding matrices.) In this case, the precoding matrices F[0]-F[15] are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   237 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       
                         8 
                         × 
                         k 
                       
                       + 
                       i 
                     
                     ] 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           α 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               0 
                             
                           
                         
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                       
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   Xk 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ( 
                               
                                 
                                   
                                     i 
                                     ⁢ 
                                     π 
                                   
                                   4 
                                 
                                 + 
                                 Xk 
                                 + 
                                 
                                   
                                     7 
                                     ⁢ 
                                     π 
                                   
                                   8 
                                 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   227 
                 
               
             
           
         
       
     
     Here, i=0, 1, 2, 3, 4, 5, 6, 7, and k=0, 1. 
     In this case, when M=2, precoding matrices F[0]-F[15] are generated (the precoding matrices F[0]-F[15] may be in any order, and the matrices F[0]-F[15] may each be different). Symbol number 16i may be precoded using F[0], symbol number 16i+1 may be precoded using F[1], . . . , and symbol number 16i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , 14, 15). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) 
     Summarizing the above considerations, with reference to Equations 82-85, N-period (cycle) precoding matrices are represented by the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   238 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           α 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                             
                           
                         
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                    
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ( 
                               
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                 + 
                                 λ 
                                 + 
                                 δ 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   228 
                 
               
             
           
         
       
     
     Here, since the period (cycle) has N slots, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). Furthermore, the N×M period (cycle) precoding matrices based on Equation 228 are represented by the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   239 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       
                         N 
                         × 
                         k 
                       
                       + 
                       i 
                     
                     ] 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           α 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                             
                           
                         
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                    
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 + 
                                 
                                   X 
                                   k 
                                 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ( 
                               
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                 + 
                                 
                                   X 
                                   k 
                                 
                                 + 
                                 λ 
                                 + 
                                 δ 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   229 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     Precoding matrices F[0]-F[N×M−1] are thus generated (the precoding matrices F[0]-F[N×M−1] may be in any order for the N×M slots in the period (cycle)). Symbol number N×M×i may be precoded using F[0], symbol number N×M×i+1 may be precoded using F[1], . . . , and symbol number N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , N×M−2, N×M−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) 
     Generating the precoding matrices in this way achieves a precoding matrix hopping scheme with a large period (cycle), allowing for the position of poor reception points to be easily changed, which may lead to improved data reception quality. Note that while the N×M period (cycle) precoding matrices have been set to Equation 229, the N×M period (cycle) precoding matrices may be set to the following equation, as described above. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   240 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       
                         N 
                         × 
                         k 
                       
                       + 
                       i 
                     
                     ] 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           α 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                               + 
                               
                                 X 
                                 k 
                               
                             
                           
                         
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                    
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     
                                       X 
                                       k 
                                     
                                     + 
                                     λ 
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ( 
                               
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                 + 
                                 λ 
                                 + 
                                 δ 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   230 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     In Equations 229 and 230, when 0 radians≤δ&lt;2π radians, the matrices are a unitary matrix when δ=π radians and are a non-unitary matrix when δ≠π radians. In the present scheme, use of a non-unitary matrix for π/2 radians≤|δ|&lt;π radians is one characteristic structure (the conditions for δ being similar to other embodiments), and excellent data reception quality is obtained. Use of a unitary matrix is another structure, and as described in detail in Embodiment 10 and Embodiment 16, if N is an odd number in Equations 229 and 230, the probability of obtaining excellent data reception quality increases. 
     Embodiment 9 
     The present embodiment describes a scheme for regularly hopping between precoding matrices using a unitary matrix. 
     As described in Embodiment 8, in the scheme of regularly hopping between precoding matrices over a period (cycle) with N slots, the precoding matrices prepared for the N slots with reference to Equations 82-85 are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   241 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           α 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                             
                           
                         
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                    
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ( 
                               
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                 + 
                                 λ 
                                 + 
                                 δ 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   231 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). (Let α&gt;0.) Since a unitary matrix is used in the present embodiment, the precoding matrices in Equation 231 may be represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   242 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   ⁢ 
                   
                     1 
                     
                       
                         
                           α 
                           2 
                         
                         + 
                         1 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             e 
                             
                               j 
                               ⁢ 
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                             
                           
                         
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                    
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             α 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             e 
                             
                               j 
                               ( 
                               
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                 + 
                                 λ 
                                 + 
                                 π 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   232 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). (Let α&gt;0.) From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment 3, the following condition is important for achieving excellent data reception quality.
 
Math 243
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2, . . . , N− 2, N− 1)  Condition #17
 
     (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
Math 244
 
 e   j(θ     11     (x)−θ     21     (x)−π)   ≠e   j(θ     11     (y)−θ     21     (y)−π)  for ∀ x,∀y  ( x≠y;x,y= 0,1,2, . . . , N− 2, N− 1)  Condition #18
 
     (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.) 
     Embodiment 6 describes the distance between poor reception points. In order to increase the distance between poor reception points, it is important for the number of slots N to be an odd number three or greater. The following explains this point. 
     In order to distribute the poor reception points evenly with regards to phase in the complex plane, as described in Embodiment 6, Condition #19 and Condition #20 are provided. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   245 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       e 
                       
                         j 
                         ( 
                           
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             
                               x 
                               + 
                               1 
                             
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             
                               x 
                               + 
                               1 
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     
                       e 
                       
                         j 
                         ( 
                           
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             x 
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             x 
                             ) 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             2 
                             ⁢ 
                             π 
                           
                           N 
                         
                         ) 
                       
                     
                     ⁢ 
                         
                     for 
                     ⁢ 
                         
                     
                       ∀ 
                         
                       
                         x 
                         ⁡ 
                         ( 
                         
                           
                             x 
                             = 
                             0 
                           
                           , 
                           1 
                           , 
                           2 
                           , 
                           … 
                               
                           , 
                           
                             N 
                             - 
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #19 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   246 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       e 
                       
                         j 
                         ( 
                           
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             
                               x 
                               + 
                               1 
                             
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             
                               x 
                               + 
                               1 
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     
                       e 
                       
                         j 
                         ( 
                           
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             x 
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             x 
                             ) 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           - 
                           
                             
                               2 
                               ⁢ 
                               π 
                             
                             N 
                           
                         
                         ) 
                       
                     
                     ⁢ 
                         
                     for 
                     ⁢ 
                         
                     
                       ∀ 
                         
                       
                         x 
                         ⁡ 
                         ( 
                         
                           
                             x 
                             = 
                             0 
                           
                           , 
                           1 
                           , 
                           2 
                           , 
                           … 
                               
                           , 
                           
                             N 
                             - 
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #20 
                 
               
             
           
         
       
     
     In other words, Condition #19 means that the difference in phase is 2π/N radians. On the other hand, Condition #20 means that the difference in phase is −2π/N radians. 
     Letting θ 11 (0)−θ 21 (0)=0 radians, and letting α&lt;1, the distribution of poor reception points for s 1  and for s 2  in the complex plane for an N=3 period (cycle) is shown in  FIG.  43 A , and the distribution of poor reception points for s 1  and for s 2  in the complex plane for an N=4 period (cycle) is shown in  FIG.  43 B . Letting θ 11 (0)−θ 21 (0)=0 radians, and letting α&gt;1, the distribution of poor reception points for s 1  and for s 2  in the complex plane for an N=3 period (cycle) is shown in  FIG.  44 A , and the distribution of poor reception points for s 1  and for s 2  in the complex plane for an N=4 period (cycle) is shown in  FIG.  44 B . 
     In this case, when considering the phase between a line segment from the origin to a poor reception point and a half line along the real axis defined by real ≥0 (see  FIG.  43 A ), then for either α&gt;1 or α&lt;1, when N=4, the case always occurs wherein the phase for the poor reception points for s 1  and the phase for the poor reception points for s 2  are the same value. (See  4301 ,  4302  in  FIG.  43 B, and  4401 ,  4402    in  FIG.  44 B .) In this case, in the complex plane, the distance between poor reception points becomes small. On the other hand, when N=3, the phase for the poor reception points for s 1  and the phase for the poor reception points for s 2  are never the same value. 
     Based on the above, considering how the case always occurs wherein the phase for the poor reception points for s 1  and the phase for the poor reception points for s 2  are the same value when the number of slots N in the period (cycle) is an even number, setting the number of slots N in the period (cycle) to an odd number increases the probability of a greater distance between poor reception points in the complex plane as compared to when the number of slots N in the period (cycle) is an even number. However, when the number of slots N in the period (cycle) is small, for example when N≤16, the minimum distance between poor reception points in the complex plane can be guaranteed to be a certain length, since the number of poor reception points is small. Accordingly, when N≤16, even if N is an even number, cases do exist where data reception quality can be guaranteed. 
     Therefore, in the scheme for regularly hopping between precoding matrices based on Equation 232, when the number of slots N in the period (cycle) is set to an odd number, the probability of improving data reception quality is high. Precoding matrices F[0]-F[N−1] are generated based on Equation 232 (the precoding matrices F[0]-F[N−1] may be in any order for the N slots in the period (cycle)). Symbol number Ni may be precoded using F[0], symbol number Ni+1 may be precoded using F[1], . . . , and symbol number N×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , N−2, N−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) Furthermore, when the modulation scheme for both s 1  and s 2  is 16QAM, if α is set as follows, 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   247 
                 
               
               
                  
               
             
             
               
                 
                   α 
                   = 
                   
                     
                       
                         2 
                       
                       + 
                       4 
                     
                     
                       
                         2 
                       
                       + 
                       2 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   233 
                 
               
             
           
         
       
     
     the advantageous effect of increasing the minimum distance between 16×16=256 signal points in the I-Q plane for a specific LOS environment may be achieved. 
     In the present embodiment, the scheme of structuring N different precoding matrices for a precoding hopping scheme with an N-slot time period (cycle) has been described. In this case, as the N different precoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] are prepared. In the present embodiment, an example of a single carrier transmission scheme has been described, and therefore the case of arranging symbols in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1] in the time domain (or the frequency domain) has been described. The present invention is not, however, limited in this way, and the N different precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1] generated in the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaption in this case, precoding weights may be changed by arranging symbols in the frequency domain and in the frequency-time domain. Note that a precoding hopping scheme with an N-slot time period (cycle) has been described, but the same advantageous effects may be obtained by randomly using N different precoding matrices. In other words, the N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots N in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the N different precoding matrices of the present embodiment are included, the probability of excellent reception quality increases. In this case, Condition #17 and Condition #18 can be replaced by the following conditions. (The number of slots in the period (cycle) is considered to be N.)
 
Math 248
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∃ x,∃y  ( x≠y;x,y= 0,1,2, . . . , N− 2, N− 1)  Condition #17′
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
Math 249
 
 e   j(θ     11     (x)−θ     21     (x)−π)   ≠e   j(θ     11     (y)−θ     21     (y)−π)  for ∃ x,∃y  ( x≠y;x,y= 0,1,2, . . . , N− 2, N− 1)  Condition #18′
 
     (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.) 
     Embodiment 10 
     The present embodiment describes a scheme for regularly hopping between precoding matrices using a unitary matrix that differs from the example in Embodiment 9. 
     In the scheme of regularly hopping between precoding matrices over a period (cycle) with 2N slots, the precoding matrices prepared for the 2N slots are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   250 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       for 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   234 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             ⁢ 
             
               1 
               
                 
                   
                     α 
                     2 
                   
                   + 
                   1 
                 
               
             
             ⁢ 
             
               ( 
               
                 
                   
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           
                             θ 
                             11 
                           
                           ( 
                           i 
                           ) 
                         
                       
                     
                   
                   
                     
                       α 
                       × 
                       
                         e 
                         
                           j 
                           ⁢ 
                              
                           
                             ( 
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       α 
                       × 
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       e 
                       
                         j 
                         ( 
                         
                           
                             
                               θ 
                               21 
                             
                             ( 
                             i 
                             ) 
                           
                           + 
                           λ 
                           + 
                           π 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Let α be a fixed value (not depending on i), where α&gt;0. 
     
       
         
           
             Math 
             ⁢ 
             
                  
                 
             
             ⁢ 
             251 
           
         
       
       
         
           
             
               
                 
                   
                     
                       for 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   235 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                 + 
                                 λ 
                                 + 
                                 π 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     Let α be a fixed value (not depending on i), where α&gt;0. (Let the α in Equation 234 and the α in Equation 235 be the same value.) 
     From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment 3, the following conditions are important in Equation 234 for achieving excellent data reception quality.
 
Math 252
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2, . . . , N− 2, N− 1)  Condition #21
 
     (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
Math 253
 
 e   j(θ     11     (x)−θ     21     (x)−π)   ≠e   j(θ     11     (y)−θ     21     (y)−π)  for ∀ x,∀y  ( x≠y;x,y= 0,1,2, . . . , N− 2, N− 1)  Condition #22
 
     (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.) 
     Addition of the following condition is considered.
 
Math 254
 
θ 11 ( x )=θ 11 ( x+N ) for ∀ x  ( x= 0,1,2, . . . , N− 2, N− 1)
 
and
 
θ 21 ( y )=θ 21 ( y+N ) for ∀ y  ( y= 0,1,2, . . . , N− 2, N− 1)  Condition #23
 
     Next, in order to distribute the poor reception points evenly with regards to phase in the complex plane, as described in Embodiment 6, Condition #24 and Condition #25 are provided. 
     
       
         
           
             Math 
             ⁢ 
             
                  
                 
             
             ⁢ 
             255 
           
         
       
       
         
           
             
               
                 
                   
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 x 
                                 + 
                                 i 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               x 
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               x 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   = 
                   
                     e 
                     
                       j 
                       ⁡ 
                       ( 
                       
                         
                           2 
                           ⁢ 
                           π 
                         
                         N 
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #24 
                 
               
             
           
         
       
       
         
           
             for 
             ⁢ 
                 
             
               ∀ 
               
                 x 
                 ⁡ 
                 ( 
                 
                   
                     x 
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                 
                 ) 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
             
                  
                 
             
             ⁢ 
             256 
           
         
       
       
         
           
             
               
                 
                   
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               x 
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               x 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   = 
                   
                     e 
                     
                       j 
                       ⁡ 
                       ( 
                       
                         - 
                         
                           
                             2 
                             ⁢ 
                             π 
                           
                           N 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #25 
                 
               
             
           
         
       
       
         
           
             for 
             ⁢ 
                 
             
               ∀ 
               
                 x 
                 ⁡ 
                 ( 
                 
                   
                     x 
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                 
                 ) 
               
             
           
         
       
     
     In other words, Condition #24 means that the difference in phase is 2π/N radians. On the other hand, Condition #25 means that the difference in phase is −2π/N radians. 
     Letting θ 11 (0)−θ 21 (0)=0 radians, and letting α&gt;1, the distribution of poor reception points for s 1  and for s 2  in the complex plane when N=4 is shown in  FIGS.  45 A and  45 B . As is clear from  FIGS.  45 A and  45 B , in the complex plane, the minimum distance between poor reception points for s 1  is kept large, and similarly, the minimum distance between poor reception points for s 2  is also kept large. Similar conditions are created when α&lt;1. Furthermore, making the same considerations as in Embodiment 9, the probability of a greater distance between poor reception points in the complex plane increases when N is an odd number as compared to when N is an even number. However, when N is small, for example when N≤16, the minimum distance between poor reception points in the complex plane can be guaranteed to be a certain length, since the number of poor reception points is small. Accordingly, when N≤16, even if N is an even number, cases do exist where data reception quality can be guaranteed. 
     Therefore, in the scheme for regularly hopping between precoding matrices based on Equations 234 and 235, when N is set to an odd number, the probability of improving data reception quality is high. Precoding matrices F[0]-F[2N−1] are generated based on Equations 234 and 235 (the precoding matrices F[0]-F[2N−1] may be arranged in any order for the 2N slots in the period (cycle)). Symbol number 2Ni may be precoded using F[0], symbol number 2Ni+1 may be precoded using F[1], . . . , and symbol number 2N×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , 2N−2, 2N−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) Furthermore, when the modulation scheme for both s 1  and s 2  is 16QAM, if α is set as in Equation 233, the advantageous effect of increasing the minimum distance between 16×16=256 signal points in the I-Q plane for a specific LOS environment may be achieved. 
     The following conditions are possible as conditions differing from Condition #23:
 
Math 257
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ   21   (y))  for ∀ x,∀y  ( x≠y;x,y=N,N+ 1 ,N+ 2, . . . ,2 N− 2,2 N− 1)  Condition #26
 
     (where x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . , 2N−2, 2N−1 (each of x and y being an integer in a range of N to 2N−1); and x≠y.)
 
Math 258
 
 e   j(θ     11     (x)−θ     21     (x)−π)   ≠e   j(θ     11     (y)−θ     21     (y)−π)  for ∀ x,∀y  ( x≠y;x,y=N,N+ 1 ,N+ 2, . . . ,2 N− 2,2 N− 1)  Condition #27
 
     (where x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . , 2N−2, 2N−1 (each of x and y being an integer in a range of N to 2N−1); and x≠y.) 
     In this case, by satisfying Condition #21, Condition #22, Condition #26, and Condition #27, the distance in the complex plane between poor reception points for s 1  is increased, as is the distance between poor reception points for s 2 , thereby achieving excellent data reception quality. 
     In the present embodiment, the scheme of structuring 2N different precoding matrices for a precoding hopping scheme with a 2N-slot time period (cycle) has been described. In this case, as the 2N different precoding matrices, F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] are prepared. In the present embodiment, an example of a single carrier transmission scheme has been described, and therefore the case of arranging symbols in the order F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] in the time domain (or the frequency domain) has been described. The present invention is not, however, limited in this way, and the 2N different precoding matrices F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] generated in the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaption in this case, precoding weights may be changed by arranging symbols in the frequency domain and in the frequency-time domain. Note that a precoding hopping scheme with a 2N-slot time period (cycle) has been described, but the same advantageous effects may be obtained by randomly using 2N different precoding matrices. In other words, the 2N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots 2N in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the 2N different precoding matrices of the present embodiment are included, the probability of excellent reception quality increases. 
     Embodiment 11 
     The present embodiment describes a scheme for regularly hopping between precoding matrices using a non-unitary matrix. 
     In the scheme of regularly hopping between precoding matrices over a period (cycle) with 2N slots, the precoding matrices prepared for the 2N slots are represented as follows. 
     
       
         
           
             Math 
             ⁢ 
             
                  
                 
             
             ⁢ 
             259 
           
         
       
       
         
           
             
               
                 
                   
                     
                       for 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   236 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               11 
                             
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                 + 
                                 λ 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   θ 
                                   21 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                               + 
                               δ 
                             
                             ) 
                           
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     Let α be a fixed value (not depending on i), where α&gt;0. Furthermore, let δ≠π radians. 
     
       
         
           
             Math 
             ⁢ 
             
                  
                 
             
             ⁢ 
             260 
           
         
       
       
         
           
             
               
                 
                   
                     
                       for 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   237 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                 + 
                                 λ 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               11 
                             
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   θ 
                                   21 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                               + 
                               δ 
                             
                             ) 
                           
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     Let α be a fixed value (not depending on i), where α&gt;0. (Let the α in Equation 236 and the α in Equation 237 be the same value.) 
     From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment 3, the following conditions are important in Equation 236 for achieving excellent data reception quality.
 
Math 261
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #28
 
     (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
Math 262
 
 e   j(θ     11     (x)−θ     21     (x)−δ)   ≠e   j(θ     11     (y)−θ     21     (y)−δ)  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #29
 
     (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.) 
     Addition of the following condition is considered.
 
Math 263
 
θ 11 ( x )=θ 11 ( x+N ) for ∀ x  ( x= 0,1,2, . . . , N− 2, N− 1)
 
and
 
θ 21 ( y )=θ 21 ( y+N ) for ∀ y  ( y= 0,1,2, . . . , N− 2, N− 1)  Condition #30
 
     Note that instead of Equation 237, the precoding matrices in the following Equation may be provided. 
     
       
         
           
             Math 
             ⁢ 
             
                  
                 
             
             ⁢ 
             264 
           
         
       
       
         
           
             
               
                 
                   
                     
                       for 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     238 
                   
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ( 
                             
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             λ 
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                 + 
                                 λ 
                                 - 
                                 δ 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     Let α be a fixed value (not depending on i), where α&gt;0. (Let the α in Equation 236 and the α in Equation 238 be the same value.) 
     As an example, in order to distribute the poor reception points evenly with regards to phase in the complex plane, as described in Embodiment 6, Condition #31 and Condition #32 are provided. 
     
       
         
           
             Math 
             ⁢ 
             
                  
                 
             
             ⁢ 
             265 
           
         
       
       
         
           
             
               
                 
                   
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               x 
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               x 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   = 
                   
                     e 
                     
                       j 
                       ⁡ 
                       ( 
                       
                         
                           2 
                           ⁢ 
                           π 
                         
                         N 
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #31 
                 
               
             
           
         
       
       
         
           
             for 
             ⁢ 
                 
             
               ∀ 
               
                 x 
                 ⁡ 
                 ( 
                 
                   
                     x 
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                 
                 ) 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
             
                  
                 
             
             ⁢ 
             266 
           
         
       
       
         
           
             
               
                 
                   
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               x 
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               x 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   = 
                   
                     e 
                     
                       j 
                       ⁡ 
                       ( 
                       
                         - 
                         
                           
                             2 
                             ⁢ 
                             π 
                           
                           N 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #32 
                 
               
             
           
         
       
       
         
           
             for 
             ⁢ 
                 
             
               ∀ 
               
                 x 
                 ⁡ 
                 ( 
                 
                   
                     x 
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                 
                 ) 
               
             
           
         
       
     
     In other words, Condition #31 means that the difference in phase is 2π/N radians. On the other hand, Condition #32 means that the difference in phase is −2π/N radians. 
     Letting θ 11 (0)−θ 21 (0)=0 radians, letting α&gt;1, and letting δ=(3π)/4 radians, the distribution of poor reception points for s 1  and for s 2  in the complex plane when N=4 is shown in  FIGS.  46 A and  46 B . With these settings, the period (cycle) for hopping between precoding matrices is increased, and the minimum distance between poor reception points for s 1 , as well as the minimum distance between poor reception points for s 2 , in the complex plane is kept large, thereby achieving excellent reception quality. An example in which α&gt;1, 6=(3π)/4 radians, and N=4 has been described, but the present invention is not limited in this way. Similar advantageous effects may be obtained for π/2 radians≤|δ|&lt;π radians, α&gt;0, and α≠1. 
     The following conditions are possible as conditions differing from Condition #30:
 
Math 267
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∀ x,∀y  ( x≠y;x,y=N,N+ 1 ,N+ 2, . . . ,2 N− 2,2 N− 1)  Condition #33
 
     (where x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . , 2N−2, 2N−1 (each of x and y being an integer in a range of N to 2N−1); and x≠y.)
 
Math 268
 
 e   j(θ     11     (x)−θ     21     (x)−π)   ≠e   j(θ     11     (y)−θ     21     (y)−π)  for ∀ x,∀y  ( x≠y;x,y=N,N+ 1 ,N+ 2, . . . ,2 N− 2,2 N− 1)  Condition #34
 
(where x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . , 2N−2, 2N−1 (each of x and y being an integer in a range of N to 2N−1); and x≠y.)
 
     In this case, by satisfying Condition #28, Condition #29, Condition #33, and Condition #34, the distance in the complex plane between poor reception points for s 1  is increased, as is the distance between poor reception points for s 2 , thereby achieving excellent data reception quality. 
     In the present embodiment, the scheme of structuring 2N different precoding matrices for a precoding hopping scheme with a 2N-slot time period (cycle) has been described. In this case, as the 2N different precoding matrices, F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] are prepared. In the present embodiment, an example of a single carrier transmission scheme has been described, and therefore the case of arranging symbols in the order F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] in the time domain (or the frequency domain) has been described. The present invention is not, however, limited in this way, and the 2N different precoding matrices F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] generated in the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaption in this case, precoding weights may be changed by arranging symbols in the frequency domain and in the frequency-time domain. Note that a precoding hopping scheme with a 2N-slot time period (cycle) has been described, but the same advantageous effects may be obtained by randomly using 2N different precoding matrices. In other words, the 2N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots 2N in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the 2N different precoding matrices of the present embodiment are included, the probability of excellent reception quality increases. 
     Embodiment 12 
     The present embodiment describes a scheme for regularly hopping between precoding matrices using a non-unitary matrix. 
     In the scheme of regularly hopping between precoding matrices over a period (cycle) with N slots, the precoding matrices prepared for the N slots are represented as follows. 
             Math   ⁢                ⁢   269                       F   [   i   ]     =       1         α   2     +   1         ⁢     (           e     j   ⁢       θ   11     (   i   )               α   ×     e         j   ⁢       θ   11     (   i   )       +   λ     )                   α   ×     e     j   ⁢       θ   21     (   i   )                 e     j   (             θ   21     (   i   )     +   λ   -   δ     )             )                 Equation   ⁢         239                 
Let α be a fixed value (not depending on i), where α&gt;0. Furthermore, let δ·π radians (a fixed value not depending on i), and i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1).
 
     From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment 3, the following conditions are important in Equation 239 for achieving excellent data reception quality.
 
Math 270
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #35
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
Math 271
 
 e   j(θ     11     (x)−θ     21     (x)−δ)   ≠e   j(θ     11     (y)−θ     21     (y)−δ)  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #36
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
     As an example, in order to distribute the poor reception points evenly with regards to phase in the complex plane, as described in Embodiment 6, Condition #37 and Condition #38 are provided. 
     
       
         
           
             Math 
             ⁢ 
             
                  
                 
             
             ⁢ 
             272 
           
         
       
       
         
           
             
               
                 
                   
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               x 
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               x 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   = 
                   
                     e 
                     
                       j 
                       ⁡ 
                       ( 
                       
                         
                           2 
                           ⁢ 
                           π 
                         
                         N 
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #37 
                 
               
             
           
         
       
       
         
           
             for 
             ⁢ 
                 
             
               ∀ 
               
                 x 
                 ⁡ 
                 ( 
                 
                   
                     x 
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                 
                 ) 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
             
                  
                 
             
             ⁢ 
             273 
           
         
       
       
         
           
             
               
                 
                   
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               x 
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               x 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   = 
                   
                     e 
                     
                       j 
                       ⁡ 
                       ( 
                       
                         - 
                         
                           
                             2 
                             ⁢ 
                             π 
                           
                           N 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #38 
                 
               
             
           
         
       
       
         
           
             for 
             ⁢ 
                 
             
               ∀ 
               
                 x 
                 ⁡ 
                 ( 
                 
                   
                     x 
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                 
                 ) 
               
             
           
         
       
     
     In other words, Condition #37 means that the difference in phase is 2π/N radians. On the other hand, Condition #38 means that the difference in phase is −2π/N radians. 
     In this case, if π/2 radians≤|δ|&lt;π radians, α&gt;0, and α≠1, the distance in the complex plane between poor reception points for s 1  is increased, as is the distance between poor reception points for s 2 , thereby achieving excellent data reception quality. Note that Condition #37 and Condition #38 are not always necessary. 
     In the present embodiment, the scheme of structuring N different precoding matrices for a precoding hopping scheme with an N-slot time period (cycle) has been described. In this case, as the N different precoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] are prepared. In the present embodiment, an example of a single carrier transmission scheme has been described, and therefore the case of arranging symbols in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1] in the time domain (or the frequency domain) has been described. The present invention is not, however, limited in this way, and the N different precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1] generated in the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaption in this case, precoding weights may be changed by arranging symbols in the frequency domain and in the frequency-time domain. Note that a precoding hopping scheme with an N-slot time period (cycle) has been described, but the same advantageous effects may be obtained by randomly using N different precoding matrices. In other words, the N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots N in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the N different precoding matrices of the present embodiment are included, the probability of excellent reception quality increases. In this case, Condition #35 and Condition #36 can be replaced by the following conditions. (The number of slots in the period (cycle) is considered to be N.)
 
Math 274
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∃ x,∃y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #35′
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
Math 275
 
 e   j(θ     11     (x)−θ     21     (x)−δ)   ≠e   j(θ     11     (y)−θ     21     (y)−δ)  for ∃ x,∃y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #36′
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
     Embodiment 13 
     The present embodiment describes a different example than Embodiment 8. 
     In the scheme of regularly hopping between precoding matrices over a period (cycle) with 2N slots, the precoding matrices prepared for the 2N slots are represented as follows. 
             Math   ⁢                ⁢   276                         for   ⁢         i     =   0     ,   1   ,   2   ,   …         ,     N   -   2     ,     N   -     1   :                 Equation   ⁢         240                         F   [   i   ]     =       1         α   2     +   1         ⁢     (           e     j   ⁢       θ   11     (   i   )               α   ×     e     j   (             θ   11     (   i   )     +   λ     )                   α   ×     e     j   ⁢       θ   21     (   i   )                 e     j   (             θ   21     (   i   )     +   λ   +   δ     )             )             
Let α be a fixed value (not depending on i), where α&gt;0. Furthermore, let δ≠π radians.
 
     
       
         
           
             Math 
             ⁢ 
             
                  
                 
             
             ⁢ 
             277 
           
         
       
       
         
           
             
               
                 
                   
                     
                       for 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   241 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                 + 
                                 λ 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               11 
                             
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         e 
                         
                           j 
                           ( 
                             
                           
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             λ 
                             + 
                             δ 
                           
                           ) 
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     Let α be a fixed value (not depending on i), where α&gt;0. (Let the α in Equation 240 and the α in Equation 241 be the same value.) 
     Furthermore, the 2×N×M period (cycle) precoding matrices based on Equations 240 and 241 are represented by the following equations. 
     
       
         
           
             Math 
             ⁢ 
             
                  
                 
             
             ⁢ 
             278 
           
         
       
       
         
           
             
               
                 
                   
                     
                       for 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     242 
                   
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               11 
                             
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ( 
                               
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                 + 
                                 
                                   X 
                                   k 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ( 
                             
                           
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               X 
                               k 
                             
                             + 
                             λ 
                             + 
                             δ 
                           
                           ) 
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     In this case, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     
       
         
           
             Math 
             ⁢ 
             
                  
                 
             
             ⁢ 
             279 
           
         
       
       
         
           
             
               
                 
                   
                     
                       for 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   243 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       α 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             λ 
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           
                             θ 
                             11 
                           
                           ( 
                           i 
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     
                       e 
                       
                         j 
                         ( 
                           
                         
                           
                             
                               θ 
                               21 
                             
                             ( 
                             i 
                             ) 
                           
                           + 
                           λ 
                           + 
                           δ 
                           + 
                           
                             Y 
                             k 
                           
                         
                         ) 
                       
                     
                   
                   
                     
                       α 
                       × 
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             
                               i 
                               + 
                               
                                 Y 
                                 k 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     In this case, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). Furthermore, Xk=Yk may be true, or Xk≠Yk may be true. 
     Precoding matrices F[0]-F[2×N×M−1] are thus generated (the precoding matrices F[0]-F[2×N×M−1] may be in any order for the 2×N×M slots in the period (cycle)). Symbol number 2×N×M×i may be precoded using F[0], symbol number 2×N×M×i+1 may be precoded using F[1], . . . , and symbol number 2×N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , 2×N×M−2, 2×N×M−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) 
     Generating the precoding matrices in this way achieves a precoding matrix hopping scheme with a large period (cycle), allowing for the position of poor reception points to be easily changed, which may lead to improved data reception quality. 
     The 2×N×M period (cycle) precoding matrices in Equation 242 may be changed to the following equation. 
     
       
         
           
             Math 
             ⁢ 
             
                  
                 
             
             ⁢ 
             280 
           
         
       
       
         
           
             
               
                 
                   
                     
                       for 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   244 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               
                                 X 
                                 k 
                               
                             
                             ) 
                           
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ( 
                               
                             
                               
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                 ⁢ 
                                 
                                   X 
                                   k 
                                 
                               
                               + 
                               λ 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ( 
                             
                           
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             λ 
                             + 
                             δ 
                           
                           ) 
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     In this case, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     The 2×N×M period (cycle) precoding matrices in Equation 243 may also be changed to any of Equations 245-247. 
     
       
         
           
             Math 
             ⁢ 
             
                  
                 
             
             ⁢ 
             281 
           
         
       
       
         
           
             
               
                 
                   
                     
                       for 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   245 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ( 
                               
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                               + 
                               
                                 Y 
                                 k 
                               
                             
                             ) 
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               11 
                             
                             ( 
                             
                               i 
                               + 
                               
                                 Y 
                                 k 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         e 
                         
                           j 
                           ( 
                             
                           
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             λ 
                             + 
                             δ 
                           
                           ) 
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     In this case, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     
       
         
           
             Math 
             ⁢ 
             
                  
                 
             
             ⁢ 
             282 
           
         
       
       
         
           
             
               
                 
                   
                     
                       for 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   246 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             
                               i 
                               + 
                               
                                 Y 
                                 k 
                               
                             
                             ) 
                           
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ( 
                               
                             
                               
                                 
                                   θ 
                                   21 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                               - 
                               δ 
                               + 
                               
                                 Y 
                                 k 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     In this case, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   283 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       for 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   247 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         α 
                         × 
                         
                           e 
                             
                           
                             j 
                             ⁢ 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 i 
                                 + 
                                 
                                   Y 
                                   k 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         e 
                           
                         
                           j 
                           ( 
                             
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             λ 
                             + 
                             
                               Y 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                             
                           
                             j 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                 + 
                                 λ 
                                 - 
                                 δ 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     In this case, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     Focusing on poor reception points, if Equations 242 through 247 satisfy the following conditions,
 
Math 284
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #39
 
     (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
Math 285
 
 e   j(θ     11     (x)−θ     21     (x)−δ)   ≠e   j(θ     11     (y)−θ     21     (y)−δ)  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #40
 
     (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
Math 286
 
θ 11 ( x )=θ 11 ( x+N ) for ∀ x  ( x= 0,1,2, . . . , N− 2, N− 1)
 
and
 
θ 21 ( y )=θ 21 ( y+N ) for ∀ y  ( y= 0,1,2, . . . , N− 2, N− 1)  Condition #41
 
     then excellent data reception quality is achieved. Note that in Embodiment 8, Condition #39 and Condition #40 should be satisfied. 
     Focusing on Xk and Yk, if Equations 242 through 247 satisfy the following conditions,
 
Math 287
 
 X   a   ≠X   b +2× s ×π for ∀ a,∀b  ( a≠b;a,b= 0,1,2, . . . , M− 2, M− 1)  Condition #42
 
     (a is 0, 1, 2, . . . , M−2, M−1; b is 0, 1, 2, . . . , M−2, M−1 (each of a and b being an integer in a range of 0 to M−1); and a≠b.) 
     (Here, s is an integer.)
 
Math 288
 
 Y   a   ≠Y   b +2× u ×π for ∀ a,∀b  ( a≠b;a,b= 0,1,2, . . . , M− 2, M− 1)  Condition #43
 
(a is 0, 1, 2, . . . , M−2, M−1; b is 0, 1, 2, . . . , M−2, M−1 (each of a and b being an integer in a range of 0 to M−1); and a≠b.)
 
     (Here, u is an integer.) 
     then excellent data reception quality is achieved. Note that in Embodiment 8, Condition #42 should be satisfied. 
     In Equations 242 and 247, when 0 radians≤δ&lt;2π (radians, the matrices are a unitary matrix when δ=π radians and are a non-unitary matrix when δ≠π radians. In the present scheme, use of a non-unitary matrix for π/2 radians≤|δ|&lt;π radians is one characteristic structure, and excellent data reception quality is obtained. Use of a unitary matrix is another structure, and as described in detail in Embodiment 10 and Embodiment 16, if N is an odd number in Equations 242 through 247, the probability of obtaining excellent data reception quality increases. 
     Embodiment 14 
     The present embodiment describes an example of differentiating between usage of a unitary matrix and a non-unitary matrix as the precoding matrix in the scheme for regularly hopping between precoding matrices. 
     The following describes an example that uses a two-by-two precoding matrix (letting each element be a complex number), i.e. the case when two modulated signals (s 1 ( t ) and s 2 ( t )) that are based on a modulation scheme are precoded, and the two precoded signals are transmitted by two antennas. 
     When transmitting data using a scheme of regularly hopping between precoding matrices, the mapping units  306 A and  306 B in the transmission device in  FIG.  3    and  FIG.  13    hop the modulation scheme in accordance with the frame structure signal  313 . The relationship between the modulation level (the number of signal points for the modulation scheme in the I-Q plane) of the modulation scheme and the precoding matrices is described. 
     The advantage of the scheme of regularly hopping between precoding matrices is that, as described in Embodiment 6, excellent data reception quality is achieved in an LOS environment. In particular, when the reception device performs ML calculation or applies APP (or Max-log APP) based on ML calculation, the advantageous effect is considerable. Incidentally, ML calculation greatly impacts circuit scale (calculation scale) in accordance with the modulation level of the modulation scheme. For example, when two precoded signals are transmitted from two antennas, and the same modulation scheme is used for two modulated signals (signals based on the modulation scheme before precoding), the number of candidate signal points in the I-Q plane (received signal points  1101  in  FIG.  11   ) is 4×4=16 when the modulation scheme is QPSK, 16×16=256 when the modulation scheme is 16QAM, 64×64=4096 when the modulation scheme is 64QAM, 256×256=65,536 when the modulation scheme is 256QAM, and 1024×1024=1,048,576 when the modulation scheme is 256QAM. In order to keep the calculation scale of the reception device down to a certain circuit size, when the modulation scheme is QPSK, 16QAM, or 64QAM, ML calculation ((Max-log) APP based on ML calculation) is used, and when the modulation scheme is 256QAM or 1024QAM, linear operation such as MMSE or ZF is used in the reception device. (In some cases, ML calculation may be used for 256QAM.) 
     When such a reception device is assumed, consideration of the Signal-to-Noise Power Ratio (SNR) after separation of multiple signals indicates that a unitary matrix is appropriate as the precoding matrix when the reception device performs linear operation such as MMSE or ZF, whereas either a unitary matrix or a non-unitary matrix may be used when the reception device performs ML calculation. Taking any of the above embodiments into consideration, when two precoded signals are transmitted from two antennas, the same modulation scheme is used for two modulated signals (signals based on the modulation scheme before precoding), a non-unitary matrix is used as the precoding matrix in the scheme for regularly hopping between precoding matrices, the modulation level of the modulation scheme is equal to or less than 64 (or equal to or less than 256), and a unitary matrix is used when the modulation level is greater than 64 (or greater than 256), then for all of the modulation schemes supported by the transmission system, there is an increased probability of achieving the advantageous effect whereby excellent data reception quality is achieved for any of the modulation schemes while reducing the circuit scale of the reception device. 
     When the modulation level of the modulation scheme is equal to or less than 64 (or equal to or less than 256) as well, in some cases use of a unitary matrix may be preferable. Based on this consideration, when a plurality of modulation schemes are supported in which the modulation level is equal to or less than 64 (or equal to or less than 256), it is important that in some cases, in some of the plurality of supported modulation schemes where the modulation level is equal to or less than 64, a non-unitary matrix is used as the precoding matrix in the scheme for regularly hopping between precoding matrices. 
     The case of transmitting two precoded signals from two antennas has been described above as an example, but the present invention is not limited in this way. In the case when N precoded signals are transmitted from N antennas, and the same modulation scheme is used for N modulated signals (signals based on the modulation scheme before precoding), a threshold β N  may be established for the modulation level of the modulation scheme. When a plurality of modulation schemes for which the modulation level is equal to or less than β N  are supported, in some of the plurality of supported modulation schemes where the modulation level is equal to or less than β N , a non-unitary matrix is used as the precoding matrices in the scheme for regularly hopping between precoding matrices, whereas for modulation schemes for which the modulation level is greater than β N , a unitary matrix is used. In this way, for all of the modulation schemes supported by the transmission system, there is an increased probability of achieving the advantageous effect whereby excellent data reception quality is achieved for any of the modulation schemes while reducing the circuit scale of the reception device. (When the modulation level of the modulation scheme is equal to or less than β N , a non-unitary matrix may always be used as the precoding matrix in the scheme for regularly hopping between precoding matrices.) 
     In the above description, the same modulation scheme has been described as being used in the modulation scheme for simultaneously transmitting N modulated signals. The following, however, describes the case in which two or more modulation schemes are used for simultaneously transmitting N modulated signals. 
     As an example, the case in which two precoded signals are transmitted by two antennas is described. The two modulated signals (signals based on the modulation scheme before precoding) are either modulated with the same modulation scheme, or when modulated with different modulation schemes, are modulated with a modulation scheme having a modulation level of 2 a1  or a modulation level of 2 a2 . In this case, when the reception device uses ML calculation ((Max-log) APP based on ML calculation), the number of candidate signal points in the I-Q plane (received signal points  1101  in  FIG.  11   ) is 2 a1× 2 a2 =2 a1+a2 . As described above, in order to achieve excellent data reception quality while reducing the circuit scale of the reception device, a threshold 2 β  may be provided for 2 a1+a2 , and when 2 a1+a2 ≤2 β , a non-unitary matrix may be used as the precoding matrix in the scheme for regularly hopping between precoding matrices, whereas a unitary matrix may be used when 2 a1+a2 &gt;2 β . 
     Furthermore, when 2 a1+a2 ≤2 β , in some cases use of a unitary matrix may be preferable. Based on this consideration, when a plurality of combinations of modulation schemes are supported for which 2 a1+a2 ≤2 β , it is important that in some of the supported combinations of modulation schemes for which 2 a1+a2 ≤2 β , a non-unitary matrix is used as the precoding matrix in the scheme for regularly hopping between precoding matrices. 
     As an example, the case in which two precoded signals are transmitted by two antennas has been described, but the present invention is not limited in this way. For example, N modulated signals (signals based on the modulation scheme before precoding) may be either modulated with the same modulation scheme or, when modulated with different modulation schemes, the modulation level of the modulation scheme for the i th  modulated signal may be 2 ai  (where i=1, 2, . . . , N−1, N). 
     In this case, when the reception device uses ML calculation ((Max−log) APP based on ML calculation), the number of candidate signal points in the I-Q plane (received signal points  1101  in  FIG.  11   ) is 2 a1 ×2 a2 × . . . ×2 ai × . . . ×2 aN =2 a1+a2+ . . . +ai+ . . . +aN . As described above, in order to achieve excellent data reception quality while reducing the circuit scale of the reception device, a threshold 2 β  may be provided for 2 a1+a2+ . . . +ai+ . . . +aN . 
                   Math   ⁢         289                          2       a   ⁢   1         +     a   ⁢   2     +   …   +     a   ⁢   i     +   …   +     a   ⁢   N         =       2   Y     ≤     2   β         ⁢   
   where   ⁢   
     Y   =       ∑     i   =   1     N           a   i                 Condition   ⁢         #44               
When a plurality of combinations of a modulation schemes satisfying Condition #44 are supported, in some of the supported combinations of modulation schemes satisfying Condition #44, a non-unitary matrix is used as the precoding matrix in the scheme for regularly hopping between precoding matrices.
 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   290 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       2 
                       
                         
                           a 
                           ⁢ 
                           1 
                         
                           
                         + 
                         
                           a 
                           ⁢ 
                           2 
                         
                         + 
                         … 
                         + 
                         
                           a 
                           ⁢ 
                           i 
                         
                         + 
                         … 
                         + 
                         
                           a 
                           ⁢ 
                           N 
                         
                       
                     
                     = 
                     
                       
                         2 
                         Y 
                       
                       &gt; 
                       
                         2 
                         β 
                       
                     
                   
                   ⁢ 
                   
 
                   where 
                   ⁢ 
                   
 
                   
                     Y 
                     = 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         N 
                       
                         
                       
                         a 
                         i 
                       
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #45 
                 
               
             
           
         
       
     
     By using a unitary matrix in all of the combinations of modulation schemes satisfying Condition #45, then for all of the modulation schemes supported by the transmission system, there is an increased probability of achieving the advantageous effect whereby excellent data reception quality is achieved while reducing the circuit scale of the reception device for any of the combinations of modulation schemes. (A non-unitary matrix may be used as the precoding matrix in the scheme for regularly hopping between precoding matrices in all of the supported combinations of modulation schemes satisfying Condition #44.) 
     Embodiment 15 
     The present embodiment describes an example of a system that adopts a scheme for regularly hopping between precoding matrices using a multi-carrier transmission scheme such as OFDM. 
       FIGS.  47 A and  47 B  show an example according to the present embodiment of frame structure in the time and frequency domains for a signal transmitted by a broadcast station (base station) in a system that adopts a scheme for regularly hopping between precoding matrices using a multi-carrier transmission scheme such as OFDM. (The frame structure is set to extend from time $ 1  to time $T.)  FIG.  47 A  shows the frame structure in the time and frequency domains for the stream s 1  described in Embodiment 1, and  FIG.  47 B  shows the frame structure in the time and frequency domains for the stream s 2  described in Embodiment 1. Symbols at the same time and the same (sub)carrier in stream s 1  and stream s 2  are transmitted by a plurality of antennas at the same time and the same frequency. 
     In  FIGS.  47 A and  47 B , the (sub)carriers used when using OFDM are divided as follows: a carrier group #A composed of (sub)carrier a−(sub)carrier a+Na, a carrier group #B composed of (sub)carrier b−(sub)carrier b+Nb, a carrier group #C composed of (sub)carrier c−(sub)carrier c+Nc, a carrier group #D composed of (sub)carrier d−(sub)carrier d+Nd, . . . . In each subcarrier group, a plurality of transmission schemes are assumed to be supported. By supporting a plurality of transmission schemes, it is possible to effectively capitalize on the advantages of the transmission schemes. For example, in  FIGS.  47 A and  47 B , a spatial multiplexing MIMO system, or a MIMO system with a fixed precoding matrix is used for carrier group #A, a MIMO system that regularly hops between precoding matrices is used for carrier group #B, only stream s 1  is transmitted in carrier group #C, and space-time block coding is used to transmit carrier group #D. 
       FIGS.  48 A and  48 B  show an example according to the present embodiment of frame structure in the time and frequency domains for a signal transmitted by a broadcast station (base station) in a system that adopts a scheme for regularly hopping between precoding matrices using a multi-carrier transmission scheme such as OFDM.  FIGS.  48 A and  48 B  show a frame structure at a different time than  FIGS.  47 A and  47 B , from time $X to time $X+T′. In  FIGS.  48 A and  48 B , as in  FIGS.  47 A and  47 B , the (sub)carriers used when using OFDM are divided as follows: a carrier group #A composed of (sub)carrier a−(sub)carrier a+Na, a carrier group #B composed of (sub)carrier b−(sub)carrier b+Nb, a carrier group #C composed of (sub)carrier c−(sub)carrier c+Nc, a carrier group #D composed of (sub)carrier d−(sub)carrier d+Nd, . . . . The difference between  FIGS.  47 A and  47 B  and  FIGS.  48 A and  48 B  is that in some carrier groups, the transmission scheme used in  FIGS.  47 A and  47 B  differs from the transmission scheme used in  FIGS.  48 A and  48 B . In  FIGS.  48 A and  48 B , space-time block coding is used to transmit carrier group #A, a MIMO system that regularly hops between precoding matrices is used for carrier group #B, a MIMO system that regularly hops between precoding matrices is used for carrier group #C, and only stream s 1  is transmitted in carrier group #D. 
     Next, the supported transmission schemes are described. 
       FIG.  49    shows a signal processing scheme when using a spatial multiplexing MIMO system or a MIMO system with a fixed precoding matrix.  FIG.  49    bears the same numbers as in  FIG.  6   . A weighting unit  600 , which is a baseband signal in accordance with a certain modulation scheme, receives as inputs a stream s 1 ( t ) ( 307 A), a stream s 2 ( t ) ( 307 B), and information  315  regarding the weighting scheme, and outputs a modulated signal z 1 ( t ) ( 309 A) after weighting and a modulated signal z 2 ( t ) ( 309 B) after weighting. Here, when the information  315  regarding the weighting scheme indicates a spatial multiplexing MIMO system, the signal processing in scheme # 1  of  FIG.  49    is performed. Specifically, the following processing is performed. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   291 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 e 
                                 
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                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 s 
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                                   ( 
                                   t 
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                                 ⁢ 
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                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         
                           ( 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
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                                 1 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 
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                                   ⁢ 
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                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
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                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                           
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                       = 
                       
                         ( 
                         
                           
                             
                               
                                 s 
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                                   t 
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                                   ( 
                                   t 
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                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   250 
                 
               
             
           
         
       
     
     When a scheme for transmitting one modulated signal is supported, from the standpoint of transmission power, Equation 250 may be represented as Equation 251. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   292 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         1 
                         
                           2 
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
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                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 s 
                                 ⁢ 
                                 1 
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                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
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                                 ⁢ 
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                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         
                           1 
                           
                             2 
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 1 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 
                                   s 
                                   ⁢ 
                                   1 
                                   ⁢ 
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   s 
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                           
                           ) 
                         
                       
                       = 
                       
                         ( 
                         
                           
                             
                               
                                 
                                   1 
                                   
                                     2 
                                   
                                 
                                 ⁢ 
                                 s 
                                 ⁢ 
                                 1 
                                 ⁢ 
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   1 
                                   
                                     2 
                                   
                                 
                                 ⁢ 
                                 s 
                                 ⁢ 
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                                   ( 
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                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   251 
                 
               
             
           
         
       
     
     When the information  315  regarding the weighting scheme indicates a MIMO system in which precoding matrices are regularly hopped between, signal processing in scheme # 2 , for example, of  FIG.  49    is performed. Specifically, the following processing is performed. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   293 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   θ 
                                   11 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     θ 
                                     21 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   252 
                 
               
             
           
         
       
     
     Here, θ 11 , θ 12 , λ, and δ are fixed values. 
       FIG.  50    shows the structure of modulated signals when using space-time block coding. A space-time block coding unit ( 5002 ) in  FIG.  50    receives, as input, a baseband signal based on a certain modulation signal. For example, the space-time block coding unit ( 5002 ) receives symbol s 1 , symbol s 2 , . . . as inputs. As shown in  FIG.  50   , space-time block coding is performed, z 1 ( 5003 A) becomes “s 1  as symbol # 0 ”, “−s 2 * as symbol # 0 ”, “s 3  as symbol # 2 ”, “−s 4 * as symbol s 3 ” . . . , and z 2 ( 5003 B) becomes “s 2  as symbol # 0 ”, “s 1 * as symbol # 1 ”, “s 4  as symbol # 2 ”, “s 3 * as symbol # 3 ” . . . . In this case, symbol #X in z 1  and symbol #X in z 2  are transmitted from the antennas at the same time, over the same frequency. 
     In  FIGS.  47 A,  47 B,  48 A, and  48 B , only symbols transmitting data are shown. In practice, however, it is necessary to transmit information such as the transmission scheme, modulation scheme, error correction scheme, and the like. For example, as in  FIG.  51   , these pieces of information can be transmitted to a communication partner by regular transmission with only one modulated signal z 1 . It is also necessary to transmit symbols for estimation of channel fluctuation, i.e. for the reception device to estimate channel fluctuation (for example, a pilot symbol, reference symbol, preamble, a Phase Shift Keying (PSK) symbol known at the transmission and reception sides, and the like). In  FIGS.  47 A,  47 B,  48 A, and  48 B , these symbols are omitted. In practice, however, symbols for estimating channel fluctuation are included in the frame structure in the time and frequency domains. Accordingly, each carrier group is not composed only of symbols for transmitting data. (The same is true for Embodiment 1 as well.) 
       FIG.  52    is an example of the structure of a transmission device in a broadcast station (base station) according to the present embodiment. A transmission scheme determining unit ( 5205 ) determines the number of carriers, modulation scheme, error correction scheme, coding rate for error correction coding, transmission scheme, and the like for each carrier group and outputs a control signal ( 5206 ). 
     A modulated signal generating unit # 1  ( 5201 _ 1 ) receives, as input, information ( 5200 _ 1 ) and the control signal ( 5206 ) and, based on the information on the transmission scheme in the control signal ( 5206 ), outputs a modulated signal z 1  ( 5202 _ 1 ) and a modulated signal z 2  ( 5203 _ 1 ) in the carrier group #A of  FIGS.  47 A,  47 B,  48 A, and  48 B . 
     Similarly, a modulated signal generating unit # 2  ( 5201 _ 2 ) receives, as input, information ( 5200 _ 2 ) and the control signal ( 5206 ) and, based on the information on the transmission scheme in the control signal ( 5206 ), outputs a modulated signal z 1  ( 5202 _ 2 ) and a modulated signal z 2  ( 5203 _ 2 ) in the carrier group #B of  FIGS.  47 A,  47 B,  48 A, and  48 B . 
     Similarly, a modulated signal generating unit # 3  ( 5201 _ 3 ) receives, as input, information ( 5200 _ 3 ) and the control signal ( 5206 ) and, based on the information on the transmission scheme in the control signal ( 5206 ), outputs a modulated signal z 1  ( 5202 _ 3 ) and a modulated signal z 2  ( 5203 _ 3 ) in the carrier group #C of  FIGS.  47 A,  47 B,  48 A, and  48 B . 
     Similarly, a modulated signal generating unit # 4  ( 5201 _ 4 ) receives, as input, information ( 5200 _ 4 ) and the control signal ( 5206 ) and, based on the information on the transmission scheme in the control signal ( 5206 ), outputs a modulated signal z 1  ( 5202 _ 4 ) and a modulated signal z 2  ( 5203 _ 4 ) in the carrier group #D of  FIGS.  47 A,  47 B,  48 A, and  48 B . 
     While not shown in the figures, the same is true for modulated signal generating unit # 5  through modulated signal generating unit #M−1. 
     Similarly, a modulated signal generating unit #M ( 5201 _M) receives, as input, information ( 5200 _M) and the control signal ( 5206 ) and, based on the information on the transmission scheme in the control signal ( 5206 ), outputs a modulated signal z 1  ( 5202 _M) and a modulated signal z 2  ( 5203 _M) in a certain carrier group. 
     An OFDM related processor ( 5207 _ 1 ) receives, as inputs, the modulated signal z 1  ( 5202 _ 1 ) in carrier group #A, the modulated signal z 1  ( 5202 _ 2 ) in carrier group #B, the modulated signal z 1  ( 5202 _ 3 ) in carrier group #C, the modulated signal z 1  ( 5202 _ 4 ) in carrier group #D, . . . , the modulated signal z 1  ( 5202 _M) in a certain carrier group #M, and the control signal ( 5206 ), performs processing such as reordering, inverse Fourier transform, frequency conversion, amplification, and the like, and outputs a transmission signal ( 5208 _ 1 ). The transmission signal ( 5208 _ 1 ) is output as a radio wave from an antenna ( 5209 _ 1 ). 
     Similarly, an OFDM related processor ( 5207 _ 2 ) receives, as inputs, the modulated signal z 1  ( 5203 _ 1 ) in carrier group #A, the modulated signal z 1  ( 5203 _ 2 ) in carrier group #B, the modulated signal z 1  ( 5203 _ 3 ) in carrier group #C, the modulated signal z 1  ( 5203 _ 4 ) in carrier group #D, . . . , the modulated signal z 1  ( 5203 _M) in a certain carrier group #M, and the control signal ( 5206 ), performs processing such as reordering, inverse Fourier transform, frequency conversion, amplification, and the like, and outputs a transmission signal ( 5208 _ 2 ). The transmission signal ( 5208 _ 2 ) is output as a radio wave from an antenna ( 5209 _ 2 ). 
       FIG.  53    shows an example of a structure of the modulated signal generating units # 1 -#M in  FIG.  52   . An error correction encoder ( 5302 ) receives, as inputs, information ( 5300 ) and a control signal ( 5301 ) and, in accordance with the control signal ( 5301 ), sets the error correction coding scheme and the coding rate for error correction coding, performs error correction coding, and outputs data ( 5303 ) after error correction coding. (In accordance with the setting of the error correction coding scheme and the coding rate for error correction coding, when using LDPC coding, turbo coding, or convolutional coding, for example, depending on the coding rate, puncturing may be performed to achieve the coding rate.) 
     An interleaver ( 5304 ) receives, as input, error correction coded data ( 5303 ) and the control signal ( 5301 ) and, in accordance with information on the interleaving scheme included in the control signal ( 5301 ), reorders the error correction coded data ( 5303 ) and outputs interleaved data ( 5305 ). 
     A mapping unit ( 5306 _ 1 ) receives, as input, the interleaved data ( 5305 ) and the control signal ( 5301 ) and, in accordance with the information on the modulation scheme included in the control signal ( 5301 ), performs mapping and outputs a baseband signal ( 5307 _ 1 ). 
     Similarly, a mapping unit ( 5306 _ 2 ) receives, as input, the interleaved data ( 5305 ) and the control signal ( 5301 ) and, in accordance with the information on the modulation scheme included in the control signal ( 5301 ), performs mapping and outputs a baseband signal ( 5307 _ 2 ). 
     A signal processing unit ( 5308 ) receives, as input, the baseband signal ( 5307 _ 1 ), the baseband signal ( 5307 _ 2 ), and the control signal ( 5301 ) and, based on information on the transmission scheme (for example, in this embodiment, a spatial multiplexing MIMO system, a MIMO scheme using a fixed precoding matrix, a MIMO scheme for regularly hopping between precoding matrices, space-time block coding, or a transmission scheme for transmitting only stream s 1 ) included in the control signal ( 5301 ), performs signal processing. The signal processing unit ( 5308 ) outputs a processed signal z 1  ( 5309 _ 1 ) and a processed signal z 2  ( 5309 _ 2 ). Note that when the transmission scheme for transmitting only stream s 1  is selected, the signal processing unit ( 5308 ) does not output the processed signal z 2  ( 5309 _ 2 ). Furthermore, in  FIG.  53   , one error correction encoder is shown, but the present invention is not limited in this way. For example, as shown in  FIG.  3   , a plurality of encoders may be provided. 
       FIG.  54    shows an example of the structure of the OFDM related processors ( 5207 _ 1  and  5207 _ 2 ) in  FIG.  52   . Elements that operate in a similar way to  FIG.  14    bear the same reference signs. A reordering unit ( 5402 A) receives, as input, the modulated signal z 1  ( 5400 _ 1 ) in carrier group #A, the modulated signal z 1  ( 5400 _ 2 ) in carrier group #B, the modulated signal z 1  ( 5400 _ 3 ) in carrier group #C, the modulated signal z 1  ( 5400 _ 4 ) in carrier group #D, . . . , the modulated signal z 1  ( 5400 _M) in a certain carrier group, and a control signal ( 5403 ), performs reordering, and output reordered signals  1405 A and  1405 B. Note that in  FIGS.  47 A,  47 B,  48 A,  48 B, and  51   , an example of allocation of the carrier groups is described as being formed by groups of subcarriers, but the present invention is not limited in this way. Carrier groups may be formed by discrete subcarriers at each time interval. Furthermore, in  FIGS.  47 A,  47 B,  48 A,  48 B, and  51   , an example has been described in which the number of carriers in each carrier group does not change over time, but the present invention is not limited in this way. This point will be described separately below. 
       FIGS.  55 A and  55 B  show an example of frame structure in the time and frequency domains for a scheme of setting the transmission scheme for each carrier group, as in  FIGS.  47 A,  47 B,  48 A,  48 B, and  51   . In  FIGS.  55 A and  55 B , control information symbols are labeled  5500 , individual control information symbols are labeled  5501 , data symbols are labeled  5502 , and pilot symbols are labeled  5503 . Furthermore,  FIG.  55 A  shows the frame structure in the time and frequency domains for stream s 1 , and  FIG.  55 B  shows the frame structure in the time and frequency domains for stream s 2 . 
     The control information symbols are for transmitting control information shared by the carrier group and are composed of symbols for the transmission and reception devices to perform frequency and time synchronization, information regarding the allocation of (sub)carriers, and the like. The control information symbols are set to be transmitted from only stream s 1  at time $ 1 . 
     The individual control information symbols are for transmitting control information on individual subcarrier groups and are composed of information on the transmission scheme, modulation scheme, error correction coding scheme, coding rate for error correction coding, block size of error correction codes, and the like for the data symbols, information on the insertion scheme of pilot symbols, information on the transmission power of pilot symbols, and the like. The individual control information symbols are set to be transmitted from only stream s 1  at time $ 1 . 
     The data symbols are for transmitting data (information), and as described with reference to  FIGS.  47 A through  50   , are symbols of one of the following transmission schemes, for example: a spatial multiplexing MIMO system, a MIMO scheme using a fixed precoding matrix, a MIMO scheme for regularly hopping between precoding matrices, space-time block coding, or a transmission scheme for transmitting only stream s 1 . Note that in carrier group #A, carrier group #B, carrier group #C, and carrier group #D, data symbols are shown in stream s 2 , but when the transmission scheme for transmitting only stream s 1  is used, in some cases there are no data symbols in stream s 2 . 
     The pilot symbols are for the reception device to perform channel estimation, i.e. to estimate fluctuation corresponding to h 11 (t), h 12 (t), h 21 (t), and h 22 (t) in Equation 36. (In this embodiment, since a multi-carrier transmission scheme such as an OFDM scheme is used, the pilot symbols are for estimating fluctuation corresponding to h 11 (t), h 12 (t), h 21 (t), and h 22 (t) in each subcarrier.) Accordingly, the PSK transmission scheme, for example, is used for the pilot symbols, which are structured to form a pattern known by the transmission and reception devices. Furthermore, the reception device may use the pilot symbols for estimation of frequency offset, estimation of phase distortion, and time synchronization. 
       FIG.  56    shows an example of the structure of a reception device for receiving modulated signals transmitted by the transmission device in  FIG.  52   . Elements that operate in a similar way to  FIG.  7    bear the same reference signs. 
     In  FIG.  56   , an OFDM related processor ( 5600 _X) receives, as input, a received signal  702 _X, performs predetermined processing, and outputs a processed signal  704 _X. Similarly, an OFDM related processor ( 5600 _Y) receives, as input, a received signal  702 _Y, performs predetermined processing, and outputs a processed signal  704 _Y. 
     The control information decoding unit  709  in  FIG.  56    receives, as input, the processed signals  704 _X and  704 _Y, extracts the control information symbols and individual control information symbols in  FIGS.  55 A and  55 B  to obtain the control information transmitted by these symbols, and outputs a control signal  710  that includes the obtained information. 
     The channel fluctuation estimating unit  705 _ 1  for the modulated signal z 1  receives, as inputs, the processed signal  704 _X and the control signal  710 , performs channel estimation in the carrier group required by the reception device (the desired carrier group), and outputs a channel estimation signal  706 _ 1 . 
     Similarly, the channel fluctuation estimating unit  705 _ 2  for the modulated signal z 2  receives, as inputs, the processed signal  704 _X and the control signal  710 , performs channel estimation in the carrier group required by the reception device (the desired carrier group), and outputs a channel estimation signal  706 _ 2 . 
     Similarly, the channel fluctuation estimating unit  705 _ 1  for the modulated signal z 1  receives, as inputs, the processed signal  704 _Y and the control signal  710 , performs channel estimation in the carrier group required by the reception device (the desired carrier group), and outputs a channel estimation signal  708 _ 1 . 
     Similarly, the channel fluctuation estimating unit  705 _ 2  for the modulated signal z 2  receives, as inputs, the processed signal  704 _Y and the control signal  710 , performs channel estimation in the carrier group required by the reception device (the desired carrier group), and outputs a channel estimation signal  708 _ 2 . 
     The signal processing unit  711  receives, as inputs, the signals  706 _ 1 ,  706 _ 2 ,  708 _ 1 ,  708 _ 2 ,  704 _X,  704 _Y, and the control signal  710 . Based on the information included in the control signal  710  on the transmission scheme, modulation scheme, error correction coding scheme, coding rate for error correction coding, block size of error correction codes, and the like for the data symbols transmitted in the desired carrier group, the signal processing unit  711  demodulates and decodes the data symbols and outputs received data  712 . 
       FIG.  57    shows the structure of the OFDM related processors ( 5600 _X,  5600 _Y) in  FIG.  56   . A frequency converter ( 5701 ) receives, as input, a received signal ( 5700 ), performs frequency conversion, and outputs a frequency converted signal ( 5702 ). 
     A Fourier transformer ( 5703 ) receives, as input, the frequency converted signal ( 5702 ), performs a Fourier transform, and outputs a Fourier transformed signal ( 5704 ). 
     As described above, when using a multi-carrier transmission scheme such as an OFDM scheme, carriers are divided into a plurality of carrier groups, and the transmission scheme is set for each carrier group, thereby allowing for the reception quality and transmission speed to be set for each carrier group, which yields the advantageous effect of construction of a flexible system. In this case, as described in other embodiments, allowing for choice of a scheme of regularly hopping between precoding matrices offers the advantages of obtaining high reception quality, as well as high transmission speed, in an LOS environment. While in the present embodiment, the transmission schemes to which a carrier group can be set are “a spatial multiplexing MIMO system, a MIMO scheme using a fixed precoding matrix, a MIMO scheme for regularly hopping between precoding matrices, space-time block coding, or a transmission scheme for transmitting only stream s 1 ”, but the transmission schemes are not limited in this way. Furthermore, the space-time coding is not limited to the scheme described with reference to  FIG.  50   , nor is the MIMO scheme using a fixed precoding matrix limited to scheme # 2  in  FIG.  49   , as any structure with a fixed precoding matrix is acceptable. In the present embodiment, the case of two antennas in the transmission device has been described, but when the number of antennas is larger than two as well, the same advantageous effects may be achieved by allowing for selection of a transmission scheme for each carrier group from among “a spatial multiplexing MIMO system, a MIMO scheme using a fixed precoding matrix, a MIMO scheme for regularly hopping between precoding matrices, space-time block coding, or a transmission scheme for transmitting only stream s 1 ”. 
       FIGS.  58 A and  58 B  show a scheme of allocation into carrier groups that differs from  FIGS.  47 A,  47 B,  48 A,  48 B, and  51   . In  FIGS.  47 A,  47 B,  48 A,  48 B,  51 ,  55 A, and  55 B , carrier groups have described as being formed by groups of subcarriers. In  FIGS.  58 A and  58 B , on the other hand, the carriers in a carrier group are arranged discretely.  FIGS.  58 A and  58 B  show an example of frame structure in the time and frequency domains that differs from  FIGS.  47 A,  47 B,  48 A,  48 B,  51 ,  55 A, and  55 B .  FIGS.  58 A and  58 B  show the frame structure for carriers  1  through H, times $ 1  through $K. Elements that are similar to  FIGS.  55 A and  55 B  bear the same reference signs. Among the data symbols in  FIGS.  58 A and  58 B , the “A” symbols are symbols in carrier group A, the “B” symbols are symbols in carrier group B, the “C” symbols are symbols in carrier group C, and the “D” symbols are symbols in carrier group D. The carrier groups can thus be similarly implemented by discrete arrangement along (sub)carriers, and the same carrier need not always be used in the time domain. This type of arrangement yields the advantageous effect of obtaining time and frequency diversity gain. 
     In  FIGS.  47 A,  47 B,  48 A,  48 B,  51 ,  58 A, and  58 B , the control information symbols and the individual control information symbols are allocated to the same time in each carrier group, but these symbols may be allocated to different times. Furthermore, the number of (sub)carriers used by a carrier group may change over time. 
     Embodiment 16 
     Like Embodiment 10, the present embodiment describes a scheme for regularly hopping between precoding matrices using a unitary matrix when N is an odd number. 
     In the scheme of regularly hopping between precoding matrices over a period (cycle) with 2N slots, the precoding matrices prepared for the 2N slots are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   294 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       for 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   253 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               11 
                             
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁡ 
                             ( 
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             λ 
                             + 
                             π 
                           
                           ) 
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     Let α be a fixed value (not depending on i), where α&gt;0. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   295 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       for 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   254 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         α 
                         × 
                         
                           e 
                             
                           
                             j 
                             ⁢ 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         e 
                           
                         
                           j 
                           ( 
                             
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             λ 
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                             
                           
                             j 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                 + 
                                 λ 
                                 + 
                                 π 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     Let α be a fixed value (not depending on i), where α&gt;0. (Let the α in Equation 253 and the α in Equation 254 be the same value.) 
     From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment 3, the following conditions are important in Equation 253 for achieving excellent data reception quality.
 
Math 296
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #46
 
     (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
Math 297
 
 e   j(θ     11     (x)−θ     21     (x)−π)   ≠e   j(θ     11     (y)−θ     21     (y)−π)  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #47
 
     (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.) 
     Addition of the following condition is considered.
 
Math 298
 
θ 11 ( x )=θ 11 ( x+N ) for ∀ x  ( x= 0,1,2, . . . , N− 2, N− 1)
 
and
 
θ 21 ( y )=θ 21 ( y+N ) for ∀ y  ( y= 0,1,2, . . . , N− 2, N− 1)  Condition #48
 
     Next, in order to distribute the poor reception points evenly with regards to phase in the complex plane, as described in Embodiment 6, Condition #49 and Condition #50 are provided. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   299 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       e 
                       
                         j 
                         ( 
                           
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             
                               x 
                               + 
                               i 
                             
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             
                               x 
                               + 
                               1 
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     
                       e 
                       
                         j 
                         ( 
                           
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             x 
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             x 
                             ) 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             2 
                             ⁢ 
                             π 
                           
                           N 
                         
                         ) 
                       
                     
                     ⁢ 
                         
                     for 
                     ⁢ 
                         
                     
                       ∀ 
                       
                         x 
                         ⁡ 
                         ( 
                         
                           
                             x 
                             = 
                             0 
                           
                           , 
                           1 
                           , 
                           2 
                           , 
                           … 
                               
                           , 
                           
                             N 
                             - 
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #49 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   300 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       e 
                       
                         j 
                         ( 
                           
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             
                               x 
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                             ) 
                           
                           - 
                           
                             
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                               21 
                             
                             ( 
                             
                               x 
                               + 
                               1 
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     
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                         j 
                         ( 
                           
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             x 
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             x 
                             ) 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           - 
                           
                             
                               2 
                               ⁢ 
                               π 
                             
                             N 
                           
                         
                         ) 
                       
                     
                     ⁢ 
                         
                     for 
                     ⁢ 
                         
                     
                       ∀ 
                       
                         x 
                         ⁡ 
                         ( 
                         
                           
                             x 
                             = 
                             0 
                           
                           , 
                           1 
                           , 
                           2 
                           , 
                           … 
                               
                           , 
                           
                             N 
                             - 
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #50 
                 
               
             
           
         
       
     
     In other words, Condition #49 means that the difference in phase is 2π/N radians. On the other hand, Condition #50 means that the difference in phase is −2π/N radians. 
     Letting θ 11 (0)−θ 21 (0)=0 radians, and letting α&gt;1, the distribution of poor reception points for s 1  and for s 2  in the complex plane for N=3 is shown in  FIGS.  60 A and  60 B . As is clear from  FIGS.  60 A and  60 B , in the complex plane, the minimum distance between poor reception points for s 1  is kept large, and similarly, the minimum distance between poor reception points for s 2  is also kept large. Similar conditions are created when α&lt;1. Furthermore, upon comparison with  FIGS.  45 A and  45 B  in Embodiment 10, making the same considerations as in Embodiment 9, the probability of a greater distance between poor reception points in the complex plane increases when N is an odd number as compared to when N is an even number. However, when N is small, for example when N≤16, the minimum distance between poor reception points in the complex plane can be guaranteed to be a certain length, since the number of poor reception points is small. Accordingly, when N≤16, even if N is an even number, cases do exist where data reception quality can be guaranteed. 
     Therefore, in the scheme for regularly hopping between precoding matrices based on Equations 253 and 254, when N is set to an odd number, the probability of improving data reception quality is high. Precoding matrices F[0]-F[2N−1] are generated based on Equations 253 and 254 (the precoding matrices F[0]-F[2N−1] may be in any order for the 2N slots in the period (cycle)). Symbol number 2Ni may be precoded using F[0], symbol number 2Ni+1 may be precoded using F[1], . . . , and symbol number 2N×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , 2N−2, 2N−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) Furthermore, when the modulation scheme for both s 1  and s 2  is 16QAM, if α is set as in Equation 233, the advantageous effect of increasing the minimum distance between 16×16=256 signal points in the I-Q plane for a specific LOS environment may be achieved. 
     The following conditions are possible as conditions differing from Condition #48:
 
Math 301
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∀ x,∀y  ( x≠y;x,y=N,N+ 1 ,N+ 2, . . . ,2 N− 2,2 N− 1)  Condition #51
 
(where x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . , 2N−2, 2N−1 (each of x and y being an integer in a range of N to 2N−1); and x≠y.)
 
Math 302
 
 e   j(θ     11     (x)−θ     21     (x)−π)   ≠e   j(θ     11     (y)−θ     21     (y)−π)  for ∀ x,∀y  ( x≠y;x,y=N,N+ 1 ,N+ 2, . . . ,2 N− 2,2 N− 1)  Condition #52
 
(where x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . , 2N−2, 2N−1 (each of x and y being an integer in a range of N to 2N−1); and x≠y.)
 
     In this case, by satisfying Condition #46, Condition #47, Condition #51, and Condition #52, the distance in the complex plane between poor reception points for s 1  is increased, as is the distance between poor reception points for s 2 , thereby achieving excellent data reception quality. 
     In the present embodiment, the scheme of structuring 2N different precoding matrices for a precoding hopping scheme with a 2N-slot time period (cycle) has been described. In this case, as the 2N different precoding matrices, F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] are prepared. In the present embodiment, an example of a single carrier transmission scheme has been described, and therefore the case of arranging symbols in the order F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] in the time domain (or the frequency domain) has been described. The present invention is not, however, limited in this way, and the 2N different precoding matrices F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] generated in the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaption in this case, precoding weights may be changed by arranging symbols in the frequency domain and in the frequency-time domain. Note that a precoding hopping scheme with a 2N-slot time period (cycle) has been described, but the same advantageous effects may be obtained by randomly using 2N different precoding matrices. In other words, the 2N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots 2N in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the 2N different precoding matrices of the present embodiment are included, the probability of excellent reception quality increases. 
     Embodiment 17 
     The present embodiment describes a concrete example of the scheme of regularly changing precoding weights, based on Embodiment 8. 
       FIG.  6    relates to the weighting scheme (precoding scheme) in the present embodiment. The weighting unit  600  integrates the weighting units  308 A and  308 B in  FIG.  3   . As shown in  FIG.  6   , the stream s 1 ( t ) and the stream s 2 ( t ) correspond to the baseband signals  307 A and  307 B in  FIG.  3   . In other words, the streams s 1 ( t ) and s 2 ( t ) are the baseband signal in-phase components I and quadrature components Q when mapped according to a modulation scheme such as QPSK, 16QAM, 64QAM, or the like. 
     As indicated by the frame structure of  FIG.  6   , in the stream s 1 ( t ), a signal at symbol number u is represented as s 1 ( u ), a signal at symbol number u+1 as s 1 ( u +1), and so forth. Similarly, in the stream s 2 ( t ), a signal at symbol number u is represented as s 2 ( u ), a signal at symbol number u+1 as s 2 ( u +1), and so forth. The weighting unit  600  receives the baseband signals  307 A (s 1 ( t )) and  307 B (s 2 ( t )) and the information  315  regarding weighting information in  FIG.  3    as inputs, performs weighting in accordance with the information  315  regarding weighting, and outputs the signals  309 A (z 1 ( t )) and  309 B (z 2 ( t )) after weighting in  FIG.  3   . 
     At this point, when for example a precoding matrix hopping scheme with an N=8 period (cycle) as in Example #8 in Embodiment 6 is used, z 1 ( t ) and z 2 ( t ) are represented as follows. For symbol number 8i (where i is an integer greater than or equal to zero): 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   303 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 8 
                                 ⁢ 
                                 i 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 8 
                                 ⁢ 
                                 i 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       k 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   255 
                 
               
             
           
         
       
     
     Here, j is an imaginary unit, and k=0. 
     For symbol number 8i+1: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   304 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       k 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   256 
                 
               
             
           
         
       
     
     Here, k=1. 
     For symbol number 8i+2: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   305 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 2 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 2 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       k 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   2 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   2 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   257 
                 
               
             
           
         
       
     
     Here, k=2. 
     For symbol number 8i+3: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   306 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 3 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 3 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       k 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   3 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   3 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   258 
                 
               
             
           
         
       
     
     Here, k=3. 
     For symbol number 8i+4: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   307 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 4 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 4 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       k 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   4 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   4 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   259 
                 
               
             
           
         
       
     
     Here, k=4. 
     For symbol number 8i+5: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   308 
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 5 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 5 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       k 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   5 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   5 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   260 
                 
               
             
           
         
       
     
     Here, k=5. 
     For symbol number 8i+6: 
     
       
         
           
             
               
                 
                                     
                   
                     Math 
                     ⁢ 
                         
                     309 
                   
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 6 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 6 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       k 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   6 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   6 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   261 
                 
               
             
           
         
       
     
     Here, k=6. 
     For symbol number 8i+7: 
     
       
         
           
             
               
                 
                                     
                   
                     Math 
                     ⁢ 
                         
                     310 
                   
                 
               
               
                  
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 7 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   8 
                                   ⁢ 
                                   i 
                                 
                                 + 
                                 7 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                                   
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       k 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               s 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   7 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               s 
                               ⁢ 
                               2 
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     8 
                                     ⁢ 
                                     i 
                                   
                                   + 
                                   7 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   262 
                 
               
             
           
         
       
     
     Here, k=7. 
     The symbol numbers shown here can be considered to indicate time. As described in other embodiments, in Equation 262, for example, z 1 (8i+7) and z 2 (8i+7) at time 8i+7 are signals at the same time, and the transmission device transmits z 1  (8i+7) and z 2 (8i+7) over the same (shared/common) frequency. In other words, letting the signals at time T be s 1 (T), s 2 (T), z 1 (T), and z 2 (T), then z 1 (T) and z 2 (T) are sought from some sort of precoding matrices and from s 1 (T) and s 2 (T), and the transmission device transmits z 1 (T) and z 2 (T) over the same (shared/common) frequency (at the same time). Furthermore, in the case of using a multi-carrier transmission scheme such as OFDM or the like, and letting signals corresponding to s 1 , s 2 , z 1 , and z 2  for (sub)carrier L and time T be s 1 (T, L), s 2 (T, L), z 1 (T, L), and z 2 (T, L), then z 1 (T, L) and z 2 (T, L) are sought from some sort of precoding matrices and from s 1 (T, L) and s 2 (T, L), and the transmission device transmits z 1 (T, L) and z 2 (T, L) over the same (shared/common) frequency (at the same time). In this case, the appropriate value of α is given by Equation 198 or Equation 200. Also, different values of α may be set in Equations 255-262. That is to say, when two equations (Equations X and Y) are extracted from Equations 255-262, the value of α given by Equation X may be different from the value of α given by Equation Y. 
     The present embodiment describes a precoding hopping scheme that increases period (cycle) size, based on the above-described precoding matrices of Equation 190. 
     Letting the period (cycle) of the precoding hopping scheme be 8M, 8M different precoding matrices are represented as follows. 
     
       
         
           
             
               
                 
                                      
                   
                     Math 
                     ⁢ 
                         
                     311 
                   
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       
                         8 
                         × 
                         k 
                       
                       + 
                       i 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                     + 
                                     
                                       
                                         k 
                                         ⁢ 
                                         π 
                                       
                                       
                                         4 
                                         ⁢ 
                                         M 
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       k 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   263 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, 3, 4, 5, 6, 7, and k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     For example, letting M=2 and α&lt;1, the poor reception points for s 1  (◯) and for s 2  (□) at k=0 are represented as in  FIG.  42 A . Similarly, the poor reception points for s 1  (◯) and for s 2  (□) at k=1 are represented as in  FIG.  42 B . In this way, based on the precoding matrices in Equation 190, the poor reception points are as in  FIG.  42 A , and by using, as the precoding matrices, the matrices yielded by multiplying each term in the second line on the right-hand side of Equation 190 by e jX  (see Equation 226), the poor reception points are rotated with respect to  FIG.  42 A  (see  FIG.  42 B ). (Note that the poor reception points in  FIG.  42 A  and  FIG.  42 B  do not overlap. Even when multiplying by e jX , the poor reception points should not overlap, as in this case. Furthermore, the matrices yielded by multiplying each term in the first line on the right-hand side of Equation 190, rather than in the second line on the right-hand side of Equation 190, by e jX  may be used as the precoding matrices.) In this case, the precoding matrices F[0]-F[15] are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   312 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       
                         8 
                         × 
                         k 
                       
                       + 
                       i 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       4 
                                     
                                     + 
                                     Xk 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     4 
                                   
                                   + 
                                   Xk 
                                   + 
                                   
                                     
                                       7 
                                       ⁢ 
                                       π 
                                     
                                     8 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   264 
                 
               
             
           
         
       
     
     Here, i=0, 1, 2, 3, 4, 5, 6, 7, and k=0, 1. 
     In this case, when M=2, precoding matrices F[0]-F[15] are generated (the precoding matrices F[0]-F[15] may be in any order. Also, matrices F[0]-F[15] may be different matrices). Symbol number 16i may be precoded using F[0], symbol number 16i+1 may be precoded using F[1], . . . , and symbol number 16i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , 14, 15). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) Summarizing the above considerations, with reference to Equations 82-85, N-period (cycle) precoding matrices are represented by the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   313 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         i 
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   265 
                 
               
             
           
         
       
     
     Here, since the period (cycle) has N slots, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). Furthermore, the N×M period (cycle) precoding matrices based on Equation 265 are represented by the following equation. 
     
       
         
           
             
               
                 
                                    
                   
                     Math 
                     ⁢ 
                         
                     314 
                   
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       
                         N 
                         × 
                         k 
                       
                       + 
                       i 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         i 
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     Xk 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   Xk 
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   266 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M  1 ). 
     In this case, precoding matrices F[0]-F[N×M−1] are generated. (Precoding matrices F[0]-F[N×M−1] may be in any order for the N×M slots in the period (cycle)). Symbol number N×M×i may be precoded using F[0], symbol number N×M×i+1 may be precoded using F[1], . . . , and symbol number N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , N×M−2, N×M−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) 
     Generating the precoding matrices in this way achieves a precoding matrix hopping scheme with a large period (cycle), allowing for the position of poor reception points to be easily changed, which may lead to improved data reception quality. Note that while the N×M period (cycle) precoding matrices have been set to Equation 266, the N×M period (cycle) precoding matrices may be set to the following equation, as described above. 
     
       
         
           
             
               
                 
                                    
                   
                     Math 
                     ⁢ 
                         
                     315 
                   
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       
                         N 
                         × 
                         k 
                       
                       + 
                       i 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   
                                     X 
                                     k 
                                   
                                 
                                 ) 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         i 
                                         ) 
                                       
                                       + 
                                       
                                         X 
                                         k 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   267 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     In Equations 265 and 266, when 0 radians≤δ&lt;2π (radians, the matrices are a unitary matrix when δ=n radians and are a non-unitary matrix when δ≠π radians. In the present scheme, use of a non-unitary matrix for π/2 radians≤|δ|&lt;π radians is one characteristic structure (the conditions for δ being similar to other embodiments), and excellent data reception quality is obtained. However, not limited to this, a unitary matrix may be used instead. 
     In the present embodiment, as one example of the case where λ is treated as a fixed value, a case where λ=0 radians is described. However, in view of the mapping according to the modulation scheme, λ may be set to a fixed value defined as λ=π/2 radians, λ=π radians, or λ=(3π)/2 radians. (For example, λ may be set to a fixed value defined as λ=π radians in the precoding matrices of the precoding scheme in which hopping between precoding matrices is performed regularly.) With this structure, as is the case where λ is set to a value defined as λ=0 radians, a reduction in circuit size is achieved. 
     Embodiment 18 
     The present embodiment describes a scheme for regularly hopping between precoding matrices using a unitary matrix based on Embodiment 9. 
     As described in Embodiment 8, in the scheme of regularly hopping between precoding matrices over a period (cycle) with N slots, the precoding matrices prepared for the N slots with reference to Equations 82-85 are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   316 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         i 
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   268 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). (α&gt;0.) Since a unitary matrix is used in the present embodiment, the precoding matrices in Equation 268 may be represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   317 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         i 
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   269 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). (α&gt;0.) From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment 3, the following condition is important for achieving excellent data reception quality.
 
Math 318
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #53
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; and x≠y.)
 
Math 319
 
 e   j(θ     11     (x)−θ     21     (x)−π)   ≠e   j(θ     11     (y)−θ     21     (y)−π)  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #54
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; and x≠y.)
 
     Embodiment 6 has described the distance between poor reception points. In order to increase the distance between poor reception points, it is important for the number of slots N to be an odd number three or greater. The following explains this point. 
     In order to distribute the poor reception points evenly with regards to phase in the complex plane, as described in Embodiment 6, Condition #55 and Condition #56 are provided. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   320 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               x 
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               x 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         
                           e 
                           j 
                         
                         ( 
                         
                           
                             2 
                             ⁢ 
                             π 
                           
                           N 
                         
                         ) 
                       
                       ⁢ 
                           
                       for 
                     
                   
                   ⁢ 
                   
 
                   
                     ∀ 
                     
                       x 
                       ⁡ 
                       ( 
                       
                         
                           x 
                           = 
                           0 
                         
                         , 
                         1 
                         , 
                         2 
                         , 
                         … 
                             
                         , 
                         
                           N 
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #55 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   321 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               x 
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               x 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         
                           e 
                           j 
                         
                         ( 
                         
                           - 
                           
                             
                               2 
                               ⁢ 
                               π 
                             
                             N 
                           
                         
                         ) 
                       
                       ⁢ 
                           
                       for 
                     
                   
                   ⁢ 
                   
 
                   
                     ∀ 
                     
                       x 
                       ⁢ 
                       
                         ( 
                         
                           
                             x 
                             = 
                             0 
                           
                           , 
                           1 
                           , 
                           2 
                           , 
                           … 
                               
                           , 
                           
                             N 
                             - 
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #56 
                 
               
             
           
         
       
     
     Letting θ 11 (0)−θ 21 (0)=0 radians, and letting α&lt;1, the distribution of poor reception points for s 1  and for s 2  in the complex plane for an N=3 period (cycle) is shown in  FIG.  43 A , and the distribution of poor reception points for s 1  and for s 2  in the complex plane for an N=4 period (cycle) is shown in  FIG.  43 B . Letting θ 11 (0)−θ 21 (0)=0 radians, and letting α&gt;1, the distribution of poor reception points for s 1  and for s 2  in the complex plane for an N=3 period (cycle) is shown in  FIG.  44 A , and the distribution of poor reception points for s 1  and for s 2  in the complex plane for an N=4 period (cycle) is shown in  FIG.  44 B . 
     In this case, when considering the phase between a line segment from the origin to a poor reception point and a half line along the real axis defined by real ≥0 (see  FIG.  43 A ), then for either α&gt;1 for α&lt;1, when N=4, the case always occurs wherein the phase for the poor reception points for s 1  and the phase for the poor reception points for s 2  are the same value. (See  4301 ,  4302  in  FIG.  43 B, and  4401 ,  4402    in  FIG.  44 B .) In this case, in the complex plane, the distance between poor reception points becomes small. On the other hand, when N=3, the phase for the poor reception points for s 1  and the phase for the poor reception points for s 2  are never the same value. 
     Based on the above, considering how the case always occurs wherein the phase for the poor reception points for s 1  and the phase for the poor reception points for s 2  are the same value when the number of slots N in the period (cycle) is an even number, setting the number of slots N in the period (cycle) to an odd number increases the probability of a greater distance between poor reception points in the complex plane as compared to when the number of slots N in the period (cycle) is an even number. However, when the number of slots N in the period (cycle) is small, for example when N≤16, the minimum distance between poor reception points in the complex plane can be guaranteed to be a certain length, since the number of poor reception points is small. Accordingly, when N≤16, even if N is an even number, cases do exist where data reception quality can be guaranteed. 
     Therefore, in the scheme for regularly hopping between precoding matrices based on Equation 269, when the number of slots N in the period (cycle) is set to an odd number, the probability of improving data reception quality is high. Precoding matrices F[0]-F[N−1] are generated based on Equation 269 (the precoding matrices F[0]-F[N−1] may be in any order for the N slots in the period (cycle)). Symbol number Ni may be precoded using F[0], symbol number Ni+1 may be precoded using F[1], . . . , and symbol number N×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , N−2, N−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) Furthermore, when the modulation scheme for both s 1  and s 2  is 16QAM, if α is set as follows, 
             Math   ⁢         322                     α   =         2     +   4         2     +   2                 Equation   ⁢         270                 
the advantageous effect of increasing the minimum distance between 16×16=256 signal points in the I-Q plane for a specific LOS environment may be achieved.
 
       FIG.  94    shows signal point layout in the I-Q plane for 16QAM. In  FIG.  94   , signal point  9400  is a signal point when bits to be transmitted (input bits) b 0 -b 3  represent a value “(b 0 , b 1 , b 2 , b 3 )=(1, 0, 0, 0)” (as shown in  FIG.  94   ), and its coordinates in the I-Q plane are (−3×g, 3×g). With regard to the signal points other than signal point  9400 , the bits to be transmitted and the coordinates in the I-Q plane can be identified from  FIG.  94   . 
       FIG.  95    shows signal point layout in the I-Q plane for QPSK. In  FIG.  95   , signal point  9500  is a signal point when bits to be transmitted (input bits) b 0  and b 1  represent a value “(b 0 , b 1 )=(1, 0)” (as shown in  FIG.  95   ), and its coordinates in the I-Q plane are (−1×g, 1×g). With regard to the signal points other than signal point  9500 , the bits to be transmitted and the coordinates in the I-Q plane can be identified from  FIG.  95   . 
     Also, when the modulation scheme for s 1  is QPSK modulation and the modulation scheme for s 2  is 16QAM, if α is set as follows, 
             Math   ⁢         323                     α   =         2     +   3   +     5           2     +   3   -     5                   Equation   ⁢         271                 
the advantageous effect of increasing the minimum distance between candidate signal points in the I-Q plane for a specific LOS environment may be achieved.
 
     Note that a signal point layout in the I-Q plane for 16QAM is shown in  FIG.  94   , and a signal point layout in the I-Q plane for QPSK is shown in  FIG.  95   . Here, if g in  FIG.  94    is set as follows, 
             Math   ⁢         324                     g   =     z     10               Equation   ⁢         272               
h in  FIG.  94    is obtained as follows.
 
     
       
         
           
             Math 
             ⁢ 
                 
             325 
           
         
       
       
         
           
             
               
                 
                   h 
                   = 
                   
                     z 
                     
                       2 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     273 
                   
                 
               
             
           
         
       
     
     As an example of the precoding matrices prepared for the N slots based on Equation 269, the following matrices are considered: 
     
       
         
           
             Math 
             ⁢ 
                 
             326 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       0 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   274 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             327 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       1 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     2 
                                     5 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       2 
                                       5 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   275 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             328 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       2 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     4 
                                     5 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       4 
                                       5 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   276 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             329 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       3 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     6 
                                     5 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       6 
                                       5 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   277 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             330 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       4 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     8 
                                     5 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       8 
                                       5 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   278 
                 
               
             
           
         
       
     
     Note that, in order to restrict the calculation scale of the above precoding in the transmission device, θ 11 (i)=0 radians and λ=0 radians may be set in Equation 269. In this case, however, in Equation 269, λ may vary depending on i, or may be the same value. That is to say, in Equation 269, λ in F[i=x] and λ F[i=y] (x≠y) may be the same value or may be different values. 
     As the value to which α is set, the above-described set value is one of effective values. However, not limited to this, a may be set, for example, for each value of i in the precoding matrix F[i] as described in Embodiment 17. (That is to say, in F[i], α is not necessarily be always set to a constant value for i). 
     In the present embodiment, the scheme of structuring N different precoding matrices for a precoding hopping scheme with an N-slot time period (cycle) has been described. In this case, as the N different precoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] are prepared. In the single carrier transmission scheme, symbols are arranged in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1] in the time domain (or the frequency domain in the case of the multi-carrier transmission scheme). The present invention is not, however, limited in this way, and the N different precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1] generated in the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaptation in this case, precoding weights may be changed by arranging symbols in the frequency domain and in the frequency-time domain. Note that a precoding hopping scheme with an N-slot time period (cycle) has been described, but the same advantageous effects may be obtained by randomly using N different precoding matrices. In other words, the N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots N in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the N different precoding matrices of the present embodiment are included, the probability of excellent reception quality increases. In this case, Condition #55 and Condition #56 can be replaced by the following conditions. (The number of slots in the period (cycle) is considered to be N.)
 
Math 331
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∃ x,∃y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #55′
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; and x≠y.)
 
Math 332
 
 e   j(θ     11     (x)−θ     21     (x)−π)   ≠e   j(θ     11     (y)−θ     21     (y)−π)  for ∃ x,∃y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #56′
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; and x≠y.)
 
     In the present embodiment, as one example of the case where λ is treated as a fixed value, a case where λ=0 radians is described. However, in view of the mapping according to the modulation scheme, λ may be set to a fixed value defined as λ=π/2 radians, λ=π radians, or λ=(3π)/2 radians. (For example, λ may be set to a fixed value defined as λ=π radians in the precoding matrices of the precoding scheme in which hopping between precoding matrices is performed regularly.) With this structure, as is the case where λ is set to a value defined as λ=0 radians, a reduction in circuit size is achieved. 
     Embodiment 19 
     The present embodiment describes a scheme for regularly hopping between precoding matrices using a unitary matrix based on Embodiment 10. 
     In the scheme of regularly hopping between precoding matrices over a period (cycle) with 2N slots, the precoding matrices prepared for the 2N slots are represented as follows. 
             Math   ⁢         333                           When   ⁢         i     =   0     ,   1   ,   2   ,   …         ,     N   -   2     ,     N   -     1   :         ⁢   
       F   [   i   ]     =       1         α   2     +   1         ⁢     (           e     j   ⁢       θ   11     (   i   )               α   ×     e     j   (             θ   11     (   i   )     +   λ     )                   α   ×     e     j   ⁢       θ   21     (   i   )                 e     j   (             θ   21     (   i   )     +   λ   +   π     )             )                   Equation   ⁢         279                 
α&gt;0, and α is a fixed value (regardless of i).
 
             Math   ⁢         334                           When   ⁢         i     =   N     ,     N   +   1     ,     N   +   2     ,   …         ,       2   ⁢   N     -   2     ,       2   ⁢   N     -     1   :         ⁢   
       F   [   i   ]     =       1         α   2     +   1         ⁢     (           α   ×     e     j   ⁢       θ   11     (   i   )                 e     j   (             θ   11     (   i   )     +   λ     )                 e     j   ⁢       θ   21     (   i   )               α   ×     e     j   (             θ   21     (   i   )     +   λ   +   π     )               )                 Equation   ⁢         280               
α&gt;0, and α is a fixed value (regardless of i).
 
(The value of α in Equation 279 is the same as the value of α in Equation 280.) (The value of α may be set as α&lt;0.)
 
     From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment 3, the following condition is important for achieving excellent data reception quality.
 
Math 335
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #57
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; and x≠y.)
 
Math 336
 
 e   j(θ     11     (x)−θ     21     (x)−π)   ≠e   j(θ     11     (y)−θ     21     (y)−π)  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #58
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; and x≠y.)
 
     Addition of the following condition is considered.
 
Math 337
 
θ 11 ( x )=θ 11 ( x+N ) for ∀ x  ( x= 0,1,2, . . . , N− 2, N− 1)
 
and
 
θ 21 ( y )=θ 21 ( y+N ) for ∀ y  ( y= 0,1,2, . . . , N− 2, N− 1)  Condition #59
 
     Next, in order to distribute the poor reception points evenly with regards to phase in the complex plane, as described in Embodiment 6, Condition #60 and Condition #61 are provided. 
     
       
         
           
             Math 
             ⁢ 
                 
             338 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               x 
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               x 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               2 
                               ⁢ 
                               π 
                             
                             N 
                           
                           ) 
                         
                       
                       ⁢ 
                           
                       for 
                     
                   
                   ⁢ 
                   
 
                   
                     ∀ 
                     
                       x 
                       ⁡ 
                       ( 
                       
                         
                           x 
                           = 
                           0 
                         
                         , 
                         1 
                         , 
                         2 
                         , 
                         … 
                             
                         , 
                         
                           N 
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #60 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             339 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               x 
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               x 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             - 
                             
                               
                                 2 
                                 ⁢ 
                                 π 
                               
                               N 
                             
                           
                           ) 
                         
                       
                       ⁢ 
                           
                       for 
                     
                   
                   ⁢ 
                   
 
                   
                     ∀ 
                     
                       x 
                       ⁢ 
                       
                         ( 
                         
                           
                             x 
                             = 
                             0 
                           
                           , 
                           1 
                           , 
                           2 
                           , 
                           … 
                               
                           , 
                           
                             N 
                             - 
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #61 
                 
               
             
           
         
       
     
     Letting θ 11 (0)−θ 21 (0)=0 radians, and letting α&gt;1, the distribution of poor reception points for s 1  and for s 2  in the complex plane for N=4 is shown in  FIGS.  43 A and  43 B . As is clear from  FIGS.  43 A and  43 B , in the complex plane, the minimum distance between poor reception points for s 1  is kept large, and similarly, the minimum distance between poor reception points for s 2  is also kept large. Similar conditions are created when α&lt;1. Furthermore, making the same considerations as in Embodiment 9, the probability of a greater distance between poor reception points in the complex plane increases when N is an odd number as compared to when N is an even number. However, when N is small, for example when N≤16, the minimum distance between poor reception points in the complex plane can be guaranteed to be a certain length, since the number of poor reception points is small. Accordingly, when N≤16, even if N is an even number, cases do exist where data reception quality can be guaranteed. 
     Therefore, in the scheme for regularly hopping between precoding matrices based on Equations 279 and 280, when N is set to an odd number, the probability of improving data reception quality is high. Note that precoding matrices F[0]-F[2N−1] have been generated based on Equations 279 and 280. (The precoding matrices F[0]-F[2N−1] may be in any order for the 2N slots in the period (cycle)). Symbol number 2Ni may be precoded using F[0], symbol number 2Ni+1 may be precoded using F[1], . . . , and symbol number 2N×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , 2N−2, 2N−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) Furthermore, when the modulation scheme for both s 1  and s 2  is 16QAM, if α is set as in Equation 270, the advantageous effect of increasing the minimum distance between 16×16=256 signal points in the I-Q plane for a specific LOS environment may be achieved. 
     Also, when the modulation scheme for s 1  is QPSK modulation and the modulation scheme for s 2  is 16QAM, if α is set as in Equation 271, the advantageous effect of increasing the minimum distance between candidate signal points in the I-Q plane for a specific LOS environment may be achieved. Note that a signal point layout in the I-Q plane for 16QAM is shown in  FIG.  60   , and a signal point layout in the I-Q plane for QPSK is shown in  FIG.  94   . Here, if “g” in  FIG.  60    is set as in Equation 272, follows, “h” in  FIG.  94    is obtained as in Equation 273. 
     The following conditions are possible as conditions differing from Condition #59:
 
Math 340
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∀ x,∀y  ( x≠y;x,y=N,N+ 1 ,N+ 2, . . . ,2 N− 2,2 N− 1)  Condition #62
 
(x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . , 2N−2, 2N−1; and x≠y.)
 
Math 341
 
 e   j(θ     11     (x)−θ     21     (x)−π)   ≠e   j(θ     11     (y)−θ     21     (y)−π)  for ∀ x,∀y  ( x≠y;x,y=N,N+ 1 ,N+ 2, . . . ,2 N− 2,2 N− 1)  Condition #63
 
(x is N, N+1, N+2N−2, . . . 2N−1; y is N, N+1, N+2N−2, . . . 2N−1; and x≠y.)
 
     In this case, by satisfying Condition #57 and Condition #58 and Condition #62 and Condition #63, the distance in the complex plane between poor reception points for s 1  is increased, as is the distance between poor reception points for s 2 , thereby achieving excellent data reception quality. 
     As an example of the precoding matrices prepared for the 2N slots based on Equations 279 and 280, the following matrices are considered when N=15: 
     
       
         
           
             Math 
             ⁢ 
                 
             342 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       0 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   281 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             343 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       1 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     2 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       2 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   282 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             344 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       2 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     4 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       4 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   283 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             345 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       3 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     6 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       6 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   284 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             346 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       4 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     8 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       8 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   285 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             347 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       5 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     10 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       10 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   286 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             348 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       6 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     12 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       12 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   287 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             349 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       7 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     14 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       14 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   288 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             350 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       8 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     16 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       16 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   289 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             351 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       9 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     18 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       18 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   290 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             352 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       10 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     20 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       20 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   291 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             353 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       11 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     22 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       22 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   292 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             354 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       12 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     24 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       24 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   293 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             355 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       13 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     26 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       26 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   294 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             356 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       14 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     28 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       28 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   295 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             357 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       15 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   296 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             358 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       16 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     2 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       2 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   297 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             359 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       17 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     4 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       4 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   298 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             360 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       18 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     6 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       6 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   299 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             361 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       19 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     8 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       8 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   300 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             362 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       20 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     10 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       10 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   301 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             363 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       21 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     12 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       12 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   302 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             364 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       22 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     14 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       14 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   303 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             365 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       23 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     16 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       16 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   304 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             366 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       24 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     18 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       18 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   305 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             367 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       25 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     20 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       20 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   306 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             368 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       26 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     22 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       22 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   307 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             369 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       27 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     24 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       24 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   308 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             370 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       28 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     26 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       26 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   309 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             371 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       29 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     28 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 ( 
                                 
                                   
                                     j 
                                     ⁢ 
                                     
                                       28 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   310 
                 
               
             
           
         
       
     
     Note that, in order to restrict the calculation scale of the above precoding in the transmission device, θ 11 (i)=0 radians and λ=0 radians may be set in Equation 279, and θ21(i)=0 radians and λ=0 radians may be set in Equation 280. 
     In this case, however, in Equations 279 and 280, λ may be set as a value that varies depending on i, or may be set as the same value. That is to say, in Equations 279 and 280, λ in F[i=x] and λ in F[i=y] (x≠y) may be the same value or may be different values. As another scheme, λ is set as a fixed value in Equation 279, λ is set as a fixed value in Equation 280, and the fixed values of λ in Equations 279 and 280 are set as different values. (As still another scheme, the fixed values of λ in Equations 279 and 280 are used.) 
     As the value to which α is set, the above-described set value is one of effective values. However, not limited to this, a may be set, for example, for each value of i in the precoding matrix F[i] as described in Embodiment 17. (That is to say, in F[i], α is not necessarily be always set to a constant value for i.) 
     In the present embodiment, the scheme of structuring 2N different precoding matrices for a precoding hopping scheme with a 2N-slot time period (cycle) has been described. In this case, as the 2N different precoding matrices, F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] are prepared. In the single carrier transmission scheme, symbols are arranged in the order F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] in the time domain (or the frequency domain in the case of the multi-carrier transmission scheme). The present invention is not, however, limited in this way, and the 2N different precoding matrices F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] generated in the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaptation in this case, precoding weights may be changed by arranging symbols in the frequency domain and in the frequency-time domain. Note that a precoding hopping scheme with a 2N-slot time period (cycle) has been described, but the same advantageous effects may be obtained by randomly using 2N different precoding matrices. In other words, the 2N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots 2N in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the 2N different precoding matrices of the present embodiment are included, the probability of excellent reception quality increases. 
     In the present embodiment, as one example of the case where λ is treated as a fixed value, a case where λ=0 radians is described. However, in view of the mapping according to the modulation scheme, λ may be set to a fixed value defined as λ=π/2 radians, λ=π radians, or λ=(3π)/2 radians. (For example, λ may be set to a fixed value defined as λ=π radians in the precoding matrices of the precoding scheme in which hopping between precoding matrices is performed regularly.) With this structure, as is the case where λ is set to a value defined as λ=0 radians, a reduction in circuit size is achieved. 
     Embodiment 20 
     The present embodiment describes a scheme for regularly hopping between precoding matrices using a unitary matrix based on Embodiment 13. 
     In the scheme of regularly hopping between precoding matrices over a period (cycle) with 2N slots, the precoding matrices prepared for the 2N slots are represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             372 
           
         
       
       
         
           
             
               
                 
                   
                     
                       When 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                     
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     311 
                   
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               11 
                             
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                     
                       
                         a 
                         × 
                         
                           e 
                           
                             j 
                             ( 
                               
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ( 
                             
                           
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             λ 
                             + 
                             δ 
                           
                           ) 
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     Let α be a fixed value (not depending on i), where α&gt;0. 
     
       
         
           
             Math 
             ⁢ 
                 
             373 
           
         
       
       
         
           
             
               
                 
                   
                     
                       When 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     312 
                   
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ( 
                               
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                             
                             ) 
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ( 
                             
                           
                             
                               θ 
                               11 
                             
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         e 
                         
                           j 
                           ( 
                             
                           
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             λ 
                             + 
                             δ 
                           
                           ) 
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     Let α be a fixed value (not depending on i), where α&gt;0. (The value of α may be set as α&lt;0.) 
     Furthermore, the 2×N×M period (cycle) precoding matrices based on Equations 311 and 312 are represented by the following equations. 
     
       
         
           
             Math 
             ⁢ 
                 
             374 
           
         
       
       
         
           
             
               
                 
                   
                     
                       When 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                     
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   313 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               11 
                             
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                     
                       
                         a 
                         × 
                         
                           e 
                           
                             j 
                             ( 
                               
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ( 
                               
                             
                               
                                 
                                   θ 
                                   21 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               
                                 X 
                                 k 
                               
                             
                             ) 
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ( 
                             
                           
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               X 
                               k 
                             
                             + 
                             λ 
                             + 
                             δ 
                           
                           ) 
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     In this case, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     
       
         
           
             Math 
             ⁢ 
                 
             375 
           
         
       
       
         
           
             
               
                 
                   
                     
                       When 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   314 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ( 
                               
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                             
                             ) 
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               11 
                             
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         e 
                         
                           j 
                           ( 
                             
                           
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             λ 
                             + 
                             δ 
                             + 
                             
                               Y 
                               k 
                             
                           
                           ) 
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 i 
                                 + 
                                 
                                   Y 
                                   k 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     In this case, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). Furthermore, Xk=Yk may be true, or Xk≠Yk may be true. 
     In this case, precoding matrices F[0]-F[2N×M−1] are generated. (Precoding matrices F[0]-F[2×N×M−1] may be in any order for the 2×N×M slots in the period (cycle)). Symbol number 2×N×M×i may be precoded using F[0], symbol number 2×N×M×i+1 may be precoded using F[1], . . . , and symbol number 2×N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , 2×N×M−2, 2×N×M−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) 
     Generating the precoding matrices in this way achieves a precoding matrix hopping scheme with a large period (cycle), allowing for the position of poor reception points to be easily changed, which may lead to improved data reception quality. 
     The 2×N×M period (cycle) precoding matrices in Equation 313 may be changed to the following equation. 
     
       
         
           
             Math 
             ⁢ 
                 
             376 
           
         
       
       
         
           
             
               
                 
                   
                     
                       When 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     315 
                   
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ( 
                               
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                             
                             ) 
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               11 
                             
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         e 
                         
                           j 
                           ( 
                             
                           
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             λ 
                             + 
                             δ 
                             + 
                             
                               Y 
                               k 
                             
                           
                           ) 
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                               + 
                               
                                 Y 
                                 k 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     In this case, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     The 2×N×M period (cycle) precoding matrices in Equation 314 may also be changed to any of Equations 316-318. 
     
       
         
           
             Math 
             ⁢ 
                 
             377 
           
         
       
       
         
           
             
               
                 
                   
                     
                       When 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     316 
                   
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ( 
                               
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                               + 
                               
                                 Y 
                                 k 
                               
                             
                             ) 
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               
                                 Y 
                                 k 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         e 
                         
                           j 
                           ( 
                             
                           
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             λ 
                             + 
                             δ 
                           
                           ) 
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     In this case, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     
       
         
           
             Math 
             ⁢ 
                 
             378 
           
         
       
       
         
           
             
               
                 
                   
                     
                       When 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     317 
                   
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         e 
                         
                           j 
                           ( 
                             
                           
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               Y 
                               k 
                             
                           
                           ) 
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ( 
                               
                             
                               
                                 
                                   θ 
                                   21 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                               - 
                               δ 
                               + 
                               
                                 Y 
                                 k 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     In this case, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     
       
         
           
             Math 
             ⁢ 
                 
             379 
           
         
       
       
         
           
             
               
                 
                   
                     
                       When 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   318 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               
                 1 
                 
                   
                     
                       α 
                       2 
                     
                     + 
                     1 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ( 
                               
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               
                                 Y 
                                 k 
                               
                             
                             ) 
                           
                         
                       
                     
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                               + 
                               
                                 Y 
                                 k 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                     
                       
                         α 
                         × 
                         
                           e 
                           
                             j 
                             ( 
                               
                             
                               
                                 
                                   θ 
                                   21 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               + 
                               λ 
                               - 
                               δ 
                             
                             ) 
                           
                         
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     In this case, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     Focusing on poor reception points, if Equations 313 through 318 satisfy the following conditions,
 
Math 380
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #64
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
Math 381
 
 e   j(θ     11     (x)−θ     21     (x)−δ)   ≠e   j(θ     11     (y)−θ     21     (y)−δ)  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #65
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
Math 382
 
θ 11 ( x )=θ 11 ( x+N ) for ∀ x  ( x= 0,1,2, . . . , N− 2, N− 1)
 
and
 
θ 21 ( y )=θ 21 ( y+N ) for ∀ y  ( y= 0,1,2, . . . , N− 2, N− 1)  Condition #66
 
then excellent data reception quality is achieved. Note that in Embodiment 8, Condition #39 and Condition #40 should be satisfied.
 
     Focusing on Xk and Yk, if Equations 313 through 318 satisfy the following conditions,
 
Math 383
 
 X   a   ≠X   b +2× s ×π for ∀ a,∀b  ( a≠b;a,b= 0,1,2, . . . , M− 2, M− 1)  Condition #67
 
(a is 0, 1, 2, . . . , M−2, M−1; b is 0, 1, 2, . . . , M−2, M−1 (each of a and b being an integer in a range of 0 to M−1); and a≠b.) (Here, s is an integer.)
 
Math 384
 
 Y   a   ≠Y   b +2× u ×π for ∀ a,∀b  ( a≠b;a,b= 0,1,2, . . . , M− 2, M− 1)  Condition #68
 
(a is 0, 1, 2, . . . , M−2, M−1; b is 0, 1, 2, . . . , M−2, M−1 (each of a and b being an integer in a range of 0 to M−1); and a≠b.) (Here, u is an integer.), then excellent data reception quality is achieved. Note that in Embodiment 8, Condition #42 should be satisfied. In Equations 313 and 318, when 0 radians≤δ&lt;2π radians, the matrices are a unitary matrix when δ=π radians and are a non-unitary matrix when δ≠π radians. In the present scheme, use of a non-unitary matrix for π/2 radians≤|δ|&lt;π radians is one characteristic structure, and excellent data reception quality is obtained, but use of a unitary matrix is also possible.
 
     The following provides an example of precoding matrices in the precoding hopping scheme of the present embodiment. The following matrices are considered when N=5, M=2 as an example of the 2×N×M period (cycle) precoding matrices based on Equations 313 through 318: 
     
       
         
           
             Math 
             ⁢ 
                 
             385 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       0 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   319 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             386 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       1 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         2 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   320 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             387 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       2 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         4 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         4 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   321 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             388 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       3 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         6 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         6 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   322 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             389 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       4 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         8 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         8 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   323 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             390 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       5 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   324 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             391 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       6 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     2 
                                     5 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         2 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   325 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             392 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       7 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     4 
                                     5 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         4 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   326 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             393 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       8 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     6 
                                     5 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         6 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   327 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             394 
           
         
       
       
         
           
             
               
                 
                   
                     f 
                     [ 
                     
                       i 
                       = 
                       9 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     8 
                                     5 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         8 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   328 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             395 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       10 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       0 
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     π 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   329 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             396 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       11 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           2 
                                           5 
                                         
                                         ⁢ 
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         2 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   330 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             397 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       12 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           4 
                                           5 
                                         
                                         ⁢ 
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         4 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   331 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             398 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       13 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           6 
                                           5 
                                         
                                         ⁢ 
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         6 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   332 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             399 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       14 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           8 
                                           5 
                                         
                                         ⁢ 
                                         π 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         8 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   333 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             400 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       15 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     0 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       0 
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   334 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             401 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       16 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     2 
                                     5 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         2 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     0 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       0 
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   335 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             402 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       17 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     4 
                                     5 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         4 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     0 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       0 
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   336 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             403 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       18 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     6 
                                     5 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         6 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     0 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       0 
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   337 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             404 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       19 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     8 
                                     5 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         8 
                                         5 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     0 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       0 
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   338 
                 
               
             
           
         
       
     
     In this way, in the above example, in order to restrict the calculation scale of the above precoding in the transmission device, λ=0 radians, δ=π radians, X1=0 radians, and X2=π radians are set in Equation 313, and λ=0 radians, δ=π radians, Y1=0 radians, and Y2=π radians are set in Equation 314. In this case, however, in Equations 313 and 314, λ may be set as a value that varies depending on i, or may be set as the same value. That is to say, in Equations 313 and 314, λ in F[i=x] and λ in F[i=y] (x≠y) may be the same value or may be different values. As another scheme, λ is set as a fixed value in Equation 313, λ is set as a fixed value in Equation 314, and the fixed values of λ in Equations 313 and 314 are set as different values. (As still another scheme, the fixed values of λ in Equations 313 and 314 are used.) 
     As the value to which α is set, the set value described in Embodiment 18 is one of effective values. However, not limited to this, a may be set, for example, for each value of i in the precoding matrix F[i] as described in Embodiment 17. (That is to say, in F[i], α is not necessarily be always set to a constant value for i.) 
     In the present embodiment, as one example of the case where λ is treated as a fixed value, a case where λ=0 radians is described. However, in view of the mapping according to the modulation scheme, λ may be set to a fixed value defined as λ=π/2 radians, λ=π radians, or λ=(3π)/2 radians. (For example, λ may be set to a fixed value defined as λ=π radians in the precoding matrices of the precoding scheme in which hopping between precoding matrices is performed regularly.) With this structure, as is the case where λ is set to a value defined as λ=0 radians, a reduction in circuit size is achieved. 
     Embodiment 21 
     The present embodiment describes an example of the precoding scheme of Embodiment 18 in which hopping between precoding matrices is performed regularly. 
     As an example of the precoding matrices prepared for the N slots based on Equation 269, the following matrices are considered: 
     
       
         
           
             Math 
             ⁢ 
                 
             405 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       0 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   339 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             406 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       1 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     2 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         2 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   340 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             407 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       2 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     4 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         4 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   341 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             408 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       3 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     6 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         6 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   342 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             409 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       4 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     8 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         8 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   343 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             410 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       5 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     10 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         10 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   344 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             411 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       6 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     12 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         12 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   345 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             412 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       7 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     14 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         14 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   346 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             413 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       8 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     16 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         16 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   347 
                 
               
             
           
         
       
     
     In the above equations, there is a special case where a can be set to 1. In this case, Equations 339 through 347 are represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             414 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       0 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   348 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             415 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       1 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   2 
                                   9 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         2 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   349 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             416 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       2 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   4 
                                   9 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         4 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   350 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             417 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       3 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   6 
                                   9 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         6 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   351 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             418 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       4 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   8 
                                   9 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         8 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   352 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             419 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       5 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   10 
                                   9 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         10 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   353 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             420 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       6 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   12 
                                   9 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         12 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   354 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             421 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       7 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   14 
                                   9 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         14 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   355 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             422 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       8 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   16 
                                   9 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         16 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   356 
                 
               
             
           
         
       
     
     As another example, as an example of the precoding matrices prepared for the N slots based on Equation 269, the following matrices are considered when N=15: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   423 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       0 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   357 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   424 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       1 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     2 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         2 
                                         15 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   358 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   425 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       2 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     4 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         4 
                                         15 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   359 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   426 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       3 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     6 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         6 
                                         15 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   360 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   427 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       4 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     8 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         8 
                                         15 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   361 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   428 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       5 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     10 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         10 
                                         15 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   362 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   429 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       6 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     12 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         12 
                                         15 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   363 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   430 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       7 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     14 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         14 
                                         15 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   364 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   431 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       8 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     16 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         16 
                                         15 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   365 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   432 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       9 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     18 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         18 
                                         15 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   366 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   433 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       10 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     20 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         20 
                                         15 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   367 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   434 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       11 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     22 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         22 
                                         15 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   368 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   435 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       12 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     24 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         24 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   369 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   436 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       13 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     26 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         26 
                                         15 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   370 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   437 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       14 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     28 
                                     15 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         28 
                                         15 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   371 
                 
               
             
           
         
       
     
     In the above equations, there is a special case where a can be set to 1. In this case, Equations 357 through 371 are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   438 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       0 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   372 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   439 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       1 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   2 
                                   15 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       2 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   373 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   440 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       2 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   4 
                                   15 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       4 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   374 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   441 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       3 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   6 
                                   15 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       6 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   375 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   442 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       4 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   8 
                                   15 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       8 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   376 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   443 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       5 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   10 
                                   15 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       10 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   377 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   444 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       6 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   12 
                                   15 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       12 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   378 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   445 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       7 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   14 
                                   15 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       14 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   379 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   446 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       8 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   16 
                                   15 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       16 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   380 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   447 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       9 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   18 
                                   15 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       18 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   381 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   448 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       10 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   20 
                                   15 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       20 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   382 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   449 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       11 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   22 
                                   15 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       22 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   383 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   450 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       12 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   24 
                                   9 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       24 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   384 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   451 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       13 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   26 
                                   15 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       26 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   385 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   452 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       14 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   28 
                                   15 
                                 
                                 ⁢ 
                                 π 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       28 
                                       15 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   386 
                 
               
             
           
         
       
     
     In the present example, α is set to 1. However, the value to which α is set is not limited to this. For example, the set value of α may be applied to the following case. That is to say, as shown in  FIG.  3    or the like, the encoder performs an error correction coding. The value of α may be varied depending on the coding rate for error correction coding used in the error correction coding. For example, there is considered a scheme in which α is set to 1 when the coding rate is 1/2, and to a value other than 1 such as a value satisfying the relationship α&gt;1 (or α&lt;1) when the coding rate is 2/3. With this structure, in the reception device, excellent data reception quality may be achieved regardless of the coding rate. (Excellent data reception quality may be achieved even if α is set as a fixed value.) 
     As another example, as described in Embodiment 17, α may be set for each value of i in the precoding matrix F[i]. (That is to say, in F[i], α is not necessarily be always set to a constant value for i.) 
     In the present embodiment, the scheme of structuring N different precoding matrices for a precoding hopping scheme with an N-slot time period (cycle) has been described. In this case, as the N different precoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] are prepared. In the single carrier transmission scheme, symbols are arranged in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1] in the time domain (or the frequency domain in the case of the multi-carrier transmission scheme). The present invention is not, however, limited in this way, and the N different precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1] generated in the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaptation in this case, precoding weights may be changed by arranging symbols in the frequency domain and in the frequency-time domain. Note that a precoding hopping scheme with an N-slot time period (cycle) has been described, but the same advantageous effects may be obtained by randomly using N different precoding matrices. In other words, the N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Embodiment 22 
     The present embodiment describes an example of the precoding scheme of Embodiment 19 in which hopping between precoding matrices is performed regularly. 
     As an example of the precoding matrices prepared for the 2N slots based on Equations 279 and 280, the following matrices are considered when N=9: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   453 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       0 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   387 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   454 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       1 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     2 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       2 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   388 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   455 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       2 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     4 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       4 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   389 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   456 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       3 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     6 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       6 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   390 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   457 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       4 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     8 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       8 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   391 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   458 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       5 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     10 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       10 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   392 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   459 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       6 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     12 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       12 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   393 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   460 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       7 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     14 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       14 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   394 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   461 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       8 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     16 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       16 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   395 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   462 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       9 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   396 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   463 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       10 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     2 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       2 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   397 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   464 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       11 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     4 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       4 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   398 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   465 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       12 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     6 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       6 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   399 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   466 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       13 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     8 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       8 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   400 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   467 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       14 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     10 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       10 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   401 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   468 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       15 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     12 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       12 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   402 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   469 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       16 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     14 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       14 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   403 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   470 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       17 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     16 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       16 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   404 
                 
               
             
           
         
       
     
     In the above equations, there is a special case where a can be set to 1. In this case, Equations 387 through 404 are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   471 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       0 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   405 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   472 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       1 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     2 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         2 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   406 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   473 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       2 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     4 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         4 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   407 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   474 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       3 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     6 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         6 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   408 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   475 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       4 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     8 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         8 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   409 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   476 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       5 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     10 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         10 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   410 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   477 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       6 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     12 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         12 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   411 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   478 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       7 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     14 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         14 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   412 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   479 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       8 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     16 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         16 
                                         9 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   413 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   480 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       9 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   414 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   481 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       10 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     2 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       2 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   415 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   482 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       11 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     4 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       4 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   416 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   483 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       12 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     6 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       6 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   417 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   484 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       13 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     8 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       8 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   418 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   485 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       14 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     10 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       10 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   419 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   486 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       15 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     12 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       12 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   420 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   487 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       16 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     14 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       14 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   421 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   488 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       17 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     16 
                                     9 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       16 
                                       9 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   422 
                 
               
             
           
         
       
     
     Also, α may be set to 1 in Equations 281 through 310 presented in Embodiment 19. As the value to which α is set, the above-described set value is one of effective values. However, not limited to this, α may be set, for example, for each value of i in the precoding matrix F[i] as described in Embodiment 17. (That is to say, in F[i], α is not necessarily be always set to a constant value for i.) 
     In the present embodiment, the scheme of structuring 2N different precoding matrices for a precoding hopping scheme with a 2N-slot time period (cycle) has been described. In this case, as the 2N different precoding matrices, F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] are prepared. In the single carrier transmission scheme, symbols are arranged in the order F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] in the time domain (or the frequency domain in the case of the multi-carrier transmission scheme). The present invention is not, however, limited in this way, and the 2N different precoding matrices F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] generated in the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaptation in this case, precoding weights may be changed by arranging symbols in the frequency domain and in the frequency-time domain. Note that a precoding hopping scheme with a 2N-slot time period (cycle) has been described, but the same advantageous effects may be obtained by randomly using 2N different precoding matrices. In other words, the 2N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots 2N in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the 2N different precoding matrices of the present embodiment are included, the probability of excellent reception quality increases. 
     Embodiment 23 
     In Embodiment 9, a scheme for regularly hopping between precoding matrices with use of a unitary matrix has been described. In the present embodiment, a scheme for regularly hopping between precoding matrices with use of a matrix different from that in Embodiment 9 is described. 
     First, a precoding matrix F, a basic precoding matrix, is expressed by the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   489 
                 
               
               
                  
               
             
             
               
                 
                   F 
                   = 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   μ 
                                   11 
                                 
                               
                             
                           
                         
                         
                           
                             B 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   μ 
                                   12 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             C 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   μ 
                                   21 
                                 
                               
                             
                           
                         
                         
                           0 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   423 
                 
               
             
           
         
       
     
     In Equation 423, A, B, and C are real numbers, μ 11 , μ 12 , and μ 21  are real numbers, and the units of them are radians. In the scheme of regularly hopping between precoding matrices over a period (cycle) with N slots, the precoding matrices prepared for the N slots are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   490 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             × 
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     μ 
                                     11 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             B 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                     
                                   
                                     
                                       μ 
                                       12 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             C 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                     
                                   
                                     
                                       μ 
                                       21 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           0 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   424 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). Also, A, B, and C are fixed values regardless of i, and μ 11 , μ 12 , and μ 21  are fixed values regardless of i. If a matrix represented by the format of Equation 424 is treated as a precoding matrix, “0” is present as one element of the precoding matrix, thus it has an advantageous effect that the poor reception points described in other embodiments can be reduced. 
     Also, another basic precoding matrix different from that expressed by Equation 423 is expressed by the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   491 
                 
               
               
                  
               
             
             
               
                 
                   F 
                   = 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   μ 
                                   11 
                                 
                               
                             
                           
                         
                         
                           
                             B 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   μ 
                                   12 
                                 
                               
                             
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             D 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   μ 
                                   22 
                                 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   425 
                 
               
             
           
         
       
     
     In Equation 425, A, B, and C are real numbers, μ 11 , μ 12 , and μ 22  are real numbers, and the units of them are radians. In the scheme of regularly hopping between precoding matrices over a period (cycle) with N slots, the precoding matrices prepared for the N slots are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   492 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             × 
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     μ 
                                     11 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             B 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                     
                                   
                                     
                                       μ 
                                       12 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             D 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                     
                                   
                                     
                                       μ 
                                       22 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   426 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). Also, A, B, and D are fixed values regardless of i, and μ 11 , μ 12 , and μ 22  are fixed values regardless of i. If a matrix represented by the format of Equation 426 is treated as a precoding matrix, “0” is present as one element of the precoding matrix, thus it has an advantageous effect that the poor reception points described in other embodiments can be reduced. 
     Also, another basic precoding matrix different from those expressed by Equations 423 and 425 is expressed by the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   493 
                 
               
               
                  
               
             
             
               
                 
                   F 
                   = 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   μ 
                                   11 
                                 
                               
                             
                           
                         
                         
                           0 
                         
                       
                       
                         
                           
                             C 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   μ 
                                   21 
                                 
                               
                             
                           
                         
                         
                           
                             D 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   μ 
                                   22 
                                 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   427 
                 
               
             
           
         
       
     
     In Equation 427, A, C, and D are real numbers, μ 11 , μ 12 , and μ 22  are real numbers, and the units of them are radians. In the scheme of regularly hopping between precoding matrices over a period (cycle) with N slots, the precoding matrices prepared for the N slots are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   494 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             × 
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     μ 
                                     11 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           0 
                         
                       
                       
                         
                           
                             C 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                     
                                   
                                     
                                       μ 
                                       21 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             D 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                     
                                   
                                     
                                       μ 
                                       22 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   428 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). Also, A, C, and D are fixed values regardless of i, and μ 11 , μ 21 , and μ 22  are fixed values regardless of i. If a matrix represented by the format of Equation 428 is treated as a precoding matrix, “0” is present as one element of the precoding matrix, thus it has an advantageous effect that the poor reception points described in other embodiments can be reduced. 
     Also, another basic precoding matrix different from those expressed by Equations 423, 425, and 427 is expressed by the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                     
                   495 
                 
               
               
                  
               
             
             
               
                 
                   F 
                   = 
                   
                     ( 
                     
                       
                         
                           0 
                         
                         
                           
                             B 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   μ 
                                   12 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             C 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   μ 
                                   21 
                                 
                               
                             
                           
                         
                         
                           
                             D 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   μ 
                                   22 
                                 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   429 
                 
               
             
           
         
       
     
     In Equation 429, B, C, and D are real numbers, μ 12 , μ 21 , and μ 22  are real numbers, and the units of them are radians. In the scheme of regularly hopping between precoding matrices over a period (cycle) with N slots, the precoding matrices prepared for the N slots are represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             496 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           0 
                         
                         
                           
                             B 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     12 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             C 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     21 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             D 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     22 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   430 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). Also, B, C, and D are fixed values regardless of i, and μ 12 , μ 21 , and μ 22  are fixed values regardless of i. If a matrix represented by the format of Equation 430 is treated as a precoding matrix, “0” is present as one element of the precoding matrix, thus it has an advantageous effect that the poor reception points described in other embodiments can be reduced. From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment 3, the following conditions are important for achieving excellent data reception quality.
 
Math 497
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #69
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
Math 498
 
 e   j(θ     11     (x)−θ     21     (x)−π)   ≠e   j(θ     11     (y)−θ     21     (y)−π)  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #70
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
     In order to distribute the poor reception points evenly with regards to phase in the complex plane, as described in Embodiment 6, Condition #71 and Condition #72 are provided. 
     
       
         
           
             Math 
             ⁢ 
                 
             499 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               x 
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               x 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               2 
                               ⁢ 
                               π 
                             
                             N 
                           
                           ) 
                         
                       
                       ⁢ 
                           
                       for 
                     
                   
                   ⁢ 
                       
                   
 
                   
                     ∀ 
                     
                       x 
                       ⁡ 
                       ( 
                       
                         
                           x 
                           = 
                           0 
                         
                         , 
                         1 
                         , 
                         2 
                         , 
                         … 
                            
                         , 
                         
                           N 
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #71 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             500 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               x 
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               x 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             - 
                             
                               
                                 2 
                                 ⁢ 
                                 π 
                               
                               N 
                             
                           
                           ) 
                         
                       
                       ⁢ 
                           
                       for 
                     
                   
                   ⁢ 
                       
                   
 
                   
                     ∀ 
                     
                       x 
                       ⁡ 
                       ( 
                       
                         
                           x 
                           = 
                           0 
                         
                         , 
                         1 
                         , 
                         2 
                         , 
                         … 
                            
                         , 
                         
                           N 
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #72 
                 
               
             
           
         
       
     
     With this structure, the reception device can avoid poor reception points in the LOS environment, and thus can obtain the advantageous effect of improving the data reception quality. 
     Note that, as an example of the above-described scheme for regularly hopping between precoding matrices, there is a scheme for fixing θ 11 (i) to 0 radians (θ 11 (i) is set to a constant value regardless of i. In this case, θ 11 (i) may be set to a value other than 0 radians.) so that θ 11 (i) and θ 21 (i) satisfy the above-described conditions. Also, there is a scheme for not fixing θ 11 (i) to 0 radians, but fixing θ 21 (i) to 0 radians (θ 21 (i) is set to a constant value regardless of i. In this case, θ 21 (i) may be set to a value other than 0 radians.) so that θ 11 (i) and θ 21 (i) satisfy the above-described conditions. 
     The present embodiment describes the scheme of structuring N different precoding matrices for a precoding hopping scheme with an N-slot time period (cycle). In this case, as the N different precoding matrices, F[0], F[1], F[2], . . . , F[N 2], F[N−1] are prepared. In a single carrier transmission scheme, symbols are arranged in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1] in the time domain (or the frequency domain in the case of multi-carrier transmission scheme). However, this is not the only example, and the N different precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1] generated according to the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaption in this case, precoding weights may be changed by arranging symbols in the frequency domain or in the frequency-time domains. Note that a precoding hopping scheme with an N-slot time period (cycle) has been described, but the same advantageous effects may be obtained by randomly using N different precoding matrices. In other words, the N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots N in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the N different precoding matrices of the present embodiment are included, the probability of excellent reception quality increases. In this case, Condition #69 and Condition #70 can be replaced by the following conditions. (The number of slots in the period (cycle) is considered to be N.)
 
Math 501
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∃ x,∃y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #73
 
     (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
Math 502
 
 e   j(θ     11     (x)−θ     21     (x)−π)   ≠e   j(θ     11     (y)−θ     21     (y)−π)  for ∃ x,∃y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #74
 
     (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.) 
     Embodiment 24 
     In Embodiment 10, the scheme for regularly hopping between precoding matrices using a unitary matrix is described. However, the present embodiment describes a scheme for regularly hopping between precoding matrices using a matrix different from that used in Embodiment 10. 
     In the scheme of regularly hopping between precoding matrices over a period (cycle) with 2N slots, the precoding matrices prepared for the 2N slots are represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             503 
           
         
       
       
         
           
             
               
                 
                   
                     Here 
                     , 
                     
                       i 
                       = 
                       0 
                     
                     , 
                     1 
                     , 
                     2 
                     , 
                     … 
                        
                     , 
                     
                       N 
                       - 
                       2 
                     
                     , 
                     
                       N 
                       - 
                       1. 
                     
                   
                   ⁢ 
                   
 
                   
                     
                       F 
                       [ 
                       i 
                       ] 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               A 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       μ 
                                       11 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               B 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       μ 
                                       12 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               C 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       μ 
                                       21 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             0 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   431 
                 
               
             
           
         
       
     
     Here, let A, B, and C be real numbers, and μ 11 , μ 12 , and μ 21  be real numbers expressed in radians. In addition, A, B, and C are fixed values not depending on i. Similarly, μ 11 , μ 12 , and μ 21  are fixed values not depending on i. 
     
       
         
           
             Math 
             ⁢ 
                 
             504 
           
         
       
       
         
           
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                      
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   432 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       α 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               11 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       β 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               12 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     0 
                   
                   
                     
                       δ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               22 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, let α, β, and δ be real numbers, and v 11 , v 12 , and v 22  be real numbers expressed in radians. In addition, α, β, and δ are fixed values not depending on i. Similarly, v 11 , v 12 , and v 22  are fixed values not depending on i. 
     The precoding matrices prepared for the 2N slots different from those in Equations 431 and 432 are represented by the following equations. 
     
       
         
           
             Math 
             ⁢ 
                 
             505 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         For 
                         ⁢ 
                             
                         i 
                       
                       = 
                       0 
                     
                     , 
                     1 
                     , 
                     2 
                     , 
                     … 
                        
                     , 
                     
                       N 
                       - 
                       2 
                     
                     , 
                     
                       N 
                       - 
                       
                         1 
                         : 
                       
                     
                   
                   ⁢ 
                   
 
                   
                     
                       F 
                       [ 
                       i 
                       ] 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               A 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       μ 
                                       11 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               B 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       μ 
                                       12 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               C 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       μ 
                                       21 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             0 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   433 
                 
               
             
           
         
       
     
     Here, let A, B, and C be real numbers, and μ 11 , μ 12 , and μ 21  be real numbers expressed in radians. In addition, A, B, and C are fixed values not depending on i. Similarly, μ 11 , μ 12 , and μ 21  are fixed values not depending on i. 
     
       
         
           
             Math 
             ⁢ 
                 
             506 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         For 
                         ⁢ 
                             
                         i 
                       
                       = 
                       N 
                     
                     , 
                     
                       N 
                       + 
                       1 
                     
                     , 
                     
                       N 
                       + 
                       2 
                     
                     , 
                     … 
                        
                     , 
                     
                       
                         2 
                         ⁢ 
                         N 
                       
                       - 
                       2 
                     
                     , 
                     
                       
                         2 
                         ⁢ 
                         N 
                       
                       - 
                       
                         1 
                         : 
                       
                     
                   
                   ⁢ 
                   
 
                   
                     
                       F 
                       [ 
                       i 
                       ] 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             0 
                           
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       ν 
                                       12 
                                     
                                     + 
                                     
                                       
                                         ψ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               γ 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       ν 
                                       21 
                                     
                                     + 
                                     
                                       
                                         ψ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               δ 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       ν 
                                       22 
                                     
                                     + 
                                     
                                       
                                         ψ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   434 
                 
               
             
           
         
       
     
     Here, let β, γ, and δ be real numbers, and v 12 , v 21 , and v 22  be real numbers expressed in radians. In addition, β, γ, and δ are fixed values not depending on i. Similarly, v 12 , v 21 , and v 22  are fixed values not depending on i. 
     The precoding matrices prepared for the 2N slots different from those described above are represented by the following equations. 
     
       
         
           
             Math 
             ⁢ 
                 
             507 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         For 
                         ⁢ 
                             
                         i 
                       
                       = 
                       0 
                     
                     , 
                     1 
                     , 
                     2 
                     , 
                     … 
                        
                     , 
                     
                       N 
                       - 
                       2 
                     
                     , 
                     
                       N 
                       - 
                       
                         1 
                         : 
                       
                     
                   
                   ⁢ 
                   
 
                   
                     
                       F 
                       [ 
                       i 
                       ] 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               A 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       μ 
                                       11 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             0 
                           
                         
                         
                           
                             
                               C 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       μ 
                                       21 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               D 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       μ 
                                       22 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   435 
                 
               
             
           
         
       
     
     Here, let A, C, and D be real numbers, and μ 11 , μ 21 , and μ 22  be real numbers expressed in radians. In addition, A, C, and D are fixed values not depending on i. Similarly, μ 11 , μ 21 , and μ 22  are fixed values not depending on i. 
     
       
         
           
             Math 
             ⁢ 
                 
             508 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         For 
                         ⁢ 
                             
                         i 
                       
                       = 
                       N 
                     
                     , 
                     
                       N 
                       + 
                       1 
                     
                     , 
                     
                       N 
                       + 
                       2 
                     
                     , 
                     … 
                        
                     , 
                     
                       
                         2 
                         ⁢ 
                         N 
                       
                       - 
                       2 
                     
                     , 
                     
                       
                         2 
                         ⁢ 
                         N 
                       
                       - 
                       
                         1 
                         : 
                       
                     
                   
                   ⁢ 
                   
 
                   
                     
                       F 
                       [ 
                       i 
                       ] 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       ν 
                                       11 
                                     
                                     + 
                                     
                                       
                                         ψ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       ν 
                                       12 
                                     
                                     + 
                                     
                                       
                                         ψ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               δ 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       ν 
                                       22 
                                     
                                     + 
                                     
                                       
                                         ψ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   436 
                 
               
             
           
         
       
     
     Here, let α, β, and δ be real numbers, and v 11 , v 12 , and v 22  be real numbers expressed in radians. In addition, α, β, and δ are fixed values not depending on i. Similarly, v 11 , v 12 , and v 22  are fixed values not depending on i. 
     The precoding matrices prepared for the 2N slots different from those described above are represented by the following equations. 
     
       
         
           
             Math 
             ⁢ 
                 
             509 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         For 
                         ⁢ 
                             
                         i 
                       
                       = 
                       0 
                     
                     , 
                     1 
                     , 
                     2 
                     , 
                     … 
                        
                     , 
                     
                       N 
                       - 
                       2 
                     
                     , 
                     
                       N 
                       - 
                       
                         1 
                         : 
                       
                     
                   
                   ⁢ 
                   
 
                   
                     
                       F 
                       [ 
                       i 
                       ] 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               A 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       μ 
                                       11 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             0 
                           
                         
                         
                           
                             
                               C 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       μ 
                                       21 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               D 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       μ 
                                       22 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     Equation 
                     ⁢ 
                         
                     437 
                   
                 
               
             
           
         
       
     
     Here, let A, C, and D be real numbers, and μ 11 , μ 21 , and μ 22  be real numbers expressed in radians. In addition, A, C, and D are fixed values not depending on i. Similarly, μ 11 , μ 21 , and μ 22  are fixed values not depending on i. 
     
       
         
           
             Math 
             ⁢ 
                 
             510 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         For 
                         ⁢ 
                             
                         i 
                       
                       = 
                       N 
                     
                     , 
                     
                       N 
                       + 
                       1 
                     
                     , 
                     
                       N 
                       + 
                       2 
                     
                     , 
                     … 
                        
                     , 
                     
                       
                         2 
                         ⁢ 
                         N 
                       
                       - 
                       2 
                     
                     , 
                     
                       
                         2 
                         ⁢ 
                         N 
                       
                       - 
                       
                         1 
                         : 
                       
                     
                   
                   ⁢ 
                   
 
                   
                     
                       F 
                       [ 
                       i 
                       ] 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             0 
                           
                           
                             
                               β 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       ν 
                                       12 
                                     
                                     + 
                                     
                                       
                                         ψ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               γ 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       ν 
                                       21 
                                     
                                     + 
                                     
                                       
                                         ψ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               δ 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       ν 
                                       22 
                                     
                                     + 
                                     
                                       
                                         ψ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   438 
                 
               
             
           
         
       
     
     Here, let β, γ, and δ be real numbers, and v 12 , v 21 , and v 22  be real numbers expressed in radians. In addition, β, γ, and δ are fixed values not depending on i. Similarly, v 12 , v 21 , and v 22  are fixed values not depending on i. 
     Making the same considerations as in Condition #5 (Math 106) and Condition #6 (Math 107) of Embodiment 3, the following conditions are important for achieving excellent data reception quality.
 
Math 511
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y)−π)  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #75
 
     (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
Math 512
 
 e   j(ψ     11     (x)−ψ     21     (x))   ≠e   j(ψ     11     (y)−ψ     21     (y))  for ∀ x,∀y  ( x≠y;x,y=N,N+ 1 ,N+ 2, . . . ,2 N− 2,2 N− 1)   Condition #76
 
     (x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . , 2N−2, 2N−1 (each of x and y being an integer in a range of N to 2N−1); and x≠y.) 
     Next, in order to distribute the poor reception points evenly with regards to phase in the complex plane, as described in Embodiment 6, Condition #77 or Condition #78 is provided. 
     
       
         
           
             Math 
             ⁢ 
                 
             513 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               x 
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               x 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               2 
                               ⁢ 
                               π 
                             
                             N 
                           
                           ) 
                         
                       
                       ⁢ 
                           
                       for 
                     
                   
                   ⁢ 
                       
                   
 
                   
                     ∀ 
                     
                       x 
                       ⁡ 
                       ( 
                       
                         
                           x 
                           = 
                           0 
                         
                         , 
                         1 
                         , 
                         2 
                         , 
                         … 
                            
                         , 
                         
                           N 
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #77 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             514 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               x 
                               ) 
                             
                             - 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               x 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             - 
                             
                               
                                 2 
                                 ⁢ 
                                 π 
                               
                               N 
                             
                           
                           ) 
                         
                       
                       ⁢ 
                           
                       for 
                     
                   
                   ⁢ 
                       
                   
 
                   
                     ∀ 
                     
                       x 
                       ⁡ 
                       ( 
                       
                         
                           x 
                           = 
                           0 
                         
                         , 
                         1 
                         , 
                         2 
                         , 
                         … 
                            
                         , 
                         
                           N 
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #78 
                 
               
             
           
         
       
     
     Similarly, in order to distribute the poor reception points evenly with regards to phase in the complex plane, Condition #79 or Condition #80 is provided. 
     
       
         
           
             Math 
             ⁢ 
                 
             515 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               x 
                               ) 
                             
                             - 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               x 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               2 
                               ⁢ 
                               π 
                             
                             N 
                           
                           ) 
                         
                       
                       ⁢ 
                           
                       for 
                     
                   
                   ⁢ 
                       
                   
 
                   
                     ∀ 
                     
                       x 
                       ⁡ 
                       ( 
                       
                         
                           x 
                           = 
                           N 
                         
                         , 
                         
                           N 
                           + 
                           1 
                         
                         , 
                         
                           N 
                           + 
                           2 
                         
                         , 
                         … 
                            
                         , 
                         
                           
                             2 
                             ⁢ 
                             N 
                           
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #79 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             516 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                             - 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               
                                 x 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               x 
                               ) 
                             
                             - 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               x 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             - 
                             
                               
                                 2 
                                 ⁢ 
                                 π 
                               
                               N 
                             
                           
                           ) 
                         
                       
                       ⁢ 
                           
                       for 
                     
                   
                   ⁢ 
                       
                   
 
                   
                     ∀ 
                     
                       x 
                       ⁡ 
                       ( 
                       
                         
                           x 
                           = 
                           N 
                         
                         , 
                         
                           N 
                           + 
                           1 
                         
                         , 
                         
                           N 
                           + 
                           2 
                         
                         , 
                         … 
                            
                         , 
                         
                           
                             2 
                             ⁢ 
                             N 
                           
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #80 
                 
               
             
           
         
       
     
     The above arrangement ensures to reduce the number of poor reception points described in the other embodiments because one of the elements of precoding matrices is “0”. In addition, the reception device is enabled to improve reception quality because poor reception points are effectively avoided especially in an LOS environment. 
     In an alternative scheme to the above-described precoding scheme of regularly hopping between precoding matrices, θ 11 (i) is fixed, for example, to 0 radians (a fixed value not depending on i, and a value other than 0 radians may be applicable) and θ 11 (i) and θ 21 (i) satisfy the conditions described above. In another alternative scheme, θ 21 (i) instead of θ 11 (i) is fixed, for example, to 0 radians (a fixed value not depending on i, and a value other than 0 radians may be applicable) and θ 11 (i) and θ 21 (i) satisfy the conditions described above. 
     Similarly, in another alternative scheme, Ψ 11 (i) is fixed, for example, to 0 radians (a fixed value not depending on i, and a value other than 0 radians may be applicable) and Ψ 11 (i) and Ψ 21 (i) satisfy the conditions described above. Similarly, in another alternative scheme, Ψ 21 (i) instead of Ψ 11 (i) is fixed, for example, to 0 radians (a fixed value not depending on i, and a value other than 0 radians may be applicable) and Ψ 11 (i) and Ψ 21 (i) satisfy the conditions described above. 
     The present embodiment describes the scheme of structuring 2N different precoding matrices for a precoding hopping scheme with a 2N-slot time period (cycle). In this case, as the 2N different precoding matrices, F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] are prepared. In a single carrier transmission scheme, symbols are arranged in the order F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] in the time domain (or the frequency domain in the case of multi-carrier). However, this is not the only example, and the 2N different precoding matrices F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] generated in the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaption in this case, precoding weights may be changed by arranging symbols in the frequency domain or in the frequency-time domain. Note that a precoding hopping scheme with a 2N-slot time period (cycle) has been described, but the same advantageous effects may be obtained by randomly using 2N different precoding matrices. In other words, the 2N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots 2N in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the 2N different precoding matrices of the present embodiment are included, the probability of excellent reception quality increases. 
     Embodiment 25 
     The present embodiment describes a scheme for increasing the period (cycle) size of precoding hops between the precoding matrices, by applying Embodiment 17 to the precoding matrices described in Embodiment 23. 
     As described in Embodiment 23, in the scheme of regularly hopping between precoding matrices over a period (cycle) with N slots, the precoding matrices prepared for the N slots are represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             517 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     11 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             B 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     12 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             C 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     21 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           0 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   439 
                 
               
             
           
         
       
     
     Here, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). In addition, A, B, and C are fixed values not depending on i. Similarly, μ 11 , μ 12 , and μ 21  are fixed values not depending on i. Furthermore, the N×M period (cycle) precoding matrices based on Equation 439 are represented by the following equation. 
     
       
         
           
             Math 
             ⁢ 
                 
             518 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       
                         N 
                         × 
                         k 
                       
                       + 
                       i 
                     
                     ] 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     11 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             B 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     12 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             C 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     21 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   
                                     X 
                                     k 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           0 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   440 
                 
               
             
           
         
       
     
     Here, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). Precoding matrices F[0] to F[N×M−1] are thus generated (the precoding matrices F[0] to F[N×M−1] may be in any order for the N×M slots in the period (cycle)). Symbol number N×M×i may be precoded using F[0], symbol number N×M×i+1 may be precoded using F[1], . . . , and symbol number N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , N×M−2, N×M−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) 
     Generating the precoding matrices in this way achieves a precoding matrix hopping scheme with a large period (cycle), allowing for the position of poor reception points to be easily changed, which may lead to improved data reception quality. Note that while the N×M period (cycle) precoding matrices have been set to Equation 440, the N×M period (cycle) precoding matrices may be set to the following equation, as described above. 
     
       
         
           
                               
             
               Math 
               ⁢ 
                   
               519 
             
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       
                         N 
                         × 
                         k 
                       
                       + 
                       i 
                     
                     ] 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     11 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   
                                     X 
                                     k 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             B 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     12 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   
                                     X 
                                     k 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             C 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     21 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           0 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   441 
                 
               
             
           
         
       
     
     Here, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     As described in Embodiment 23, in the scheme of regularly hopping between precoding matrices over a period (cycle) with N slots that is different from the above-described N slots, the precoding matrices prepared for the N slots are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   520 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     11 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             B 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     12 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             D 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     22 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   442 
                 
               
             
           
         
       
     
     Here, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). In addition, A, B, and D are fixed values not depending on i. Similarly, μ 11 , μ 12 , and μ 22  are fixed values not depending on i. Furthermore, the N×M period (cycle) precoding matrices based on Equation 441 are represented by the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   521 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       
                         N 
                         × 
                         k 
                       
                       + 
                       i 
                     
                     ] 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     11 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             B 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     12 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             D 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     22 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   
                                     X 
                                     k 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   443 
                 
               
             
           
         
       
     
     Here, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     Precoding matrices F[0] to F[N×M−1] are thus generated (the precoding matrices F[0] to F[N×M−1] may be in any order for the N×M slots in the period (cycle)). Symbol number N×M×i may be precoded using F[0], symbol number N×M×i+1 may be precoded using F[1], . . . , and symbol number N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , N×M−2, N×M−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) 
     Generating the precoding matrices in this way achieves a precoding matrix hopping scheme with a large period (cycle), allowing for the position of poor reception points to be easily changed, which may lead to improved data reception quality. Note that while the N×M period (cycle) precoding matrices have been set to Equation 443, the N×M period (cycle) precoding matrices may be set to the following equation, as described above. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   522 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       
                         N 
                         × 
                         k 
                       
                       + 
                       i 
                     
                     ] 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     11 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   
                                     X 
                                     k 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             B 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     12 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   
                                     X 
                                     k 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             D 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     22 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   444 
                 
               
             
           
         
       
     
     Here, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     As described in Embodiment 23, in the scheme of regularly hopping between precoding matrices over a period (cycle) with N slots that is different from the above-described N slots, the precoding matrices prepared for the N slots are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   523 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     11 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           0 
                         
                       
                       
                         
                           
                             C 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     21 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             D 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     22 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   445 
                 
               
             
           
         
       
     
     Here, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). In addition, A, C, and D are fixed values not depending on i. Similarly, μ 11 , μ 21 , and μ 22  are fixed values not depending on i. Furthermore, the N×M period (cycle) precoding matrices based on Equation 445 are represented by the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   524 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       
                         N 
                         × 
                         k 
                       
                       + 
                       i 
                     
                     ] 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     11 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           0 
                         
                       
                       
                         
                           
                             C 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     21 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   
                                     X 
                                     k 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             D 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     22 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   
                                     X 
                                     k 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   446 
                 
               
             
           
         
       
     
     Here, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     Precoding matrices F[0] to F[N×M−1] are thus generated (the precoding matrices F[0] to F[N×M−1] may be in any order for the N×M slots in the period (cycle)). Symbol number N×M×i may be precoded using F[0], symbol number N×M×i+1 may be precoded using F[1], . . . , and symbol number N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , N×M−2, N×M−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) 
     Generating the precoding matrices in this way achieves a precoding matrix hopping scheme with a large period (cycle), allowing for the position of poor reception points to be easily changed, which may lead to improved data reception quality. Note that while the N×M period (cycle) precoding matrices have been set to Equation 446, the N×M period (cycle) precoding matrices may be set to the following equation, as described above. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   525 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       
                         N 
                         × 
                         k 
                       
                       + 
                       i 
                     
                     ] 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             A 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     11 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   
                                     X 
                                     k 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           0 
                         
                       
                       
                         
                           
                             C 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     21 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             D 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     22 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   447 
                 
               
             
           
         
       
     
     Here, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     As described in Embodiment 23, in the scheme of regularly hopping between precoding matrices over a period (cycle) with N slots that is different from the above-described N slots, the precoding matrices prepared for the N slots are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   526 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           0 
                         
                         
                           
                             B 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     12 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             C 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     21 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             D 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     22 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   448 
                 
               
             
           
         
       
     
     Here, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). In addition, B, C, and D are fixed values not depending on i. Similarly, μ 11 , μ 12 , μ 21 , and μ 22  are fixed values not depending on i. Furthermore, the N×M period (cycle) precoding matrices based on Equation 448 are represented by the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   527 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       
                         N 
                         × 
                         k 
                       
                       + 
                       i 
                     
                     ] 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           0 
                         
                         
                           
                             B 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     12 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             C 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     21 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   
                                     X 
                                     k 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             D 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     22 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   
                                     X 
                                     k 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   449 
                 
               
             
           
         
       
     
     Here, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     Precoding matrices F[0] to F[N×M−1] are thus generated (the precoding matrices F[0] to F[N×M−1] may be in any order for the N×M slots in the period (cycle)). Symbol number N×M×i may be precoded using F[0], symbol number N×M×i+1 may be precoded using F[1], . . . , and symbol number N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , N×M−2, N×M−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) 
     Generating the precoding matrices in this way achieves a precoding matrix hopping scheme with a large period (cycle), allowing for the position of poor reception points to be easily changed, which may lead to improved data reception quality. Note that while the N×M period (cycle) precoding matrices have been set to Equation 449, the N×M period (cycle) precoding matrices may be set to the following equation, as described above. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   528 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       
                         N 
                         × 
                         k 
                       
                       + 
                       i 
                     
                     ] 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           0 
                         
                         
                           
                             B 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     12 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   
                                     X 
                                     k 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             C 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     21 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             D 
                             × 
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     μ 
                                     22 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   450 
                 
               
             
           
         
       
     
     Here, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     The present embodiment describes the scheme of structuring N×M different precoding matrices for a precoding hopping scheme with N×M slots in the time period (cycle). In this case, as the N×M different precoding matrices, F[0], F[1], F[2], . . . , F[N×M−2], F[N×M−1] are prepared. In a single carrier transmission scheme, symbols are arranged in the order F[0], F[1], F[2], . . . , F[N×M−2], F[N×M−1] in the time domain (or the frequency domain in the case of multi-carrier). However, this is not the only example, and the N×M different precoding matrices F[0], F[1], F[2], . . . , F[N×M−2], F[N×M−1] generated in the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaption in this case, precoding weights may be changed by arranging symbols in the frequency domain or in the frequency-time domain. Note that a precoding hopping scheme with N×M slots in the time period (cycle) has been described, but the same advantageous effects may be obtained by randomly using N×M different precoding matrices. In other words, the N×M different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots N×M in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the N×M different precoding matrices of the present embodiment are included, the probability of excellent reception quality increases. 
     Embodiment 26 
     The present embodiment describes a scheme for increasing the period (cycle) size of precoding hops between the precoding matrices, by applying Embodiment 20 to the precoding matrices described in Embodiment 24. 
     In the scheme of regularly hopping between precoding matrices over a period (cycle) with 2N slots, the precoding matrices prepared for the 2N slots are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   529 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   451 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       A 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               11 
                             
                             + 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       B 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               12 
                             
                             + 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     
                       C 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               21 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     0 
                   
                 
               
               ) 
             
           
         
       
     
     Here, let A, B, and C be real numbers, and μ 11 , μ 12 , and μ 21  be real numbers expressed in radians. In addition, A, B, and C are fixed values not depending on i. Similarly, μ 11 , μ 12 , and μ 21  are fixed values not depending on i. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   530 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   452 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       α 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               11 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       β 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               12 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     0 
                   
                   
                     
                       δ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               21 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, let α, β, and δ be real numbers, and v 11 , v 12 , and v 22  be real numbers expressed in radians. In addition, α, β, and δ are fixed values not depending on i. Similarly, v 11 , v 12 , and v 22  are fixed values not depending on i. Furthermore, the 2×N×M period (cycle) precoding matrices based on Equations 451 and 452 are represented by the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   531 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   453 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       A 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               11 
                             
                             + 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       B 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               12 
                             
                             + 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     
                       C 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               21 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               X 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     0 
                   
                 
               
               ) 
             
           
         
       
     
     Here, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   532 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   454 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       α 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               11 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       β 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               12 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     0 
                   
                   
                     
                       δ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               21 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               Y 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). In addition, Xk=Yk may be true or Xk≠Yk may be true. 
     Precoding matrices F[0] to F[2×N×M−1] are thus generated (the precoding matrices F[0] to F[2×N×M−1] may be in any order for the 2×N×M slots in the period (cycle)). Symbol number 2×N×M×i may be precoded using F[0], symbol number 2×N×M×i+1 may be precoded using F[1], . . . , and symbol number 2×N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , 2×N×M−2, 2×N×M−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) 
     Generating the precoding matrices in this way achieves a precoding matrix hopping scheme with a large period (cycle), allowing for the position of poor reception points to be easily changed, which may lead to improved data reception quality. 
     The 2×N×M period (cycle) precoding matrices in Equation 453 may be changed to the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   533 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   455 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       A 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               11 
                             
                             + 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               X 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       B 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               12 
                             
                             + 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               X 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     
                       C 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               21 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     0 
                   
                 
               
               ) 
             
           
         
       
     
     Here, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     The 2×N×M period (cycle) precoding matrices in Equation 454 may be changed to the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   532 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   454 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       α 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               11 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               Y 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       β 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               12 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               Y 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     0 
                   
                   
                     
                       δ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               21 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     Another example is shown below. In the scheme of regularly hopping between precoding matrices over a period (cycle) with 2N slots, the precoding matrices prepared for the 2N slots are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   535 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   457 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       A 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               11 
                             
                             + 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       B 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               12 
                             
                             + 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     
                       C 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               21 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     0 
                   
                 
               
             
           
         
       
     
     Here, let A, B, and C be real numbers, and μ 11 , μ 12 , and μ 21  be real numbers expressed in radians. In addition, A, B, and C are fixed values not depending on i. Similarly, μ 11 , μ 12 , and μ 21  are fixed values not depending on i. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   536 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   458 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               ( 
               
                 
                   
                     0 
                   
                   
                     
                       β 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               12 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     
                       γ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               21 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       δ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               22 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, let β, γ, and δ be real numbers, and v 12 , v 21 , and v 22  be real numbers expressed in radians. In addition, β, γ, and δ are fixed values not depending on i. Similarly, v 12 , v 21 , and v 22  are fixed values not depending on i. Furthermore, the 2×N×M period (cycle) precoding matrices based on Equations 457 and 458 are represented by the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   537 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   459 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       A 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               11 
                             
                             + 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       B 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               12 
                             
                             + 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     
                       C 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               21 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               X 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     0 
                   
                 
               
               ) 
             
           
         
       
     
     Here, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   538 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   460 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               ( 
               
                 
                   
                     0 
                   
                   
                     
                       β 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               12 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     
                       γ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               21 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               Y 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       δ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               22 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               Y 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). Furthermore, Xk=Yk may be true, or Xk≠Yk may be true. 
     Precoding matrices F[0] to F[2×N×M−1] are thus generated (the precoding matrices F[0] to F[2×N×M−1] may be in any order for the 2×N×M slots in the period (cycle)). Symbol number 2×N×M×i may be precoded using F[0], symbol number 2×N×M×i+1 may be precoded using F[1], . . . , and symbol number 2×N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , 2×N×M−2, 2×N×M−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) 
     Generating the precoding matrices in this way achieves a precoding matrix hopping scheme with a large period (cycle), allowing for the position of poor reception points to be easily changed, which may lead to improved data reception quality. 
     The 2×N×M period (cycle) precoding matrices in Equation 459 may be changed to the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   539 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   461 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       A 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               11 
                             
                             + 
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 i 
                                 ) 
                               
                               ⁢ 
                               
                                 X 
                                 k 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       B 
                       × 
                       
                         
                           e 
                           j 
                         
                         ( 
                         
                           
                             μ 
                             12 
                           
                           + 
                           
                             
                               θ 
                               11 
                             
                             ( 
                             i 
                             ) 
                           
                           + 
                           
                             X 
                             k 
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     
                       C 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               21 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     0 
                   
                 
               
               ) 
             
           
         
       
     
     Here, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     The 2×N×M period (cycle) precoding matrices in Equation 460 may be changed to the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   540 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   462 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               ( 
               
                 
                   
                     0 
                   
                   
                     
                       β 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               12 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               Y 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     
                       γ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               21 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       δ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               22 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     Another example is shown below. In the scheme of regularly hopping between precoding matrices over a period (cycle) with 2N slots, the precoding matrices prepared for the 2N slots are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   541 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   463 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       A 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               11 
                             
                             + 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     0 
                   
                 
                 
                   
                     
                       C 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               21 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       D 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               22 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, let A, C, and D be real numbers, and μ 11 , μ 21 , and μ 22  be real numbers expressed in radians. In addition, A, C, and D are fixed values not depending on i. Similarly, μ 11 , μ 21 , and μ 22  are fixed values not depending on i. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   542 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   464 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       α 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               11 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       β 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               12 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     0 
                   
                   
                     
                       δ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               22 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, let α, β, and δ be real numbers, and v 11 , v 12 , and v 22  be real numbers expressed in radians. In addition, α, β, and δ are fixed values not depending on i. Similarly, v 11 , v 12 , and v 22  are fixed values not depending on i. Furthermore, the 2×N×M period (cycle) precoding matrices based on Equations 463 and 464 are represented by the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   543 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   465 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       A 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               11 
                             
                             + 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     0 
                   
                 
                 
                   
                     
                       C 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               21 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               X 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       D 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               22 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               X 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   544 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   466 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       α 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               11 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       β 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               12 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     0 
                   
                   
                     
                       δ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               22 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               Y 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). Furthermore, Xk=Yk may be true, or Xk≠Yk may be true. 
     Precoding matrices F[0] to F[2×N×M−1] are thus generated (the precoding matrices F[0] to F[2×N×M−1] may be in any order for the 2×N×M slots in the period (cycle)). Symbol number 2×N×M×i may be precoded using F[0], symbol number 2×N×M×i+1 may be precoded using F[1], . . . , and symbol number 2×N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , 2×N×M−2, 2×N×M−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) 
     Generating the precoding matrices in this way achieves a precoding matrix hopping scheme with a large period (cycle), allowing for the position of poor reception points to be easily changed, which may lead to improved data reception quality. 
     The 2×N×M period (cycle) precoding matrices in Equation 465 may be changed to the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   545 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   467 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       A 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               11 
                             
                             + 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               X 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     0 
                   
                 
                 
                   
                     
                       C 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               21 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       D 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               22 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     The 2×N×M period (cycle) precoding matrices in Equation 466 may be changed to the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   546 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   468 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       α 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               11 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               Y 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       β 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               12 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               Y 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     0 
                   
                   
                     
                       δ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               22 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     Another example is shown below. In the scheme of regularly hopping between precoding matrices over a period (cycle) with 2N slots, the precoding matrices prepared for the 2N slots are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   547 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   469 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       A 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               11 
                             
                             + 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     0 
                   
                 
                 
                   
                     
                       C 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               21 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       D 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               22 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, let A, C, and D be real numbers, and μ 11 , μ 21 , and μ 22  be real numbers expressed in radians. In addition, A, C, and D are fixed values not depending on i. Similarly, μ 11 , μ 21 , and μ 22  are fixed values not depending on i. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   548 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   470 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               i 
               ] 
             
             = 
             
               ( 
               
                 
                   
                     0 
                   
                   
                     
                       β 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               12 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     
                       γ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               21 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       δ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               v 
                               22 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, let β, γ, and δ be real numbers, and v 12 , v 21 , and v 22  be real numbers expressed in radians. In addition, β, γ, and δ are fixed values not depending on i. Similarly, v 12 , v 21 , and v 22  are fixed values not depending on i. Furthermore, the 2×N×M period (cycle) precoding matrices based on Equations 469 and 470 are represented by the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   549 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   471 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       A 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               11 
                             
                             + 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     0 
                   
                 
                 
                   
                     
                       C 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               21 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               X 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       D 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               22 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               X 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     
       
         
           
             Math 
             ⁢ 
                 
             550 
           
         
       
       
         
           
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   472 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               ( 
               
                 
                   
                     0 
                   
                   
                     
                       β 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               12 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     
                       γ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               21 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               Y 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       δ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               22 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               Y 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). Furthermore, Xk=Yk may be true, or Xk≠Yk may be true. 
     Precoding matrices F[0] to F[2×N×M−1] are thus generated (the precoding matrices F[0] to F[2×N×M−1] may be in any order for the 2×N×M slots in the period (cycle)). Symbol number 2×N×M×i may be precoded using F[0], symbol number 2×N×M×i+1 may be precoded using F[1], . . . , and symbol number 2×N×M×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , 2×N×M−2, 2×N×M−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) 
     Generating the precoding matrices in this way achieves a precoding matrix hopping scheme with a large period (cycle), allowing for the position of poor reception points to be easily changed, which may lead to improved data reception quality. 
     The 2×N×M period (cycle) precoding matrices in Equation 471 may be changed to the following equation. 
     
       
         
           
             Math 
             ⁢ 
                 
             551 
           
         
       
       
         
           
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     0 
                   
                   , 
                   1 
                   , 
                   2 
                   , 
                   … 
                       
                   , 
                   
                     N 
                     - 
                     2 
                   
                   , 
                   
                     N 
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   473 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               ( 
               
                 
                   
                     
                       A 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               11 
                             
                             + 
                             
                               
                                 θ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               X 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     0 
                   
                 
                 
                   
                     
                       C 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               21 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       D 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               μ 
                               22 
                             
                             + 
                             
                               
                                 θ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     The 2×N×M period (cycle) precoding matrices in Equation 472 may be changed to the following equation. 
     
       
         
           
             Math 
             ⁢ 
                 
             552 
           
         
       
       
         
           
             
               
                 
                   
                     
                       For 
                       ⁢ 
                           
                       i 
                     
                     = 
                     N 
                   
                   , 
                   
                     N 
                     + 
                     1 
                   
                   , 
                   
                     N 
                     + 
                     2 
                   
                   , 
                   … 
                       
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     2 
                   
                   , 
                   
                     
                       2 
                       ⁢ 
                       N 
                     
                     - 
                     
                       1 
                       : 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   474 
                 
               
             
           
         
       
       
         
           
             
               F 
               [ 
               
                 
                   2 
                   × 
                   N 
                   × 
                   k 
                 
                 + 
                 i 
               
               ] 
             
             = 
             
               ( 
               
                 
                   
                     0 
                   
                   
                     
                       β 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               12 
                             
                             + 
                             
                               
                                 ψ 
                                 11 
                               
                               ( 
                               i 
                               ) 
                             
                             + 
                             
                               Y 
                               k 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     
                       γ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               21 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       δ 
                       × 
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             
                               ν 
                               22 
                             
                             + 
                             
                               
                                 ψ 
                                 21 
                               
                               ( 
                               i 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     Here, k=0, 1, . . . , M−2, M−1 (k being an integer in a range of 0 to M−1). 
     Focusing on poor reception points in the above examples, the following conditions are important.
 
Math 553
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #81
 
     (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
Math 554
 
 e   j(ψ     11     (x)−ψ     21     (x))   ≠e   j(ψ     11     (y)−ψ     21     (y))  for ∀ x,∀y  ( x≠y;x,y=N,N+ 1 ,N+ 2, . . . ,2 N− 2,2 N− 1)   Condition #82
 
     (x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . 2N−2, 2N−1 (each of x and y being an integer in a range of N to 2N−1); and x≠y.)
 
Math 555
 
θ 11 ( x )=θ 11 ( x+N ) for ∀ x  ( x= 0,1,2, . . . , N− 2, N− 1)
 
and
 
θ 21 ( y )=θ 21 ( y+N ) for ∀ y  ( y= 0,1,2, . . . , N− 2, N− 1)  Condition #83
 
Math 556
 
ψ 11 ( x )=ψ 11 ( x+N ) for ∀ x  ( x=N,N+ 1 ,N+ 2, . . . ,2 N− 2,2 N− 1)
 
and
 
ψ 21 ( y )=ψ 21 ( y+N ) for ∀ y  ( y=N,N+ 1 ,N+ 2, . . . ,2 N− 2,2 N− 1)  Condition #84
 
     By satisfying the conditions shown above, excellent data reception quality is achieved. Furthermore, the following conditions should be satisfied (See Embodiment 24).
 
Math 557
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #85
 
     (x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1 (each of x and y being an integer in a range of 0 to N−1); and x≠y.)
 
Math 558
 
 e   j(ψ     11     (x)−ψ     21     (x))   ≠e   j(ψ     11     (y)−ψ     21     (y))  for ∀ x,∀y  ( x≠y;x,y=N,N+ 1 ,N+ 2, . . . ,2 N− 2,2 N− 1)   Condition #86
 
     (x is N, N+1, N+2, . . . , 2N−2, 2N−1; y is N, N+1, N+2, . . . , 2N−2, 2N−1 (each of x and y being an integer in a range of N to 2N−1); and x≠y.) 
     Focusing on Xk and Yk, the following conditions are noted.
 
Math 559
 
 X   a   ≠X   b +2× s ×π for ∀ a,∀b  ( a≠b;a,b= 0,1,2, . . . , M− 2, M− 1)  Condition #87
 
     (a is 0, 1, 2, . . . , M−2, M−1; b is 0, 1, 2, . . . , M−2, M−1 (each of a and b being an integer in a range of 0 to M−1); and a≠b.) 
     Here, s is an integer.
 
Math 560
 
 Y   a   ≠Y   b +2× u ×π for ∀ a,∀b  ( a≠b;a,b= 0,1,2, . . . , M− 2, M− 1)  Condition #88
 
     (a is 0, 1, 2, . . . , M−2, M−1; b is 0, 1, 2, . . . , M−2, M−1 (each of a and b being an integer in a range of 0 to M−1); and a≠b.) 
     (Here, u is an integer.) 
     By satisfying the two conditions shown above, excellent data reception quality is achieved. In Embodiment 25, Condition #87 should be satisfied. 
     The present embodiment describes the scheme of structuring 2×N×M different precoding matrices for a precoding hopping scheme with 2N×M slots in the time period (cycle). In this case, as the 2×N×M different precoding matrices, F[0], F[1], F[2], . . . , F[2×N×M−2], F[2×N×M−1] are prepared. In a single carrier transmission scheme, symbols are arranged in the order F[0], F[1], F[2], . . . , F[2×N×M−2], F[2×N×M−1] in the time domain (or the frequency domain in the case of multi-carrier). However, this is not the only example, and the 2×N×M different precoding matrices F[0], F[1], F[2], . . . , F[2×N×M−2], F[2×N×M−1] generated in the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaption in this case, precoding weights may be changed by arranging symbols in the frequency domain or in the frequency-time domain. Note that a precoding hopping scheme with 2×N×M slots the time period (cycle) has been described, but the same advantageous effects may be obtained by randomly using 2×N×M different precoding matrices. In other words, the 2×N×M different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots 2×N×M in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the 2×N×M different precoding matrices of the present embodiment are included, the probability of excellent reception quality increases. 
     Embodiment A1 
     In the present embodiment, a detailed description is given of a scheme for adapting the above-described transmission schemes that regularly hops between precoding matrices to a communications system compliant with the DVB (Digital Video Broadcasting)-T2 (T: Terrestrial) standard (DVB for a second generation digital terrestrial television broadcasting system). 
       FIG.  61    is an overview of the frame structure of a signal a signal transmitted by a broadcast station according to the DVB-T2 standard. According to the DVB-T2 standard, an OFDM scheme is employed. Thus, frames are structured in the time and frequency domains.  FIG.  61    shows the frame structure in the time and frequency domains. The frame is composed of P1 Signalling data ( 6101 ), L1 Pre-Signalling data ( 6102 ), L1 Post-Signalling data ( 6103 ), Common PLP ( 6104 ), and PLPs # 1  to #N ( 6105 _ 1  to  6105 _N) (PLP: Physical Layer Pipe). (Here, L1 Pre-Signalling data ( 6102 ) and L1 Post-Signalling data ( 6103 ) are referred to as P2 symbols.) As above, the frame composed of P1 Signalling data ( 6101 ), L1 Pre-Signalling data ( 6102 ), L1 Post-Signalling data ( 6103 ), Common PLP ( 6104 ), and PLPs # 1  to #N ( 6105 _ 1  to  6105 _N) is referred to as a T2 frame, which is a unit of frame structure. 
     The P1 Signalling data ( 6101 ) is a symbol for use by a reception device for signal detection and frequency synchronization (including frequency offset estimation). Also, the P1 Signalling data ( 6101 ) transmits information including information indicating the FFT (Fast Fourier Transform) size, and information indicating which of SISO (Single-Input Single-Output) and MISO (Multiple-Input Single-Output) is employed to transmit a modulated signal. (The SISO scheme is for transmitting one modulated signal, whereas the MISO scheme is for transmitting a plurality of modulated signals using space-time block coding.) 
     The L1 Pre-Signalling data ( 6102 ) transmits information including: information about the guard interval used in transmitted frames; information about PAPR (Peak to Average Power Ratio) method; information about the modulation scheme, error correction scheme (FEC: Forward Error Correction), and coding rate of the error correction scheme all used in transmitting L1 Post-Signalling data; information about the size of L1 Post-Signalling data and the information size; information about the pilot pattern; information about the cell (frequency region) unique number; and information indicating which of the normal mode and extended mode (the respective modes differs in the number of subcarriers used in data transmission) is used. 
     The L1 Post-Signalling data ( 6103 ) transmits information including: information about the number of PLPs; information about the frequency region used; information about the unique number of each PLP; information about the modulation scheme, error correction scheme, coding rate of the error correction scheme all used in transmitting the PLPs; and information about the number of blocks transmitted in each PLP. 
     The Common PLP ( 6104 ) and PLPs # 1  to #N ( 6105 _ 1  to  6105 N) are fields used for transmitting data. 
     In the frame structure shown in  FIG.  61   , the P1 Signalling data ( 6101 ), L1 Pre-Signalling data ( 6102 ), L1 Post-Signalling data ( 6103 ), Common PLP ( 6104 ), and PLPs # 1  to #N ( 6105 _ 1  to  6105 _N) are illustrated as being transmitted by time-sharing. In practice, however, two or more of the signals are concurrently present.  FIG.  62    shows such an example. As shown in  FIG.  62   , L1 Pre-Signalling data, L1 Post-Signalling data, and Common PLP may be present at the same time, and PLP # 1  and PLP # 2  may be present at the same time. That is, the signals constitute a frame using both time-sharing and frequency-sharing. 
       FIG.  63    shows an example of the structure of a transmission device obtained by applying the above-described schemes of regularly hopping between precoding matrices to a transmission device compliant with the DVB-T2 standard (i.e., to a transmission device of a broadcast station). A PLP signal generating unit  6302  receives PLP transmission data (transmission data for a plurality of PLPs)  6301  and a control signal  6309  as input, performs mapping of each PLP according to the error correction scheme and modulation scheme indicated for the PLP by the information included in the control signal  6309 , and outputs a (quadrature) baseband signal  6303  carrying a plurality of PLPs. 
     A P2 symbol signal generating unit  6305  receives P2 symbol transmission data  6304  and the control signal  6309  as input, performs mapping according to the error correction scheme and modulation scheme indicated for each P2 symbol by the information included in the control signal  6309 , and outputs a (quadrature) baseband signal  6306  carrying the P2 symbols. 
     A control signal generating unit  6308  receives P1 symbol transmission data  6307  and P2 symbol transmission data  6304  as input, and then outputs, as the control signal  6309 , information about the transmission scheme (the error correction scheme, coding rate of the error correction, modulation scheme, block length, frame structure, selected transmission schemes including a transmission scheme that regularly hops between precoding matrices, pilot symbol insertion scheme, IFFT (Inverse Fast Fourier Transform)/FFT, method of reducing PAPR, and guard interval insertion scheme) of each symbol group shown in  FIG.  61    (P1 Signalling data ( 6101 ), L1 Pre-Signalling data ( 6102 ), L1 Post-Signalling data ( 6103 ), Common PLP ( 6104 ), PLPs # 1  to #N ( 6105 _ 1  to  6105 _N)). A frame structuring unit  6310  receives, as input, the baseband signal  6303  carrying PLPs, the baseband signal  6306  carrying P2 symbols, and the control signal  6309 . On receipt of the input, the frame structuring unit  6310  changes the order of input data in frequency domain and time domain based on the information about frame structure included in the control signal, and outputs a (quadrature) baseband signal  6311 _ 1  corresponding to stream  1  and a (quadrature) baseband signal  6311 _ 2  corresponding to stream  2  both in accordance with the frame structure. 
     A signal processing unit  6312  receives, as input, the baseband signal  6311 _ 1  corresponding to stream  1 , the baseband signal  6311 _ 2  corresponding to stream  2 , and the control signal  6309  and outputs a modulated signal  1  ( 6313 _ 1 ) and a modulated signal  2  ( 6313 _ 2 ) each obtained as a result of signal processing based on the transmission scheme indicated by information included in the control signal  6309 . The characteristic feature noted here lies in the following. That is, when a transmission scheme that regularly hops between precoding matrices is selected, the signal processing unit hops between precoding matrices and performs weighting (precoding) in a manner similar to  FIGS.  6 ,  22 ,  23 , and  26   . Thus, precoded signals so obtained are the modulated signal  1  ( 6313 _ 1 ) and modulated signal  2  ( 6313 _ 2 ) obtained as a result of the signal processing. 
     A pilot inserting unit  6314 _ 1  receives, as input, the modulated signal  1  ( 6313 _ 1 ) obtained as a result of the signal processing and the control signal  6309 , inserts pilot symbols into the received modulated signal  1  ( 6313 _ 1 ), and outputs a modulated signal  6315 _ 1  obtained as a result of the pilot signal insertion. Note that the pilot symbol insertion is carried out based on information indicating the pilot symbol insertion scheme included the control signal  6309 . 
     A pilot inserting unit  6314 _ 2  receives, as input, the modulated signal  2  ( 6313 _ 2 ) obtained as a result of the signal processing and the control signal  6309 , inserts pilot symbols into the received modulated signal  2  ( 6313 _ 2 ), and outputs a modulated signal  6315 _ 2  obtained as a result of the pilot symbol insertion. Note that the pilot symbol insertion is carried out based on information indicating the pilot symbol insertion scheme included the control signal  6309 . 
     An IFFT (Inverse Fast Fourier Transform) unit  6316 _ 1  receives, as input, the modulated signal  6315 _ 1  obtained as a result of the pilot symbol insertion and the control signal  6309 , and applies IFFT based on the information about the IFFT method included in the control signal  6309 , and outputs a signal  6317 _ 1  obtained as a result of the IFFT. 
     An IFFT unit  6316 _ 2  receives, as input, the modulated signal  6315 _ 2  obtained as a result of the pilot symbol insertion and the control signal  6309 , and applies IFFT based on the information about the IFFT method included in the control signal  6309 , and outputs a signal  6317 _ 2  obtained as a result of the IFFT. 
     A PAPR reducing unit  6318 _ 1  receives, as input, the signal  6317 _ 1  obtained as a result of the IFFT and the control signal  6309 , performs processing to reduce PAPR on the received signal  6317 _ 1 , and outputs a signal  6319 _ 1  obtained as a result of the PAPR reduction processing. Note that the PAPR reduction processing is performed based on the information about the PAPR reduction included in the control signal  6309 . 
     A PAPR reducing unit  6318 _ 2  receives, as input, the signal  6317 _ 2  obtained as a result of the IFFT and the control signal  6309 , performs processing to reduce PAPR on the received signal  6317 _ 2 , and outputs a signal  6319 _ 2  obtained as a result of the PAPR reduction processing. Note that the PAPR reduction processing is carried out based on the information about the PAPR reduction included in the control signal  6309 . 
     A guard interval inserting unit  6320 _ 1  receives, as input, the signal  6319 _ 1  obtained as a result of the PAPR reduction processing and the control signal  6309 , inserts guard intervals into the received signal  6319 _ 1 , and outputs a signal  6321 _ 1  obtained as a result of the guard interval insertion. Note that the guard interval insertion is carried out based on the information about the guard interval insertion scheme included in the control signal  6309 . 
     A guard interval inserting unit  6320 _ 2  receives, as input, the signal  6319 _ 2  obtained as a result of the PAPR reduction processing and the control signal  6309 , inserts guard intervals into the received signal  6319 _ 2 , and outputs a signal  6321 _ 2  obtained as a result of the guard interval insertion. Note that the guard interval insertion is carried out based on the information about the guard interval insertion scheme included in the control signal  6309 . 
     A P1 symbol inserting unit  6322  receives, as input, the signal  6321 _ 1  obtained as a result of the guard interval insertion, the signal  6321 _ 2  obtained as a result of the guard interval insertion, and the P1 symbol transmission data  6307 , generates a P1 symbol signal from the P1 symbol transmission data  6307 , adds the P1 symbol to the signal  6321 _ 1  obtained as a result of the guard interval insertion, and adds the P1 symbol to the signal  6321 _ 2  obtained as a result of the guard interval insertion. Then, the P1 symbol inserting unit  6322  outputs a signal  6323 _ 1  obtained as a result of the processing related to P1 symbol and a signal  6323 _ 2  obtained as a result of the processing related to P1 symbol. Note that a P1 symbol signal may be added to both the signals  6323 _ 1  and  6323 _ 2  or to one of the signals  6323 _ 1  and  6323 _ 2 . In the case where the P1 symbol signal is added to one of the signals  6323 _ 1  and  6323 _ 2 , the following is noted. For purposes of description, an interval of the signal to which a P1 symbol is added is referred to as a P1 symbol interval. Then, the signal to which a P1 signal is not added includes, as a baseband signal, a zero signal in an interval corresponding to the P1 symbol interval of the other signal. A wireless processing unit  6324 _ 1  receives the signal  6323 _ 1  obtained as a result of the processing related to P1 symbol, performs processing such as frequency conversion, amplification, and the like, and outputs a transmission signal  6325 _ 1 . The transmission signal  6325 _ 1  is then output as a radio wave from an antenna  6326 _ 1 . 
     A wireless processing unit  6324 _ 2  receives the signal  6323 _ 2  obtained as a result of the processing related to P1 symbol, performs processing such as frequency conversion, amplification, and the like, and outputs a transmission signal  6325 _ 2 . The transmission signal  6325 _ 2  is then output as a radio wave from an antenna  6326 _ 2 . 
     Next, a detailed description is given of the frame structure of a transmission signal and the transmission scheme of control information (information carried by the P1 symbol and P2 symbols) employed by a broadcast station (base station) in the case where the scheme of regularly hopping between precoding matrices is adapted to a DVB-T2 system. 
       FIG.  64    shows an example of the frame structure in the time and frequency domains, in the case where a plurality of PLPs are transmitted after transmission of P1 symbol, P2 symbols, and Common PLP. In  FIG.  64   , stream s 1  uses subcarriers # 1  to #M in the frequency domain. Similarly, stream s 2  uses subcarriers # 1  to #M in the frequency domain. Therefore, when streams s 1  and s 2  both have a symbol in the same subcarrier and at the same time, symbols of the two streams are present at the same frequency. In the case where precoding performed includes the precoding according to the scheme for regularly hopping between precoding matrices as described in the other embodiments, streams s 1  and s 2  are subjected to weighting performed using the precoding matrices and z 1  and z 2  are output from the respective antennas. 
     As shown in  FIG.  64   , in interval  1 , a symbol group  6401  of PLP # 1  is transmitted using streams s 1  and s 2 , and the data transmission is carried out using the spatial multiplexing MIMO system shown in  FIG.  49    or the MIMO system with a fixed precoding matrix. 
     In interval  2 , a symbol group  6402  of PLP # 2  is transmitted using stream s 1 , and the data transmission is carried out by transmitting one modulated signal. 
     In interval  3 , a symbol group  6403  of PLP # 3  is transmitted using streams s 1  and s 2 , and the data transmission is carried out using a precoding scheme of regularly hopping between precoding matrices. 
     In interval  4 , a symbol group  6404  of PLP # 4  is transmitted using streams s 1  and s 2 , and the data transmission is carried out using space-time block coding shown in  FIG.  50   . Note that the symbol arrangement used in space-time block coding is not limited to the arrangement in the time domain. Alternatively, the symbol arrangement may be in the frequency domain or in symbol groups formed in the time and frequency domains. In addition, the space-time block coding is not limited to the one shown in  FIG.  50   . 
     In the case where a broadcast station transmits PLPs in the frame structure shown in  FIG.  64   , a reception device receiving the transmission signal shown in  FIG.  64    needs to know the transmission scheme used for each PLP. As has been already described above, it is therefore necessary to transmit information indicating the transmission scheme for each PLP, using L1 Post-Signalling data ( 6103  shown in  FIG.  61   ), which is a P2 symbol. The following describes an example of the scheme of structuring a P1 symbol used herein and the scheme of structuring a P2 symbol used herein. 
     Table 3 shows a specific example of control information transmitted using a P1 symbol. 
     
       
         
           
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
             
            
               
                   
                 S1 
                 000: T2_SISO (One modulated signal transmission compliant  
               
               
                   
                   
                 with DVB-T2 standard) 
               
               
                   
                   
                 001: T2_MISO (Transmission using space-time block coding  
               
               
                   
                   
                 compliant with DVB-T2 standard) 
               
               
                   
                   
                 010: NOT_T2 (compliant with standard other than DVB-T2) 
               
               
                   
               
            
           
         
       
     
     According to the DVB-T2 standard, the control information S1 (three bits) enables the reception device to determine whether or not the DVB-T2 standard is used and also to determine, if DVB-T2 is used, which transmission scheme is used. If the three bits are set to “000”, the S1 information indicates that the modulated signal transmitted in accordance with “transmission of a modulated signal compliant with the DVB-T2 standard”. 
     If the three bits are set to “001”, the S1 information indicates that the modulated signal transmitted is in accordance with “transmission using space-time block coding compliant with the DVB-T2 standard”. 
     In the DVB-T2 standard, the bit sets “010” to “111” are “Reserved” for future use. In order to adapt the present invention in a manner to establish compatibility with the DVB-T2, the three bits constituting the S1 information may be set to “010” (or any bit set other than “000” and “001”) to indicate that the modulated signal transmitted is compliant with a standard other than DVB-T2. On determining that the S1 information received is set to “010”, the reception device is informed that the modulated signal transmitted from the broadcast station is compliant with a standard other than DVB-T2. 
     Next, a description is given of examples of the scheme of structuring a P2 symbol in the case where a modulated signal transmitted by the broadcast station is compliant with a standard other than DVB-T2. The first example is directed to a scheme in which P2 symbol compliant with the DVB-T2 standard is used. 
     Table 4 shows a first example of control information transmitted using L1 Post-Signalling data, which is one of P2 symbols. 
     
       
         
           
               
               
             
               
                 TABLE 4 
               
               
                   
               
             
            
               
                 PLP_MODE 
                 00: SISO/SIMO 
               
               
                 (2 bits) 
                 01: MISO/MIMO (Space-time block code) 
               
               
                   
                 10: MIMO (Precoding scheme of regularly hopping  
               
               
                   
                 between precoding matrices) 
               
               
                   
                 11: MIMO (MIMO system with fixed preceding matrix  
               
               
                   
                 or Spatial multiplexing MIMO system) 
               
               
                   
               
            
           
         
       
     
     SISO: Single-Input Single-Output (one modulated signal is transmitted and receive with one antenna) 
     SIMO: Single-Input Multiple-Output (one modulated signal is transmitted and received with a plurality of antennas) 
     MISO: Multiple-Input Single-Output (a plurality of modulated signals are transmitted from a plurality of antennas and received with one antenna) 
     MIMO: Multiple-Input Multiple-Output (a plurality of modulated signals are transmitted from a plurality of antennas and received with a plurality of antennas) 
     The 2-bit information “PLP_MODE” shown in Table 4 is control information used to indicate the transmission scheme used for each PLP as shown in  FIG.  64    (PLPs # 1  to # 4  in  FIG.  64   ). That is, a separate piece of “PLP_MODE” information is provided for each PLP. That is, in the example shown in  FIG.  64   , PLP_MODE for PLP # 1 , PLP_MODE for PLP # 2 , PLP_MODE for PLP # 3 , PLP_MODE for PLP # 4  . . . are transmitted from the broadcast station. As a matter of course, by demodulating (and also performing error correction) those pieces of information, the terminal at the receiving end is enabled to recognize the transmission scheme that the broadcast station used for transmitting each PLP. 
     When the PLP_MODE is set to “00”, the data transmission by a corresponding PLP is carried out by “transmitting one modulated signal”. When the PLP_MODE is set to “01”, the data transmission by a corresponding PLP is carried out by “transmitting a plurality of modulated signals obtained by space-time block coding”. When the PLP_MODE is set to “10”, the data transmission by a corresponding PLP is carried out using a “precoding scheme of regularly hopping between precoding matrices”. When the PLP_MODE is set to “11”, the data transmission by a corresponding PLP is carried out using a “MIMO system with a fixed precoding matrix or spatial multiplexing MIMO system”. 
     Note that when the PLP_MODE is set to “01” to “11”, the information indicating the specific processing conducted by the broadcast station (for example, the specific hopping scheme used in the scheme of regularly hopping between precoding matrices, the specific space-time block coding scheme used, and the structure of precoding matrices used) needs to be notified to the terminal. The following describes the scheme of structuring control information that includes such information and that is different from the example shown in Table 4. 
     Table 5 shows a second example of control information transmitted using L1 Post-Signalling data, which is one of P2 symbols. The second example shown in Table 5 is different from the first example shown in Table 4. 
     
       
         
           
               
               
             
               
                 TABLE 5 
               
               
                   
               
             
            
               
                 PLP_MODE  
                 0: SISO/SIMO 
               
               
                 (1 bit) 
                 1: MISO/MIMO 
               
               
                   
                 (Space-time block coding, or 
               
               
                   
                 Precoding scheme of regularly hopping between 
               
               
                   
                 precoding matrices, or 
               
               
                   
                 MIMO system with fixed precoding matrix, or 
               
               
                   
                 Spatial multiplexing MIMO system) 
               
               
                 MIMO_MODE  
                 0: Precoding scheme of regularly hopping between 
               
               
                 (1 bit) 
                 precoding matrices --- OFF 
               
               
                   
                 1: Precoding scheme of regularly hopping between 
               
               
                   
                 precoding matrices --- ON 
               
               
                 MIMO_  
                 00: Space-time block coding 
               
               
                 PATTERN 
                 01: MIMO system with fixed precoding matrix and 
               
               
                 #1 (2 bits) 
                 Precoding matrix #1 
               
               
                   
                 10: MIMO system with fixed precoding matrix and 
               
               
                   
                 Precoding matrix #2 
               
               
                   
                 11: Spatial multiplexing MIMO system 
               
               
                 MIMO_  
                 00: Precoding scheme of regularly hopping between 
               
               
                 PATTERN 
                 precoding matrices, using precoding matrix hopping 
               
               
                 #2 (2 bits) 
                 scheme #1 
               
               
                   
                 01: Precoding scheme of regularly hopping between 
               
               
                   
                 precoding matrices, using precoding matrix hopping 
               
               
                   
                 scheme #2 
               
               
                   
                 10: Precoding scheme of regularly hopping between 
               
               
                   
                 recoding matrices, using precoding matrix hopping 
               
               
                   
                 scheme #3 
               
               
                   
                 11: Precoding scheme of regularly hopping between 
               
               
                   
                 precoding matrices, using precoding matrix hopping 
               
               
                   
                 scheme #4 
               
               
                   
               
            
           
         
       
     
     As shown in Table 5, the control information includes “PLP_MODE” which is one bit long, “MIMO_MODE” which is one bit long, “MIMO_PATTERN # 1 ” which is two bits long, and “MIMO_PATTERN # 2 ” which is two bits long. As shown in  FIG.  64   , these four pieces of control information is to notify the transmission scheme of a corresponding one of PLPs (PLPs # 1  to # 4  in the example shown in  FIG.  64   ). Thus, a set of four pieces of information is provided for each PLP. That is, in the example shown in  FIG.  64   , the broadcast station transmits a set of PLP_MODE information, MIMO_MODE information, MIMO_PATTERN # 1  information, and MIMO_PATTERN # 2  information for PLP # 1 , a set of PLP_MODE information, MIMO_MODE information, MIMO_PATTERN # 1  information, and MIMO_PATTERN # 2  information for PLP # 2 , a set of PLP_MODE information, MIMO_MODE information, MIMO_PATTERN # 1  information, and MIMO_PATTERN # 2  information for PLP # 3 , a set of PLP_MODE information, MIMO_MODE information, MIMO_PATTERN # 1  information, and MIMO_PATTERN # 2  information for PLP # 4  . . . . As a matter of course, by demodulating (and also performing error correction) those pieces of information, the terminal at the receiving end is enabled to recognize the transmission scheme that the broadcast station used for transmitting each PLP. 
     With the PLP_MODE set to “0”, the data transmission by a corresponding PLP is carried out by “transmitting one modulated signal”. With the PLP_MODE set to “1”, the data transmission by a corresponding PLP is carried out by “transmitting a plurality of modulated signals obtained by space-time block coding”, “precoding scheme of regularly hopping between precoding matrices”, “MIMO system with a fixed precoding matrix”, or “spatial multiplexing MIMO system”. 
     With the “PLP_MODE” set to “1”, the “MIMO_MODE” information is made effective. With “MIMO_MODE” set to “0”, data transmission is carried out by a scheme other than the “precoding scheme of regularly hopping between precoding matrices”. With “MIMO_MODE” set to “1”, on the other hand, data transmission is carried out by the “precoding scheme of regularly hopping between precoding matrices”. 
     With “PLP_MODE” set to “1” and “MIMO_MODE” set to “0”, the “MIMO_PATTERN # 1 ” information is made effective. With “MIMO_PATTERN # 1 ” set to “00”, data transmission is carried out using space-time block coding. With “MIMO_PATTERN” set to “01”, data transmission is carried out using a precoding scheme in which weighting is performed using a fixed precoding matrix # 1 . With “MIMO_PATTERN” set to “10”, data transmission is carried out using a precoding scheme in which weighting is performed using a fixed precoding matrix # 2  (Note that the precoding matrix # 1  and precoding matrix # 2  are mutually different). When “MIMO_PATTERN” set to “11”, data transmission is carried out using spatial multiplexing MIMO system (Naturally, it may be construed that Scheme  1  shown in  FIG.  49    is selected here). 
     With “PLP_MODE” set to “1” and “MIMO_MODE” set to “1”, the “MIMO_PATTERN # 2 ” information is made effective. Then, with “MIMO_PATTERN # 2 ” set to “00”, data transmission is carried out using the precoding matrix hopping scheme # 1  according to which precoding matrices are regularly hopped. With “MIMO_PATTERN # 2 ” set to “01”, data transmission is carried out using the precoding matrix hopping scheme # 2  according to which precoding matrices are regularly hopped. With “MIMO_PATTERN # 2 ” set to “10”, data transmission is carried out using the precoding matrix hopping scheme # 3  according to which precoding matrices are regularly hopped. With “MIMO_PATTERN # 2 ” set to “11”, data transmission is carried out using the precoding matrix hopping scheme # 4  according to which precoding matrices are regularly hopped. Note that the precoding matrix hopping schemes # 1  to # 4  are mutually different. Here, to define a scheme being different, it is supposed that #A and #B are mutually different schemes and then one of the following is true.
         The precoding matrices used in #A include the same matrices used in #b but the periods (cycles) of the matrices are different.   The precoding matrices used in #A include precoding matrices not used in #B.   None of the precoding matrices used in #A is used in #B.       

     In the above description, the control information shown in Tables 4 and 5 is transmitted on L1 Post-Signalling data, which is one of P2 symbols. According to the DVB-T2 standard, however, the amount of information that can be transmitted as P2 symbols is limited. Therefore, addition of information shown in Tables 4 and 5 to the information required in the DVB-T2 standard to be transmitted using P2 symbols may result in an amount exceeding the maximum amount that can be transmitted as P2 symbols. In such a case, Signalling PLP ( 6501 ) may be provided as shown in  FIG.  65    to transmit control information required by a standard other than the DVB-T2 standard (that is, data transmission is carried out using both L1 Post-Signalling data and Signalling PLP). In the example shown in  FIG.  65   , the same frame structure as shown in  FIG.  61    is used. However, the frame structure is not limited to this specific example. For example, similarly to L1 Pre-signalling data and other data shown in  FIG.  62   , Signalling PLP may be allocated to a specific carrier range in a specific time domain in the time and frequency domains. In short, Signalling PLP may be allocated in the time and frequency domains in any way. 
     As described above, the present embodiment allows for choice of a scheme of regularly hopping between precoding matrices while using a multi-carrier scheme, such as an OFDM scheme, without compromising the compatibility with the DVB-T2 standard. This offers the advantages of obtaining high reception quality, as well as high transmission speed, in an LOS environment. While in the present embodiment, the transmission schemes to which a carrier group can be set are “a spatial multiplexing MIMO system, a MIMO scheme using a fixed precoding matrix, a MIMO scheme for regularly hopping between precoding matrices, space-time block coding, or a transmission scheme for transmitting only stream s 1 ”, but the transmission schemes are not limited in this way. Furthermore, the MIMO scheme using a fixed precoding matrix limited to scheme # 2  in  FIG.  49   , as any structure with a fixed precoding matrix is acceptable. 
     Furthermore, the above description is directed to a scheme in which the schemes selectable by the broadcast station are “a spatial multiplexing MIMO system, a MIMO scheme using a fixed precoding matrix, a MIMO scheme for regularly hopping between precoding matrices, space-time block coding, or a transmission scheme for transmitting only stream s 1 ”. However, it is not necessary that all of the transmission schemes are selectable. Any of the following examples is also possible.
         A transmission scheme in which any of the following is selectable: a MIMO scheme using a fixed precoding matrix, a MIMO scheme for regularly hopping between precoding matrices, space-time block coding, and a transmission scheme for transmitting only stream s 1 .   A transmission scheme in which any of the following is selectable: a MIMO scheme using a fixed precoding matrix, a MIMO scheme for regularly hopping between precoding matrices, and space-time block coding.   A transmission scheme in which any of the following is selectable: a MIMO scheme using a fixed precoding matrix, a MIMO scheme for regularly hopping between precoding matrices, and a transmission scheme for transmitting only stream s 1 .   A transmission scheme in which any of the following is selectable: a MIMO scheme for regularly hopping between precoding matrices, space-time block coding, and a transmission scheme for transmitting only stream s 1 .   A transmission scheme in which any of the following is selectable: a MIMO scheme using a fixed precoding matrix, and a MIMO scheme for regularly hopping between precoding matrices.   A transmission scheme in which any of the following is selectable: a MIMO scheme for regularly hopping between precoding matrices, and space-time block coding.   A transmission scheme in which any of the following is selectable: a MIMO scheme for regularly hopping between precoding matrices, and a transmission scheme for transmitting only stream s 1 .
 
As listed above, as long as a MIMO scheme for regularly hopping between precoding matrices is included as a selectable scheme, the advantageous effects of high-speed data transmission is obtained in an LOS environment, in addition to excellent reception quality for the reception device.
       

     Here, it is necessary to set the control information S1 in P1 symbols as described above. In addition, as P2 symbols, the control information may be set differently from a scheme (the scheme for setting the transmission scheme of each PLP) shown in Table 4. Table 6 shows one example of such a scheme. 
     
       
         
           
               
               
               
             
               
                 TABLE 6 
               
               
                   
               
             
            
               
                   
                 PLP-MODE 
                 00: SISO/SIMO 
               
               
                   
                 (2 bits) 
                 01: MISO/MIMO (Space-time block code) 
               
               
                   
                   
                 10: MIMO (Precoding scheme of regularly hopping  
               
               
                   
                   
                 between precoding matrices) 
               
               
                   
                   
                 11: Reserved 
               
               
                   
               
            
           
         
       
     
     Table 6 differs from Table 4 in that the “PLP_MODE” set to “11” is “Reserved.” In this way, the number of bits constituting the “PLP_MODE” shown in Tables 4 and 6 may be increased or decreased depending on the number of selectable PLP transmission schemes, in the case where the selectable transmission schemes are as shown in the above examples. 
     The same holds with respect to Table 5. For example, if the only MIMO scheme supported is a precoding scheme of regularly hopping between precoding matrices, the control information “MIMO_MODE” is no longer necessary. Furthermore, the control information “MIMO_PATTERN # 1 ” may not be necessary in the case, for example, where a MIMO scheme using a fixed precoding matrix is not supported. Furthermore, the control information “MIMO_PATTERN # 1 ” may be one bit long instead of two bits long, in the case where, for example, no more than one precoding matrix is required for a MIMO scheme using a fixed precoding matrix. Furthermore, the control information “MIMO_PATTERN # 1 ” may be two bits long or more in the case where a plurality of precoding matrices are selectable. 
     The same applies to “MIMO_PATTERN # 2 ”. That is, the control information “MIMO_PATTERN # 2 ” may be one bit long instead of two bits long, in the case where no more than one precoding scheme of regularly hopping between precoding matrices is available. Alternatively, the control information “MIMO_PATTERN # 2 ” may be two bits long or more in the case where a plurality of precoding schemes of regularly hopping between precoding matrices are selectable. 
     In the present embodiment, the description is directed to the transmission device having two antennas, but the number of antennas is not limited to two. With a transmission device having more than two antennas, the control information may be transmitted in the same manner. Yet, to enable the modulated signal transmission with the use of four antennas in addition to the modulated signal transmission with the use of two antennas, there may be a case where the number of bits constituting respective pieces of control information needs to be increased. In such a modification, it still holds that the control information is transmitted by the P1 symbol and the control information is transmitted by P2 symbols as set forth above. 
     The above description is directed to the frame structure of PLP symbol groups transmitted by a broadcast station in a time-sharing transmission scheme as shown in  FIG.  64   . 
       FIG.  66    shows another example of a symbol arranging scheme in the time and frequency domains, which is different from the symbol arranging scheme shown in  FIG.  64   . The symbols shown in  FIG.  66    are of the stream s 1  and s 2  and to be transmitted after the transmission of P1 symbol, P2 symbols, and Common PLP. In  FIG.  66   , each symbol denoted by “# 1 ” represents one symbol of the symbol group of PLP # 1  shown in  FIG.  64   . Similarly, each symbol denoted as “# 2 ” represents one symbol of the symbol group of PLP # 2  shown in  FIG.  64   , each symbol denoted as “# 3 ” represents one symbol of the symbol group of PLP # 3  shown in  FIG.  64   , and each symbol denoted as “# 4 ” represents one symbol of the symbol group of PLP shown in  FIG.  64   . Similarly to  FIG.  64   , PLP # 1  transmits data using spatial multiplexing MIMO system shown in  FIG.  49    or the MIMO system with a fixed precoding matrix. In addition, PLP # 2  transmits data thereby to transmit one modulated signal. PLP # 3  transmits data using a precoding scheme of regularly hopping between precoding matrices. PLP # 4  transmits data using space-time block coding shown in  FIG.  50   . Note that the symbol arrangement used in space-time block coding is not limited to the arrangement in the time domain. Alternatively, the symbol arrangement may be in the frequency domain or in symbol groups formed in the time and frequency domains. In addition, space-time block coding is not limited to the one shown in  FIG.  50   . 
     In  FIG.  66   , where streams s 1  and s 2  both have a symbol in the same subcarrier and at the same time, symbols of the two streams are present at the same frequency. In the case where precoding performed includes the precoding according to the scheme for regularly hopping between precoding matrices as described in the other embodiments, streams s 1  and s 2  are subjected to weighting performed using the precoding matrices, and z 1  and z 2  are output from the respective antennas. 
       FIG.  66    differs from  FIG.  64    in the following points. That is, the example shown in  FIG.  64    is an arrangement of a plurality of PLPs using time-sharing, whereas the example shown in  FIG.  66    is an arrangement of a plurality of PLPs using both time-sharing and frequency-sharing. That is, for example, at time  1 , a symbol of PLP # 1  and a symbol of PLP # 2  are both present. Similarly, at time  3 , a symbol of PLP # 3  and a symbol of PLP # 4  are both present. In this way, PLP symbols having different index numbers (#X; X=1, 2 . . . ) may be allocated on a symbol-by-symbol basis (for each symbol composed of one subcarrier per time). 
     For the sake of simplicity,  FIG.  66    only shows symbols denoted by “# 1 ” and “# 2 ” at time  1 . However, this is not a limiting example, and PLP symbols having any index numbers other than “# 1 ” and “# 2 ” may be present at time  1 . In addition, the relation between subcarriers present at time  1  and PLP index numbers are not limited to that shown in  FIG.  66   . Alternatively, a PLP symbol having any index number may be allocated to any subcarrier. Similarly, in addition, a PLP symbol having any index number may be allocated to any subcarrier at any time other than time  1 . 
       FIG.  67    shows another example of a symbol arranging scheme in the time and frequency domains, which is different from the symbol arranging scheme shown in  FIG.  64   . The symbols shown in  FIG.  67    are of the stream s 1  and s 2  and to be transmitted after the transmission of P1 symbol, P2 symbols, and Common PLP. The characterizing feature of the example shown in  FIG.  67    is that the “transmission scheme for transmitting only stream s 1 ” is not selectable in the case where PLP transmission for T2 frames is carried out basically with a plurality of antennas. 
     Therefore, data transmission by the symbol group  6701  of PLP # 1  shown in  FIG.  67    is carried out by “a spatial multiplexing MIMO system or a MIMO scheme using a fixed precoding matrix”. Data transmission by the symbol group  6702  of PLP # 2  is carried out using “a precoding scheme of regularly hopping between precoding matrices”. Data transmission by the symbol group  6703  of PLP # 3  is carried out by “space-time block coding”. Note that data transmission by the PLP symbol group  6703  of PLP # 3  and the following symbol groups in T2 frame is carried out by using one of “a spatial multiplexing MIMO system or a MIMO scheme using a fixed precoding matrix,” “a precoding scheme of regularly hopping between precoding matrices” and “space-time block coding”. 
       FIG.  68    shows another example of a symbol arranging scheme in the time and frequency domains, which is different from the symbol arranging scheme shown in  FIG.  66   . The symbols shown in  FIG.  66    are of the stream s 1  and s 2  and to be transmitted after the transmission of P1 symbol, P2 symbols, and Common PLP. In  FIG.  68   , each symbol denoted by “# 1 ” represents one symbol of the symbol group of PLP # 1  shown in  FIG.  67   . Similarly, each symbol denoted as “# 2 ” represents one symbol of the symbol group of PLP # 2  shown in  FIG.  67   , each symbol denoted as “# 3 ” represents one symbol of the symbol group of PLP # 3  shown in  FIG.  67   , and each symbol denoted as “# 4 ” represents one symbol of the symbol group of PLP shown in  FIG.  67   . Similarly to  FIG.  67   , PLP # 1  transmits data using spatial multiplexing MIMO system shown in  FIG.  49    or the MIMO system with a fixed precoding matrix. PLP # 2  transmits data using a precoding scheme of regularly hopping between precoding matrices. PLP # 3  transmits data using space-time block coding shown in  FIG.  50   . Note that the symbol arrangement used in the space-time block coding is not limited to the arrangement in the time domain. Alternatively, the symbol arrangement may be in the frequency domain or in symbol groups formed in the time and frequency domains. In addition, the space-time block coding is not limited to the one shown in  FIG.  50   . 
     In  FIG.  68   , where streams s 1  and s 2  both have a symbol in the same subcarrier and at the same time, symbols of the two streams are present at the same frequency. In the case where precoding performed includes the precoding according to the scheme for regularly hopping between precoding matrices as described in the other embodiments, streams s 1  and s 2  are subjected to weighting performed using the precoding matrices and z 1  and z 2  are output from the respective antennas. 
       FIG.  68    differs from  FIG.  67    in the following points. That is, the example shown in  FIG.  67    is an arrangement of a plurality of PLPs using time-sharing, whereas the example shown in  FIG.  68    is an arrangement of a plurality of PLPs using both time-sharing and frequency-sharing. That is, for example, at time  1 , a symbol of PLP # 1  and a symbol of PLP # 2  are both present. In this way, PLP symbols having different index numbers (#X; X=1, 2 . . . ) may be allocated on a symbol-by-symbol basis (for each symbol composed of one subcarrier per time). 
     For the sake of simplicity,  FIG.  68    only shows symbols denoted by “# 1 ” and “# 2 ” at time  1 . However, this is not a limiting example, and PLP symbols having any index numbers other than “# 1 ” and “# 2 ” may be present at time  1 . In addition, the relation between subcarriers present at time  1  and PLP index numbers are not limited to that shown in  FIG.  68   . Alternatively, a PLP symbol having any index number may be allocated to any subcarrier. Similarly, in addition, a PLP symbol having any index number may be allocated to any subcarrier at any time other than time  1 . Alternatively, on the other hand, only one PLP symbol may be allocated at a specific time as at time t 3 . That is, in a framing scheme of arranging PLP symbols in the time and frequency domains, any allocation is applicable. 
     As set forth above, no PLPs using “a transmission scheme for transmitting only stream s 1 ” exist in the T2 frame, so that the dynamic range of a signal received by the terminal is ensured to be narrow. As a result, the advantageous effect is achieved that the probability of excellent reception quality increases. 
     Note that the description of  FIG.  68    is described using an example in which the transmission scheme selected is one of “spatial multiplexing MIMO system or a MIMO scheme using a fixed precoding matrix”, “a precoding scheme of regularly hopping between precoding matrices”, and “space-time block coding”. Yet, it is not necessary that all of these transmission schemes are selectable. For example, the following combinations of the transmission schemes may be made selectable.
         “a precoding scheme of regularly hopping between precoding matrices”, “space-time block coding”, and “a MIMO scheme using a fixed precoding matrix” are selectable.   “a precoding scheme of regularly hopping between precoding matrices” and “space-time block coding” are selectable.   “a precoding scheme of regularly hopping between precoding matrices” and “a MIMO scheme using a fixed precoding matrix” are selectable.       

     The above description relates to an example in which the T2 frame includes a plurality of PLPs. The following describes an example in which T2 frame includes one PLP only. 
       FIG.  69    shows an example of frame structure in the time and frequency domains for stream s 1  and s 2  in the case where only one PLP exits in T2 frame. In  FIG.  69   , the denotation “control symbol” represents a symbol such as P1 symbol, P2 symbol, or the like. In the example shown in  FIG.  69   , the first T2 frame is transmitted using interval  1 . Similarly, the second T2 frame is transmitted using interval  2 , the third T2 frame is transmitted using interval  3 , and the fourth T2 frame is transmitted using interval  4 . 
     In the example shown in  FIG.  69   , in the first T2 frame, a symbol group  6801  for PLP # 1 - 1  is transmitted and the transmission scheme selected is “spatial multiplexing MIMO system or MIMO scheme using a fixed precoding matrix”. 
     In the second T2 frame, a symbol group  6802  for PLP # 2 - 1  is transmitted and the transmission scheme selected is “a scheme for transmitting one modulated signal”. 
     In the third T2 frame, a symbol group  6803  for PLP # 3 - 1  is transmitted and the transmission scheme selected is “a precoding scheme of regularly hopping between precoding matrices”. 
     In the fourth T2 frame, a symbol group  6804  for PLP # 4 - 1  is transmitted and the transmission scheme selected is “space-time block coding”. Note that the symbol arrangement used in the space-time block coding is not limited to the arrangement in the time domain. Alternatively, the symbol arrangement may be in the frequency domain or in symbol groups formed in the time and frequency domains. In addition, the space-time block coding is not limited to the one shown in  FIG.  50   . 
     In  FIG.  69   , where streams s 1  and s 2  both have a symbol in the same subcarrier and at the same time, symbols of the two streams are present at the same frequency. In the case where precoding performed includes the precoding according to the scheme for regularly hopping between precoding matrices as described in the other embodiments, streams s 1  and s 2  are subjected to weighting performed using the precoding matrices and z 1  and z 2  are output from the respective antennas. 
     In the above manner, a transmission scheme may be set for each PLP in consideration of the data transmission speed and the data reception quality at the receiving terminal, so that increase in data transmission seeped and excellent reception quality are both achieved. As an example scheme of structuring control information, the control information indicating, for example, the transmission scheme and other information of P1 symbol and P2 symbols (and also Signalling PLP where applicable) may be configured in a similar manner to Tables 3-6. The difference is as follows. In the frame structure shown, for example, in  FIG.  64   , one T2 frame includes a plurality of PLPs. Thus, it is necessary to provide the control information indicating the transmission scheme and the like for each PLP. On the other hand, in the frame structure shown, for example, in  FIG.  69   , one T2 frame includes one PLP only. Thus, it is sufficient to provide the control information indicating the transmission scheme and the like only for the one PLP. 
     Although the above description is directed to the scheme of transmitting information about the PLP transmission scheme using P1 symbol and P2 symbols (and Signalling PLPs where applicable), the following describes in particular the scheme of transmitting information about the PLP transmission scheme without using P2 symbols. 
       FIG.  70    shows a frame structure in the time and frequency domains for the case where a terminal at a receiving end of data broadcasting by a broadcast station supporting a standard other than the DVB-T2 standard. In  FIG.  70   , the same reference signs are used to denote the blocks that operate in a similar way to those shown in  FIG.  61   . The frame shown in  FIG.  70    is composed of P1 Signalling data ( 6101 ), first Signalling data ( 7001 ), second Signalling data ( 7002 ), Common PLP ( 6104 ), and PLPs # 1  to N ( 6105 _ 1  to  6105 _N) (PLP: Physical Layer Pipe). In this way, a frame composed of P1 Signalling data ( 6101 ), first Signalling data ( 7001 ), second Signalling data ( 7002 ), Common PLP ( 6104 ), PLPs # 1  to N ( 6105 _ 1  to  6105 _N) constitutes one frame unit. 
     By the P1 Signalling data ( 6101 ), data indicating that the symbol is for a reception device to perform signal detection and frequency synchronization (including frequency offset estimation) is transmitted. In this example, in addition, data identifying whether or not the frame supports the DVB-T2 standard needs to be transmitted. For example, by S1 shown in Table 3, data indicating whether or not the signal supports the DVB-T2 standard needs to be transmitted. 
     By the first 1 Signalling data ( 7001 ), the following information may be transmitted for example: information about the guard interval used in the transmission frame; information about the method of PAPR (Peak to Average Power Ratio); information about the modulation scheme, error correction scheme, coding rate of the error correction scheme all of which are used in transmitting the second Signalling data; information about the size of the second Signalling data and about information size; information about the pilot pattern; information about the cell (frequency domain) unique number; and information indicating which of the norm mode and extended mode is used. Here, it is not necessary that the first Signalling data ( 7001 ) transmits data supporting the DVB-T2 standard. By L2 Post-Signalling data ( 7002 ), the following information may be transmitted for example: information about the number of PLPs; information about the frequency domain used; information about the unique number of each PLP; information about the modulation scheme, error correction scheme, coding rate of the error correction scheme all of which are used in transmitting the PLPs; and information about the number of blocks transmitted in each PLP. 
     In the frame structure shown in  FIG.  70   , first Signalling data ( 7001 ), second Signalling data ( 7002 ), L1 Post-Signalling data ( 6103 ), Common PLP ( 6104 ), PLPs # 1  to #N ( 6105 _ 1  to  6105 _N) are appear to be transmitted by time sharing. In practice, however, two or more of the signals are concurrently present.  FIG.  71    shows such an example. As shown in  FIG.  71   , first Signalling data, second Signalling data, and Common PLP may be present at the same time, and PLP # 1  and PLP # 2  may be present at the same time. That is, the signals constitute a frame using both time-sharing and frequency-sharing. 
       FIG.  72    shows an example of the structure of a transmission device obtained by applying the above-described schemes of regularly hopping between precoding matrices to a transmission device (of a broadcast station, for example) that is compliant with a standard other than the DVB-T2 standard. In  FIG.  72   , the same reference signs are used to denote the components that operate in a similar way to those shown in  FIG.  63    and the description of such components are the same as above. A control signal generating unit  6308  receives transmission data  7201  for the first and second Signalling data, transmission data  6307  for P1 symbol as input. As output, the control signal generating unit  6308  outputs a control signal  6309  carrying information about the transmission scheme of each symbol group shown in  FIG.  70   . (The information about the transmission scheme output herein includes: error correction coding, coding rate of the error correction, modulation scheme, block length, frame structure, the selected transmission schemes including a transmission scheme that regularly hops between precoding matrices, pilot symbol insertion scheme, information about IFFT (Inverse Fast Fourier Transform)/FFT and the like, information about the method of reducing PAPR, and information about guard interval insertion scheme.) 
     The control signal generating unit  7202  receives the control signal  6309  and the transmission data  7201  for first and second Signalling data as input. The control signal generating unit  7202  then performs error correction coding and mapping based on the modulation scheme, according to the information carried in the control signal  6309  (namely, information about the error correction of the first and second Signalling data, information about the modulation scheme) and outputs a (quadrature) baseband signal  7203  of the first and second Signalling data. 
     Next, a detailed description is given of the frame structure of a transmission signal and the transmission scheme of control information (information carried by the P1 symbol and first and second 2 Signalling data) employed by a broadcast station (base station) in the case where the scheme of regularly hopping between precoding matrices is adapted to a system compliant with a standard other than the DVB-T2 standard. 
       FIG.  64    shows an example of the frame structure in the time and frequency domains, in the case where a plurality of PLPs are transmitted after transmission of P1 symbol, first and second 2 Signalling data, and Common PLP. In  FIG.  64   , stream s 1  uses subcarriers # 1  to #M in the frequency domain. Similarly, stream s 2  uses subcarriers # 1  to #M in the frequency domain. Therefore, when streams s 1  and s 2  both have a symbol in the same subcarrier and at the same time, symbols of the two streams are present at the same frequency. In the case where precoding performed includes the precoding according to the scheme for regularly hopping between precoding matrices as described in the other embodiments, streams s 1  and s 2  are subjected to weighting performed using the precoding matrices and z 1  and z 2  are output from the respective antennas. 
     As shown in  FIG.  64   , in interval  1 , a symbol group  6401  of PLP # 1  is transmitted using streams s 1  and s 2 , and the data transmission is carried out using the spatial multiplexing MIMO system shown in  FIG.  49    or the MIMO system with a fixed precoding matrix. 
     In interval  2 , a symbol group  6402  of PLP # 2  is transmitted using stream s 1 , and the data transmission is carried out by transmitting one modulated signal. 
     In interval  3 , a symbol group  6403  of PLP # 3  is transmitted using streams s 1  and s 2 , and the data transmission is carried out using a precoding scheme of regularly hopping between precoding matrices. 
     In interval  4 , a symbol group  6404  of PLP # 4  is transmitted using streams s 1  and s 2 , and the data transmission is carried out using the space-time block coding shown in  FIG.  50   . Note that the symbol arrangement used in the space-time block coding is not limited to the arrangement in the time domain. Alternatively, the symbol arrangement may be in the frequency domain or in symbol groups formed in the time and frequency domains. In addition, the space-time block coding is not limited to the one shown in  FIG.  50   . 
     In the case where a broadcast station transmits PLPs in the frame structure shown in  FIG.  64   , a reception device receiving the transmission signal shown in  FIG.  64    needs to know the transmission scheme used for each PLP. As has been already described above, it is therefore necessary to transmit information indicating the transmission scheme for each PLP, using the first and second Signalling data. The following describes an example of the scheme of structuring a P1 symbol used herein and the scheme of structuring first and second Signalling data used herein. Specific examples of control information transmitted using a P1 symbol are as shown in Table 3. According to the DVB-T2 standard, the control information S1 (three bits) enables the reception device to determine whether or not the DVB-T2 standard is used and also determine, if DVB-T2 is used, the transmission scheme used. If the three bits are set to “000”, the S1 information indicates that the modulated signal transmitted is in compliant with “transmission of a modulated signal compliant with the DVB-T2 standard”. 
     If the three bits are set to “001”, the S1 information indicates that the modulated signal transmitted is in compliant with “transmission using space-time block coding compliant with the DVB-T2 standard”. 
     In the DVB-T2 standard, the bit sets “010” to “111” are “Reserved” for future use. In order to adapt the present invention in a manner to establish compatibility with the DVB-T2, the three bits constituting the S1 information may be set to “010” (or any bit set other than “000” and “001”) to indicate that the modulated signal transmitted is compliant with a standard other than DVB-T2. On determining that the S1 information received is set to “010”, the reception device is informed that the modulated signal transmitted from the broadcast station is compliant with a standard other than DVB-T2. 
     Next, a description is given of examples of the scheme of structuring first and second Signalling data in the case where a modulated signal transmitted by the broadcast station is compliant with a standard other than DVB-T2. A first example of the control information for the first and second Signalling data is as shown in Table 4. 
     The 2-bit information “PLP_MODE” shown in Table 4 is control information used to indicate the transmission scheme used for each PLP as shown in  FIG.  64    (PLPs # 1  to # 4  in  FIG.  64   ). That is, a separate piece of “PLP_MODE” information is provided for each PLP. That is, in the example shown in  FIG.  64   , PLP_MODE for PLP # 1 , PLP_MODE for PLP # 2 , PLP_MODE for PLP # 3 , PLP_MODE for PLP # 4  . . . are transmitted from the broadcast station. As a matter of course, by demodulating (and also performing error correction) those pieces of information, the terminal at the receiving end is enabled to recognize the transmission scheme that the broadcast station used for transmitting each PLP. 
     With the PLP_MODE set to “00”, the data transmission by a corresponding PLP is carried out by “transmitting one modulated signal”. When the PLP_MODE is set to “01”, the data transmission by a corresponding PLP is carried out by “transmitting a plurality of modulated signals obtained by space-time block coding”. When the PLP_MODE is set to “10”, the data transmission by a corresponding PLP is carried out using a “precoding scheme of regularly hopping between precoding matrices”. When the PLP_MODE is set to “11”, the data transmission by a corresponding PLP is carried out using a “MIMO system with a fixed precoding matrix or spatial multiplexing MIMO system”. 
     Note that when the PLP_MODE is set to “01” to “11”, the information indicating the specific processing conducted by the broadcast station (for example, the specific hopping scheme used in the scheme of regularly hopping between precoding matrices, the specific space-time block coding scheme used, and the structure of precoding matrices used) needs to be notified to the terminal. The following describes the scheme of structuring control information that includes such information and that is different from the example shown in Table 4. 
     A second example of the control information for the first and second Signalling data is as shown in Table 5. 
     As shown in Table 5, the control information includes “PLP_MODE” which is one bit long, “MIMO_MODE” which is one bit long, “MIMO_PATTERN # 1 ” which is two bits long, and “MIMO_PATTERN # 2 ” which is two bits long. As shown in  FIG.  64   , these four pieces of control information is to notify the transmission scheme of a corresponding one of PLPs (PLPs # 1  to # 4  in the example shown in  FIG.  64   ). Thus, a set of four pieces of information is provided for each PLP. That is, in the example shown in  FIG.  64   , the broadcast station transmits a set of PLP_MODE information, MIMO_MODE information, MIMO_PATTERN # 1  information, and MIMO_PATTERN # 2  information for PLP # 1 , a set of PLP_MODE information, MIMO_MODE information, MIMO_PATTERN # 1  information, and MIMO_PATTERN # 2  information for PLP # 2 , a set of PLP_MODE information, MIMO_MODE information, MIMO_PATTERN # 1  information, and MIMO_PATTERN # 2  information for PLP # 3 , a set of PLP_MODE information, MIMO_MODE information, MIMO_PATTERN # 1  information, and MIMO_PATTERN # 2  information for PLP # 4  . . . . As a matter of course, by demodulating (and also performing error correction) those pieces of information, the terminal at the receiving end is enabled to recognize the transmission scheme that the broadcast station used for transmitting each PLP. 
     With the PLP_MODE set to “0”, the data transmission by a corresponding PLP is carried out by “transmitting one modulated signal”. With the PLP_MODE set to “1”, the data transmission by a corresponding PLP is carried out by “transmitting a plurality of modulated signals obtained by space-time block coding”, “precoding scheme of regularly hopping between precoding matrices”, “MIMO system with a fixed precoding matrix or spatial multiplexing MIMO system”, or “spatial multiplexing MIMO system”. 
     With the “PLP_MODE” set to “1”, the “MIMO_MODE” information is made effective. With “MIMO_MODE” set to “0”, data transmission is carried out by a scheme other than the “precoding scheme of regularly hopping between precoding matrices”. With “MIMO_MODE” set to “1”, on the other hand, data transmission is carried out by the “precoding scheme of regularly hopping between precoding matrices”. 
     With “PLP_MODE” set to “1” and “MIMO_MODE” set to “0”, the “MIMO_PATTERN # 1 ” information is made effective. With “MIMO_PATTERN # 1 ” set to “00”, data transmission is carried out using space-time block coding. With “MIMO_PATTERN” set to “01”, data transmission is carried out using a precoding scheme in which weighting is performed using a fixed precoding matrix # 1 . With “MIMO_PATTERN” set to “10”, data transmission is carried out using a precoding scheme in which weighting is performed using a fixed precoding matrix # 2  (Note that the precoding matrix # 1  and precoding matrix # 2  are mutually different). When “MIMO_PATTERN” set to “11”, data transmission is carried out using spatial multiplexing MIMO system (Naturally, it may be construed that Scheme  1  shown in  FIG.  49    is selected here). 
     With “PLP_MODE” set to “1” and “MIMO_MODE” set to “1”, the “MIMO_PATTERN # 2 ” information is made effective. With “MIMO_PATTERN # 2 ” set to “00”, data transmission is carried out using the precoding matrix hopping scheme # 1  according to which precoding matrices are regularly hopped. With “MIMO_PATTERN # 2 ” set to “01”, data transmission is carried out using the precoding matrix hopping scheme # 2  according to which precoding matrices are regularly hopped. With “MIMO_PATTERN # 3 ” set to “10”, data transmission is carried out using the precoding matrix hopping scheme # 2  according to which precoding matrices are regularly hopped. With “MIMO_PATTERN # 4 ” set to “11”, data transmission is carried out using the precoding matrix hopping scheme # 2  according to which precoding matrices are regularly hopped. Note that the precoding matrix hopping schemes # 1  to # 4  are mutually different. Here, to define a scheme being different, it is supposed that #A and #B are mutually different schemes. Then one of the following is true.
         The precoding matrices used in #A include the same matrices used in #b but the periods (cycles) of the matrices are different.   The precoding matrices used in #A include precoding matrices not used in #B.   None of the precoding matrices used in #A is used in #B.       

     In the above description, the control information shown in Tables 4 and 5 is transmitted by first and second Signalling data. In this case, the advantage of eliminating the need to specifically use PLPs to transmit control information is achieved. 
     As described above, the present embodiment allows for choice of a scheme of regularly hopping between precoding matrices while using a multi-carrier scheme, such as an OFDM scheme and while allowing a standard other than DVB-T2 to be distinguished from DVB-T2. This offers the advantages of obtaining high reception quality, as well as high transmission speed, in an LOS environment. While in the present embodiment, the transmission schemes to which a carrier group can be set are “a spatial multiplexing MIMO system, a MIMO scheme using a fixed precoding matrix, a MIMO scheme for regularly hopping between precoding matrices, space-time block coding, or a transmission scheme for transmitting only stream s 1 ”, but the transmission schemes are not limited in this way. Furthermore, the MIMO scheme using a fixed precoding matrix limited to scheme # 2  in  FIG.  49   , as any structure with a fixed precoding matrix is acceptable. 
     Furthermore, the above description is directed to a scheme in which the schemes selectable by the broadcast station are “a spatial multiplexing MIMO system, a MIMO scheme using a fixed precoding matrix, a MIMO scheme for regularly hopping between precoding matrices, space-time block coding, or a transmission scheme for transmitting only stream s 1 ”. However, it is not necessary that all of the transmission schemes are selectable. Any of the following examples is also possible.
         A transmission scheme in which any of the following is selectable: a MIMO scheme using a fixed precoding matrix, a MIMO scheme for regularly hopping between precoding matrices, space-time block coding, and a transmission scheme for transmitting only stream s 1 .   A transmission scheme in which any of the following is selectable: a MIMO scheme using a fixed precoding matrix, a MIMO scheme for regularly hopping between precoding matrices, and space-time block coding.   A transmission scheme in which any of the following is selectable: a MIMO scheme using a fixed precoding matrix, a MIMO scheme for regularly hopping between precoding matrices, and a transmission scheme for transmitting only stream s 1 .   A transmission scheme in which any of the following is selectable: a MIMO scheme for regularly hopping between precoding matrices, space-time block coding, and a transmission scheme for transmitting only stream s 1 .   A transmission scheme in which any of the following is selectable: a MIMO scheme using a fixed precoding matrix, and a MIMO scheme for regularly hopping between precoding matrices.   A transmission scheme in which any of the following is selectable: a MIMO scheme for regularly hopping between precoding matrices, and space-time block coding.   A transmission scheme in which any of the following is selectable: a MIMO scheme for regularly hopping between precoding matrices, and a transmission scheme for transmitting only stream s 1 .       

     As listed above, as long as a MIMO scheme for regularly hopping between precoding matrices is included as a selectable scheme, the advantageous effects of high-speed data transmission is obtained in an LOS environment, in addition to excellent reception quality for the reception device. 
     Here, it is necessary to set the control information S1 in P1 symbols as described above. In addition, as first and second Signalling data, the control information may be set differently from a scheme (the scheme for setting the transmission scheme of each PLP) shown in Table 4. Table 6 shows one example of such a scheme. 
     Table 6 differs from Table 4 in that the “PLP_MODE” set to “11” is “Reserved” In this way, the number of bits constituting the “PLP_MODE” shown in Tables 4 and 6 may be increased or decreased depending on the number of selectable PLP transmission schemes, which varies as in the examples listed above. 
     The same holds with respect to Table 5. For example, if the only MIMO scheme supported is a precoding scheme of regularly hopping between precoding matrices, the control information “MIMO_MODE” is no longer necessary. Furthermore, the control information “MIMO_PATTERN # 1 ” may not be necessary in the case, for example, where a MIMO scheme using a fixed precoding matrix is not supported. Furthermore, the control information “MIMO_PATTERN # 1 ” may not necessarily be two bits long and may alternatively be one bit long in the case where, for example, no more than one precoding matrix is required for such a MIMO scheme using a fixed precoding matrix. Furthermore, the control information “MIMO_PATTERN # 1 ” may be two bits long or more in the case where a plurality of precoding matrices are selectable. 
     The same applies to “MIMO_PATTERN # 2 ”. That is, the control information “MIMO_PATTERN # 2 ” may be one bit long instead of two bits long, in the case where no more than one precoding scheme of regularly hopping between precoding matrices is available. Alternatively, the control information “MIMO_PATTERN # 2 ” may be two bits long or more in the case where a plurality of precoding schemes of regularly hopping between precoding matrices are selectable. 
     In the present embodiment, the description is directed to the transmission device having two antennas, but the number of antennas is not limited to two. With a transmission device having more than two antennas, the control information may be transmitted in the same manner. Yet, to enable the modulated signal transmission with the use of four antennas in addition to the modulated signal transmission with the use of two antennas may require that the number of bits constituting respective pieces of control information needs to be increased. In such a modification, it still holds that the control information is transmitted by the P1 symbol and the control information is transmitted by first and second Signalling data as set forth above. 
     The above description is directed to the frame structure of PLP symbol groups transmitted by a broadcast station in a time-sharing transmission scheme as shown in  FIG.  64   . 
       FIG.  66    shows another example of a symbol arranging scheme in the time and frequency domains, which is different from the symbol arranging scheme shown in  FIG.  64   . The symbols shown in  FIG.  66    are of the stream s 1  and s 2  and to be transmitted after the transmission of the P1 symbol, first and second Signalling data, and Common PLP. 
     In  FIG.  66   , each symbol denoted by “# 1 ” represents one symbol of the symbol group of PLP # 1  shown in  FIG.  67   . Similarly, each symbol denoted as “# 2 ” represents one symbol of the symbol group of PLP # 2  shown in  FIG.  64   , each symbol denoted as “# 3 ” represents one symbol of the symbol group of PLP shown in  FIG.  64   , and each symbol denoted as “# 4 ” represents one symbol of the symbol group of PLP # 4  shown in  FIG.  64   . Similarly to  FIG.  64   , PLP # 1  transmits data using spatial multiplexing MIMO system shown in  FIG.  49    or the MIMO system with a fixed precoding matrix. In addition, PLP # 2  transmits data thereby to transmit one modulated signal. PLP # 3  transmits data using a precoding scheme of regularly hopping between precoding matrices. PLP # 4  transmits data using space-time block coding shown in  FIG.  50   . Note that the symbol arrangement used in the space-time block coding is not limited to the arrangement in the time domain. Alternatively, the symbol arrangement may be in the frequency domain or in symbol groups formed in the time and frequency domains. In addition, the space-time block coding is not limited to the one shown in  FIG.  50   . 
     In  FIG.  66   , where streams s 1  and s 2  both have a symbol in the same subcarrier and at the same time, symbols of the two streams are present at the same frequency. In the case where precoding performed includes the precoding according to the scheme for regularly hopping between precoding matrices as described in the other embodiments, streams s 1  and s 2  are subjected to weighting performed using the precoding matrices and z 1  and z 2  are output from the respective antennas. 
       FIG.  66    differs from  FIG.  64    in the following points. That is, the example shown in  FIG.  64    is an arrangement of a plurality of PLPs using time-sharing, whereas the example shown in  FIG.  66    is an arrangement of a plurality of PLPs using both time-sharing and frequency-sharing. That is, for example, at time  1 , a symbol of PLP # 1  and a symbol of PLP # 2  are both present. Similarly, at time  3 , a symbol of PLP # 3  and a symbol of PLP # 4  are both present. In this way, PLP symbols having different index numbers (#X; X=1, 2 . . . ) may be allocated on a symbol-by-symbol basis (for each symbol composed of one subcarrier per time). 
     For the sake of simplicity,  FIG.  66    only shows symbols denoted by “# 1 ” and “# 2 ” at time  1 . However, this is not a limiting example, and PLP symbols having any index numbers other than “# 1 ” and “# 2 ” may be present at time  1 . In addition, the relation between subcarriers present at time  1  and PLP index numbers are not limited to that shown in  FIG.  66   . Alternatively, a PLP symbol having any index number may be allocated to any subcarrier. Similarly, in addition, a PLP symbol having any index number may be allocated to any subcarrier at any time other than time  1 . 
       FIG.  67    shows another example of a symbol arranging scheme in the time and frequency domains, which is different from the symbol arranging scheme shown in  FIG.  64   . The symbols shown in  FIG.  67    are of the stream s 1  and s 2  and to be transmitted after the transmission of the P1 symbol, first and second Signalling data, and Common PLP. The characterizing feature of the example shown in  FIG.  67    is that the “transmission scheme for transmitting only stream s 1 ” is not selectable in the case where PLP transmission for T2 frames is carried out basically with a plurality of antennas. 
     Therefore, data transmission by the symbol group  6701  of PLP # 1  shown in  FIG.  67    is carried out by “a spatial multiplexing MIMO system or a MIMO scheme using a fixed precoding matrix”. Data transmission by the symbol group  6702  of PLP # 2  is carried out using “a precoding scheme of regularly hopping between precoding matrices”. Data transmission by the symbol group  6703  of PLP # 3  is carried out by “space-time block coding”. Note that data transmission by the PLP symbol group  6703  of PLP # 3  and the following symbol groups in unit frame is carried out by using one of “a spatial multiplexing MIMO system or a MIMO scheme using a fixed precoding matrix,” “a precoding scheme of regularly hopping between precoding matrices” and “space-time block coding”. 
       FIG.  68    shows another example of a symbol arranging scheme in the time and frequency domains, which is different from the symbol arranging scheme shown in  FIG.  66   . The symbols shown in  FIG.  68    are of the stream s 1  and s 2  and to be transmitted after the transmission of the P1 symbol, first and second Signalling data, and Common PLP. 
     In  FIG.  68   , each symbol denoted by “# 1 ” represents one symbol of the symbol group of PLP # 1  shown in  FIG.  67   . Similarly, each symbol denoted as “# 2 ” represents one symbol of the symbol group of PLP # 2  shown in  FIG.  67   , each symbol denoted as “# 3 ” represents one symbol of the symbol group of PLP shown in  FIG.  67   , and each symbol denoted as “# 4 ” represents one symbol of the symbol group of PLP # 4  shown in  FIG.  67   . Similarly to  FIG.  67   , PLP # 1  transmits data using spatial multiplexing MIMO system shown in  FIG.  49    or the MIMO system with a fixed precoding matrix. PLP # 2  transmits data using a precoding scheme of regularly hopping between precoding matrices. PLP # 3  transmits data using space-time block coding shown in  FIG.  50   . Note that the symbol arrangement used in the space-time block coding is not limited to the arrangement in the time domain. Alternatively, the symbol arrangement may be in the frequency domain or in symbol groups formed in the time and frequency domains. In addition, the space-time block coding is not limited to the one shown in  FIG.  50   . 
     In  FIG.  68   , where streams s 1  and s 2  both have a symbol in the same subcarrier and at the same time, symbols of the two streams are present at the same frequency. In the case where precoding performed includes the precoding according to the scheme for regularly hopping between precoding matrices as described in the other embodiments, streams s 1  and s 2  are subjected to weighting performed using the precoding matrices and z 1  and z 2  are output from the respective antennas. 
       FIG.  68    differs from  FIG.  67    in the following points. That is, the example shown in  FIG.  67    is an arrangement of a plurality of PLPs using time-sharing, whereas the example shown in  FIG.  68    is an arrangement of a plurality of PLPs using both time-sharing and frequency-sharing. That is, for example, at time  1 , a symbol of PLP # 1  and a symbol of PLP # 2  are both present. In this way, PLP symbols having different index numbers (#X; X=1, 2, . . . ) may be allocated on a symbol-by-symbol basis (for each symbol composed of one subcarrier per time). 
     For the sake of simplicity,  FIG.  68    only shows symbols denoted by “# 1 ” and “# 2 ” at time  1 . However, this is not a limiting example, and PLP symbols having any index numbers other than “# 1 ” and “# 2 ” may be present at time  1 . In addition, the relation between subcarriers present at time  1  and PLP index numbers are not limited to that shown in  FIG.  68   . Alternatively, a PLP symbol having any index number may be allocated to any subcarrier. Similarly, in addition, a PLP symbol having any index number may be allocated to any subcarrier at any time other than time  1 . Alternatively, on the other hand, only one PLP symbol may be allocated at a specific time as at time t 3 . That is, in a framing scheme of arranging PLP symbols in the time and frequency domains, any allocation is applicable. 
     As set forth above, no PLPs using “a transmission scheme for transmitting only stream s 1 ” exist in a unit frame, so that the dynamic range of a signal received by the terminal is ensured to be narrow. As a result, the advantageous effect is achieved that the probability of excellent reception quality increases. 
     Note that the description of  FIG.  68    is described using an example in which the transmission scheme selected is one of “spatial multiplexing MIMO system or a MIMO scheme using a fixed precoding matrix”, “a precoding scheme of regularly hopping between precoding matrices”, and “space-time block coding”. Yet, it is not necessary that all of these transmission schemes are selectable. For example, the following combinations of the transmission schemes may be made selectable.
         A “precoding scheme of regularly hopping between precoding matrices”, “space-time block coding”, and “MIMO scheme using a fixed precoding matrix” are selectable.   A “precoding scheme of regularly hopping between precoding matrices” and “space-time block coding” are selectable.   A “precoding scheme of regularly hopping between precoding matrices” and “MIMO scheme using a fixed precoding matrix” are selectable.       

     The above description relates to an example in which a unit frame includes a plurality of PLPs. The following describes an example in which a unit frame includes one PLP only. 
       FIG.  69    shows an example of frame structure in the time and frequency domains for stream s 1  and s 2  in the case where only one PLP exits in a unit frame. 
     In  FIG.  69   , the denotation “control symbol” represents a symbol such as P1 symbol, first and second Signalling data, or the like. In the example shown in  FIG.  69   , the first unit frame is transmitted using interval  1 . Similarly, the second unit frame is transmitted using interval  2 , the third unit frame is transmitted using interval  3 , and the fourth unit frame is transmitted using interval  4 . 
     In the example shown in  FIG.  69   , in the first unit frame, a symbol group  6801  for PLP # 1 - 1  is transmitted and the transmission scheme selected is “spatial multiplexing MIMO system or MIMO scheme using a fixed precoding matrix”. 
     In the second unit frame, a symbol group  6802  for PLP # 2 - 1  is transmitted and the transmission scheme selected is “a scheme for transmitting one modulated signal.” 
     In the third unit frame, a symbol group  6803  for PLP # 3 - 1  is transmitted and the transmission scheme selected is “a precoding scheme of regularly hopping between precoding matrices”. 
     In the fourth unit frame, a symbol group  6804  for PLP # 4 - 1  is transmitted and the transmission scheme selected is “space-time block coding”. Note that the symbol arrangement used in the space-time block coding is not limited to the arrangement in the time domain. Alternatively, the symbols may be arranged in the frequency domain or in symbol groups formed in the time and frequency domains. In addition, the space-time block coding is not limited to the one shown in  FIG.  50   . 
     In  FIG.  69   , where streams s 1  and s 2  both have a symbol in the same subcarrier and at the same time, symbols of the two streams are present at the same frequency. In the case where precoding performed includes the precoding according to the scheme for regularly hopping between precoding matrices as described in the other embodiments, streams s 1  and s 2  are subjected to weighting performed using the precoding matrices and z 1  and z 2  are output from the respective antennas. 
     In the above manner, a transmission scheme may be set for each PLP in consideration of the data transmission speed and the data reception quality at the receiving terminal, so that increase in data transmission seeped and excellent reception quality are both achieved. As an example scheme of structuring control information, the control information indicating, for example, the transmission scheme and other information of the P1 symbol and first and second Signalling data may be configured in a similar manner to Tables 3-6. The difference is as follows. In the frame structure shown, for example, in  FIG.  64   , one unit frame includes a plurality of PLPs. Thus, it is necessary to provide the control information indicating the transmission scheme and the like for each PLP. On the other hand, in the frame structure shown, for example, in  FIG.  69   , one unit frame includes one PLP only. Thus, it is sufficient to provide the control information indicating the transmission scheme and the like only for the one PLP. 
     The present embodiment has described how a precoding scheme of regularly hopping between precoding matrices is applied to a system compliant with the DVB standard. Embodiments 1 to 16 have described examples of the precoding scheme of regularly hopping between precoding matrices. However, the scheme of regularly hopping between precoding matrices is not limited to the schemes described in Embodiments 1 to 16. The present embodiment can be implemented in the same manner by using a scheme comprising the steps of (i) preparing a plurality of precoding matrices, (ii) selecting, from among the prepared plurality of precoding matrices, one precoding matrix for each slot, and (iii) performing the precoding while regularly hopping between precoding matrices to be used for each slot. 
     Although control information has unique names in the present embodiment, the names of the control information do not influence the present invention. 
     Embodiment A2 
     The present embodiment provides detailed descriptions of a reception scheme and the structure of a reception device used in a case where a scheme of regularly hopping between precoding matrices is applied to a communication system compliant with the DVB-T2 standard, which is described in Embodiment A1. 
       FIG.  73    shows, by way of example, the structure of a reception device of a terminal used in a case where the transmission device of the broadcast station shown in  FIG.  63    has adopted a scheme of regularly hopping between precoding matrices. In  FIG.  73   , the elements that operate in the same manner as in  FIGS.  7  and  56    have the same reference signs thereas. 
     Referring to  FIG.  73   , a P1 symbol detection/demodulation unit  7301  performs signal detection and temporal frequency synchronization by receiving a signal transmitted by a broadcast station and detecting a P1 symbol based on the inputs, namely signals  704 _X and  704 _Y that have been subjected to signal processing. The P1 symbol detection/demodulation unit  7301  also obtains control information included in the P1 symbol (by applying demodulation and error correction decoding) and outputs P1 symbol control information  7302 . The P1 symbol control information  7302  is input to OFDM related processors  5600 _X and  5600 _Y. Based on the input information, the OFDM related processors  5600 _X and  5600 _Y change a signal processing scheme for the OFDM scheme (this is because, as described in Embodiment A1, the P1 symbol includes information on a scheme for transmitting the signal transmitted by the broadcast station). 
     Signals  704 _X and  704 _Y that have been subjected to signal processing, as well as the P1 symbol control information  7302 , are input to a P2 symbol demodulation unit  7303  (note, a P2 symbol may include a signalling PLP). The P2 symbol demodulation unit  7303  performs signal processing and demodulation (including error correction decoding) based on the P1 symbol control information, and outputs P2 symbol control information  7304 . 
     The P1 symbol control information  7302  and the P2 symbol control information  7304  are input to a control signal generating unit  7305 . The control signal generating unit  7305  forms a set of pieces of control information (relating to receiving operations) and outputs the same as a control signal  7306 . As illustrated in  FIG.  73   , the control signal  7306  is input to each unit. 
     A signal processing unit  711  receives, as inputs, the signals  706 _ 1 ,  706 _ 2 ,  708 _ 1 ,  708 _ 2 ,  704 _X,  704 _Y, and the control signal  7306 . Based on the information included in the control signal  7306  on the transmission scheme, modulation scheme, error correction coding scheme, coding rate for error correction coding, block size of error correction codes, and the like used to transmit each PLP, the signal processing unit  711  performs demodulation processing and decoding processing, and outputs received data  712 . 
     Here, the signal processing unit  711  may perform demodulation processing by using Equation 41 of Math 41 and Equation 143 of Math 153 in a case where any of the following transmission schemes is used for to transmit each PLP: a spatial multiplexing MIMO system; a MIMO scheme employing a fixed precoding matrix; and a precoding scheme of regularly hopping between precoding matrices. Note that the channel matrix (H) can be obtained from the resultant outputs from channel fluctuation estimating units ( 705 _ 1 ,  705 _ 2 ,  707 _ 1  and  707 _ 2 ). The matrix structure of the precoding matrix (F or W) differs depending on the transmission scheme actually used. Especially, when the precoding scheme of regularly hopping between precoding matrices is used, the precoding matrices to be used are hopped between and demodulation is performed every time. Also, when space-time block coding is used, demodulation is performed by using values obtained from channel estimation and a received (baseband) signal. 
       FIG.  74    shows, by way of example, the structure of a reception device of a terminal used in a case where the transmission device of the broadcast station shown in  FIG.  72    has adopted a scheme of regularly hopping between precoding matrices. In  FIG.  74   , the elements that operate in the same manner as in  FIGS.  7 ,  56  and  73    have the same reference signs thereas. 
     The reception device shown in  FIG.  74    and the reception device shown in  FIG.  73    are different in that the reception device shown in  FIG.  73    can obtain data by receiving signals conforming to the DVB-T2 standard and signals conforming to standards other than the DVB-T2 standard, whereas the reception device shown in  FIG.  74    can obtain data by receiving only signals conforming to standards other than the DVB-T2 standard. Referring to  FIG.  74   , a P1 symbol detection/demodulation unit  7301  performs signal detection and temporal frequency synchronization by receiving a signal transmitted by a broadcast station and detecting a P1 symbol based on the inputs, namely signals  704 _X and  704 _Y that have been subjected to signal processing. The P1 symbol detection/demodulation unit  7301  also obtains control information included in the P1 symbol (by applying demodulation and error correction decoding) and outputs P1 symbol control information  7302 . The P1 symbol control information  7302  is input to OFDM related processors  5600 _X and  5600 _Y. Based on the input information, the OFDM related processors  5600 _X and  5600 _Y change a signal processing scheme for the OFDM scheme. (This is because, as described in Embodiment A1, the P1 symbol includes information on a scheme for transmitting the signal transmitted by the broadcast station.) 
     Signals  704 _X and  704 _Y that have been subjected to signal processing, as well as the P1 symbol control information  7302 , are input to a first/second signalling data demodulation unit  7401 . The first/second signalling data demodulation unit  7401  performs signal processing and demodulation (including error correction decoding) based on the P1 symbol control information, and outputs first/second signalling data control information  7402 . 
     The P1 symbol control information  7302  and the first/second signalling data control information  7402  are input to a control signal generating unit  7305 . The control signal generating unit  7305  forms a set of pieces of control information (relating to receiving operations) and outputs the same as a control signal  7306 . As illustrated in  FIG.  74   , the control signal  7306  is input to each unit. 
     A signal processing unit  711  receives, as inputs, the signals  706 _ 1 ,  706 _ 2 ,  708 _ 1 ,  708 _ 2 ,  704 _X,  704 _Y, and the control signal  7306 . Based on the information included in the control signal  7306  on the transmission scheme, modulation scheme, error correction coding scheme, coding rate for error correction coding, block size of error correction codes, and the like used to transmit each PLP, the signal processing unit  711  performs demodulation processing and decoding processing, and outputs received data  712 . 
     Here, the signal processing unit  711  may perform demodulation processing by using Equation 41 of Math 41 and Equation 143 of Math 153 in a case where any of the following transmission schemes is used to transmit each PLP: a spatial multiplexing MIMO system; a MIMO scheme employing a fixed precoding matrix; and a precoding scheme of regularly hopping between precoding matrices. Note that the channel matrix (H) can be obtained from the resultant outputs from channel fluctuation estimating units ( 705 _ 1 ,  705 _ 2 ,  707 _ 1  and  707 _ 2 ). The matrix structure of the precoding matrix (F or W) differs depending on the transmission scheme actually used. Especially, when the precoding scheme of regularly hopping between precoding matrices is used, the precoding matrices to be used are hopped between and demodulation is performed every time. Also, when space-time block coding is used, demodulation is performed by using values obtained from channel estimation and a received (baseband) signal. 
       FIG.  75    shows the structure of a reception device of a terminal compliant with both the DVB-T2 standard and standards other than the DVB-T2 standard. In  FIG.  75   , the elements that operate in the same manner as in  FIGS.  7 ,  56  and  73    have the same reference signs thereas. 
     The reception device shown in  FIG.  75    is different from the reception devices shown in  FIGS.  73  and  74    in that the reception device shown in  FIG.  75    comprises a P2 symbol or first/second signalling data demodulation unit  7501  so as to be able to demodulate both signals compliant with the DVB-T2 standard and signals compliant with standards other than the DVB-T2 standard. 
     Signals  704 _X and  704 _Y that have been subjected to signal processing, as well as P1 symbol control information  7302 , are input to the P2 symbol or first/second signalling data demodulation unit  7501 . Based on the P1 symbol control information, the P2 symbol or first/second signalling data demodulation unit  7501  judges whether the received signal is compliant with the DVB-T2 standard or with a standard other than the DVB-T2 standard (this judgment can be made with use of, for example, Table 3), performs signal processing and demodulation (including error correction decoding), and outputs control information  7502  that includes information indicating the standard with which the received signal is compliant. Other operations are similar to  FIGS.  73  and  74   . 
     As set forth above, the structure of the reception device described in the present embodiment allows obtaining data with high reception quality by receiving the signal transmitted by the transmission device of the broadcast station, which has been described in Embodiment A1, and by performing appropriate signal processing. Especially, when receiving a signal associated with a precoding scheme of regularly hopping between precoding matrices, both the data transmission efficiency and the data reception quality can be improved in an LOS environment. 
     As the present embodiment has described the structure of the reception device that corresponds to the transmission scheme used by the broadcast station described in Embodiment A1, the reception device is provided with two receive antennas in the present embodiment. However, the number of antennas provided in the reception device is not limited to two. The present embodiment can be implemented in the same manner when the reception device is provided with three or more antennas. In this case, the data reception quality can be improved due to an increase in the diversity gain. Furthermore, when the transmission device of the broadcast station is provided with three or more transmit antennas and transmits three or more modulated signals, the present embodiment can be implemented in the same manner by increasing the number of receive antennas provided in the reception device of the terminal. In this case, it is preferable that the precoding scheme of regularly hopping between precoding matrices be used as a transmission scheme. 
     Note that Embodiments 1 to 16 have described examples of the precoding scheme of regularly hopping between precoding matrices. However, the scheme of regularly hopping between precoding matrices is not limited to the schemes described in Embodiments 1 to 16. The present embodiment can be implemented in the same manner by using a scheme comprising the steps of (i) preparing a plurality of precoding matrices, (ii) selecting, from among the prepared plurality of precoding matrices, one precoding matrix for each slot, and (iii) performing the precoding while regularly hopping between precoding matrices to be used for each slot. 
     Embodiment A3 
     In the system described in Embodiment A1 where the precoding scheme of regularly hopping between precoding matrices is applied to the DVB-T2 standard, there is control information for designating a pilot insertion pattern in L1 pre-signalling. The present embodiment describes how to apply the precoding scheme of regularly hopping between precoding matrices when the pilot insertion pattern is changed in the L1 pre-signalling. 
       FIGS.  76 A,  76 B,  77 A and  77 B  show examples of a frame structure represented in a frequency-time domain for the DVB-T2 standard in a case where a plurality of modulated signals are transmitted from a plurality of antennas using the same frequency band. In each of  FIGS.  76 A to  77 B , the horizontal axis represents frequency and carrier numbers are shown therealong, whereas the vertical axis represents time.  FIGS.  76 A and  77 A  each show a frame structure for a modulated signal z 1  pertaining to the embodiments that have been described so far.  FIGS.  76 B and  77 B  each show a frame structure for a modulated signal z 2  pertaining to the embodiments that have been described so far. Indexes “f 0 , f 1 , f 2 , . . . ” are assigned as carrier numbers, and indexes “t 1 , t 2 , t 3 , . . . ” are assigned as time. In  FIGS.  76 A to  77 B , symbols that are assigned the same carrier number and the same time exist over the same frequency at the same time. 
       FIGS.  76 A to  77 B  show examples of positions in which pilot symbols are inserted according to the DVB-T2 standard (when a plurality of modulated signals are transmitted by using a plurality of antennas according to the DVB-T2, there are eight schemes regarding the positions in which pilots are inserted;  FIGS.  76 A to  77 B  show two of such schemes).  FIGS.  76 A to  77 B  show two types of symbols, namely, symbols as pilots and symbols for data transmission (“data transmission symbols”). As described in other embodiments, when a precoding scheme of regularly hopping between precoding matrices or a precoding scheme employing a fixed precoding matrix is used, data transmission symbols in the modulated signal z 1  are obtained as a result of performing weighting on the streams s 1  and s 2 , and data transmission symbols in the modulated signal z 2  are obtained as a result of performing weighting on the streams s 1  and s 2 . When the space-time block coding or the spatial multiplexing MIMO system is used, data transmission symbols in the modulated signal z 1  are either for the stream s 1  or for the stream s 2 , and data transmission symbols in the modulated signal z 2  are either for the stream s 1  or for the stream s 2 . 
     In  FIGS.  76 A to  77 B , the symbols as pilots are each assigned an index “PP1” or “PP2”. A pilot symbol with the index “PP1” and a pilot symbol with the index “PP2” are structured by using different schemes. As mentioned earlier, according to the DVB-T2 standard, the broadcast station can designate one of the eight pilot insertion schemes (that differ from one another in the frequency of insertion of pilot symbols in a frame).  FIGS.  76 A to  77 B  show two of the eight pilot insertion schemes. Information on one of the eight pilot insertion schemes selected by the broadcast station is transmitted to a transmission destination (terminal) as L1 pre-signalling data of P2 symbols, which has been described in Embodiment A1. 
     Next, a description is given of how to apply the precoding scheme of regularly hopping between precoding matrices in association with a pilot insertion scheme. By way of example, it is assumed here that 10 different types of precoding matrices F are prepared for the precoding scheme of regularly hopping between precoding matrices, and these 10 different types of precoding matrices F are expressed as F[0], F[1], F[2], F[3], F[4], F[5], F[6], F[7], F[8], and F[9].  FIGS.  78 A and  78 B  show the result of allocating the precoding matrices to the frame structure represented in the frequency-time domains shown in  FIGS.  76 A and  76 B  when the precoding scheme of regularly hopping between precoding matrices is applied.  FIGS.  79 A and  79 B  show the result of allocating the precoding matrices to the frame structure represented in the frequency-time domains shown in  FIGS.  77 A and  77 B  when the precoding scheme of regularly hopping between precoding matrices is applied. For example, in both of the frame structure for the modulated signal z 1  shown in  FIG.  78 A  and the frame structure for the modulated signal z 2  shown in  FIG.  78 B , a symbol at the carrier f 1  and the time t 1  shows “# 1 ”. This means that precoding is performed on this symbol by using the precoding matrix F[1]. Likewise, in  FIGS.  78 A to  79 B , a symbol at the carrier fx and the time ty showing “#Z” denotes that precoding is performed on this symbol by using the precoding matrix F[Z] (here, x=0, 1, 2, . . . , and y=1, 2, 3, . . . ). 
     It should be naturally appreciated that different schemes for inserting pilot symbols (different insertion intervals) are used for the frame structure represented in the frequency-time domain shown in  FIGS.  78 A and  78 B  and the frame structure represented in the frequency-time domain shown in  FIGS.  79 A and  79 B . Furthermore, the precoding scheme of regularly hopping between the coding matrices is not applied to pilot symbols. For this reason, even if all of the signals shown in  FIGS.  78 A to  79 B  are subjected to the same precoding scheme that regularly hops between precoding matrices over a certain period (cycle) (i.e., the same number of different precoding matrices are prepared for this scheme applied to all of the signals shown in  FIGS.  78 A to  79 B ), a precoding matrix allocated to a symbol at a certain carrier and a certain time in  FIGS.  78 A and  78 B  may be different from a precoding matrix allocated to the corresponding symbol in  FIGS.  79 A and  79 B . This is apparent from  FIGS.  78 A to  79 B . For example, in  FIGS.  78 A and  78 B , a symbol at the carrier f 5  and the time t 2  shows “# 7 ”, meaning that precoding is performed thereon by using the precoding matrix F[7]. On the other hand, in  FIGS.  79 A and  79 B , a symbol at the carrier f 5  and the time t 2  shows “# 8 ”, meaning that precoding is performed thereon by using the precoding matrix F[8]. 
     Therefore, the broadcast station transmits control information indicating a pilot pattern (pilot insertion scheme) using the L1 pre-signalling data. Note, when the broadcast station has selected the precoding scheme of regularly hopping between precoding matrices as a scheme for transmitting each PLP based on control information shown in Table 4 or 5, the control information indicating the pilot pattern (pilot insertion scheme) may additionally indicate a scheme for allocating the precoding matrices (hereinafter “precoding matrix allocation scheme”) prepared for the precoding scheme of regularly hopping between precoding matrices. Hence, the reception device of the terminal that receives modulated signals transmitted by the broadcast station can acknowledge the precoding matrix allocation scheme used in the precoding scheme of regularly hopping between precoding matrices by obtaining the control information indicating the pilot pattern, which is included in the L1 pre-signalling data (on the premise that the broadcast station has selected the precoding scheme of regularly hopping between precoding matrices as a scheme for transmitting each PLP based on control information shown in Table 4 or 5). Although the description of the present embodiment has been given with reference to L1 pre-signalling data, in the case of the frame structure shown in  FIG.  70    where no P2 symbol exists, the control information indicating the pilot pattern and the precoding matrix allocation scheme used in the precoding scheme of regularly hopping between precoding matrices is included in first signalling data and second signalling data. 
     The following describes another example. For example, the above description is also true of a case where the precoding matrices used in the precoding scheme of regularly hopping between precoding matrices are determined at the same time as designation of a modulation scheme, as shown in Table 2. In this case, by transmitting only the pieces of control information indicating a pilot pattern, a scheme for transmitting each PLP and a modulation scheme from P2 symbols, the reception device of the terminal can estimate, via obtainment of these pieces of control information, the precoding matrix allocation scheme used in the precoding scheme of regularly hopping between precoding matrices (note, the allocation is performed in the frequency-time domain). Assume a case where the precoding matrices used in the precoding scheme of regularly hopping between precoding matrices are determined at the same time as designation of a modulation scheme and an error correction coding scheme, as shown in Table 1B. In this case also, by transmitting only the pieces of control information indicating a pilot pattern, a scheme for transmitting each PLP and a modulation scheme, as well as an error correction coding scheme, from P2 symbols, the reception device of the terminal can estimate, via obtainment of these pieces of information, the precoding matrix allocation scheme used in the precoding scheme of regularly hopping between precoding matrices (note, the allocation is performed in the frequency-time domain). 
     However, unlike the cases of Tables 1B and 2, a precoding matrix hopping scheme used in the precoding scheme of regularly hopping between precoding matrices is transmitted, as indicated by Table 5, in any of the following situations (i) to (iii): (i) when one of two or more different schemes of regularly hopping between precoding matrices can be selected even if the modulation scheme is determined (examples of such two or more different schemes include: precoding schemes that regularly hop between precoding matrices over different periods (cycles); and precoding schemes that regularly hop between precoding matrices, where the precoding matrices used in one scheme is different from those used in another; (ii) when one of two or more different schemes of regularly hopping between precoding matrices can be selected even if the modulation scheme and the error correction scheme are determined; and (iii) when one of two or more different schemes of regularly hopping between precoding matrices can be selected even if the error correction scheme is determined. In any of these situations (i) to (iii), it is permissible to transmit information on the precoding matrix allocation scheme used in the precoding scheme of regularly hopping between precoding matrices, in addition to the precoding matrix hopping scheme used in the precoding scheme of regularly hopping between precoding matrices (note, the allocation is performed in the frequency-time domain). 
     Table 7 shows an example of the structure of control information for the information on the precoding matrix allocation scheme used in the precoding scheme of regularly hopping between precoding matrices (note, the allocation is performed in the frequency-time domain). 
     
       
         
           
               
               
               
             
               
                 TABLE 7 
               
               
                   
               
             
            
               
                   
                 MATRIX_FRAME_ 
                 00: Preceding matrix allocation scheme 
               
               
                   
                 ARRANGEMENT 
                 #1 in frames 
               
               
                   
                 (2 bits) 
                 01: Precoding matrix allocation scheme 
               
               
                   
                   
                 #2 in frames 
               
               
                   
                   
                 10: Precoding matrix allocation scheme 
               
               
                   
                   
                 #3 in frames 
               
               
                   
                   
                 11: Precoding matrix allocation scheme 
               
               
                   
                   
                 #4 in frames 
               
               
                   
               
            
           
         
       
     
     By way of example, assume a case where the transmission device of the broadcast station has selected the pilot insertion pattern shown in  FIGS.  76 A and  76 B , and selected a scheme A as the precoding scheme of regularly hopping between precoding matrices. In this case, the transmission device of the broadcast station can select either the precoding matrix allocation scheme shown in  FIGS.  78 A and  78 B  or the precoding matrix allocation scheme shown in  FIGS.  80 A and  80 B  (note, the allocation is performed in the frequency-time domain). For example, when the transmission device of the broadcast station has selected the precoding matrix allocation scheme shown in  FIGS.  78 A and  78 B , “MATRIX_FRAME_ARRANGEMENT” in Table 7 is set to “00”. On the other hand, when the transmission device has selected the precoding matrix allocation scheme shown in  FIGS.  80 A and  80 B , “MATRIX_FRAME_ARRANGEMENT” in Table 7 is set to “01”. Then, the reception device of the terminal can acknowledge the precoding matrix allocation scheme by obtaining the control information shown in Table 7 (note, the allocation is performed in the frequency-time domain). Note that the control information shown in Table 7 can be transmitted by using P2 symbols, or by using first signalling data and second signalling data. 
     As set forth above, by implementing the precoding matrix allocation scheme used in the precoding scheme of regularly hopping between precoding matrices based on the pilot insertion scheme, and by properly transmitting the information indicative of the precoding matrix allocation scheme to the transmission destination (terminal), the reception device of the terminal can achieve the advantageous effect of improving both the data transmission efficiency and the data reception quality. 
     The present embodiment has described a case where the broadcast station transmits two signals. However, the present embodiment can be implemented in the same manner when the transmission device of the broadcast station is provided with three or more transmit antennas and transmits three or more modulated signals. Embodiments 1 to 16 have described examples of the precoding scheme of regularly hopping between precoding matrices. However, the scheme of regularly hopping between precoding matrices is not limited to the schemes described in Embodiments 1 to 16. The present embodiment can be implemented in the same manner by using a scheme comprising the steps of (i) preparing a plurality of precoding matrices, (ii) selecting, from among the prepared plurality of precoding matrices, one precoding matrix for each slot, and (iii) performing the precoding while regularly hopping between precoding matrices to be used for each slot. 
     Embodiment A4 
     In the present embodiment, a description is given of a repetition scheme used in a precoding scheme of regularly hopping between precoding matrices in order to improve the data reception quality. 
       FIGS.  3 ,  4 ,  13 ,  40  and  53    each show the structure of a transmission device employing the precoding scheme of regularly hopping between precoding matrices. On the other hand, the present embodiment describes the examples where repetition is used in the precoding scheme of regularly hopping between precoding matrices. 
       FIG.  81    shows an example of the structure of the signal processing unit pertaining to a case where repetition is used in the precoding scheme of regularly hopping between precoding matrices. In light of  FIG.  53   , the structure of  FIG.  81    corresponds to the signal processing unit  5308 . 
     A baseband signal  8101 _ 1  shown in  FIG.  81    corresponds to the baseband signal  5307 _ 1  shown in  FIG.  53   . The baseband signal  8101 _ 1  is obtained as a result of mapping, and constitutes the stream s 1 . Likewise, a baseband signal  8101 _ 2  shown in  FIG.  81    corresponds to the baseband signal  5307 _ 2  shown in  FIG.  53   . The baseband signal  8101 _ 2  is obtained as a result of mapping, and constitutes the stream s 2 . 
     The baseband signal  8101 _ 1  and a control signal  8104  are input to a signal processing unit (duplicating unit)  8102 _ 1 . The signal processing unit (duplicating unit)  8102 _ 1  generates duplicates of the baseband signal in accordance with the information on the number of repetitions included in the control signal  8104 . For example, in a case where the information on the number of repetitions included in the control signal  8104  indicates four repetitions, provided that the baseband signal  8101 _ 1  includes signals s 11 , s 12 , s 13 , s 14 , . . . arranged in the stated order along the time axis, the signal processing unit (duplicating unit)  8102 _ 1  generates a duplicate of each signal four times, and outputs the resultant duplicates. That is, after the four repetitions, the signal processing unit (duplicating unit)  8102 _ 1  outputs, as the baseband signal  8103 _ 1 , four pieces of s 11  (i.e., s 11 , s 11 , s 11 , s 11 ), four pieces of s 12  (i.e., s 12 , s 12 , s 12 , s 12 ), four pieces of s 13  (i.e., s 13 , s 13 , s 13 , s 13 ), four pieces of s 14  (i.e., s 14 , s 14 , s 14 , s 14 ) and so on, in the stated order along the time axis. 
     The baseband signal  8101 _ 2  and the control signal  8104  are input to a signal processing unit (duplicating unit)  8102 _ 2 . The signal processing unit (duplicating unit)  8102 _ 2  generates duplicates of the baseband signal in accordance with the information on the number of repetitions included in the control signal  8104 . For example, in a case where the information on the number of repetitions included in the control signal  8104  indicates four repetitions, provided that the baseband signal  8101 _ 2  includes signals s 21 , s 22 , s 23 , s 24 , . . . arranged in the stated order along the time axis, the signal processing unit (duplicating unit)  8102 _ 2  generates a duplicate of each signal four times, and outputs the resultant duplicates. That is, after the four repetitions, the signal processing unit (duplicating unit)  8102 _ 2  outputs, as the baseband signal  8103 _ 2 , four pieces of s 21  (i.e., s 21 , s 21 , s 21 , s 21 ), four pieces of s 22  (i.e., s 22 , s 22 , s 22 , s 22 ), four pieces of s 23  (i.e., s 23 , s 23 , s 23 , s 13 ), four pieces of s 24  (i.e., s 14 , s 24 , s 24 , s 24 ) and so on, in the stated order along the time axis. 
     The baseband signals  8103 _ 1  and  8103 _ 2  obtained as a result of repetitions, as well as the control signal  8104 , are input to a weighting unit (precoding operation unit)  8105 . The weighting unit (precoding operation unit)  8105  performs precoding based on the information on the precoding scheme of regularly hopping between precoding matrices, which is included in the control signal  8104 . More specifically, the weighting unit (precoding operation unit)  8105  performs weighting on the baseband signals  8103 _ 1  and  8103 _ 2  obtained as a result of repetitions, and outputs baseband signals  8106 _ 1  and  8106 _ 2  on which the precoding has been performed (here, the baseband signals  8106 _ 1  and  8106 _ 2  are respectively expressed as z 1 ( i ) and z 2 ( i ), where i represents the order (along time or frequency)). 
     Provided that the baseband signals  8103 _ 1  and  8103 _ 2  obtained as a result of repetitions are respectively y 1 ( i ) and y 2 ( i ) and the precoding matrix is F(i), the following relationship is satisfied. 
     
       
         
           
             Math 
             ⁢ 
                 
             561 
           
         
       
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             ⁢ 
                             1 
                             ⁢ 
                             
                               ( 
                               i 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             z 
                             ⁢ 
                             2 
                             ⁢ 
                             
                               ( 
                               i 
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       F 
                       ⁡ 
                       ( 
                       i 
                       ) 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               y 
                               ⁢ 
                               1 
                               ⁢ 
                               
                                 ( 
                                 i 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               y 
                               ⁢ 
                               2 
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                                 ( 
                                 i 
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                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   475 
                 
               
             
           
         
       
     
     Provided that N precoding matrices prepared for the precoding scheme of regularly hopping between precoding matrices are F[0], F[1], F[2], F[3], . . . , F[N−1] (where N is an integer larger than or equal to two), one of the precoding matrices F[0], F[1], F[2], F[3], . . . , F[N−1] is used as F(i) in Equation 475. 
     By way of example, assume that i=0, 1, 2, 3; y 1 ( i ) represents four duplicated baseband signals s 11 , s 11 , s 11 , s 11 ; and y 2 ( i ) represents four duplicated baseband signals s 21 , s 21 , s 21 , s 21 . Under this assumption, it is important that the following condition be met.
 
For  ∀ α ∀ β, the relationship  F (α)≠ F (β) is satisfied (for α,β=0,1,2,3 and α≠β).  Math 562
 
     The following description is derived by generalizing the above. Assume that the number of repetitions is K; i=g 0 , g 1 , g 2 , . . . , g K-1  (i.e., g j  where j is an integer in a range of 0 to K−1); and y 1 ( i ) represents s 11 . Under this assumption, it is important that the following condition be met.
 
For  ∀ α ∀ β, the relationship  F (α)≠ F (β) is satisfied (for α,β= g   j  ( j  being an integer in a range of 0 to  K− 1) and α≠β).  Math 563
 
     Likewise, assume that the number of repetitions is K; i=h 0 , h 1 , h 2 , . . . , h K-1  (i.e., h j  where j is an integer in a range of 0 to K−1); and y 2 ( i ) represents s 21 . Under this assumption, it is important that the following condition be met.
 
For  ∀ α ∀ β, the relationship  F (α)≠ F (β) is satisfied (for α,β= h   j  ( j  being an integer in a range of 0 to  K− 1) and α≠β).  Math 564
 
     Here, the relationship g j =h j  may be or may not be satisfied. This way, the identical streams generated through the repetitions are transmitted while using different precoding matrices therefor, and thus the advantageous effect of improving the data reception quality is achieved. 
     The present embodiment has described a case where the broadcast station transmits two signals. However, the present embodiment can be implemented in the same manner when the transmission device of the broadcast station is provided with three or more transmit antennas and transmits three or more modulated signals. Assume that the number of transmitted signals is Q; the number of repetitions is K; i=g 0 , g 1 , g 2 , g K-1  (i.e., g j  where j is an integer in a range of 0 to K−1); and yb(i) represents sb 1  (where b is an integer in a range of 1 to Q). Under this assumption, it is important that the following condition be met.
 
For  ∀ α ∀ β, the relationship  F (α)≠ F (β) is satisfied (for α,β= g   j  ( j  being an integer in a range of 0 to  K− 1) and α≠β).  Math 565
 
     Note that F(i) is a precoding matrix pertaining to a case where the number of transmitted signals is Q. 
     Next, an embodiment different from the embodiment illustrated in  FIG.  81    is described with reference to  FIG.  82   . In  FIG.  82   , the elements that operate in the same manner as in  FIG.  81    have the same reference signs thereas. The structure shown in  FIG.  82    is different from the structure shown in  FIG.  81    in that data pieces are reorders so as to transmit identical data pieces from different antennas. 
     A baseband signal  8101 _ 1  shown in  FIG.  82    corresponds to the baseband signal  5307 _ 1  shown in  FIG.  53   . The baseband signal  8101 _ 1  is obtained as a result of mapping, and constitutes the s 1  stream. Similarly, a baseband signal  8101 _ 2  shown in  FIG.  81    corresponds to the baseband signal  5307 _ 2  shown in  FIG.  53   . The baseband signal  8101 _ 2  is obtained as a result of mapping, and constitutes the s 2  stream. 
     The baseband signal  8101 _ 1  and the control signal  8104  are input to a signal processing unit (duplicating unit)  8102 _ 1 . The signal processing unit (duplicating unit)  8102 _ 1  generates duplicates of the baseband signal in accordance with the information on the number of repetitions included in the control signal  8104 . For example, in a case where the information on the number of repetitions included in the control signal  8104  indicates four repetitions, provided that the baseband signal  8101 _ 1  includes signals s 11 , s 12 , s 13 , s 14 , . . . arranged in the stated order along the time axis, the signal processing unit (duplicating unit)  8102 _ 1  generates a duplicate of each signal four times, and outputs the resultant duplicates. That is, after the four repetitions, the signal processing unit (duplicating unit)  8102 _ 1  outputs, as the baseband signal  8103 _ 1 , four pieces of s 11  (i.e., s 11 , s 11 , s 11 , s 11 ), four pieces of s 12  (i.e., s 12 , s 12 , s 12 , s 12 ), four pieces of s 13  (i.e., s 13 , s 13 , s 13 , s 13 ), four pieces of s 14  (i.e., s 14 , s 14 , s 14 , s 14 ) and so on, in the stated order along the time axis. 
     The baseband signal  8101 _ 2  and the control signal  8104  are input to a signal processing unit (duplicating unit)  8102 _ 2 . The signal processing unit (duplicating unit)  8102 _ 2  generates duplicates of the baseband signal in accordance with the information on the number of repetitions included in the control signal  8104 . For example, in a case where the information on the number of repetitions included in the control signal  8104  indicates four repetitions, provided that the baseband signal  8101 _ 2  includes signals s 21 , s 22 , s 23 , s 24 , . . . arranged in the stated order along the time axis, the signal processing unit (duplicating unit)  8102 _ 1  generates a duplicate of each signal four times, and outputs the resultant duplicates. That is, after the four repetitions, the signal processing unit (duplicating unit)  8102 _ 2  outputs, as the baseband signal  8103 _ 2 , four pieces of s 21  (i.e., s 21 , s 21 , s 21 , s 21 ), four pieces of s 22  (i.e., s 22 , s 22 , s 22 , s 22 ), four pieces of s 23  (i.e., s 23 , s 23 , s 23 , s 23 ), four pieces of s 24  (i.e., s 24 , s 24 , s 24 , s 24 ) and so on, in the stated order along the time axis. 
     The baseband signals  8103 _ 1  and  8103 _ 2  obtained as a result of repetitions, as well as the control signal  8104 , are input to a reordering unit  8201 . The reordering unit  8201  reorders the data pieces in accordance with information on a repetition scheme included in the control signal  8104 , and outputs baseband signals  8202 _ 1  and  8202 _ 2  obtained as a result of reordering. For example, assume that the baseband signal  8103 _ 1  obtained as a result of repetitions is composed of four pieces of s 11  (s 11 , s 11 , s 11 , s 11 ) arranged along the time axis, and the baseband signal  8103 _ 2  obtained as a result of repetitions is composed of four pieces of s 21  (s 21 , s 21 , s 21 , s 21 ) arranged along the time axis. In  FIG.  82   , s 11  is output as both y 1 ( i ) and y 2 ( i ) of Equation 475, and s 21  is similarly output as both y 1 ( i ) and y 2 ( i ) of Equation 475. Likewise, the reordering similar to the reordering performed on s 11  is performed on s 12 , s 13 , . . . , and the reordering similar to the reordering performed on s 21  is performed on s 22 , s 23 , . . . . Hence, the baseband signal  8202 _ 1  obtained as a result of reordering includes s 11 , s 21 , s 11 , s 21 , s 12 , s 22 , s 12 , s 22 , s 13 , s 23 , s 13 , s 23 , . . . arranged in the stated order, which are equivalent to y 1 ( i ) of Equation 475. Although the pieces of s 11  and s 21  are arranged in the order s 11 , s 21 , s 11  and s 21  in the above description, the pieces of s 11  and s 21  are not limited to being arranged in this way, but may be arranged in any order. Similarly, the pieces of s 12  and s 22 , as well as the pieces of s 13  and s 23 , may be arranged in any order. The baseband signal  8202 _ 2  obtained as a result of reordering includes s 21 , s 11 , s 21 , s 11 , s 22 , s 12 , s 22 , s 12 , s 23 , s 13 , s 23 , s 13 , . . . in the stated order, which are equivalent to y 2 ( i ) of Equation 475. Although the pieces of s 11  and s 21  are arranged in the order s 21 , s 11 , s 21  and s 11  in the above description, the pieces of s 11  and s 21  are not limited to being arranged in this way, but may be arranged in any order. Similarly, the pieces of s 12  and s 22 , as well as the pieces of s 13  and s 23 , may be arranged in any order. 
     The baseband signals  8202 _ 1  and  8202 _ 2  obtained as a result of reordering, as well as the control signal  8104 , are input to a weighting unit (precoding operation unit)  8105 . The weighting unit (precoding operation unit)  8105  performs precoding based on the information on the precoding scheme of regularly hopping between precoding matrices, which is included in the control signal  8104 . More specifically, the weighting unit (precoding operation unit)  8105  performs weighting on the baseband signals  8202 _ 1  and  8202 _ 2  obtained as a result of reordering, and outputs baseband signals  8106 _ 1  and  8106 _ 2  on which the precoding has been performed (here, the baseband signals  8106 _ 1  and  8106 _ 2  are respectively expressed as z 1 ( i ) and z 2 ( i ), where i represents the order (along time or frequency)). 
     As described earlier, under the assumption that the baseband signals  8202 _ 1  and  8202 _ 2  obtained as a result of reordering are respectively y 1 ( i ) and y 2 ( i ) and the precoding matrix is F(i), the relationship in Equation 475 is satisfied. 
     Provided that N precoding matrices prepared for the precoding scheme of regularly hopping between precoding matrices are F[0], F[1], F[2], F[3], . . . , F[N−1] (where N is an integer larger than or equal to two), one of the precoding matrices F[0], F[1], F[2], F[3], . . . , F[N−1] is used as F(i) in Equation 475. 
     Although it has been described above that four repetitions are performed, the number of repetitions is not limited to four. As with the structure shown in  FIG.  81   , the structure shown in  FIG.  82    also achieves high reception quality when the relationships set out in Math 304 to Math 307 are satisfied. 
     The structure of the reception device is illustrated in  FIGS.  7  and  56   . By taking advantage of fulfillment of the relationships set out in Equation 144 and Equation 475, the signal processing unit demodulates bits transmitted by each of s 11 , s 12 , s 13 , s 14 , . . . , and bits transmitted by each of s 21 , s 22 , s 23 , s 24 , . . . . Note that each bit may be calculated as a log-likelihood ratio or as a hard-decision value. Furthermore, by taking advantage of the fact that K repetitions are performed on s 11 , it is possible to obtain highly reliable estimate values for bits transmitted by s 1 . Likewise, by taking advantage of the fact that K repetitions are performed on s 12 , s 13 , . . . , and on s 21 , s 22 , s 23 , . . . , it is possible to obtain highly reliable estimate values for bits transmitted by s 12 , s 13 , . . . , and by s 21 , s 22 , s 23 , . . . . 
     The present embodiment has described a scheme for applying a precoding scheme of regularly hopping between precoding matrices in the case where the repetitions are performed. When there are two types of slots, i.e., slots over which data is transmitted after performing the repetitions, and slots over which data is transmitted without performing the repetitions, either of a precoding scheme of regularly hopping between precoding matrices or a precoding scheme employing a fixed precoding matrix may be used as a transmission scheme for the slots over which data is transmitted without performing the repetitions. Put another way, in order for the reception device to achieve high data reception quality, it is important that the transmission scheme pertaining to the present embodiment be used for the slots over which data is transmitted after performing the repetitions. 
     In the systems associated with the DVB standard that have been described in Embodiments A1 through A3, it is necessary to secure higher reception qualities for P2 symbols, first signalling data and second signalling data than for PLPs. When P2 symbols, first signalling data and second signalling data are transmitted by using the precoding scheme of regularly hopping between precoding matrices described in the present embodiment, which incorporates the repetitions, the reception quality of control information improves in the reception device. This is important for stable operations of the systems. 
     Embodiments 1 to 16 have provided examples of the precoding scheme of regularly hopping between precoding matrices described in the present embodiment. However, the scheme of regularly hopping between precoding matrices is not limited to the schemes described in Embodiments 1 to 16. The present embodiment can be implemented in the same manner by using a scheme comprising the steps of (i) preparing a plurality of precoding matrices, (ii) selecting, from among the prepared plurality of precoding matrices, one precoding matrix for each slot, and (iii) performing the precoding while regularly hopping between precoding matrices for each slot. 
     Embodiment A5 
     The present embodiment describes a scheme for transmitting modulated signals by applying common amplification to the transmission scheme described in Embodiment A1. 
       FIG.  83    shows an example of the structure of a transmission device. In  FIG.  83   , the elements that operate in the same manner as in  FIG.  52    have the same reference signs thereas. 
     Modulated signal generating units # 1  to #M (i.e.,  5201 _ 1  to  5201 _M) shown in  FIG.  83    generate the signals  6323 _ 1  and  6323 _ 2  from the input signals (input data), the signals  6323 _ 1  and  6323 _ 2  being subjected to processing for a P1 symbol and shown in  FIG.  63  or  72   . The modulated signal generating units # 1  to #M output modulated signals z 1  ( 5202 _ 1  to  5202 _M) and modulated signals z 2  ( 5203 _ 1  to  5203 _M). 
     The modulated signals z 1  ( 5202 _ 1  to  5202 _M) are input to a wireless processing unit  8301 _ 1  shown in  FIG.  83   . The wireless processing unit  8301 _ 1  performs signal processing (e.g., frequency conversion) and amplification, and outputs a modulated signal  8302 _ 1 . Thereafter, the modulated signal  8302 _ 1  is output from an antenna  8303 _ 1  as a radio wave. 
     Similarly, the modulated signals z 2  ( 5203 _ 1  to  5203 _M) are input to a wireless processing unit  8301 _ 2 . The wireless processing unit  8301 _ 2  performs signal processing (e.g., frequency conversion) and amplification, and outputs a modulated signal  8302 _ 2 . Thereafter, the modulated signal  8302 _ 2  is output from an antenna  8303 _ 2  as a radio wave. 
     As set forth above, it is permissible to use the transmission scheme described in Embodiment A1 while performing frequency conversion and amplification simultaneously on modulated signals having different frequency bands. 
     Embodiment B1 
     The following describes a structural example of an application of the transmission schemes and reception schemes shown in the above embodiments and a system using the application. 
       FIG.  84    shows an example of the structure of a system that includes devices implementing the transmission schemes and reception schemes described in the above embodiments. The transmission scheme and reception scheme described in the above embodiments are implemented in a digital broadcasting system  8400 , as shown in  FIG.  84   , that includes a broadcasting station and a variety of reception devices such as a television  8411 , a DVD recorder  8412 , a Set Top Box (STB)  8413 , a computer  8420 , an in-car television  8441 , and a mobile phone  8430 . Specifically, the broadcasting station  8401  transmits multiplexed data, in which video data, audio data, and the like are multiplexed, using the transmission schemes in the above embodiments over a predetermined broadcasting band. 
     An antenna (for example, antennas  8560  and  8440 ) internal to each reception device, or provided externally and connected to the reception device, receives the signal transmitted from the broadcasting station  8401 . Each reception device obtains the multiplexed data by using the reception schemes in the above embodiments to demodulate the signal received by the antenna. In this way, the digital broadcasting system  8400  obtains the advantageous effects of the present invention described in the above embodiments. 
     The video data included in the multiplexed data has been coded with a moving picture coding method compliant with a standard such as Moving Picture Experts Group (MPEG)-2, MPEG-4 Advanced Video Coding (AVC), VC-1, or the like. The audio data included in the multiplexed data has been encoded with an audio coding method compliant with a standard such as Dolby Audio Coding (AC)-3, Dolby Digital Plus, Meridian Lossless Packing (MLP), Digital Theater Systems (DTS), DTS-HD, Linear Pulse-Code Modulation (PCM), or the like. 
       FIG.  85    is a schematic view illustrating an exemplary structure of a reception device  8500  for carrying out the reception schemes described in the above embodiments. As illustrated in  FIG.  85   , in one exemplary structure, the reception device  8500  may be composed of a modem portion implemented on a single LSI (or a single chip set) and a codec portion implemented on another single LSI (or another single chip set). The reception device  8500  shown in  FIG.  85    corresponds to a component that is included, for example, in the television  8411 , the DVD recorder  8412 , the STB  8413 , the computer  8420 , the in-car television  8441 , the mobile phone  8430 , or the like illustrated in  FIG.  84   . The reception device  8500  includes a tuner  8501 , for transforming a high-frequency signal received by an antenna  8560  into a baseband signal, and a demodulation unit  8502 , for demodulating multiplexed data from the baseband signal obtained by frequency conversion. The reception schemes described in the above embodiments are implemented in the demodulation unit  8502 , thus obtaining the advantageous effects of the present invention described in the above embodiments. 
     The reception device  8500  includes a stream input/output unit  8520 , a signal processing unit  8504 , an audio output unit  8506 , and a video display unit  8507 . The stream input/output unit  8520  demultiplexes video and audio data from multiplexed data obtained by the demodulation unit  8502 . The signal processing unit  8504  decodes the demultiplexed video data into a video signal using an appropriate method picture decoding method and decodes the demultiplexed audio data into an audio signal using an appropriate audio decoding scheme. The audio output unit  8506 , such as a speaker, produces audio output according to the decoded audio signal. The video display unit  8507 , such as a display monitor, produces video output according to the decoded video signal. 
     For example, the user may operate the remote control  8550  to select a channel (of a TV program or audio broadcast), so that information indicative of the selected channel is transmitted to an operation input unit  8510 . In response, the reception device  8500  demodulates, from among signals received with the antenna  8560 , a signal carried on the selected channel and applies error correction decoding, so that reception data is extracted. At this time, the reception device  8500  receives control symbols included in a signal corresponding to the selected channel and containing information indicating the transmission scheme (the transmission scheme, modulation scheme, error correction scheme, and the like in the above embodiments) of the signal (exactly as described in Embodiments A1 through A4 and as shown in  FIGS.  5  and  41   ). With this information, the reception device  8500  is enabled to make appropriate settings for the receiving operations, demodulation scheme, scheme of error correction decoding, and the like to duly receive data included in data symbols transmitted from a broadcasting station (base station). Although the above description is directed to an example in which the user selects a channel using the remote control  8550 , the same description applies to an example in which the user selects a channel using a selection key provided on the reception device  8500 . 
     With the above structure, the user can view a broadcast program that the reception device  8500  receives by the reception schemes described in the above embodiments. 
     The reception device  8500  according to this embodiment may additionally include a recording unit (drive)  8508  for recording various data onto a recording medium, such as a magnetic disk, optical disc, or a non-volatile semiconductor memory. Examples of data to be recorded by the recording unit  8508  include data contained in multiplexed data that is obtained as a result of demodulation and error correction decoding by the demodulation unit  8502 , data equivalent to such data (for example, data obtained by compressing the data), and data obtained by processing the moving pictures and/or audio. (Note here that there may be a case where no error correction decoding is applied to a signal obtained as a result of demodulation by the demodulation unit  8502  and where the reception device  8500  conducts further signal processing after error correction decoding. The same holds in the following description where similar wording appears.) Note that the term “optical disc” used herein refers to a recording medium, such as Digital Versatile Disc (DVD) or BD (Blu-ray Disc), that is readable and writable with the use of a laser beam. Further, the term “magnetic disk” used herein refers to a recording medium, such as a floppy disk (FD, registered trademark) or hard disk, that is writable by magnetizing a magnetic substance with magnetic flux. Still further, the term “non-volatile semiconductor memory” refers to a recording medium, such as flash memory or ferroelectric random access memory, composed of semiconductor element(s). Specific examples of non-volatile semiconductor memory include an SD card using flash memory and a flash Solid State Drive (SSD). It should be naturally appreciated that the specific types of recording media mentioned herein are merely examples, and any other types of recording mediums may be usable. 
     With the above structure, the user can record a broadcast program that the reception device  8500  receives with any of the reception schemes described in the above embodiments, and time-shift viewing of the recorded broadcast program is possible anytime after the broadcast. 
     In the above description of the reception device  8500 , the recording unit  8508  records multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502 . However, the recording unit  8508  may record part of data extracted from the data contained in the multiplexed data. For example, the multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502  may contain contents of data broadcast service, in addition to video data and audio data. In this case, new multiplexed data may be generated by multiplexing the video data and audio data, without the contents of broadcast service, extracted from the multiplexed data demodulated by the demodulation unit  8502 , and the recording unit  8508  may record the newly generated multiplexed data. Alternatively, new multiplexed data may be generated by multiplexing either of the video data and audio data contained in the multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502 , and the recording unit  8508  may record the newly generated multiplexed data. The recording unit  8508  may also record the contents of data broadcast service included, as described above, in the multiplexed data. 
     The reception device  8500  described in this embodiment may be included in a television, a recorder (such as DVD recorder, Blu-ray recorder, HDD recorder, SD card recorder, or the like), or a mobile telephone. In such a case, the multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502  may contain data for correcting errors (bugs) in software used to operate the television or recorder or in software used to prevent disclosure of personal or confidential information. If such data is contained, the data is installed on the television or recorder to correct the software errors. Further, if data for correcting errors (bugs) in software installed in the reception device  8500  is contained, such data is used to correct errors that the reception device  8500  may have. This arrangement ensures more stable operation of the TV, recorder, or mobile phone in which the reception device  8500  is implemented. 
     Note that it may be the stream input/output unit  8503  that handles extraction of data from the whole data contained in multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502  and multiplexing of the extracted data. More specifically, under instructions given from a control unit not illustrated in the figures, such as a CPU, the stream input/output unit  8503  demultiplexes video data, audio data, contents of data broadcast service etc. from the multiplexed data demodulated by the demodulation unit  8502 , extracts specific pieces of data from the demultiplexed data, and multiplexes the extracted data pieces to generate new multiplexed data. The data pieces to be extracted from demultiplexed data may be determined by the user or determined in advance for the respective types of recording mediums. 
     With the above structure, the reception device  8500  is enabled to extract and record only data necessary to view a recorded broadcast program, which is effective to reduce the size of data to be recorded. 
     In the above description, the recording unit  8508  records multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502 . Alternatively, however, the recording unit  8508  may record new multiplexed data generated by multiplexing video data newly yielded by encoding the original video data contained in the multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502 . Here, the moving picture coding method to be employed may be different from that used to encode the original video data, so that the data size or bit rate of the new video data is smaller than the original video data. Here, the moving picture coding method used to generate new video data may be of a different standard from that used to generate the original video data. Alternatively, the same moving picture coding method may be used but with different parameters. Similarly, the recording unit  8508  may record new multiplexed data generated by multiplexing audio data newly obtained by encoding the original audio data contained in the multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502 . Here, the audio coding method to be employed may be different from that used to encode the original audio data, such that the data size or bit rate of the new audio data is smaller than the original audio data. 
     The process of converting the original video or audio data contained in the multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502  into the video or audio data of a different data size of bit rate is performed, for example, by the stream input/output unit  8503  and the signal processing unit  8504 . More specifically, under instructions given from the control unit such as the CPU, the stream input/output unit  8503  demultiplexes video data, audio data, contents of data broadcast service etc. from the multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502 . Under instructions given from the control unit, the signal processing unit  8504  converts the demultiplexed video data and audio data respectively using a moving picture coding method and an audio coding method each different from the method that was used in the conversion applied to obtain the video and audio data. Under instructions given from the control unit, the stream input/output unit  8503  multiplexes the newly converted video data and audio data to generate new multiplexed data. Note that the signal processing unit  8504  may perform the conversion of either or both of the video or audio data according to instructions given from the control unit. In addition, the sizes of video data and audio data to be obtained by encoding may be specified by a user or determined in advance for the types of recording mediums. 
     With the above arrangement, the reception device  8500  is enabled to record video and audio data after converting the data to a size recordable on the recording medium or to a size or bit rate that matches the read or write rate of the recording unit  8508 . This arrangement enables the recoding unit to duly record a program, even if the size recordable on the recording medium is smaller than the data size of the multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502 , or if the rate at which the recording unit records or reads is lower than the bit rate of the multiplexed data. Consequently, time-shift viewing of the recorded program by the user is possible anytime after the broadcast. 
     Furthermore, the reception device  8500  additionally includes a stream output interface (IF)  8509  for transmitting multiplexed data demodulated by the demodulation unit  8502  to an external device via a transport medium  8530 . In one example, the stream output IF  8509  may be a wireless communication device that transmits multiplexed data via a wireless medium (equivalent to the transport medium  8530 ) to an external device by modulating the multiplexed data in accordance with a wireless communication scheme compliant with a wireless communication standard such as Wi-Fi (registered trademark, a set of standards including IEEE 802.11a, IEEE 802.11b, IEEE 802.11g, and IEEE 802.11n), WiGiG, Wireless HD, Bluetooth, ZigBee, or the like. The stream output IF  8509  may also be a wired communication device that transmits multiplexed data via a transmission line (equivalent to the transport medium  8530 ) physically connected to the stream output IF  8509  to an external device, modulating the multiplexed data using a communication scheme compliant with wired communication standards, such as Ethernet (registered trademark), Universal Serial Bus (USB), Power Line Communication (PLC), or High-Definition Multimedia Interface (HDMI). 
     With the above structure, the user can use, on an external device, multiplexed data received by the reception device  8500  using the reception scheme described according to the above embodiments. The usage of multiplexed data by the user mentioned herein includes use of the multiplexed data for real-time viewing on an external device, recording of the multiplexed data by a recording unit included in an external device, and transmission of the multiplexed data from an external device to a yet another external device. 
     In the above description of the reception device  8500 , the stream output IF  8509  outputs multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502 . However, the reception device  8500  may output data extracted from data contained in the multiplexed data, rather than the whole data contained in the multiplexed data. For example, the multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502  may contain contents of data broadcast service, in addition to video data and audio data. In this case, the stream output IF  8509  may output multiplexed data newly generated by multiplexing video and audio data extracted from the multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502 . In another example, the stream output IF  8509  may output multiplexed data newly generated by multiplexing either of the video data and audio data contained in the multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502 . 
     Note that it may be the stream input/output unit  8503  that handles extraction of data from the whole data contained in multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502  and multiplexing of the extracted data. More specifically, under instructions given from a control unit not illustrated in the figures, such as a Central Processing Unit (CPU), the stream input/output unit  8503  demultiplexes video data, audio data, contents of data broadcast service etc. from the multiplexed data demodulated by the demodulation unit  8502 , extracts specific pieces of data from the demultiplexed data, and multiplexes the extracted data pieces to generate new multiplexed data. The data pieces to be extracted from demultiplexed data may be determined by the user or determined in advance for the respective types of the stream output IF  8509 . 
     With the above structure, the reception device  8500  is enabled to extract and output only data necessary for an external device, which is effective to reduce the communication band used to output the multiplexed data. 
     In the above description, the stream output IF  8509  outputs multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502 . Alternatively, however, the stream output IF  8509  may output new multiplexed data generated by multiplexing video data newly yielded by encoding the original video data contained in the multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502 . The new video data is encoded with a moving picture coding method different from that used to encode the original video data, so that the data size or bit rate of the new video data is smaller than the original video data. Here, the moving picture coding method used to generate new video data may be of a different standard from that used to generate the original video data. Alternatively, the same moving picture coding method may be used but with different parameters. Similarly, the stream output IF  8509  may output new multiplexed data generated by multiplexing audio data newly obtained by encoding the original audio data contained in the multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502 . The new audio data is encoded with an audio coding method different from that used to encode the original audio data, such that the data size or bit rate of the new audio data is smaller than the original audio data. 
     The process of converting the original video or audio data contained in the multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502  into the video or audio data of a different data size of bit rate is performed, for example, by the stream input/output unit  8503  and the signal processing unit  8504 . More specifically, under instructions given from the control unit, the stream input/output unit  8503  demultiplexes video data, audio data, contents of data broadcast service etc. from the multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502 . Under instructions given from the control unit, the signal processing unit  8504  converts the demultiplexed video data and audio data respectively using a moving picture coding method and an audio coding method each different from the method that was used in the conversion applied to obtain the video and audio data. Under instructions given from the control unit, the stream input/output unit  8503  multiplexes the newly converted video data and audio data to generate new multiplexed data. Note that the signal processing unit  8504  may perform the conversion of either or both of the video or audio data according to instructions given from the control unit. In addition, the sizes of video data and audio data to be obtained by conversion may be specified by the user or determined in advance for the types of the stream output IF  8509 . 
     With the above structure, the reception device  8500  is enabled to output video and audio data after converting the data to a bit rate that matches the transfer rate between the reception device  8500  and an external device. This arrangement ensures that even if multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502  is higher in bit rate than the data transfer rate to an external device, the stream output IF duly outputs new multiplexed data at an appropriate bit rate to the external device. Consequently, the user can use the new multiplexed data on another communication device. 
     Furthermore, the reception device  8500  also includes an audio and visual output interface (hereinafter, AV output IF)  8511  that outputs video and audio signals decoded by the signal processing unit  8504  to an external device via an external transport medium. In one example, the AV output IF  8511  may be a wireless communication device that transmits modulated video and audio signals via a wireless medium to an external device, using a wireless communication scheme compliant with wireless communication standards, such as Wi-Fi (registered trademark), which is a set of standards including IEEE 802.11a, IEEE 802.11b, IEEE 802.11g, and IEEE 802.11n, WiGiG, Wireless HD, Bluetooth, ZigBee, or the like. In another example, the stream output IF  8509  may be a wired communication device that transmits modulated video and audio signals via a transmission line physically connected to the stream output IF  8509  to an external device, using a communication scheme compliant with wired communication standards, such as Ethernet (registered trademark), USB, PLC, HDMI, or the like. In yet another example, the stream output IF  8509  may be a terminal for connecting a cable to output the video and audio signals in analog form. 
     With the above structure, the user is allowed to use, on an external device, the video and audio signals decoded by the signal processing unit  8504 . 
     Furthermore, the reception device  8500  additionally includes an operation input unit  8510  for receiving a user operation. According to control signals indicative of user operations input to the operation input unit  8510 , the reception device  8500  performs various operations, such as switching the power ON or OFF, switching the reception channel, switching the display of subtitle text ON or OFF, switching the display of subtitle text to another language, changing the volume of audio output of the audio output unit  8506 , and changing the settings of channels that can be received. 
     Additionally, the reception device  8500  may have a function of displaying the antenna level indicating the quality of the signal being received by the reception device  8500 . Note that the antenna level is an indicator of the reception quality calculated based on, for example, the Received Signal Strength Indication, Received Signal Strength Indicator (RSSI), received field strength, Carrier-to-noise power ratio (C/N), Bit Error Rate (BER), packet error rate, frame error rate, and channel state information of the signal received on the reception device  8500 . In other words, the antenna level is a signal indicating the level and quality of the received signal. In this case, the demodulation unit  8502  also includes a reception quality measuring unit for measuring the received signal characteristics, such as RSSI, received field strength, C/N, BER, packet error rate, frame error rate, and channel state information. In response to a user operation, the reception device  8500  displays the antenna level (i.e., signal indicating the level and quality of the received signal) on the video display unit  8507  in a manner identifiable by the user. The antenna level (i.e., signal indicating the level and quality of the received signal) may be numerically displayed using a number that represents RSSI, received field strength, C/N, BER, packet error rate, frame error rate, channel state information or the like. Alternatively, the antenna level may be displayed using an image representing RSSI, received field strength, C/N, BER, packet error rate, frame error rate, channel state information or the like. Furthermore, the reception device  8500  may display a plurality of antenna levels (signals indicating the level and quality of the received signal) calculated for each of the plurality of streams s 1 , s 2 , . . . received and separated using the reception schemes shown in the above embodiments, or one antenna level (signal indicating the level and quality of the received signal) calculated from the plurality of streams s 1 , s 2 , . . . . When video data and audio data composing a program are transmitted hierarchically, the reception device  8500  may also display the signal level (signal indicating the level and quality of the received signal) for each hierarchical level. 
     With the above structure, users are able to grasp the antenna level (signal indicating the level and quality of the received signal) numerically or visually during reception with the reception schemes shown in the above embodiments. 
     Although the reception device  8500  is described above as having the audio output unit  8506 , video display unit  8507 , recording unit  8508 , stream output IF  8509 , and AV output IF  8511 , it is not necessary for the reception device  8500  to have all of these units. As long as the reception device  8500  is provided with at least one of the units described above, the user is enabled to use multiplexed data obtained as a result of demodulation and error correction decoding by the demodulation unit  8502 . The reception device  8300  may therefore include any combination of the above-described units depending on its intended use. 
     (Multiplexed Data) 
     The following is a detailed description of an exemplary structure of multiplexed data. The data structure typically used in broadcasting is an MPEG2 transport stream (TS), so therefore the following description is given by way of an example related to MPEG2-TS. It should be naturally appreciated, however, that the data structure of multiplexed data transmitted by the transmission and reception schemes described in the above embodiments is not limited to MPEG2-TS and the advantageous effects of the above embodiments are achieved even if any other data structure is employed. 
       FIG.  86    is a view illustrating an exemplary multiplexed data structure. As illustrated in  FIG.  86   , multiplexed data is obtained by multiplexing one or more elementary streams, which are elements constituting a broadcast program (program or an event which is part of a program) currently provided through respective services. Examples of elementary streams include a video stream, audio stream, presentation graphics (PG) stream, and interactive graphics (IG) stream. In the case where a broadcast program carried by multiplexed data is a movie, the video streams represent main video and sub video of the movie, the audio streams represent main audio of the movie and sub audio to be mixed with the main audio, and the PG stream represents subtitles of the movie. The term “main video” used herein refers to video images normally presented on a screen, whereas “sub video” refers to video images (for example, images of text explaining the outline of the movie) to be presented in a small window inserted within the video images. The IG stream represents an interactive display constituted by presenting GUI components on a screen. 
     Each stream contained in multiplexed data is identified by an identifier called PID uniquely assigned to the stream. For example, the video stream carrying main video images of a movie is assigned with “0x1θ11”, each audio stream is assigned with a different one of “0x1100” to “0x111F”, each PG stream is assigned with a different one of “0x1200” to “0x121F”, each IG stream is assigned with a different one of “0x1400” to “0x141F”, each video stream carrying sub video images of the movie is assigned with a different one of “0x1B00” to “0x1B1F”, each audio stream of sub-audio to be mixed with the main audio is assigned with a different one of “0x1A00” to “0x1A1F”. 
       FIG.  87    is a schematic view illustrating an example of how the respective streams are multiplexed into multiplexed data. First, a video stream  8701  composed of a plurality of video frames is converted into a PES packet sequence  8702  and then into a TS packet sequence  8703 , whereas an audio stream  8704  composed of a plurality of audio frames is converted into a PES packet sequence  8705  and then into a TS packet sequence  8706 . Similarly, the PG stream  8711  is first converted into a PES packet sequence  8712  and then into a TS packet sequence  8713 , whereas the IG stream  8714  is converted into a PES packet sequence  8715  and then into a TS packet sequence  8716 . The multiplexed data  8717  is obtained by multiplexing the TS packet sequences ( 8703 ,  8706 ,  8713  and  8716 ) into one stream. 
       FIG.  88    illustrates the details of how a video stream is divided into a sequence of PES packets. In  FIG.  88   , the first tier shows a sequence of video frames included in a video stream. The second tier shows a sequence of PES packets. As indicated by arrows yy 1 , yy 2 , yy 3 , and yy 4  shown in  FIG.  88   , a plurality of video presentation units, namely I pictures, B pictures, and P pictures, of a video stream are separately stored into the payloads of PES packets on a picture-by-picture basis. Each PES packet has a PES header and the PES header stores a Presentation Time-Stamp (PTS) and Decoding Time-Stamp (DTS) indicating the display time and decoding time of a corresponding picture. 
       FIG.  89    illustrates the format of a TS packet to be eventually written as multiplexed data. The TS packet is a fixed length packet of 188 bytes and has a 4-byte TS header containing such information as PID identifying the stream and a 184-byte TS payload carrying actual data. The PES packets described above are divided to be stored into the TS payloads of TS packets. In the case of BD-ROM, each TS packet is attached with a TP_Extra_Header of 4 bytes to build a 192-byte source packet, which is to be written as multiplexed data. The TP_Extra_Header contains such information as an Arrival_Time_Stamp (ATS). The ATS indicates a time for starring transfer of the TS packet to the PID filter of a decoder. As shown on the lowest tier in  FIG.  89   , multiplexed data includes a sequence of source packets each bearing a source packet number (SPN), which is a number incrementing sequentially from the start of the multiplexed data. 
     In addition to the TS packets storing streams such as video, audio, and PG streams, multiplexed data also includes TS packets storing a Program Association Table (PAT), a Program Map Table (PMT), and a Program Clock Reference (PCR). The PAT in multiplexed data indicates the PID of a PMT used in the multiplexed data, and the PID of the PAT is “0”. The PMT includes PIDs identifying the respective streams, such as video, audio and subtitles, contained in multiplexed data and attribute information (frame rate, aspect ratio, and the like) of the streams identified by the respective PIDs. In addition, the PMT includes various types of descriptors relating to the multiplexed data. One of such descriptors may be copy control information indicating whether or not copying of the multiplexed data is permitted. The PCR includes information for synchronizing the Arrival Time Clock (ATC), which is the time axis of ATS, with the System Time Clock (STC), which is the time axis of PTS and DTS. More specifically, the PCR packet includes information indicating an STC time corresponding to the ATS at which the PCR packet is to be transferred. 
       FIG.  90    is a view illustrating the data structure of the PMT in detail. The PMT starts with a PMT header indicating, for example, the length of data contained in the PMT. Following the PMT header, descriptors relating to the multiplexed data are disposed. One example of a descriptor included in the PMT is copy control information described above. Following the descriptors, pieces of stream information relating to the respective streams included in the multiplexed data are arranged. Each piece of stream information is composed of stream descriptors indicating a stream type identifying a compression codec employed for a corresponding stream, a PID of the stream, and attribute information (frame rate, aspect ratio, and the like) of the stream. The PMT includes as many stream descriptors as the number of streams included in the multiplexed data. 
     When recorded onto a recoding medium, for example, the multiplexed data is recorded along with a multiplexed data information file. 
       FIG.  91    is a view illustrating the structure of the multiplexed data file information. As illustrated in  FIG.  91   , the multiplexed data information file is management information of corresponding multiplexed data and is composed of multiplexed data information, stream attribute information, and an entry map. Note that multiplexed data information files and multiplexed data are in a one-to-one relationship. 
     As illustrated in  FIG.  91   , the multiplexed data information is composed of a system rate, playback start time, and playback end time. The system rate indicates the maximum transfer rate of the multiplexed data to the PID filter of a system target decoder, which is described later. The multiplexed data includes ATSs at intervals set so as not to exceed the system rate. The playback start time is set to the time specified by the PTS of the first video frame in the multiplexed data, whereas the playback end time is set to the time calculated by adding the playback period of one frame to the PTS of the last video frame in the multiplexed data. 
       FIG.  92    illustrates the structure of stream attribute information contained in multiplexed data file information. As illustrated in  FIG.  92   , the stream attribute information includes pieces of attribute information of the respective streams included in multiplexed data, and each piece of attribute information is registered with a corresponding PID. That is, different pieces of attribute information are provided for different streams, namely a video stream, an audio stream, a PG stream and an IG stream. The video stream attribute information indicates the compression codec employed to compress the video stream, the resolutions of individual pictures constituting the video stream, the aspect ratio, the frame rate, and so on. The audio stream attribute information indicates the compression codec employed to compress the audio stream, the number of channels included in the audio stream, the language of the audio stream, the sampling frequency, and so on. These pieces of information are used to initialize a decoder before playback by a player. 
     In the present embodiment, from among the pieces of information included in the multiplexed data, the stream type included in the PMT is used. In the case where the multiplexed data is recorded on a recording medium, the video stream attribute information included in the multiplexed data information is used. More specifically, the moving picture coding method and device described in any of the above embodiments may be modified to additionally include a step or unit of setting a specific piece of information in the stream type included in the PMT or in the video stream attribute information. The specific piece of information is for indicating that the video data is generated by the moving picture coding method and device described in the embodiment. With the above structure, video data generated by the moving picture coding method and device described in any of the above embodiments is distinguishable from video data compliant with other standards. 
       FIG.  93    illustrates an exemplary structure of a video and audio output device  9300  that includes a reception device  9304  for receiving a modulated signal carrying video and audio data or data for data broadcasting from a broadcasting station (base station). Note that the structure of the reception device  9304  corresponds to the reception device  8500  illustrated in  FIG.  85   . The video and audio output device  9300  is installed with an Operating System (OS), for example, and also with a communication device  9306  (a communication device for a wireless Local Area Network (LAN) or Ethernet, for example) for establishing an Internet connection. With this structure, hypertext (World Wide Web (WWW))  9303  provided over the Internet can be displayed on a display area  9301  simultaneously with images  9302  reproduced on the display area  9301  from the video and audio data or data provided by data broadcasting. By operating a remote control (which may be a mobile phone or keyboard)  9307 , the user can make a selection on the images  9302  reproduced from data provided by data broadcasting or the hypertext  9303  provided over the Internet to change the operation of the video and audio output device  9300 . For example, by operating the remote control to make a selection on the hypertext  9303  provided over the Internet, the user can change the WWW site currently displayed to another site. Alternatively, by operating the remote control  9307  to make a selection on the images  9302  reproduced from the video or audio data or data provided by the data broadcasting, the user can transmit information indicating a selected channel (such as a selected broadcast program or audio broadcasting). In response, an interface (IF)  9305  acquires information transmitted from the remote control, so that the reception device  9304  operates to obtain reception data by demodulation and error correction decoding of a signal carried on the selected channel. At this time, the reception device  9304  receives control symbols included in a signal corresponding to the selected channel and containing information indicating the transmission scheme of the signal (exactly as described in Embodiments A1 through A4 and as shown in  FIGS.  5  and  41   ). With this information, the reception device  9304  is enabled to make appropriate settings for the receiving operations, demodulation scheme, scheme of error correction decoding, and the like to duly receive data included in data symbols transmitted from a broadcasting station (base station). Although the above description is directed to an example in which the user selects a channel using the remote control  9307 , the same description applies to an example in which the user selects a channel using a selection key provided on the video and audio output device  9300 . 
     In addition, the video and audio output device  9300  may be operated via the Internet. For example, a terminal connected to the Internet may be used to make settings on the video and audio output device  9300  for pre-programmed recording (storing). (The video and audio output device  9300  therefore would have the recording unit  8508  as illustrated in  FIG.  85   .) In this case, before starting the pre-programmed recording, the video and audio output device  9300  selects the channel, so that the reception device  9304  operates to obtain reception data by demodulation and error correction decoding of a signal carried on the selected channel. At this time, the reception device  9304  receives control symbols included in a signal corresponding to the selected channel and containing information indicating the transmission scheme (the transmission scheme, modulation scheme, error correction scheme, and the like in the above embodiments) of the signal (exactly as described in Embodiments A1 through A4 and as shown in  FIGS.  5  and  41   ). With this information, the reception device  9304  is enabled to make appropriate settings for the receiving operations, demodulation scheme, scheme of error correction decoding, and the like to duly receive data included in data symbols transmitted from a broadcasting station (base station). 
     Embodiment C1 
     Embodiment 2 describes a precoding scheme of regularly hopping between precoding matrices, and (Example #1) and (Example #2) as schemes of setting precoding matrices in consideration of poor reception points. The present embodiment is directed to generalization of (Example #1) and (Example #2) described in Embodiment 2. 
     With respect to a scheme of regularly hopping between precoding matrices with an N-slot period (cycle), a precoding matrix prepared for an N-slot period (cycle) is represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             566 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         i 
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #1 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). (Let a&gt;0.) In the present embodiment, a unitary matrix is used and the precoding matrix in Equation #1 is represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             567 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         i 
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #2 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). (Let a&gt;0.) (In order to simplify the mapping performed by the transmission device and the reception device, it is preferable that λ be one of the following fixed values: 0 radians; π/2 radians; π radians; and (3π)/2 radians.) Embodiment 2 is specifically implemented under the assumption α=1. In Embodiment 2, Equation #2 is represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             568 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #3 
                 
               
             
           
         
       
     
     In order to distribute the poor reception points evenly with regards to phase in the complex plane, as described in Embodiment 2, Condition #101 or #102 is provided in Equation #1 or #2. 
     
       
         
           
             Math 
             ⁢ 
                 
             569 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 
                                   x 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               - 
                                 
                               
                                 
                                   θ 
                                   21 
                                 
                                 ( 
                                 
                                   x 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 x 
                                 ) 
                               
                               - 
                                 
                               
                                 
                                   θ 
                                   21 
                                 
                                 ( 
                                 x 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                     
                     = 
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             π 
                             N 
                           
                           ) 
                         
                       
                       ⁢ 
                           
                       for 
                     
                   
                   ⁢ 
                   
 
                   
                     ∀ 
                     
                       x 
                       ⁡ 
                       ( 
                       
                         
                           x 
                           = 
                           0 
                         
                         , 
                         1 
                         , 
                         2 
                         , 
                         … 
                             
                         , 
                         
                           N 
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #101 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             570 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 
                                   x 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               - 
                                 
                               
                                 
                                   θ 
                                   21 
                                 
                                 ( 
                                 
                                   x 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   θ 
                                   11 
                                 
                                 ( 
                                 x 
                                 ) 
                               
                               - 
                                 
                               
                                 
                                   θ 
                                   21 
                                 
                                 ( 
                                 x 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                     
                     = 
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             - 
                             
                               π 
                               N 
                             
                           
                           ) 
                         
                       
                       ⁢ 
                           
                       for 
                     
                   
                   ⁢ 
                   
 
                   
                     ∀ 
                     
                       x 
                       ⁢ 
                       
                         ( 
                         
                           
                             x 
                             = 
                             0 
                           
                           , 
                           1 
                           , 
                           2 
                           , 
                           … 
                               
                           , 
                           
                             N 
                             - 
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #102 
                 
               
             
           
         
       
     
     Especially, when θ 11 (i) is a fixed value independent of i, Condition #103 or #104 may be provided. 
     
       
         
           
             Math 
             ⁢ 
                 
             571 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             
                               x 
                               + 
                               1 
                             
                             ) 
                           
                         
                       
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             x 
                             ) 
                           
                         
                       
                     
                     = 
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             π 
                             N 
                           
                           ) 
                         
                       
                       ⁢ 
                           
                       for 
                     
                   
                   ⁢ 
                   
 
                   
                     ∀ 
                     
                       x 
                       ⁡ 
                       ( 
                       
                         
                           x 
                           = 
                           0 
                         
                         , 
                         1 
                         , 
                         2 
                         , 
                         … 
                             
                         , 
                         
                           N 
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #103 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             572 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             
                               x 
                               + 
                               1 
                             
                             ) 
                           
                         
                       
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             x 
                             ) 
                           
                         
                       
                     
                     = 
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             - 
                             
                               π 
                               N 
                             
                           
                           ) 
                         
                       
                       ⁢ 
                           
                       for 
                     
                   
                   ⁢ 
                   
 
                   
                     ∀ 
                     
                       x 
                       ⁢ 
                       
                         ( 
                         
                           
                             x 
                             = 
                             0 
                           
                           , 
                           1 
                           , 
                           2 
                           , 
                           … 
                               
                           , 
                           
                             N 
                             - 
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #104 
                 
               
             
           
         
       
     
     Similarly, when θ 21 (i) is a fixed value independent of i, Condition #105 or #106 may be provided. 
     
       
         
           
             Math 
             ⁢ 
                 
             573 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               11 
                             
                             ( 
                             
                               x 
                               + 
                               1 
                             
                             ) 
                           
                         
                       
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               11 
                             
                             ( 
                             x 
                             ) 
                           
                         
                       
                     
                     = 
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             π 
                             N 
                           
                           ) 
                         
                       
                       ⁢ 
                           
                       for 
                     
                   
                   ⁢ 
                   
 
                   
                     ∀ 
                     
                       x 
                       ⁡ 
                       ( 
                       
                         
                           x 
                           = 
                           0 
                         
                         , 
                         1 
                         , 
                         2 
                         , 
                         … 
                             
                         , 
                         
                           N 
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #105 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             574 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               11 
                             
                             ( 
                             
                               x 
                               + 
                               1 
                             
                             ) 
                           
                         
                       
                       
                         e 
                         
                           j 
                           ⁢ 
                           
                             
                               θ 
                               11 
                             
                             ( 
                             x 
                             ) 
                           
                         
                       
                     
                     = 
                     
                       
                         e 
                         
                           j 
                           ⁡ 
                           ( 
                           
                             - 
                             
                               π 
                               N 
                             
                           
                           ) 
                         
                       
                       ⁢ 
                           
                       for 
                     
                   
                   ⁢ 
                   
 
                   
                     ∀ 
                     
                       x 
                       ⁡ 
                       ( 
                       
                         
                           x 
                           = 
                           0 
                         
                         , 
                         1 
                         , 
                         2 
                         , 
                         … 
                             
                         , 
                         
                           N 
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #106 
                 
               
             
           
         
       
     
     The following is an example of a precoding matrix using the above-mentioned unitary matrix for the scheme of regularly hopping between precoding matrices with an N-slot period (cycle). A precoding matrix that is based on Equation #2 and prepared for an N-slot period (cycle) is represented as follows. (In Equation #2, λ is 0 radians, and θ 11 (i) is 0 radians.) 
     
       
         
           
             Math 
             ⁢ 
                 
             575 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #10 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). (Let α&gt;0.) Also, Condition #103 or #104 is satisfied. In addition, θ 21  (i=0) may be set to a certain value, such as 0 radians. 
     With respect to a scheme of regularly hopping between precoding matrices with an N-slot period (cycle), another example of a precoding matrix prepared for an N-slot period (cycle) is represented as follows. (In Equation #2, λ is 0 radians, and θ 11 (i) is 0 radians.) 
     
       
         
           
             Math 
             ⁢ 
                 
             576 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #9 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). (Let α&gt;0.) Also, Condition #103 or #104 is satisfied. In addition, θ 21  (i=0) may be set to a certain value, such as 0 radians. 
     As yet another example, a precoding matrix prepared for an N-slot period (cycle) is represented as follows. (In Equation #2, λ is 0 radians, and θ 21 (i) is 0 radians.) 
     
       
         
           
             Math 
             ⁢ 
                 
             577 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ( 
                                     
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #12 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). (Let α&gt;0.) Also, Condition #105 or #106 is satisfied. In addition, θ 11  (i=0) may be set to a certain value, such as 0 radians. 
     As yet another example, a precoding matrix prepared for an N-slot period (cycle) is represented as follows. 
     (In Equation #2, λ is π radians, and θ 21 (i) is 0 radians.) 
     
       
         
           
             Math 
             ⁢ 
                 
             578 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ( 
                                     
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #13 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1) (let α&gt;0), and Condition #105 or #106 is satisfied. In addition, θ 11 =0) may be set to a certain value, such as 0 radians. 
     In view of the examples of Embodiment 2, yet another example of a precoding matrix prepared for an N-slot period (cycle) is represented as follows. (In Equation #3, λ is 0 radians, and θ 11 (i) is 0 radians.) 
     
       
         
           
             Math 
             ⁢ 
                 
             579 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                 + 
                                 π 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #14 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and Condition #103 or #104 is satisfied. In addition, θ 21  (i=0) may be set to a certain value, such as 0 radians. 
     With respect to a scheme of regularly hopping between precoding matrices with an N-slot period (cycle), yet another example of a precoding matrix prepared for an N-slot period (cycle) is represented as follows. (In Equation #3, λ is π radians, and θ 11 (i) is 0 radians.) 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   580 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #15 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and Condition #103 or #104 is satisfied. In addition, θ 21  (i=0) may be set to a certain value, such as 0 radians. 
     As yet another example, a precoding matrix prepared for an N-slot period (cycle) is represented as follows. (In Equation #3, λ is 0 radians, and θ 21 (i) is 0 radians.) 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   581 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #16 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and Condition #105 or #106 is satisfied. In addition, θ 11  (i=0) may be set to a certain value, such as 0 radians. 
     As yet another example, a precoding matrix prepared for an N-slot period (cycle) is represented as follows. (In Equation #3, λ is π radians, and θ 21 (i) is 0 radians.) 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   582 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         i 
                                         ) 
                                       
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #17 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and Condition #105 or #106 is satisfied. In addition, θ 11  (i=0) may be set to a certain value, such as 0 radians. 
     As compared to the precoding scheme of regularly hopping between precoding matrices described in Embodiment 9, the precoding scheme pertaining to the present embodiment has a probability of achieving high data reception quality even if the length of the period (cycle) pertaining to the present embodiment is reduced to approximately half of the length of the period (cycle) pertaining to Embodiment 9. Therefore, the precoding scheme pertaining to the present embodiment can reduce the number of precoding matrices to be prepared, which brings about the advantageous effect of reducing the scale of circuits for the transmission device and the reception device. The above advantageous effect can be enhanced with a transmission device that is provided with one encoder and distributes encoded data as shown in  FIG.  4   , or with a reception device corresponding to such a transmission device. 
     A preferable example of a appearing in the above examples can be obtained by using any of the schemes described in Embodiment 18. However, a is not limited to being obtained in this way. 
     In the present embodiment, the scheme of structuring N different precoding matrices for a precoding hopping scheme with an N-slot time period (cycle) has been described. In this case, the N different precoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] are prepared. In the case of a single-carrier transmission scheme, the order F[0], F[1], F[2], . . . , F[N−2], F[N−1] is maintained in the time domain (or the frequency domain). The present invention is not, however, limited in this way, and the N different precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1] generated in the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaption in this case, precoding weights may be changed by arranging symbols in the frequency domain and in the frequency-time domain. Note that a precoding hopping scheme with an N-slot period (cycle) has been described, but the same advantageous effects may be obtained by randomly using N different precoding matrices. In other words, the N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots N in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the N different precoding matrices of the present embodiment are included, the probability of excellent reception quality increases. 
     Embodiment C2 
     The following describes a precoding scheme of regularly hopping between precoding matrices that is different from Embodiment C1 where Embodiment 9 is incorporated—i.e., a scheme of implementing Embodiment C1 in a case where the number of slots in a period (cycle) is an odd number in Embodiment 9. 
     With respect to a scheme of regularly hopping between precoding matrices with an N-slot period (cycle), a precoding matrix prepared for an N-slot period (cycle) is represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   583 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         i 
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #18 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1) (let α&gt;0). In the present embodiment, a unitary matrix is used and the precoding matrix in Equation #1 is represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   584 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         i 
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #19 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1) (let α&gt;0). (In order to simplify the mapping performed by the transmission device and the reception device, it is preferable that λ be one of the following fixed values: 0 radians; π/2 radians; π radians; and (3π)/2 radians.) Specifically, it is assumed here that α=1. Here, Equation #19 is represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   585 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #20 
                 
               
             
           
         
       
     
     The precoding matrices used in the precoding scheme of regularly hopping between precoding matrices pertaining to the present embodiment are expressed in the above manner. The present embodiment is characterized in that the number of slots in an N-slot period (cycle) for the precoding scheme of regularly hopping between precoding matrices pertaining to the present embodiment is an odd number, i.e., expressed as N=2n+1. To realize an N-slot period (cycle) where N=2n+1, the number of different precoding matrices to be prepared is n+1 (note, the description of these different precoding matrices will be given later). From among the n+1 different precoding matrices, each of the n precoding matrices is used twice in one period (cycle), and the remaining one precoding matrix is used once in one period (cycle), which results in an N-slot period (cycle) where N=2n+1. The following is a detailed description of these precoding matrices. 
     Assume that the n+1 different precoding matrices, which are necessary to implement the precoding scheme of regularly hopping between precoding matrices with an N-slot period (cycle) where N=2n+1, are F[0], F[1], . . . , F[i], . . . , F[n−1], F[n] (i=0, 1, 2, . . . , n−2, n−1, n (i being an integer in a range of 0 to n)). Here, the n+1 different precoding matrices F[0], F[1], . . . , F[i], . . . , F[n−1], F[n] based on Equation #19 are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   586 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         θ 
                                         11 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ( 
                                     
                                   
                                     
                                       θ 
                                       11 
                                     
                                     + 
                                     
                                       
                                         2 
                                         ⁢ 
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       
                                         
                                           2 
                                           ⁢ 
                                           n 
                                         
                                         + 
                                         1 
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     + 
                                     
                                       
                                         2 
                                         ⁢ 
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       
                                         
                                           2 
                                           ⁢ 
                                           n 
                                         
                                         + 
                                         1 
                                       
                                     
                                     + 
                                     λ 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #21 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , n−2, n−1, n (i being an integer in a range of 0 to n). Out of the n+1 different precoding matrices according to Equation #21 (namely, F[0], F[1], . . . , F[i], . . . , F[n−1], F[n]), F[0] is used once, and each of F[1] through F[n] is used twice (i.e., F[1] is used twice, F[2] is used twice, . . . , F[n−1] is used twice, and F[n] is used twice). As a result, the precoding scheme of regularly hopping between precoding matrices with an N-slot period (cycle) where N=2n+1 is achieved, and the reception device can achieve excellent data reception quality, similarly to the case where the number of slots in a period (cycle) for the precoding scheme of regularly hopping between precoding matrices is an odd number in Embodiment 9. In this case, high data reception quality may be achieved even if the length of the period (cycle) pertaining to the present embodiment is reduced to approximately half of the length of the period (cycle) pertaining to Embodiment 9. This can reduce the number of precoding matrices to be prepared, which brings about the advantageous effect of reducing the scale of circuits for the transmission device and the reception device. The above advantageous effect can be enhanced with a transmission device that is provided with one encoder and distributes encoded data as shown in  FIG.  4   , or with a reception device corresponding to such a transmission device. 
     Especially, when λ=0 radians and θ 11 =0 radians, the above equation can be expressed as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   587 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ( 
                                     
                                   
                                     
                                       2 
                                       ⁢ 
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     
                                       
                                         2 
                                         ⁢ 
                                         n 
                                       
                                       + 
                                       1 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         2 
                                         ⁢ 
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       
                                         
                                           2 
                                           ⁢ 
                                           n 
                                         
                                         + 
                                         1 
                                       
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #22 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , n−2, n−1, n (i being an integer in a range of 0 to n). Out of the n+1 different precoding matrices according to Equation #22 (namely, F[0], F[1], . . . , F[i], . . . , F[n−1], F[n]), F[0] is used once, and each of F[1] through F[n] is used twice (i.e., F[1] is used twice, F[2] is used twice, . . . , F[n−1] is used twice, and F[n] is used twice). As a result, the precoding scheme of regularly hopping between precoding matrices with an N-slot period (cycle) where N=2n+1 is achieved, and the reception device can achieve excellent data reception quality, similarly to the case where the number of slots in a period (cycle) for the precoding scheme of regularly hopping between precoding matrices is an odd number in Embodiment 9. In this case, high data reception quality may be achieved even if the length of the period (cycle) pertaining to the present embodiment is reduced to approximately half of the length of the period (cycle) pertaining to Embodiment 9. This can reduce the number of precoding matrices to be prepared, which brings about the advantageous effect of reducing the scale of circuits for the transmission device and the reception device. 
     Especially, when λ=π radians and θ 11 =0 radians, the following equation is true. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   588 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ( 
                                     
                                   
                                     
                                       2 
                                       ⁢ 
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     
                                       
                                         2 
                                         ⁢ 
                                         n 
                                       
                                       + 
                                       1 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     
                                       
                                         2 
                                         ⁢ 
                                         n 
                                       
                                       + 
                                       1 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #23 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , n−2, n−1, n (i being an integer in a range of 0 to n). Out of the n+1 different precoding matrices according to Equation #23 (namely, F[0], F[1], . . . , F[i], . . . , F[n−1], F[n]), F[0] is used once, and each of F[1] through F[n] is used twice (i.e., F[1] is used twice, F[2] is used twice, . . . , F[n−1] is used twice, and F[n] is used twice). As a result, the precoding scheme of regularly hopping between precoding matrices with an N-slot period (cycle) where N=2n+1 is achieved, and the reception device can achieve excellent data reception quality, similarly to the case where the number of slots in a period (cycle) for the precoding scheme of regularly hopping between precoding matrices is an odd number in Embodiment 9. In this case, high data reception quality may be achieved even if the length of the period (cycle) pertaining to the present embodiment is reduced to approximately half of the length of the period (cycle) pertaining to Embodiment 9. This can reduce the number of precoding matrices to be prepared, which brings about the advantageous effect of reducing the scale of circuits for the transmission device and the reception device. 
     Furthermore, when α=1 as in the relationships shown in Equation #19 and Equation #20, Equation #21 can be expressed as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   589 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   θ 
                                   11 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   + 
                                   λ 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     θ 
                                     11 
                                   
                                   + 
                                   
                                     
                                       2 
                                       ⁢ 
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     
                                       
                                         2 
                                         ⁢ 
                                         n 
                                       
                                       + 
                                       1 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     + 
                                     
                                       
                                         2 
                                         ⁢ 
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       
                                         
                                           2 
                                           ⁢ 
                                           n 
                                         
                                         + 
                                         1 
                                       
                                     
                                     + 
                                     λ 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #24 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , n−2, n−1, n (i being an integer in a range of 0 to n). Out of the n+1 different precoding matrices according to Equation #24 (namely, F[0], F[1], . . . , F[i], . . . , F[n−1], F[n]), F[0] is used once, and each of F[1] through F[n] is used twice (i.e., F[1] is used twice, F[2] is used twice, . . . , F[n−1] is used twice, and F[n] is used twice). As a result, the precoding scheme of regularly hopping between precoding matrices with an N-slot period (cycle) where N=2n+1 is achieved, and the reception device can achieve excellent data reception quality, similarly to the case where the number of slots in a period (cycle) for the precoding scheme of regularly hopping between precoding matrices is an odd number in Embodiment 9. In this case, high data reception quality may be achieved even if the length of the period (cycle) pertaining to the present embodiment is reduced to approximately half of the length of the period (cycle) pertaining to Embodiment 9. This can reduce the number of precoding matrices to be prepared, which brings about the advantageous effect of reducing the scale of circuits for the transmission device and the reception device. 
     Similarly, when α=1 in Equation #22, the following equation is true. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   590 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     2 
                                     ⁢ 
                                     i 
                                     ⁢ 
                                     π 
                                   
                                   
                                     
                                       2 
                                       ⁢ 
                                       n 
                                     
                                     + 
                                     1 
                                   
                                 
                                 ) 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         2 
                                         ⁢ 
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       
                                         
                                           2 
                                           ⁢ 
                                           n 
                                         
                                         + 
                                         1 
                                       
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #25 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , n−2, n−1, n (i being an integer in a range of 0 to n). Out of the n+1 different precoding matrices according to Equation #25 (namely, F[0], F[1], . . . , F[i], . . . , F[n−1], F[n]), F[0] is used once, and each of F[1] through F[n] is used twice (i.e., F[1] is used twice, F[2] is used twice, . . . , F[n−1] is used twice, and F[n] is used twice). As a result, the precoding scheme of regularly hopping between precoding matrices with an N-slot period (cycle) where N=2n+1 is achieved, and the reception device can achieve excellent data reception quality, similarly to the case where the number of slots in a period (cycle) for the precoding scheme of regularly hopping between precoding matrices is an odd number in Embodiment 9. In this case, high data reception quality may be achieved even if the length of the period (cycle) pertaining to the present embodiment is reduced to approximately half of the length of the period (cycle) pertaining to Embodiment 9. This can reduce the number of precoding matrices to be prepared, which brings about the advantageous effect of reducing the scale of circuits for the transmission device and the reception device. 
     Similarly, when α=1 in Equation #23, the following equation is true. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   591 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     2 
                                     ⁢ 
                                     i 
                                     ⁢ 
                                     π 
                                   
                                   
                                     
                                       2 
                                       ⁢ 
                                       n 
                                     
                                     + 
                                     1 
                                   
                                 
                                 ) 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       i 
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                                         2 
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                                         n 
                                       
                                       + 
                                       1 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #26 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , n−2, n−1, n (i being an integer in a range of 0 to n). Out of the n+1 different precoding matrices according to Equation #26 (namely, F[0], F[1], . . . , F[i], . . . , F[n−1], F[n]), F[0] is used once, and each of F[1] through F[n] is used twice (i.e., F[1] is used twice, F[2] is used twice, . . . , F[n−1] is used twice, and F[n] is used twice). As a result, the precoding scheme of regularly hopping between precoding matrices with an N-slot period (cycle) where N=2n+1 is achieved, and the reception device can achieve excellent data reception quality, similarly to the case where the number of slots in a period (cycle) for the precoding scheme of regularly hopping between precoding matrices is an odd number in Embodiment 9. In this case, high data reception quality may be achieved even if the length of the period (cycle) pertaining to the present embodiment is reduced to approximately half of the length of the period (cycle) pertaining to Embodiment 9. This can reduce the number of precoding matrices to be prepared, which brings about the advantageous effect of reducing the scale of circuits for the transmission device and the reception device. 
     A preferable example of a appearing in the above examples can be obtained by using any of the schemes described in Embodiment 18. However, a is not limited to being obtained in this way. 
     According to the present embodiment, in the case of a single-carrier transmission scheme, the precoding matrices W[0], W[1], . . . , W[2n−1], W[2n] (which are constituted by F[0], F[1], F[2], . . . , F[n−1], F[n]) for a precoding hopping scheme with a an N-slot period (cycle) where N=2n+1 (i.e., a precoding scheme of regularly hopping between precoding matrices with an N-slot period (cycle) where N=2n+1) are arranged in the order W[0], W[1], . . . , W[2n−1], W[2n] in the time domain (or the frequency domain). The present invention is not, however, limited in this way, and the precoding matrices W[0], W[1], . . . , W[2n−1], W[2n] may be applied to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaption in this case, precoding weights may be changed by arranging symbols in the frequency domain and in the frequency-time domain. Although the above has described the precoding hopping scheme with an N-slot period (cycle) where N=2n+1, the same advantageous effects may be obtained by randomly using W[0], W[1], . . . , W[2n−1], W[2n]. In other words, W[0], W[1], . . . , W[2n−1], W[2n] do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots N=2n+1 in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the N different precoding matrices of the present embodiment are included, the probability of excellent reception quality increases. 
     Embodiment C3 
     The present embodiment provides detailed descriptions of a case where, as shown in Non-Patent Literature 12 through Non-Patent Literature 15, a Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) code (or an LDPC (block) code other than a QC-LDPC code) and a block code (e.g., a concatenated code consisting of an LDPC code and a Bose-Chaudhuri-Hocquenghem (BCH) code, and a turbo code) are used, especially when the scheme of regularly hopping between precoding matrices described in Embodiments 16 through 26 and C1 is employed. This embodiment describes an example of transmitting two streams, s 1  and s 2 . However, for the case of coding using block codes, when control information or the like is not necessary, the number of bits in a coded block matches the number of bits composing the block code (the control information or the like listed below may, however, be included therein). For the case of coding using block codes, when control information or the like (such as a cyclic redundancy check (CRC), transmission parameters, or the like) is necessary, the number of bits in a coded block is the sum of the number of bits composing the block code and the number of bits in the control information or the like. 
       FIG.  97    shows a modification of the number of symbols and of slots necessary for one coded block when using block coding.  FIG.  97    “shows a modification of the number of symbols and of slots necessary for one coded block when using block coding” for the case when, for example as shown in the transmission device in  FIG.  4   , two streams, s 1  and s 2 , are transmitted, and the transmission device has one encoder. (In this case, the transmission scheme may be either single carrier transmission, or multicarrier transmission such as OFDM.) 
     As shown in  FIG.  97   , the number of bits constituting one block that has been encoded via block coding is set to 6,000. In order to transmit these 6,000 bits, 3,000 symbols are required when the modulation scheme is QPSK, 1,500 when the modulation scheme is 16QAM, and 1,000 when the modulation scheme is 64QAM. 
     Since the transmission device in  FIG.  4    simultaneously transmits two streams, 1,500 of the 3,000 symbols when the modulation scheme is QPSK are allocated to s 1 , and 1,500 to s 2 . Therefore, 1,500 slots (the term “slot” is used here) are required to transmit the 1,500 symbols transmitted in s 1  and the 1,500 symbols transmitted in s 2 . 
     By similar reasoning, when the modulation scheme is 16QAM, 750 slots are necessary to transmit all of the bits constituting one coded block, and when the modulation scheme is 64QAM, 500 slots are necessary to transmit all of the bits constituting one block. 
     The following describes the relationship between the slots defined above and the precoding matrices in the scheme of regularly hopping between precoding matrices. 
     Here, the number of precoding matrices prepared for the scheme of regularly hopping between precoding matrices is set to five. In other words, five different precoding matrices are prepared for the weighting unit in the transmission device in  FIG.  4    (the weighting unit selects one of the plurality of precoding matrices and performs precoding for each slot). These five different precoding matrices are represented as F[0], F[1], F[2], F[3], and F[4]. 
     When the modulation scheme is QPSK, among the 1,500 slots described above for transmitting the 6,000 bits constituting one coded block, it is necessary for 300 slots to use the precoding matrix F[0], 300 slots to use the precoding matrix F[1], 300 slots to use the precoding matrix F[2], 300 slots to use the precoding matrix F[3], and 300 slots to use the precoding matrix F[4]. This is because if use of the precoding matrices is biased, the reception quality of data is greatly influenced by the precoding matrix that was used a greater number of times. 
     When the modulation scheme is 16QAM, among the 750 slots described above for transmitting the 6,000 bits constituting one coded block, it is necessary for 150 slots to use the precoding matrix F[0], 150 slots to use the precoding matrix F[1], 150 slots to use the precoding matrix F[2], 150 slots to use the precoding matrix F[3], and 150 slots to use the precoding matrix F[4]. 
     When the modulation scheme is 64QAM, among the 500 slots described above for transmitting the 6,000 bits constituting one coded block, it is necessary for 100 slots to use the precoding matrix F[0], 100 slots to use the precoding matrix F[1], 100 slots to use the precoding matrix F[2], 100 slots to use the precoding matrix F[3], and 100 slots to use the precoding matrix F[4]. 
     As described above, in the scheme of regularly hopping between precoding matrices, if there are N different precoding matrices (represented as F[0], F[1], F[2], . . . , F[N−2], and F[N−1]), when transmitting all of the bits constituting one coded block, Condition #107 should be satisfied, wherein K 0  is the number of slots using the precoding matrix F[0], K 1  is the number of slots using the precoding matrix F[1], K i  is the number of slots using the precoding matrix F[i] (i=0, 1, 2, . . . , N−1 (i being an integer in a range of 0 to N−1)), and K N−1  is the number of slots using the precoding matrix F[N−1].
 
 K   0   =K   1   = . . . =K   i   = . . . =K   N−1 , i.e.  K   a   =K   b  (for ∀ a,∀b , where  a,b= 0,1,2, . . . , N− 1 (each of  a  and  b  being an integer in a range of 0 to  N− 1), and  a≠b ).  Condition #107
 
     If the communications system supports a plurality of modulation schemes, and the modulation scheme that is used is selected from among the supported modulation schemes, then a modulation scheme for which Condition #107 is satisfied should be selected. 
     When a plurality of modulation schemes are supported, it is typical for the number of bits that can be transmitted in one symbol to vary from modulation scheme to modulation scheme (although it is also possible for the number of bits to be the same), and therefore some modulation schemes may not be capable of satisfying Condition #107. In such a case, instead of Condition #107, the following condition should be satisfied.
 
The difference between  K   a  and  K   b  is 0 or 1, i.e. | K   a   −K   b | is 0 or 1 (for ∀ a,∀b , where  a,b= 0,1,2, . . . , N− 1 (each of  a  and  b  being an integer in  a  range of 0 to  N− 1), and  a≠b ).  Condition #108
 
       FIG.  98    shows a modification of the number of symbols and of slots necessary for two coded blocks when using block coding.  FIG.  98    “shows a modification of the number of symbols and of slots necessary for two coded blocks when using block coding” for the case when, for example as shown in the transmission device in  FIG.  3    and in  FIG.  13   , two streams are transmitted, i.e. s 1  and s 2 , and the transmission device has two encoders. (In this case, the transmission scheme may be either single carrier transmission, or multicarrier transmission such as OFDM.) 
     As shown in  FIG.  98   , the number of bits constituting one block that has been encoded via block coding is set to 6,000. In order to transmit these 6,000 bits, 3,000 symbols are required when the modulation scheme is QPSK, 1,500 when the modulation scheme is 16QAM, and 1,000 when the modulation scheme is 64QAM. 
     The transmission device in  FIG.  3    or in  FIG.  13    transmits two streams simultaneously, and since two encoders are provided, different coded blocks are transmitted in the two streams. Accordingly, when the modulation scheme is QPSK, two coded blocks are transmitted in s 1  and s 2  within the same interval. For example, a first coded block is transmitted in s 1 , and a second coded block is transmitted in s 2 , and therefore, 3,000 slots are required to transmit the first and second coded blocks. 
     By similar reasoning, when the modulation scheme is 16QAM, 1,500 slots are necessary to transmit all of the bits constituting two coded blocks, and when the modulation scheme is 64QAM, 1,000 slots are necessary to transmit all of the bits constituting two blocks. 
     The following describes the relationship between the slots defined above and the precoding matrices in the scheme of regularly hopping between precoding matrices. 
     Here, the number of precoding matrices prepared for the scheme of regularly hopping between precoding matrices is set to five. In other words, five different precoding matrices are prepared for the weighting unit in the transmission device in  FIG.  3    or in  FIG.  13    (the weighting unit selects one of the plurality of precoding matrices and performs precoding for each slot). These five different precoding matrices are represented as F[0], F[1], F[2], F[3], and F[4]. 
     When the modulation scheme is QPSK, among the 3,000 slots described above for transmitting the 6,000×2 bits constituting two coded blocks, it is necessary for 600 slots to use the precoding matrix F[0], 600 slots to use the precoding matrix F[1], 600 slots to use the precoding matrix F[2], 600 slots to use the precoding matrix F[3], and 600 slots to use the precoding matrix F[4]. This is because if use of the precoding matrices is biased, the reception quality of data is greatly influenced by the precoding matrix that was used a greater number of times. 
     To transmit the first coded block, it is necessary for the slot using the precoding matrix F[0] to occur 600 times, the slot using the precoding matrix F[1] to occur 600 times, the slot using the precoding matrix F[2] to occur 600 times, the slot using the precoding matrix F[3] to occur 600 times, and the slot using the precoding matrix F[4] to occur 600 times. To transmit the second coded block, the slot using the precoding matrix F[0] should occur 600 times, the slot using the precoding matrix F[1] should occur 600 times, the slot using the precoding matrix F[2] should occur 600 times, the slot using the precoding matrix F[3] should occur 600 times, and the slot using the precoding matrix F[4] should occur 600 times. 
     Similarly, when the modulation scheme is 16QAM, among the 1,500 slots described above for transmitting the 6,000×2 bits constituting two coded blocks, it is necessary for 300 slots to use the precoding matrix F[0], 300 slots to use the precoding matrix F[1], 300 slots to use the precoding matrix F[2], 300 slots to use the precoding matrix F[3], and 300 slots to use the precoding matrix F[4]. 
     To transmit the first coded block, it is necessary for the slot using the precoding matrix F[0] to occur 300 times, the slot using the precoding matrix F[1] to occur 300 times, the slot using the precoding matrix F[2] to occur 300 times, the slot using the precoding matrix F[3] to occur 300 times, and the slot using the precoding matrix F[4] to occur 300 times. To transmit the second coded block, the slot using the precoding matrix F[0] should occur 300 times, the slot using the precoding matrix F[1] should occur 300 times, the slot using the precoding matrix F[2] should occur 300 times, the slot using the precoding matrix F[3] should occur 300 times, and the slot using the precoding matrix F[4] should occur 300 times. 
     Similarly, when the modulation scheme is 64QAM, among the 1,000 slots described above for transmitting the 6,000×2 bits constituting two coded blocks, it is necessary for 200 slots to use the precoding matrix F[0], 200 slots to use the precoding matrix F[1], 200 slots to use the precoding matrix F[2], 200 slots to use the precoding matrix F[3], and 200 slots to use the precoding matrix F[4]. 
     To transmit the first coded block, it is necessary for the slot using the precoding matrix F[0] to occur 200 times, the slot using the precoding matrix F[1] to occur 200 times, the slot using the precoding matrix F[2] to occur 200 times, the slot using the precoding matrix F[3] to occur 200 times, and the slot using the precoding matrix F[4] to occur 200 times. To transmit the second coded block, the slot using the precoding matrix F[0] should occur 200 times, the slot using the precoding matrix F[1] should occur 200 times, the slot using the precoding matrix F[2] should occur 200 times, the slot using the precoding matrix F[3] should occur 200 times, and the slot using the precoding matrix F[4] should occur 200 times. 
     As described above, in the scheme of regularly hopping between precoding matrices, if there are N different precoding matrices (represented as F[0], F[1], F[2], . . . , F[N−2], and F[N−1]), when transmitting all of the bits constituting two coded blocks, Condition #109 should be satisfied, wherein K 0  is the number of slots using the precoding matrix F[0], K 1  is the number of slots using the precoding matrix F[1], K i  is the number of slots using the precoding matrix F[i] (i=0, 1, 2, . . . , N−1 (i being an integer in a range of 0 to N−1)), and K N−1  is the number of slots using the precoding matrix F[N−1].
 
 K   0   =K   1   = . . . =K   i   = . . . =K   N−1 , i.e.  K   a   =K   b  (for ∀ a,∀b , where  a,b= 0,1,2, . . . , N− 1 (each of  a  and  b  being an integer in a range of 0 to  N− 1), and  a≠b ).  Condition #109
 
     When transmitting all of the bits constituting the first coded block, Condition #110 should be satisfied, wherein K 0,1  is the number of times the precoding matrix F[0] is used, K 1,1  is the number of times the precoding matrix F[1] is used, K i,1  is the number of times the precoding matrix F[i] is used (i=0, 1, 2, . . . , N−1 (i being an integer in a range of 0 to N−1)), and K N−1,1  is the number of times the precoding matrix F[N−1] is used.
 
 K   0,1   =K   1,1   = . . . =K   i,1   = . . . =K   N−1,1 , i.e.  K   a,1   =K   b,1  (for ∀ a,∀b , where  a,b= 0,1,2, . . . , N− 1(each of  a  and  b  being an integer in a range of 0 to  N− 1), and  a≠b ).  Condition #110
 
     When transmitting all of the bits constituting the second coded block, Condition #111 should be satisfied, wherein K 0,2  is the number of times the precoding matrix F[0] is used, K i,2  is the number of times the precoding matrix F[1] is used, K i,2  is the number of times the precoding matrix F[i] is used (i=0, 1, 2, . . . , N−1 (i being an integer in a range of 0 to N−1)), and K N−1,2  is the number of times the precoding matrix F[N−1] is used.
 
 K   0,2   =K   1,2   = . . . =K   i,2   = . . . =K   N−1,2 , i.e.  K   a,2   =K   b,2  (for ∀ a,∀b , where  a,b= 0,1,2, . . . , N− 1(each of  a  and  b  being an integer in a range of 0 to  N− 1), and  a b ).  Condition #111
 
     If the communications system supports a plurality of modulation schemes, and the modulation scheme that is used is selected from among the supported modulation schemes, the selected modulation scheme preferably satisfies Conditions #109, #110, and #111. 
     When a plurality of modulation schemes are supported, it is typical for the number of bits that can be transmitted in one symbol to vary from modulation scheme to modulation scheme (although it is also possible for the number of bits to be the same), and therefore some modulation schemes may not be capable of satisfying Conditions #109, #110, and #111. In such a case, instead of Conditions #109, #110, and #111, the following conditions should be satisfied.
 
The difference between  K   a  and  K   b  is 0 or 1, i.e. | K   a   −K   b | is 0 or 1 (for ∀ a,∀b , where  a,b= 0,1,2, . . . , N− 1 (each of  a  and  b  being an integer in a range of 0 to  N− 1), and  a≠b ).  Condition #112
 
The difference between  K   a,1  and  K   b,1  is 0 or 1, i.e. | K   a,1   −K   b,1 | is 0 or 1 (for ∀ a,∀b , where  a,b= 0,1,2, . . . , N− 1 (each of  a  and  b  being an integer in a range of 0 to  N− 1), and  a≠b ).  Condition #113
 
The difference between  K   a,2  and  K   b,2  is 0 or 1, i.e. | K   a,2    K   b,2 | is 0 or 1 (for ∀ a,∀b , where  a,b= 0,1,2, . . . , N− 1 (each of  a  and  b  being an integer in a range of 0 to  N− 1), and  a≠b ).  Condition #114
 
     Associating coded blocks with precoding matrices in this way eliminates bias in the precoding matrices that are used for transmitting coded blocks, thereby achieving the advantageous effect of improving reception quality of data by the reception device. 
     In the present embodiment, in the scheme of regularly hopping between precoding matrices, N different precoding matrices are necessary for a precoding hopping scheme with an N-slot period (cycle). In this case, F[0], F[1], F[2], . . . , F[N−2], F[N−1] are prepared as the N different precoding matrices. These precoding matrices may be arranged in the frequency domain in the order of F[0], F[1], F[2], . . . , F[N−2], F[N−1], but arrangement is not limited in this way. With N different precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1] generated in the present embodiment, precoding weights may be changed by arranging symbols in the time domain or in the frequency-time domains as in Embodiment 1. Note that a precoding hopping scheme with an N-slot period (cycle) has been described, but the same advantageous effects may be obtained by randomly using N different precoding matrices. In other words, the N different precoding matrices do not necessarily need to be used in a regular period (cycle). Here, when the conditions provided in the present embodiment are satisfied, the reception device has a high possibility of achieving excellent data reception quality. 
     Furthermore, as described in Embodiment 15, a spatial multiplexing MIMO system, a MIMO system in which precoding matrices are fixed, a space-time block coding scheme, a one-stream-only transmission mode, and modes for schemes of regularly hopping between precoding matrices may exist, and the transmission device (broadcast station, base station) may select the transmission scheme from among these modes. In this case, in the spatial multiplexing MIMO system, the MIMO system in which precoding matrices are fixed, the space-time block coding scheme, the one-stream-only transmission mode, and the modes for schemes of regularly hopping between precoding matrices, it is preferable to implement the present embodiment in the (sub)carriers for which a scheme of regularly hopping between precoding matrices is selected. 
     Embodiment C4 
     The present embodiment provides detailed descriptions of a case where, as shown in Non-Patent Literature 12 through Non-Patent Literature 15, a QC-LDPC code (or an LDPC (block) code other than a QC-LDPC code) and a block code (e.g., a concatenated code consisting of an LDPC code and a BCH code, and a turbo code) are used, especially when the scheme of regularly hopping between precoding matrices described in Embodiments C2 is employed. This embodiment describes an example of transmitting two streams, s 1  and s 2 . However, for the case of coding using block codes, when control information or the like is not necessary, the number of bits in a coded block matches the number of bits composing the block code (the control information or the like listed below may, however, be included therein). For the case of coding using block codes, when control information or the like (such as a cyclic redundancy check (CRC), transmission parameters, or the like) is necessary, the number of bits in a coded block is the sum of the number of bits composing the block code and the number of bits in the control information or the like. 
       FIG.  97    shows a modification of the number of symbols and of slots necessary for one coded block when using block coding.  FIG.  97    “shows a modification of the number of symbols and of slots necessary for one coded block when using block coding” for the case when, for example as shown in the transmission device in  FIG.  4   , two streams, s 1  and s 2 , are transmitted, and the transmission device has one encoder. (In this case, the transmission scheme may be either single carrier transmission, or multicarrier transmission such as OFDM.) 
     As shown in  FIG.  97   , the number of bits constituting one block that has been encoded via block coding is set to 6,000. In order to transmit these 6,000 bits, 3,000 symbols are required when the modulation scheme is QPSK, 1,500 when the modulation scheme is 16QAM, and 1,000 when the modulation scheme is 64QAM. 
     Since the transmission device in  FIG.  4    simultaneously transmits two streams, 1,500 of the 3,000 symbols when the modulation scheme is QPSK are allocated to s 1 , and 1,500 to s 2 . Therefore, 1,500 slots (the term “slot” is used here) are required to transmit the 1,500 symbols transmitted in s 1  and the 1,500 symbols transmitted in s 2 . 
     By similar reasoning, when the modulation scheme is 16QAM, 750 slots are necessary to transmit all of the bits constituting one coded block, and when the modulation scheme is 64QAM, 500 slots are necessary to transmit all of the bits constituting one block. 
     The following describes the relationship between the slots defined above and the precoding matrices in the scheme of regularly hopping between precoding matrices. 
     Here, five precoding matrices for realizing the precoding scheme of regularly hopping between precoding matrices with a five-slot period (cycle), as described in Embodiment C2, are expressed as W[0], W[1], W[2], W[3], and W[4] (the weighting unit of the transmission device selects one of a plurality of precoding matrices and performs precoding for each slot). 
     When the modulation scheme is QPSK, among the 1,500 slots described above for transmitting the 6,000 bits constituting one coded block, it is necessary for 300 slots to use the precoding matrix W[0], 300 slots to use the precoding matrix W[1], 300 slots to use the precoding matrix W[2], 300 slots to use the precoding matrix W[3], and 300 slots to use the precoding matrix W[4]. This is because if use of the precoding matrices is biased, the reception quality of data is greatly influenced by the precoding matrix that was used a greater number of times. 
     When the modulation scheme is 16QAM, among the 750 slots described above for transmitting the 6,000 bits constituting one coded block, it is necessary for 150 slots to use the precoding matrix W[0], 150 slots to use the precoding matrix W[1], 150 slots to use the precoding matrix W[2], 150 slots to use the precoding matrix W[3], and 150 slots to use the precoding matrix W[4]. 
     When the modulation scheme is 64QAM, among the 500 slots described above for transmitting the 6,000 bits constituting one coded block, it is necessary for 100 slots to use the precoding matrix W[0], 100 slots to use the precoding matrix W[1], 100 slots to use the precoding matrix W[2], 100 slots to use the precoding matrix W[3], and 100 slots to use the precoding matrix W[4]. 
     As described above, in the scheme of regularly hopping between precoding matrices pertaining to Embodiment C2, provided that the precoding matrices W[0], W[1], . . . , W[2n−1], and W[2n] (which are constituted by F[0], F[1], F[2], . . . , F[n−1], and F[n]; see Embodiment C2) are prepared to achieve an N-slot period (cycle) where N=2n+1, when transmitting all of the bits constituting one coded block, Condition #115 should be satisfied, wherein K 0  is the number of slots using the precoding matrix W[0], K 1  is the number of slots using the precoding matrix W[1], K i  is the number of slots using the precoding matrix W[i] (i=0, 1, 2, . . . , 2n−1, 2n (i being an integer in a range of 0 to 2n)), and K 2n  is the number of slots using the precoding matrix W[2n].
 
 K   0   =K   1   = . . . =K   i   = . . . =K   2n , i.e.  K   a   =K   b  (for ∀ a,∀b , where  a,b= 0,1,2, . . . ,2 n− 1,2 n  (each of  a  and  b  being an integer in a range of 0 to 2 n ), and  a≠b ).  Condition #115
 
     In the scheme of regularly hopping between precoding matrices pertaining to Embodiment C2, provided that the different precoding matrices F[0], F[1], F[2], . . . , F[n−1], and F[n] are prepared to achieve an N-slot period (cycle) where N=2n+1, when transmitting all of the bits constituting one coded block, Condition #115 can be expressed as follows, wherein G 0  is the number of slots using the precoding matrix F[0], G 1  is the number of slots using the precoding matrix F[1], G i  is the number of slots using the precoding matrix F[i] (i=0, 1, 2, . . . , n−1, n), and G n  is the number of slots using the precoding matrix F[n].
 
2× G   0   =G   1   = . . . =G   i   = . . . =G   n , i.e. 2× G   0   =G   a  (for ∀ a , where  a= 1,2, . . . , n− 1, n  ( a  being an integer in a range of 1 to  n )).  Condition #116
 
     If the communications system supports a plurality of modulation schemes, and the modulation scheme that is used is selected from among the supported modulation schemes, then a modulation scheme for which Condition #115 (#116) is satisfied should be selected. 
     When a plurality of modulation schemes are supported, it is typical for the number of bits that can be transmitted in one symbol to vary from modulation scheme to modulation scheme (although it is also possible for the number of bits to be the same), and therefore some modulation schemes may not be capable of satisfying Condition #115 (#116). In such a case, instead of Condition #115, the following condition should be satisfied.
 
The difference between  K   a  and  K   b  is 0 or 1, i.e. | K   a   −K   b | is 0 or 1 (for ∀ a,∀b , where  a,b= 0,1,2, . . . ,2 n− 1,2 n  (each of  a  and  b  being an integer in a range of 0 to 2 n ), and  a≠b ).  Condition #117
 
     Condition #117 can also be expressed as follows.
 
The difference between  G   a  and  G   b  is 0,1 or 2, i.e. | G   a   −G   b | is 0,1 or 2 (for ∀ a,∀b , where  a,b= 1,2, . . . , n− 1, n  (each of  a  and  b  being an integer in a range of 1 to  n ), and  a≠b ); and
 
the difference between 2× G   0  and  G   a  is 0,1 or 2, i.e. |2× G   0   −G   a | is 0,1 or 2 (for ∀ a , where  a= 1,2, . . . , n− 1, n  ( a  being an integer in a range of 1 to  n )).  Condition #118
 
       FIG.  98    shows a modification of the number of symbols and of slots necessary for one coded block when using block coding.  FIG.  98    “shows a modification of the number of symbols and of slots necessary for two coded blocks when using block coding” for the case when, for example as shown in the transmission device in  FIG.  3    and in  FIG.  13   , two streams are transmitted, i.e. s 1  and s 2 , and the transmission device has two encoders. (In this case, the transmission scheme may be either single carrier transmission, or multicarrier transmission such as OFDM.) 
     As shown in  FIG.  98   , the number of bits constituting one block that has been encoded via block coding is set to 6,000. In order to transmit these 6,000 bits, 3,000 symbols are required when the modulation scheme is QPSK, 1,500 when the modulation scheme is 16QAM, and 1,000 when the modulation scheme is 64QAM. 
     The transmission device in  FIG.  3    or in  FIG.  13    transmits two streams simultaneously, and since two encoders are provided, different coded blocks are transmitted in the two streams. Accordingly, when the modulation scheme is QPSK, two coded blocks are transmitted in s 1  and s 2  within the same interval. For example, a first coded block is transmitted in s 1 , and a second coded block is transmitted in s 2 , and therefore, 3,000 slots are required to transmit the first and second coded blocks. By similar reasoning, when the modulation scheme is 16QAM, 1,500 slots are necessary to transmit all of the bits constituting two coded blocks, and when the modulation scheme is 64QAM, 1,000 slots are necessary to transmit all of the bits constituting two blocks. 
     The following describes the relationship between the slots defined above and the precoding matrices in the scheme of regularly hopping between precoding matrices. 
     Below, the five precoding matrices prepared in Embodiment C2 to implement the precoding scheme of regularly hopping between precoding matrices with a five-slot period (cycle) are expressed as W[0], W[1], W[2], W[3], and W[4]. (The weighting unit in the transmission device selects one of a plurality of precoding matrices and performs precoding for each slot). 
     When the modulation scheme is QPSK, among the 3,000 slots described above for transmitting the 6,000×2 bits constituting two coded blocks, it is necessary for 600 slots to use the precoding matrix W[0], 600 slots to use the precoding matrix W[1], 600 slots to use the precoding matrix W[2], 600 slots to use the precoding matrix W[3], and 600 slots to use the precoding matrix W[4]. This is because if use of the precoding matrices is biased, the reception quality of data is greatly influenced by the precoding matrix that was used a greater number of times. 
     To transmit the first coded block, it is necessary for the slot using the precoding matrix W[0] to occur 600 times, the slot using the precoding matrix W[1] to occur 600 times, the slot using the precoding matrix W[2] to occur 600 times, the slot using the precoding matrix W[3] to occur 600 times, and the slot using the precoding matrix W[4] to occur 600 times. To transmit the second coded block, the slot using the precoding matrix W[0] should occur 600 times, the slot using the precoding matrix W[1] should occur 600 times, the slot using the precoding matrix W[2] should occur 600 times, the slot using the precoding matrix W[3] should occur 600 times, and the slot using the precoding matrix W[4] should occur 600 times. 
     Similarly, when the modulation scheme is 16QAM, among the 1,500 slots described above for transmitting the 6,000×2 bits constituting two coded blocks, it is necessary for 300 slots to use the precoding matrix W[0], 300 slots to use the precoding matrix W[1], 300 slots to use the precoding matrix W[2], 300 slots to use the precoding matrix W[3], and 300 slots to use the precoding matrix W[4]. 
     To transmit the first coded block, it is necessary for the slot using the precoding matrix W[0] to occur 300 times, the slot using the precoding matrix W[1] to occur 300 times, the slot using the precoding matrix W[2] to occur 300 times, the slot using the precoding matrix W[3] to occur 300 times, and the slot using the precoding matrix W[4] to occur 300 times. To transmit the second coded block, the slot using the precoding matrix W[0] should occur 300 times, the slot using the precoding matrix W[1] should occur 300 times, the slot using the precoding matrix W[2] should occur 300 times, the slot using the precoding matrix W[3] should occur 300 times, and the slot using the precoding matrix W[4] should occur 300 times. 
     Similarly, when the modulation scheme is 64QAM, among the 1,000 slots described above for transmitting the 6,000×2 bits constituting two coded blocks, it is necessary for 200 slots to use the precoding matrix W[0], 200 slots to use the precoding matrix W[1], 200 slots to use the precoding matrix W[2], 200 slots to use the precoding matrix W[3], and 200 slots to use the precoding matrix W[4]. 
     To transmit the first coded block, it is necessary for the slot using the precoding matrix W[0] to occur 200 times, the slot using the precoding matrix W[1] to occur 200 times, the slot using the precoding matrix W[2] to occur 200 times, the slot using the precoding matrix W[3] to occur 200 times, and the slot using the precoding matrix W[4] to occur 200 times. To transmit the second coded block, the slot using the precoding matrix W[0] should occur 200 times, the slot using the precoding matrix W[1] should occur 200 times, the slot using the precoding matrix W[2] should occur 200 times, the slot using the precoding matrix W[3] should occur 200 times, and the slot using the precoding matrix W[4] should occur 200 times. 
     As described above, in the scheme of regularly hopping between precoding matrices pertaining to Embodiment C2, provided that the precoding matrices W[0], W[1], . . . , W[2n−1], and W[2n] (which are constituted by F[0], F[1], F[2], . . . , F[n−1], and F[n]; see Embodiment C2) are prepared to achieve an N-slot period (cycle) where N=2n+1, when transmitting all of the bits constituting two coded blocks, Condition #119 should be satisfied, wherein K 0  is the number of slots using the precoding matrix W[0], K 1  is the number of slots using the precoding matrix W[1], K i  is the number of slots using the precoding matrix W[i] (i=0, 1, 2, . . . , 2n−1, 2n (i being an integer in a range of 0 to 2n)), and K 2n  is the number of slots using the precoding matrix W[2n].
 
 K   0   =K   1   = . . . =K   i   = . . . =K   2n , i.e.  K   a   =K   b  (for ∀ a,∀b , where  a,b= 0,1,2, . . . ,2 n −1,2 n  (each of  a  and  b  being an integer in a range of 0 to 2 n ), and  a≠b ).  Condition #119
 
     When transmitting all of the bits constituting the first coded block, Condition #120 should be satisfied, wherein K 0,1  is the number of times the precoding matrix W[0] is used, K 1,1  is the number of times the precoding matrix W[1] is used, K i,1  is the number of times the precoding matrix W[i] is used (i=0, 1, 2, . . . , 2n−1, 2n (i being an integer in a range of 0 to 2n)), and K 2n,1  is the number of times the precoding matrix W[2n] is used.
 
 K   0,1   =K   1,1   = . . . =K   i,1   = . . . =K   2n,1 , i.e.  K   a,1   =K   b,1  (for ∀ a,∀b , where  a,b= 0,1,2, . . . ,2 n −1,2 n  (each of  a  and  b  being an integer in a range of 0 to 2 n ), and  a≠b ).  Condition #120
 
     When transmitting all of the bits constituting the second coded block, Condition #121 should be satisfied, wherein K 0,2  is the number of times the precoding matrix W[0] is used, K 1,2  is the number of times the precoding matrix W[1] is used, K i,2  is the number of times the precoding matrix W[i] is used (i=0, 1, 2, . . . , 2n−1, 2n (i being an integer in a range of 0 to 2n)), and K 2n,2  is the number of times the precoding matrix W[2n] is used.
 
 K   0,2   =K   1,2   = . . . =K   i,2   = . . . =K   2n,2 , i.e.  K   a,2   =K   b,2  (for ∀ a,∀b , where  a,b= 0,1,2, . . . ,2 n −1,2 n  (each of  a  and  b  being an integer in a range of 0 to 2 n ), and  a b ).  Condition #121
 
     In the scheme of regularly hopping between precoding matrices pertaining to Embodiment C2, provided that the different precoding matrices F[0], F[1], F[2], . . . , F[n−1], and F[n] are prepared to achieve an N-slot period (cycle) where N=2n+1, when transmitting all of the bits constituting two coded blocks, Condition #119 can be expressed as follows, wherein G 0  is the number of slots using the precoding matrix F[0], G 1  is the number of slots using the precoding matrix F[1], G i  is the number of slots using the precoding matrix F[i] (i=0, 1, 2, . . . , n−1, n), and G n  is the number of slots using the precoding matrix F[n].
 
2× G   0   =G   1   = . . . =G   i   = . . . =G   n , i.e. 2× G   0   =G   a  (for ∀ a , where  a= 1,2, . . . , n− 1, n  ( a  being an integer in a range of 1 to  n )).  Condition #122
 
     When transmitting all of the bits constituting the first coded block, Condition #123 should be satisfied, wherein G 0,1  is the number of times the precoding matrix F[0] is used, K 1,1  is the number of times the precoding matrix F[1] is used, G i,1  is the number of times the precoding matrix F[i] is used (i=0, 1, 2, . . . , n−1, n), and G n,1  is the number of times the precoding matrix F[n] is used.
 
2× G   0,1   =G   1,1   = . . . =G   i,1   = . . . =G   n,1 , i.e. 2× G   0,1   =G   a,1  (for ∀ a , where  a= 1,2, . . . , n− 1, n  ( a  being an integer in a range of 1 to  n )).  Condition #123
 
     When transmitting all of the bits constituting the second coded block, Condition #124 should be satisfied, wherein G 0,2  is the number of times the precoding matrix F[0] is used, G 1,2  is the number of times the precoding matrix F[1] is used, G i,2  is the number of times the precoding matrix F[i] is used (i=0, 1, 2, . . . , n−1, n), and G n,2  is the number of times the precoding matrix F[n] is used.
 
2× G   0,2   =G   1,2   = . . . =G   i,2   = . . . =G   n,2 , i.e. 2× G   0,2   =G   a,2  (for ∀ a , where  a= 1,2, . . . , n− 1, n  ( a  being an integer in a range of 1 to  n )).  Condition #124
 
     If the communications system supports a plurality of modulation schemes, and the modulation scheme that is used is selected from among the supported modulation schemes, then a modulation scheme for which Conditions #119, #120 and #121 (#122, #123 and #124) are satisfied should be selected. When a plurality of modulation schemes are supported, it is typical for the number of bits that can be transmitted in one symbol to vary from modulation scheme to modulation scheme (although it is also possible for the number of bits to be the same), and therefore some modulation schemes may not be capable of satisfying Conditions #119, #120, and #121 (#122, #123 and #124). In such a case, instead of Conditions #119, #120, and #121, the following conditions should be satisfied.
 
The difference between  K   a  and  K   b  is 0 or 1, i.e. | K   a   −K   b | is 0 or 1 (for ∀ a,∀b , where  a,b= 0,1,2, . . . ,2 n− 1,2 n  (each of  a  and  b  being an integer in a range of 0 to 2 n ), and  a≠b ).  Condition #125
 
The difference between  K   a,1  and  K   b,1  is 0 or 1, i.e. | K   a,1   −K   b,1 | is 0 or 1 (for ∀ a,∀b , where  a,b= 0,1,2, . . . ,2 n −1,2 n  (each of  a  and  b  being an integer in a range of 0 to 2 n −1), and  a≠b ).  Condition #126
 
The difference between  K   a,2  and  K   b,2  is 0 or 1, i.e. | K   a,2    K   b,2 | is 0 or 1 (for ∀ a,∀b , where  a,b= 0,1,2, . . . ,2 n −1,2 n  (each of  a  and  b  being an integer in a range of 0 to 2 n− 1), and  a≠b ).  Condition #127
 
     Conditions #125, #126 and #127 can also be expressed as follows. Condition #128
 
The difference between  G   a  and  G   b  is 0,1 or 2, i.e. | G   a   −G   b | is 0 or 1 or 2 (for ∀ a,∀b , where  a,b= 1,2, . . . , n− 1, n  (each of  a  and  b  being an integer in a range of 1 to  n ), and  a≠b ).
 
the difference between 2× G   0  and  G   a  is 0,1 or 2, i.e. |2× G   0   −G   a | is 0,1 or 2 (for ∀ a , where  a= 1,2, . . . , n− 1, n  ( a  being an integer in a range of 1 to  n )).  Condition #128
 
The difference between  G   a,1  and  G   b,1  is 0 or 1, or 2 i.e. | G   a,1   −G   b,1 | is 0,1 or 2 (for ∀ a,∀b , where  a,b= 0,1,2, . . . , n− 1 ,n  (each of  a  and  b  being an integer in a range of 1 to  n ), and  a≠b ).
 
the difference between 2× G   0,1  and  G   a,1  is 0,1 or 2, i.e. |2× G   0,1   −G   a,1 | is 0,1 or 2 (for ∀ a , where  a= 1,2, . . . , n− 1, n  ( a  being an integer in a range of 1 to  n )).  Condition #129
 
The difference between  G   a,2  and  G   b,2  is 0,1 or 2 i.e. | G   a,2   −G   b,2 | is 0,1 or 2 (for ∀ a,∀b , where  a,b= 0,1,2, . . . , n− 1 ,n  (each of  a  and  b  being an integer in a range of 1 to  n ), and  a≠b ).
 
the difference between 2× G   0,2  and  G   a,2  is 0,1 or 2, i.e. |2× G   0,2   −G   a,2 | is 0,1 or 2 (for ∀ a , where  a= 1,2, . . . , n− 1, n  ( a  being an integer in a range of 1 to  n )).  Condition #130
 
     Associating coded blocks with precoding matrices in this way eliminates bias in the precoding matrices that are used for transmitting coded blocks, thereby achieving the advantageous effect of improving reception quality of data by the reception device. 
     In the present embodiment, precoding matrices W[0], W[1], . . . , W[2n−1], W[2n] (note that W[0], W[1], . . . , W[2n−1], W[2n] are composed of F[0], F[1], F[2], . . . , F[n−1], F[n]) for the precoding hopping scheme with the period (cycle) of N=2n+1 slots as described in Embodiment C2 (the precoding scheme of regularly hopping between precoding matrices with the period (cycle) of N=2n+1 slots) are arranged in the order W[0], W[1], . . . , W[2n−1], W[2] in the time domain (or the frequency domain) in the single carrier transmission scheme. The present invention is not, however, limited in this way, and the precoding matrices W[0], W[1], . . . , W[2n−1], W[2n] may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaption in this case, precoding weights may be changed by arranging symbols in the frequency domain and in the frequency-time domain. Note that the precoding hopping scheme with the period (cycle) of N=2n+1 slots has been described, but the same advantageous effect may be obtained by randomly using the precoding matrices W[0], W[1], . . . , W[2n−1], W[2n]. In other words, the precoding matrices W[0], W[1], . . . , W[2n−1], W[2n] do not need to be used in a regular period (cycle). In this case, when the conditions described in the present embodiment are satisfied, the probability that the reception device achieves excellent data reception quality is high. 
     Furthermore, in the precoding matrix hopping scheme with an H-slot period (cycle) (H being a natural number larger than the number of slots N=2n+1 in the period (cycle) of the above-mentioned scheme of regularly hopping between precoding matrices), when n+1 different precoding matrices of the present embodiment are included, the probability of providing excellent reception quality increases. 
     As described in Embodiment 15, there are modes such as the spatial multiplexing MIMO system, the MIMO system with a fixed precoding matrix, the space-time block coding scheme, the scheme of transmitting one stream and the scheme of regularly hopping between precoding matrices. The transmission device (broadcast station, base station) may select one transmission scheme from among these modes. In this case, from among the spatial multiplexing MIMO system, the MIMO system with a fixed precoding matrix, the space-time block coding scheme, the scheme of transmitting one stream and the scheme of regularly hopping between precoding matrices, a (sub)carrier group selecting the scheme of regularly hopping between precoding matrices may implement the present embodiment. 
     Embodiment C5 
     As shown in Non-Patent Literature 12 through Non-Patent Literature 15, the present embodiment describes a case where Embodiment C3 and Embodiment C4 are generalized when using a Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) code (or an LDPC (block) code other than a QC-LDPC code), a block code such as a concatenated code consisting of an LDPC code and a Bose-Chaudhuri-Hocquenghem (BCH) code, and a block code such as a turbo code. The following describes a case of transmitting two streams s 1  and s 2  as an example. Note that, when the control information and the like are not required to perform encoding using the block code, the number of bits constituting the coded block is the same as the number of bits constituting the block code (however, the control information and the like described below may be included). When the control information and the like (e.g. CRC (cyclic redundancy check), a transmission parameter) are required to perform encoding using the block code, the number of bits constituting the coded block can be a sum of the number of bits constituting the block code and the number of bits of the control information and the like. 
       FIG.  97    shows a change in the number of symbols and slots required for one coded block when the block code is used.  FIG.  97    shows a change in the number of symbols and slots required for one coded block when the block code is used in a case where the two streams s 1  and s 2  are transmitted and the transmission device has a single encoder, as shown in the transmission device in  FIG.  4    (note that, in this case, either the single carrier transmission or the multi-carrier transmission such as the OFDM may be used as a transmission system). 
     As shown in  FIG.  97   , let the number of bits constituting one coded block in the block code be 6000 bits. In order to transmit the 6000 bits, 3000 symbols, 1500 symbols and 1000 symbols are necessary when the modulation scheme is QPSK, 16QAM and 64QAM, respectively. 
     Since two streams are to be simultaneously transmitted in the transmission device shown in  FIG.  4   , when the modulation scheme is QPSK, 1500 symbols are allocated to s 1  and remaining 1500 symbols are allocated to s 2  out of the above-mentioned 3000 symbols. Therefore, 1500 slots (referred to as slots) are necessary to transmit 1500 symbols by s 1  and transmit 1500 symbols by s 2 . 
     Making the same considerations, 750 slots are necessary to transmit all the bits constituting one coded block when the modulation scheme is 16QAM, and 500 slots are necessary to transmit all the bits constituting one block when the modulation scheme is 64QAM. 
     The following describes the relationship between the slots defined above and precoding matrices in the scheme of regularly hopping between precoding matrices. 
     Here, let the precoding matrices for the scheme of regularly hopping between precoding matrices with a five-slot period (cycle) be W[0], W[1], W[2], W[3], W[4]. Note that at least two or more different precoding matrices may be included in W[0], W[1], W[2], W[3], W[4] (the same precoding matrices may be included in W[0], W[1], W[2], W[3], W[4]). In the weighting combination unit of the transmission device in  FIG.  4   , W[0], W[1], W[2], W[3], W[4] are used (the weighting combination unit selects one precoding matrix from among a plurality of precoding matrices in each slot, and performs precoding). 
     Out of the above-mentioned 1500 slots required to transmit 6000 bits, which is the number of bits constituting one coded block, when the modulation scheme is QPSK, 300 slots are necessary for each of a slot using the precoding matrix W[0], a slot using the precoding matrix W[1], a slot using the precoding matrix W[2], a slot using the precoding matrix W[3] and a slot using the precoding matrix W[4]. This is because, if precoding matrices to be used are biased, data reception quality is greatly influenced by a large number of precoding matrices to be used. 
     Similarly, out of the above-mentioned 750 slots required to transmit 6000 bits, which is the number of bits constituting one coded block, when the modulation scheme is 16QAM, 150 slots are necessary for each of the slot using the precoding matrix W[0], the slot using the precoding matrix W[1], the slot using the precoding matrix W[2], the slot using the precoding matrix W[3] and the slot using the precoding matrix W[4]. 
     Similarly, out of the above-mentioned 500 slots required to transmit 6000 bits, which is the number of bits constituting one coded block, when the modulation scheme is 64QAM, 100 slots are necessary for each of the slot using the precoding matrix W[0], the slot using the precoding matrix W[1], the slot using the precoding matrix W[2], the slot using the precoding matrix W[3] and the slot using the precoding matrix W[4]. 
     As described above, the precoding matrices in the scheme of regularly hopping between precoding matrices with an N-slot period (cycle) are represented as W[0], W[1], W[2], . . . , W[N−2], W[N−1]. 
     Note that W[0], W[1], W[2], . . . , W[N−2], W[N−1] are composed of at least two or more different precoding matrices (the same precoding matrices may be included in W[0], W[1], W[2], . . . , W[N−2], W[N−1]). When all the bits constituting one coded block are transmitted, letting the number of slots using the precoding matrix W[0] be K 0 , letting the number of slots using the precoding matrix W[1] be K 1 , letting the number of slots using the precoding matrix W[i] be K i  (i=0, 1, 2, . . . , N−1 (i being an integer in a range of 0 to N−1)), and letting the number of slots using the precoding matrix W[N−1] be K N−1 , the following condition should be satisfied.
 
 K   0   =K   1   = . . . =K   i   = . . . =K   N−1 , i.e.  K   a   =K   b  for ∀ a,∀b  ( a,b= 0,1,2, . . . , N− 1 ( a,b  are integers from 0 to  N− 1); a≠b ).  Condition #131
 
     When the communication system supports a plurality of modulation schemes, and a modulation scheme is selected and used from among the supported modulation schemes, Condition #94 should be satisfied. 
     When the plurality of modulation schemes are supported, however, since the number of bits that one symbol can transmit is generally different depending on modulation schemes (in some cases, the number of bits can be the same), there can be a modulation scheme that is not able to satisfy Condition #131. In such a case, instead of satisfying Condition #131, the following condition may be satisfied.
 
The difference between  K   a  and  K   b  is 0 or 1, i.e. | K   a   −K   b | is 0 or 1 for ∀ a,∀b  ( a,b= 0,1,2, . . . , N− 1 ( a,b  are integers from 0 to  N− 1); a≠b ).  Condition #132
 
       FIG.  98    shows a change in the number of symbols and slots required for two coded blocks when the block code is used.  FIG.  98    shows a change in the number of symbols and slots required for one coded block when the block code is used in a case where the two streams s 1  and s 2  are transmitted and the transmission device has two encoders, as shown in the transmission device in  FIG.  3    and the transmission device in  FIG.  13    (note that, in this case, either the single carrier transmission or the multi-carrier transmission such as the OFDM may be used as a transmission system). 
     As shown in  FIG.  98   , let the number of bits constituting one coded block in the block code be 6000 bits. In order to transmit the 6000 bits, 3000 symbols, 1500 symbols and 1000 symbols are necessary when the modulation scheme is QPSK, 16QAM and 64QAM, respectively. 
     Since two streams are to be simultaneously transmitted in the transmission device shown in  FIG.  3    and in the transmission device in  FIG.  13   , and there are two encoders, different coded blocks are to be transmitted. Therefore, when the modulation scheme is QPSK, s 1  and s 2  transmit two coded blocks within the same interval. For example, s 1  transmits a first coded block, and s 2  transmits a second coded block. Therefore, 3000 slots are necessary to transmit the first coded block and the second coded block. 
     Making the same considerations, 1500 slots are necessary to transmit all the bits constituting two coded blocks when the modulation scheme is 16QAM, and 1000 slots are necessary to transmit all the bits constituting  22  blocks when the modulation scheme is 64QAM. 
     The following describes the relationship between the slots defined above and precoding matrices in the scheme of regularly hopping between precoding matrices. 
     Here, let the precoding matrices for the scheme of regularly hopping between precoding matrices with a five-slot period (cycle) be W[0], W[1], W[2], W[3], W[4]. Note that at least two or more different precoding matrices may be included in W[0], W[1], W[2], W[3], W[4] (the same precoding matrices may be included in W[0], W[1], W[2], W[3], W[4]). In the weighting combination unit of the transmission device in  FIG.  3    and the transmission device in  FIG.  13   , W[0], W[1], W[2], W[3], W[4] are used (the weighting combination unit selects one precoding matrix from among a plurality of precoding matrices in each slot, and performs precoding). 
     Out of the above-mentioned 3000 slots required to transmit 6000×2 bits, which is the number of bits constituting two coded blocks, when the modulation scheme is QPSK, 600 slots are necessary for each of the slot using the precoding matrix W[0], the slot using the precoding matrix W[1], the slot using the precoding matrix W[2], the slot using the precoding matrix W[3] and the slot using the precoding matrix W[4]. This is because, if precoding matrices to be used are biased, data reception quality is greatly influenced by a large number of precoding matrices to be used. 
     Also, in order to transmit the first coded block, 600 slots are necessary for each of the slot using the precoding matrix W[0], the slot using the precoding matrix W[1], the slot using the precoding matrix W[2], the slot using the precoding matrix W[3] and the slot using the precoding matrix W[4]. In order to transmit the second coded block, 600 slots are necessary for each of the slot using the precoding matrix W[0], the slot using the precoding matrix W[1], the slot using the precoding matrix W[2], the slot using the precoding matrix W[3] and the slot using the precoding matrix W[4]. 
     Similarly, out of the above-mentioned 1500 slots required to transmit 6000×2 bits, which is the number of bits constituting two coded blocks, when the modulation scheme is 64QAM, 300 slots are necessary for each of the slot using the precoding matrix W[0], the slot using the precoding matrix W[1], the slot using the precoding matrix W[2], the slot using the precoding matrix W[3] and the slot using the precoding matrix W[4]. 
     Also, in order to transmit the first coded block, 300 slots are necessary for each of the slot using the precoding matrix W[0], the slot using the precoding matrix W[1], the slot using the precoding matrix W[2], the slot using the precoding matrix W[3] and the slot using the precoding matrix W[4]. In order to transmit the second coded block, 300 slots are necessary for each of the slot using the precoding matrix W[0], the slot using the precoding matrix W[1], the slot using the precoding matrix W[2], the slot using the precoding matrix W[3] and the slot using the precoding matrix W[4]. 
     Similarly, out of the above-mentioned 1000 slots required to transmit 6000×2 bits, which is the number of bits constituting two coded blocks, when the modulation scheme is 64QAM, 200 slots are necessary for each of the slot using the precoding matrix W[0], the slot using the precoding matrix W[1], the slot using the precoding matrix W[2], the slot using the precoding matrix W[3] and the slot using the precoding matrix W[4]. 
     Also, in order to transmit the first coded block, 200 slots are necessary for each of the slot using the precoding matrix W[0], the slot using the precoding matrix W[1], the slot using the precoding matrix W[2], the slot using the precoding matrix W[3] and the slot using the precoding matrix W[4]. In order to transmit the second coded block, 200 slots are necessary for each of the slot using the precoding matrix W[0], the slot using the precoding matrix W[1], the slot using the precoding matrix W[2], the slot using the precoding matrix W[3] and the slot using the precoding matrix W[4]. 
     As described above, the precoding matrices in the scheme of regularly hopping between precoding matrices with an N-slot period (cycle) are represented as W[0], W[1], W[2], . . . , W[N−2], W[N−1]. 
     Note that W[0], W[1], W[2], . . . , W[N−2], W[N−1] are composed of at least two or more different precoding matrices (the same precoding matrices may be included in W[0], W[1], W[2], . . . , W[N−2], W[N−1]). When all the bits constituting two coded blocks are transmitted, letting the number of slots using the precoding matrix W[0] be K 0 , letting the number of slots using the precoding matrix W[1] be K 1 , letting the number of slots using the precoding matrix W[i] be K i  (i=0, 1, 2, . . . , N−1 (i being an integer in a range of 0 to N−1)), and letting the number of slots using the precoding matrix W[N−1] be K N−1 , the following condition should be satisfied.
 
 K   0   =K   1   = . . . =K   i   = . . . =K   N−1 , i.e.  K   a   =K   b  for ∀ a,∀b  ( a,b= 0,1,2, . . . , N− 1 ( a,b  are integers from 0 to  N− 1); a≠b ).  Condition #133
 
     When all the bits constituting the first coded block are transmitted, letting the number of slots using the precoding matrix W[0] be K 0,1 , letting the number of slots using the precoding matrix W[1] be K 1,1 , letting the number of slots using the precoding matrix W[i] be K i,1  (i=0, 1, 2, . . . , N−1 (i being an integer in a range of 0 to N−1)), and letting the number of slots using the precoding matrix W[N−1] be K N−1,1 , the following condition should be satisfied.
 
 K   0,1   =K   1,1   = . . . =K   i,1   = . . . =K   N−1,1 , i.e.  K   a,1   =K   b,1  for ∀ a,∀b  ( a,b= 0,1,2, . . . , N− 1 ( a,b  are integers from 0 to  N− 1); a≠b ).  Condition #134
 
     When all the bits constituting the second coded block are transmitted, letting the number of slots using the precoding matrix W[0] be K 0,2 , letting the number of slots using the precoding matrix W[1] be K i,2 , letting the number of slots using the precoding matrix W[i] be K i,2  (i=0, 1, 2, . . . , N−1 (i being an integer in a range of 0 to N−1)), and letting the number of slots using the precoding matrix W[N−1] be K N−1,2  the following condition should be satisfied.
 
 K   0,2   =K   1,2   = . . . =K   i,2   = . . . =K   N−1,2 , i.e.  K   a,2   =K   b,2  for ∀ a,∀b  ( a,b= 0,1,2, . . . , N− 1 ( a,b  are integers from 0 to  N− 1); a≠b ).  Condition #135
 
     When the communication system supports a plurality of modulation schemes, and a modulation scheme is selected and used from among the supported modulation schemes, Condition #133, Condition #134 and Condition #135 should be satisfied. 
     When the plurality of modulation schemes are supported, however, since the number of bits that one symbol can transmit is generally different depending on modulation schemes (in some cases, the number of bits can be the same), there can be a modulation scheme that is not able to satisfy Condition #133, Condition #134 and Condition #135. In such a case, instead of satisfying Condition #133, Condition #134 and Condition #135, the following condition may be satisfied.
 
The difference between  K   a  and  K   b  is 0 or 1, i.e. | K   a   −K   b | is 0 or 1 for ∀ a,∀b  ( a,b= 0,1,2, . . . , N− 1 ( a,b  are integers from 0 to  N− 1); a≠b ).  Condition #136
 
The difference between  K   a,1  and  K   b,1  is 0 or 1, i.e. | K   a,1   −K   b,1 | is 0 or 1 for ∀ a,∀b  ( a,b= 0,1,2, . . . , N− 1 ( a,b  are integers from 0 to  N− 1); a≠b ).  Condition #137
 
The difference between  K   a,2  and  K   b,2  is 0 or 1, i.e. | K   a,2    K   b,2 | is 0 or 1 for ∀ a,∀b  ( a,b= 0,1,2, . . . , N− 1 ( a,b  are integers from 0 to  N− 1); a≠b ).  Condition #138
 
     By associating the coded blocks with precoding matrices as described above, precoding matrices used to transmit the coded block are unbiased. Therefore, an effect of improving data reception quality in the reception device is obtained. 
     In the present embodiment, in the scheme of regularly hopping between precoding matrices, N precoding matrices W[0], W[1], W[2], . . . , W[N−2], W[N−1] are prepared for the precoding hopping scheme with an N-slot period (cycle). There is a way to arrange precoding matrices in the order W[0], W[1], W[2], . . . , W[N−2], W[N−1] in frequency domain. The present invention is not, however, limited in this way. As described in Embodiment 1, precoding weights may be changed by arranging N precoding matrices W[0], W[1], W[2], . . . , W[N−2], W[N−1] generated in the present embodiment in time domain and in the frequency-time domain. Note that a precoding hopping scheme with the N-slot period (cycle) has been described, but the same advantageous effect may be obtained by randomly using N different precoding matrices. In other words, the N different precoding matrices do not need to be used in a regular period (cycle). In this case, when the conditions described in the present embodiment are satisfied, the probability that the reception device achieves excellent data reception quality is high. 
     As described in Embodiment 15, there are modes such as the spatial multiplexing MIMO system, the MIMO system with a fixed precoding matrix, the space-time block coding scheme, the scheme of transmitting one stream and the scheme of regularly hopping between precoding matrices. The transmission device (broadcast station, base station) may select one transmission scheme from among these modes. In this case, from among the spatial multiplexing MIMO system, the MIMO system with a fixed precoding matrix, the space-time block coding scheme, the scheme of transmitting one stream and the scheme of regularly hopping between precoding matrices, a (sub)carrier group selecting the scheme of regularly hopping between precoding matrices may implement the present embodiment. 
     Supplementary Explanation 
     In the present description, it is considered that a communication/broadcasting device such as a broadcast station, a base station, an access point, a terminal, a mobile phone, or the like is provided with the transmission device, and that a communication device such as a television, radio, terminal, personal computer, mobile phone, access point, base station, or the like is provided with the reception device. Additionally, it is considered that the transmission device and the reception device in the present invention have a communication function and are capable of being connected via some sort of interface (such as a USB) to a device for executing applications for a television, radio, personal computer, mobile phone, or the like. 
     Furthermore, in the present embodiment, symbols other than data symbols, such as pilot symbols (preamble, unique word, postamble, reference symbol, and the like), symbols for control information, and the like may be arranged in the frame in any way. While the terms “pilot symbol” and “symbols for control information” have been used here, any term may be used, since the function itself is what is important. 
     It suffices for a pilot symbol, for example, to be a known symbol modulated with PSK modulation in the transmission and reception devices (or for the reception device to be able to synchronize in order to know the symbol transmitted by the transmission device). The reception device uses this symbol for frequency synchronization, time synchronization, channel estimation (estimation of Channel State Information (CSI) for each modulated signal), detection of signals, and the like. 
     A symbol for control information is for transmitting information other than data (of applications or the like) that needs to be transmitted to the communication partner for achieving communication (for example, the modulation scheme, error correction coding scheme, coding rate of the error correction coding scheme, setting information in the upper layer, and the like). 
     Note that the present invention is not limited to the above Embodiments 1-5 and may be embodied with a variety of modifications. For example, the above embodiments describe communication devices, but the present invention is not limited to these devices and may be implemented as software for the corresponding communication scheme. 
     Furthermore, a precoding hopping scheme used in a scheme of transmitting two modulated signals from two antennas has been described, but the present invention is not limited in this way. The present invention may be also embodied as a precoding hopping scheme for similarly changing precoding weights (matrices) in the context of a scheme whereby four mapped signals are precoded to generate four modulated signals that are transmitted from four antennas, or more generally, whereby N mapped signals are precoded to generate N modulated signals that are transmitted from N antennas. 
     In the present description, the terms “precoding”, “precoding weight”, “precoding matrix” and the like are used, but any term may be used (such as “codebook”, for example) since the signal processing itself is what is important in the present invention. 
     Furthermore, in the present description, the reception device has been described as using ML calculation, APP, Max-log APP, ZF, MMSE, or the like, which yields soft decision results (log-likelihood, log-likelihood ratio) or hard decision results (“0” or “1”) for each bit of data transmitted by the transmission device. This process may be referred to as detection, demodulation, estimation, or separation. 
     Assume that precoded baseband signals z 1 ( i ), z 2 ( i ) (where i represents the order in terms of time or frequency (carrier)) are generated by precoding baseband signals s 1 ( i ) and s 2 ( i ) for two streams while regularly hopping between precoding matrices. Let the in-phase component I and the quadrature component Q of the precoded baseband signal z 1 ( i ) be I 1 (i) and Q 1 (i) respectively, and let the in-phase component I and the quadrature component Q of the precoded baseband signal z 2 ( i ) be I 2 (i) and Q 2 (i) respectively. In this case, the baseband components may be switched, and modulated signals corresponding to the switched baseband signal r 1 ( i ) and the switched baseband signal r 2 ( i ) may be transmitted from different antennas at the same time and over the same frequency by transmitting a modulated signal corresponding to the switched baseband signal r 1 ( i ) from transmit antenna  1  and a modulated signal corresponding to the switched baseband signal r 2 ( i ) from transmit antenna  2  at the same time and over the same frequency. Baseband components may be switched as follows.
         Let the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be I 1 (i) and Q 2 (i) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be I 2 (i) and Q 1 (i) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be I 1 (i) and I 2 (i) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be Q 1 (i) and Q 2 (i) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be I 2 (i) and I 1 (i) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be Q 1 (i) and Q 2 (i) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be I 1 (i) and I 2 (i) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be Q 2 (i) and Q 1 (i) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be I 2 (i) and I 1 (i) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be Q 2 (i) and Q 1 (i) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be I 1 (i) and Q 2 (i) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be Q 1 (i) and I 2 (i) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be Q 2 (i) and I 1 (i) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be I 2 (i) and Q 1 (i) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be Q 2 (i) and I 1 (i) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be Q 1 (i) and I 2 (i) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be I 1 (i) and I 2 (i) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be Q 1 (i) and Q 2 (i) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be I 2 (i) and I 1 (i) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be Q 1 (i) and Q 2 (i) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be I 1 (i) and I 2 (i) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be Q 2 (i) and Q 1 (i) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be I 2 (i) and I 1 (i) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be Q 2 (i) and Q 1 (i) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be I 1 (i) and Q 2 (i) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be I 2 (i) and Q 1 (i) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be I 1 (i) and Q 2 (i) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be Q 1 (i) and I 2 (i) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be Q 2 (i) and I 1 (i) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be I 2 (i) and Q 1 (i) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be Q 2 (i) and I 1 (i) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be Q 1 (i) and I 2 (i) respectively. In the above description, signals in two streams are precoded, and in-phase components and quadrature components of the precoded signals are switched, but the present invention is not limited in this way. Signals in more than two streams may be precoded, and the in-phase components and quadrature components of the precoded signals may be switched.       

     In the above-mentioned example, switching between baseband signals at the same time (at the same frequency ((sub)carrier)) has been described, but the present invention is not limited to the switching between baseband signals at the same time. As an example, the following description can be made.
         Let the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be I 1 (i+v) and Q 2 (i+w) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be I 2 (i+w) and Q 1 (i+v) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be I 1 (i+v) and I 2 (i+w) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be Q 1 (i+v) and Q 2 (i+w) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be I 2 (i+w) and I 1 (i+v) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be Q 1 (i+v) and Q 2 (i+w) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be I 1 (i+v) and I 2 (i+w) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be Q 2 (i+w) and Q 1 (i+v) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be I 2 (i+w) and I 1 (i+v) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be Q 2 (i+w) and Q 1 (i+v) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be I 1 (i+v) and Q 2 (i+w) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be Q 1 (i+v) and I 2 (i+w) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be Q 2 (i+w) and I 1 (i+v) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be I 2 (i+w) and Q 1 (i+v) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be Q 2 (i+w) and I 1 (i+v) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be Q 1 (i+v) and I 2 (i+w) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be I 1 (i+v) and I 2 (i+w) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be Q 1 (i+v) and Q 2 (i+w) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be I 2 (i+w) and I 1 (i+v) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be Q 1 (i+v) and Q 2 (i+w) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be I 1 (i+v) and I 2 (i+w) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be Q 2 (i+w) and Q 1 (i+v) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be I 2 (i+w) and I 1 (i+v) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be Q 2 (i+w) and Q 1 (i+v) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be I 1 (i+v) and Q 2 (i+w) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be I 2 (i+w) and Q 1 (i+v) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be I 1 (i+v) and Q 2 (i+w) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be Q 1 (i+v) and I 2 (i+w) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be Q 2 (i+w) and I 1 (i+v) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be I 2 (i+w) and Q 1 (i+v) respectively.   Let the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be Q 2 (i+w) and I 1 (i+v) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be Q 1 (i+v) and I 2 (i+w) respectively.       

       FIG.  96    explains the above description. As shown in  FIG.  96   , let the in-phase component I and the quadrature component of the precoded baseband signal z 1 ( i ) be I 1 (i) and Q 1 (i) respectively, and the in-phase component I and the quadrature component of the precoded baseband signal z 2 ( i ) be I 2 (i) and Q 2 (i) respectively. Then, let the in-phase component and the quadrature component of the switched baseband signal r 1 ( i ) be I r1 (i) and Q r1 (i) respectively, and the in-phase component and the quadrature component of the switched baseband signal r 2 ( i ) be I r2 (i) and Q r2 (i) respectively, and the in-phase component I r1 (i) and the quadrature component Q r1 (i) of the switched baseband signal r 1 ( i ) and the in-phase component I r2 ( i ) and the quadrature component Q r1 (i) of the switched baseband signal r 2 ( i ) are represented by any of the above descriptions. Note that, in this example, switching between precoded baseband signals at the same time (at the same frequency ((sub)carrier)) has been described, but the present invention may be switching between precoded baseband signals at different times (at different frequencies ((sub)carrier)), as described above. 
     In this case, modulated signals corresponding to the switched baseband signal r 1 ( i ) and the switched baseband signal r 2 ( i ) may be transmitted from different antennas at the same time and over the same frequency by transmitting a modulated signal corresponding to the switched baseband signal r 1 ( i ) from transmit antenna  1  and a modulated signal corresponding to the switched baseband signal r 2 ( i ) from transmit antenna  2  at the same time and over the same frequency. 
     Each of the transmit antennas of the transmission device and the receive antennas of the reception device shown in the figures may be formed by a plurality of antennas. 
     In this description, the symbol “∀” represents the universal quantifier, and the symbol “∃” represents the existential quantifier. 
     Furthermore, in this description, the units of phase, such as argument, in the complex plane are radians. 
     When using the complex plane, complex numbers may be shown in polar form by polar coordinates. If a complex number z=a+jb (where a and b are real numbers and j is an imaginary unit) corresponds to a point (a, b) on the complex plane, and this point is represented in polar coordinates as [r, θ], then the following math is satisfied.
 
 a=r ×cos θ
 
 b=r ×sin θ
 
 r =√{square root over ( a   2   +b   2 )}  Math 592
 
     r is the absolute value of z (r=|z|), and θ is the argument. Furthermore, z=a+jb is represented as re jθ . 
     In the description of the present invention, the baseband signal, modulated signal s 1 , modulated signal s 2 , modulated signal z 1 , and modulated signal z 2  are complex signals. Complex signals are represented as I+jQ (where j is an imaginary unit), I being the in-phase signal, and Q being the quadrature signal. In this case, I may be zero, or Q may be zero. 
       FIG.  59    shows an example of a broadcasting system that uses the scheme of regularly hopping between precoding matrices described in this description. In  FIG.  59   , a video encoder  5901  receives video images as input, encodes the video images, and outputs encoded video images as data  5902 . An audio encoder  5903  receives audio as input, encodes the audio, and outputs encoded audio as data  5904 . A data encoder  5905  receives data as input, encodes the data (for example by data compression), and outputs encoded data as data  5906 . Together, these encoders are referred to as information source encoders  5900 . 
     A transmission unit  5907  receives, as input, the data  5902  of the encoded video, the data  5904  of the encoded audio, and the data  5906  of the encoded data, sets some or all of these pieces of data as transmission data, and outputs transmission signals  5908 _ 1  through  5908 _N after performing processing such as error correction encoding, modulation, and precoding (for example, the signal processing of the transmission device in  FIG.  3   ). The transmission signals  5908 _ 1  through  5908 _N are transmitted by antennas  5909 _ 1  through  5909 _N as radio waves. 
     A reception unit  5912  receives, as input, received signals  5911 _ 1  through  5911 _M received by antennas  5910 _ 1  through  5910 _M, performs processing such as frequency conversion, decoding of precoding, log-likelihood ratio calculation, and error correction decoding (processing by the reception device in  FIG.  7   , for example), and outputs received data  5913 ,  5915 , and  5917 . Information source decoders  5919  receive, as input, the received data  5913 ,  5915 , and  5917 . A video decoder  5914  receives, as input, the received data  5913 , performs video decoding, and outputs a video signal. Video images are then shown on a television or display monitor. Furthermore, an audio decoder  5916  receives, as input, the received data  5915 , performs audio decoding, and outputs an audio signal. Audio is then produced by a speaker. A data encoder  5918  receives, as input, the received data  5917 , performs data decoding, and outputs information in the data. 
     In the above embodiments describing the present invention, the number of encoders in the transmission device when using a multi-carrier transmission scheme such as OFDM may be any number, as described above. Therefore, as in  FIG.  4   , for example, it is of course possible for the transmission device to have one encoder and to adapt a scheme of distributing output to a multi-carrier transmission scheme such as OFDM. In this case, the wireless units  310 A and  310 B in  FIG.  4    are replaced by the OFDM related processors  1301 A and  1301 B in  FIG.  13   . The description of the OFDM related processors is as per Embodiment 1. 
     The symbol arrangement scheme described in Embodiments A1 through A5 and in Embodiment 1 may be similarly implemented as a precoding scheme for regularly hopping between precoding matrices using a plurality of different precoding matrices, the precoding scheme differing from the “scheme for hopping between different precoding matrices” in the present description. The same holds true for other embodiments as well. The following is a supplementary explanation regarding a plurality of different precoding matrices. 
     Let N precoding matrices be represented as F[0], F[1], F[2], . . . , F[N−3], F[N−2], F[N−1] for a precoding scheme for regularly hopping between precoding matrices. In this case, the “plurality of different precoding matrices” referred to above are assumed to satisfy the following two conditions (Condition *1 and Condition *2).
 
Math 593
 
 F [ x ]≠ F [ y ] for ∀ x,∀y  ( x,y= 0,1,2 , . . . ,N− 3 ,N− 2 ,N− 1 ;x≠y )  Condition *1
 
     Here, x is an integer from 0 to N−1, y is an integer from 0 to N−1 and x≠y. With respect to all x and all y satisfying the above, the relationship F[x]≠F[y] holds.
 
Math 594
 
 F [ x ]= k×F [ y ]  Condition *2
 
     Letting x be an integer from 0 to N−1, y be an integer from 0 to N−1, and x≠y, for all x and all y, no real or complex number k satisfying the above equation exists. 
     The following is a supplementary explanation using a 2×2 matrix as an example. Let 2×2 matrices R and S be represented as follows: 
     
       
         
           
             
               
                 
                   R 
                   = 
                   
                     ( 
                     
                       
                         
                           a 
                         
                         
                           b 
                         
                       
                       
                         
                           c 
                         
                         
                           d 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Math 
                   ⁢ 
                       
                   595 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   S 
                   = 
                   
                     ( 
                     
                       
                         
                           e 
                         
                         
                           f 
                         
                       
                       
                         
                           g 
                         
                         
                           h 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Math 
                   ⁢ 
                       
                   596 
                 
               
             
           
         
       
     
     Let a=Ae jδ11 , b=Be jδ12 , c=Ce jδ21  and d=De jδ22 , and e=Ee jγ11 , f=Fe jγ12 , g=Ge jγ21  and h=He jγ22 . A, B, C, D, E, F, G, and H are real numbers 0 or greater, and δ 11 , δ 12 , δ 21 , δ 22 , γ 11 , γ 12 , γ 21 , and γ 22  are expressed in radians. In this case, R S means that at least one of the following holds: (1) a≠e, (2) b≠f, (3) c≠g and (4) d≠h. 
     A precoding matrix may be the matrix R wherein one of a, b, c, and d is zero. In other words, the precoding matrix may be such that (1) a is zero, and b, c, and d are not zero; (2) b is zero, and a, c, and d are not zero; (3) c is zero, and a, b, and d are not zero; or (4) d is zero, and a, b, and c are not zero. 
     In the system example in the description of the present invention, a communication system using a MIMO scheme was described, wherein two modulated signals are transmitted from two antennas and are received by two antennas. The present invention may, however, of course also be adopted in a communication system using a MISO (Multiple Input Single Output) scheme. In the case of the MISO scheme, adoption of a precoding scheme for regularly hopping between a plurality of precoding matrices in the transmission device is the same as described above. On the other hand, the reception device is not provided with the antenna  701 _Y, the wireless unit  703 _Y, the channel fluctuation estimating unit  707 _ 1  for the modulated signal z 1 , or the channel fluctuation estimating unit  707 _ 2  for the modulated signal z 2  in the structure shown in  FIG.  7   . In this case as well, however, the processing detailed in the present description may be performed to estimate data transmitted by the transmission device. Note that it is widely known that a plurality of signals transmitted at the same frequency and the same time can be received by one antenna and decoded (for one antenna reception, it suffices to perform calculation such as ML calculation (Max-log APP or the like)). In the present invention, it suffices for the signal processing unit  711  in  FIG.  7    to perform demodulation (detection) taking into consideration the precoding scheme for regularly hopping that is used at the transmitting end. 
     Programs for executing the above communication scheme may, for example, be stored in advance in ROM (Read Only Memory) and be caused to operate by a CPU (Central Processing Unit). 
     Furthermore, the programs for executing the above communication scheme may be stored in a computer-readable recording medium, the programs stored in the recording medium may be loaded in the RAM (Random Access Memory) of the computer, and the computer may be caused to operate in accordance with the programs. 
     The components in the above embodiments and the like may be typically assembled as an LSI (Large Scale Integration), a type of integrated circuit. Individual components may respectively be made into discrete chips, or part or all of the components in each embodiment may be made into one chip. While an LSI has been referred to, the terms IC (Integrated Circuit), system LSI, super LSI, or ultra LSI may be used depending on the degree of integration. Furthermore, the scheme for assembling integrated circuits is not limited to LSI, and a dedicated circuit or a general-purpose processor may be used. A FPGA (Field Programmable Gate Array), which is programmable after the LSI is manufactured, or a reconfigurable processor, which allows reconfiguration of the connections and settings of circuit cells inside the LSI, may be used. 
     Furthermore, if technology for forming integrated circuits that replaces LSIs emerges, owing to advances in semiconductor technology or to another derivative technology, the integration of functional blocks may naturally be accomplished using such technology. The application of biotechnology or the like is possible. 
     With the symbol arranging scheme described in Embodiments A1 through A5 and Embodiment 1, the present invention may be similarly implemented by replacing the “scheme of hopping between different precoding matrices” with a “scheme of regularly hopping between precoding matrices using a plurality of different precoding matrices”. Note that the “plurality of different precoding matrices” are as described above. 
     The above describes that “with the symbol arranging scheme described in Embodiments A1 through A5 and Embodiment 1, the present invention may be similarly implemented by replacing the “scheme of hopping between different precoding matrices” with a “scheme of regularly hopping between precoding matrices using a plurality of different precoding matrices”. As the “scheme of hopping between precoding matrices using a plurality of different precoding matrices”, a scheme of preparing N different precoding matrices described above, and hopping between precoding matrices using the N different precoding matrices with an H-slot period (cycle) (H being a natural number larger than N) may be used (as an example, there is a scheme described in Embodiment C2). 
     With the symbol arranging scheme described in Embodiment 1, the present invention may be similarly implemented using the precoding scheme of regularly hopping between precoding matrices described in Embodiments C1 through C5. Similarly, the present invention may be similarly implemented using the precoding scheme of regularly hopping between precoding matrices described in Embodiments C1 through C5 as the precoding scheme of regularly hopping between precoding matrices described in Embodiments A1 through A5. 
     Embodiment D1 
     The following describes the scheme of regularly hopping between precoding matrices described in Non-Patent Literatures 12 through 15 when using a Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) code (or an LDPC code other than a QC-LDPC code), a concatenated code consisting of an LDPC code and a Bose-Chaudhuri-Hocquenghem (BCH) code, and a block code such as a turbo code or a duo-binary turbo code using tail-biting. Note that the present embodiment may be implemented using either a scheme of regularly hopping between precoding matrices represented by complex numbers or a scheme of regularly hopping between precoding matrices represented by real numbers, which is described below, as the scheme of regularly hopping between precoding matrices. 
     The following describes a case of transmitting two streams s 1  and s 2  as an example. Note that, when the control information and the like are not required to perform encoding using the block code, the number of bits constituting the coded block is the same as the number of bits constituting the block code (however, the control information and the like described below may be included). When the control information and the like (e.g. CRC (cyclic redundancy check), a transmission parameter) are required to perform encoding using the block code, the number of bits constituting the coded block can be a sum of the number of bits constituting the block code and the number of bits of the control information and the like. 
       FIG.  97    shows a change in the number of symbols and slots required for one coded block when the block code is used.  FIG.  97    shows a change in the number of symbols and slots required for one coded block when the block code is used in a case where the two streams s 1  and s 2  are transmitted and the transmission device has a single encoder, as shown in the transmission device in  FIG.  4    (note that, in this case, either the single carrier transmission or the multi-carrier transmission such as the OFDM may be used as a transmission system). 
     As shown in  FIG.  97   , let the number of bits constituting one coded block in the block code be 6000 bits. In order to transmit the 6000 bits, 3000 symbols, 1500 symbols and 1000 symbols are necessary when the modulation scheme is QPSK, 16QAM and 64QAM, respectively. 
     Since two streams are to be simultaneously transmitted in the transmission device shown in  FIG.  4   , when the modulation scheme is QPSK, 1500 symbols are allocated to s 1  and remaining 1500 symbols are allocated to s 2  out of the above-mentioned 3000 symbols. Therefore, 1500 slots (referred to as slots) are necessary to transmit 1500 symbols by s 1  and transmit 1500 symbols by s 2 . 
     Making the same considerations, 750 slots are necessary to transmit all the bits constituting one coded block when the modulation scheme is 16QAM, and 500 slots are necessary to transmit all the bits constituting one block when the modulation scheme is 64QAM. 
     The present embodiment describes a scheme of initializing precoding matrices in a case where the transmission device in  FIG.  4    is compatible with the multi-carrier scheme, such as the OFDM scheme, when the precoding scheme of regularly hopping between precoding matrices described in this description is used. 
     Next, a case where the transmission device transmits modulated signals each having a frame structure shown in  FIGS.  99 A and  99 B  is considered.  FIG.  99 A  shows a frame structure in the time and frequency domain for a modulated signal z 1  (transmitted by the antenna  312 A).  FIG.  99 B  shows a frame structure in the time and frequency domain for a modulated signal z 2  (transmitted by the antenna  312 B). In this case, the modulated signal z 1  and the modulated signal z 2  are assumed to occupy the same frequency (band), and the modulated signal z 1  and the modulated signal z 2  are assumed to exist at the same time. 
     As shown in  FIG.  99 A , the transmission device transmits a preamble (control symbol) in an interval A. The preamble is a symbol for transmitting control information to the communication partner and is assumed to include information on the modulation scheme for transmitting the first coded block and the second coded block. The transmission device is to transmit the first coded block in an interval B. The transmission device is to transmit the second coded block in an interval C. 
     The transmission device transmits the preamble (control symbol) in an interval D. The preamble is a symbol for transmitting control information to the communication partner and is assumed to include information on the modulation scheme for transmitting the third coded block, the fourth coded block and so on. The transmission device is to transmit the third coded block in an interval E. The transmission device is to transmit the fourth coded block in an interval F. 
     As shown in  FIG.  99 B , the transmission device transmits a preamble (control symbol) in the interval A. The preamble is a symbol for transmitting control information to the communication partner and is assumed to include information on the modulation scheme for transmitting the first coded block and the second coded block. The transmission device is to transmit the first coded block in the interval B. The transmission device is to transmit the second coded block in the interval C. 
     The transmission device transmits the preamble (control symbol) in the interval D. The preamble is a symbol for transmitting control information to the communication partner and is assumed to include information on the modulation scheme for transmitting the third coded block, the fourth coded block and so on. The transmission device is to transmit the third coded block in the interval E. The transmission device is to transmit the fourth coded block in the interval F. 
       FIG.  100    shows the number of slots used when the coded blocks are transmitted as shown in  FIG.  97   , and, in particular, when 16QAM is used as the modulation scheme in the first coded block. In order to transmit first coded block, 750 slots are necessary. 
     Similarly,  FIG.  100    shows the number of slots used when QPSK is used as the modulation scheme in the second coded block. In order to transmit first coded block, 1500 slots are necessary. 
       FIG.  101    shows the number of slots used when the coded block is transmitted as shown in  FIG.  97   , and, in particular, when QPSK is used as the modulation scheme in the third coded block. In order to transmit third coded block, 1500 slots are necessary. 
     As described in this description, a case where phase shift is not performed for the modulated signal z 1 , i.e. the modulated signal transmitted by the antenna  312 A, and is performed for the modulated signal z 2 , i.e. the modulated signal transmitted by the antenna  312 B, is considered. In this case,  FIGS.  100  and  101    show the scheme of regularly hopping between precoding matrices. 
     First, assume that seven precoding matrices are prepared to regularly hop between the precoding matrices, and are referred to as # 0 , # 1 , # 2 , # 3 , # 4 , # 5  and # 6 . The precoding matrices are to be regularly and cyclically used. That is to say, the precoding matrices are to be regularly and cyclically changed in the order # 0 , # 1 , # 2 , # 3 , # 4 , # 5 , # 6 , # 0 , # 1 , # 2 , # 3 , # 4 , # 5 , # 6 , # 0 , # 1 , # 2 , # 3 , # 4 , # 5 , # 6 , . . . . 
     First, as shown in  FIG.  100 ,  750    slots exist in the first coded block. Therefore, starting from # 0 , the precoding matrices are arranged in the order # 0 , # 1 , # 2 , # 3 , # 4 , # 5 , # 6 , # 0 , # 1 , # 2 , . . . , # 4 , # 5 , # 6 , # 0 , and end using # 0  for the 750 th  slot. 
     Next, the precoding matrices are to be applied to each slot in the second coded block. Since this description is on the assumption that the precoding matrices are applied to the multicast communication and broadcast, one possibility is that a reception terminal does not need the first coded block and extracts only the second coded block. In such a case, even when precoding matrix # 0  is used to transmit the last slot in the first coded block, the precoding matrix # 1  is used first to transmit the second coded block. In this case, the following two schemes are considered: 
     (a) The above-mentioned terminal monitors how the first coded block is transmitted, i.e. the terminal monitors a pattern of the precoding matrix used to transmit the last slot in the first coded block, and estimates the precoding matrix to be used to transmit the first slot in the second coded block; and
 
(b) The transmission device transmits information on the precoding matrix used to transmit the first slot in the second coded block without performing (a).
 
     In the case of (a), since the terminal has to monitor transmission of the first coded block, power consumption increases. In the case of (b), transmission efficiency of data is reduced. 
     Therefore, there is room for improvement in allocation of precoding matrices as described above. In order to address the above-mentioned problems, a scheme of fixing the precoding matrix used to transmit the first slot in each coded block is proposed. Therefore, as shown in  FIG.  100   , the precoding matrix used to transmit the first slot in the second coded block is set to # 0  as with the precoding matrix used to transmit the first slot in the first coded block. 
     Similarly, as shown in  FIG.  101   , the precoding matrix used to transmit the first slot in the third coded block is set not to # 3  but to # 0  as with the precoding matrix used to transmit the first slot in the first coded block and in the second coded block. 
     With the above-mentioned scheme, an effect of suppressing the problems occurring in (a) and (b) is obtained. 
     Note that, in the present embodiment, the scheme of initializing the precoding matrices in each coded block, i.e. the scheme in which the precoding matrix used to transmit the first slot in each coded block is fixed to # 0 , is described. As a different scheme, however, the precoding matrices may be initialized in units of frames. For example, in the symbol for transmitting the preamble and information after transmission of the control symbol, the precoding matrix used in the first slot may be fixed to # 0 . 
     For example, in  FIG.  99   , a frame is interpreted as starting from the preamble, the first coded block in the first frame is first coded block, and the first coded block in the second frame is the third coded block. This exemplifies a case where “the precoding matrix used in the first slot may be fixed (to # 0 ) in units of frames” as described above using  FIGS.  100  and  101   . 
     The following describes a case where the above-mentioned scheme is applied to a broadcasting system that uses the DVB-T2 standard. The frame structure of the broadcasting system that uses the DVB-T2 standard is as described in Embodiments A1 through A3. As described in Embodiments A1 through A3 using  FIGS.  61  and  70   , by the P1 symbol, P2 symbol and control symbol group, information on transmission scheme of each PLP (for example, a transmission scheme of transmitting a single modulated signal, a transmission scheme using space-time block coding and a transmission scheme of regularly hopping between precoding matrices) and a modulation scheme being used is transmitted to a terminal. In this case, if the terminal extracts only PLP that is necessary as information to perform demodulation (including separation of signals and signal detection) and error correction decoding, power consumption of the terminal is reduced. Therefore, as described using  FIGS.  99  through  101   , the scheme in which the precoding matrix used in the first slot in the PLP transmitted using, as the transmission scheme, the precoding scheme of regularly hopping between precoding matrices is fixed (to # 0 ) is proposed. 
     For example, assume that the broadcast station transmits each symbol having the frame structure as shown in  FIGS.  61  and  70   . In this case, as an example,  FIG.  102    shows a frame structure in frequency-time domain when the broadcast station transmits PLP $ 1  (to avoid confusion, # 1  is replaced by $ 1 ) and PLP $K using the precoding scheme of regularly hopping between precoding matrices. 
     Note that, in the following description, as an example, assume that seven precoding matrices are prepared in the precoding scheme of regularly hopping between the precoding matrices, and are referred to as # 0 , # 1 , # 2 , # 3 , # 4 , # 5  and # 6 . The precoding matrices are to be regularly and cyclically used. That is to say, the precoding matrices are to be regularly and cyclically changed in the order # 0 , # 1 , # 2 , # 3 , # 4 , # 5 , # 6 , # 0 , # 1 , # 2 , # 3 , # 4 , # 5 , # 6 , # 0 , # 1 , # 2 , # 3 , # 4 , # 5 , # 6 , . . . . 
     As shown in  FIG.  102   , the slot (symbol) in PLP $ 1  starts with a time T and a carrier  3  ( 10201  in  FIG.  102   ) and ends with a time T+4 and a carrier  4  ( 10202  in  FIG.  102   ) (see  FIG.  102   ). 
     This is to say, in PLP $ 1 , the first slot is the time T and the carrier  3 , the second slot is the time T and the carrier  4 , the third slot is the time T and a carrier  5 , . . . , the seventh slot is a time T+1 and a carrier  1 , the eighth slot is the time T+1 and a carrier  2 , the ninth slot is the time T+1 and the carrier  3 , . . . , the fourteenth slot is the time T+1 and a carrier  8 , the fifteenth slot is a time T+2 and a carrier  0 , . . . . 
     The slot (symbol) in PLP $K starts with a time S and a carrier  4  ( 10203  in  FIG.  102   ) and ends with a time S+8 and the carrier  4  ( 10204  in  FIG.  102   ) (see  FIG.  102   ). 
     This is to say, in PLP $K, the first slot is the time S and the carrier  4 , the second slot is the time S and a carrier  5 , the third slot is the time S and a carrier  6 , . . . , the fifth slot is the time S and a carrier  8 , the ninth slot is a time S+1 and a carrier  1 , the tenth slot is the time S+1 and a carrier  2  . . . , the sixteenth slot is the time S+1 and the carrier  8 , the seventeenth slot is a time S+2 and a carrier  0 , . . . . 
     Note that information on slot that includes information on the first slot (symbol) and the last slot (symbol) in each PLP and is used by each PLP is transmitted by the control symbol including the P1 symbol, the P2 symbol and the control symbol group. 
     In this case, as described using  FIGS.  99  through  101   , the first slot in PLP $ 1 , which is the time T and the carrier  3  ( 10201  in  FIG.  102   ), is precoded using the precoding matrix # 0 . Similarly, the first slot in PLP $K, which is the time S and the carrier  4  ( 10203  in  FIG.  102   ), is precoded using the precoding matrix # 0  regardless of the number of the precoding matrix used in the last slot in PLP $K−1, which is the time S and the carrier  3  ( 10205  in  FIG.  102   ). 
     The first slot in another PLP transmitted using the precoding scheme of regularly hopping between the precoding matrices is also precoded using the precoding matrix # 0 . 
     With the above-mentioned scheme, an effect of suppressing the above problems occurring in (a) and (b) is obtained. 
     Naturally, the reception device extracts necessary PLP from the information on slot that is included in the control symbol including the P1 symbol, the P2 symbol and the control symbol group and is used by each PLP to perform demodulation (including separation of signals and signal detection) and error correction decoding. The reception device learns a rule of the precoding scheme of regularly hopping between the precoding matrices in advance (when there are a plurality of rules, the transmission device transmits information on the rule to be used, and the reception device learns the rule being used by obtaining the transmitted information). By synchronizing a timing of rules of hopping the precoding matrices based on the number of the first slot in each PLP, the reception device can perform demodulation of information symbols (including separation of signals and signal detection). 
     Next, a case where the broadcast station (base station) transmits a modulated signal having a frame structure shown in  FIG.  103    is considered (the frame composed of symbol groups shown in  FIG.  103    is referred to as a main frame). In  FIG.  103   , elements that operate in a similar way to  FIG.  61    bear the same reference signs. The characteristic feature is that the main frame is separated into a subframe for transmitting a single modulated signal and a subframe for transmitting a plurality of modulated signals so that gain control of received signals can easily be performed. Note that the expression “transmitting a single modulated signal” also indicates that a plurality of modulated signals that are the same as the single modulated signal transmitted from a single antenna are generated, and the generated signals are transmitted from respective antennas. 
     In  FIG.  103   , PLP # 1  ( 6105 _ 1 ) through PLP #N ( 6105 _N) constitute a subframe  10300  for transmitting a single modulated signal. The subframe  10300  is composed only of PLPs, and does not include PLP for transmitting a plurality of modulated signals. Also, PLP $ 1  ( 10302 _ 1 ) through PLP $M ( 10302 _M) constitute a subframe  10301  for transmitting a plurality of modulated signals. The subframe  10301  is composed only of PLPs, and does not include PLP for transmitting a single modulated signal. 
     In this case, as described above, when the above-mentioned precoding scheme of regularly hopping between precoding matrices is used in the subframe  10301 , the first slot in PLP (PLP $ 1  ( 10302 _ 1 ) through PLP $M ( 10302 _M)) is assumed to be precoded using the precoding matrix # 0  (referred to as initialization of the precoding matrices). The above-mentioned initialization of precoding matrices, however, is irrelevant to a PLP in which another transmission scheme, for example, one of the transmission scheme using a fixed precoding matrix, the transmission scheme using a spatial multiplexing MIMO system and the transmission scheme using the space-time block coding as described in Embodiments A1 through A3 is used in PLP $ 1  ( 10302 _ 1 ) through PLP $M ( 10302 _M). 
     As shown in  FIG.  104   , PLP $ 1  is assumed to be the first PLP in the subframe for transmitting a plurality of modulated signals in the X th  main frame. Also, PLP $ 1 ′ is assumed to be the first PLP in the subframe for transmitting a plurality of modulated signals in the Y th  main frame. Both PLP $ 1  and PLP $ 1 ′ are assumed to use the precoding scheme of regularly hopping between precoding matrices. Note that, in  FIG.  104   , elements that are similar to the elements shown in  FIG.  102    bear the same reference signs. 
     In this case, the first slot ( 10201  in  FIG.  104    (time T and carrier  3 )) in PLP $ 1 , which is the first PLP in the subframe for transmitting a plurality of modulated signals in the X th  main frame, is assumed to be precoded using the precoding matrix # 0 . 
     Similarly, the first slot ( 10401  in  FIG.  104    (time T′ and carrier  7 )) in PLP $ 1 ′, which is the first PLP in the subframe for transmitting a plurality of modulated signals in the Y th  main frame, is assumed to be precoded using the precoding matrix # 0 . 
     As described above, in each main frame, the first slot in the first PLP in the subframe for transmitting a plurality of modulated signals is characterized by being precoded using the precoding matrix # 0 . 
     This is also important to suppress the above-mentioned problems occurring in (a) and (b). 
     Note that, in the present embodiment, as shown in  FIG.  97   , a case where the two streams s 1  and s 2  are transmitted and the transmission device has a single encoder as shown in the transmission device in  FIG.  4    is taken as an example. The initialization of precoding matrices described in the present embodiment, however, is also applicable to a case where the two streams s 1  and s 2  are transmitted and the transmission device has two single encoders as shown in the transmission device in  FIG.  3   , as shown in  FIG.  98   . 
     Supplementary Explanation 2 
     In each of the above-mentioned embodiments, the precoding matrices that the weighting combination unit uses for precoding are represented by complex numbers. The precoding matrices may also be represented by real numbers (referred to as a precoding scheme represented by real numbers). 
     For example, let two mapped baseband signals (in the used modulation scheme) be s 1 ( i ) and s 2 ( i ) (where i represents time or frequency), and let two precoded baseband signals obtained by the precoding be z 1 ( i ) and z 2 ( i ). Then, let the in-phase component and the quadrature component of the mapped baseband signal s 1 ( i ) (in the used modulation scheme) be I s1 (i) and Q s1 (i) respectively, the in-phase component and the quadrature component of the mapped baseband signal s 2 ( i ) (in the used modulation scheme) be I s2 (i) and Q s2 (i) respectively, the in-phase component and the quadrature component of the precoded baseband signal z 1 ( i ) be I z1 (i) and Q z1 (i) respectively, and in-phase component and the quadrature component of the precoded baseband signal z 2 ( i ) be I z2 (i) and Q z2 (i) respectively. When the precoding matrix composed of real numbers (the precoding matrix represented by real numbers) H r  is used, the following relationship holds. 
     
       
         
           
             
               
                 
                   
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                   Math 
                   ⁢ 
                       
                   597 
                 
               
             
           
         
       
     
     The precoding matrix composed of real numbers H r , however, is represented as follows. 
     
       
         
           
             
               
                 
                   Hr 
                   = 
                   
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                   Math 
                   ⁢ 
                       
                   598 
                 
               
             
           
         
       
     
     Here, a 11 , a 12 , a 13 , a 14 , a 21 , a 22 , a 23 , a 24 , a 31 , a 32 , a 33 , a 34 , a 41 , a 42 , a 43  and a 44  are real numbers. However, {a 11 =0, a 12 =0, a 13 =0 and a 14 =0} should not hold, {a 21 =0, a 22 =0, a 23 =0 and a 24 =0} should not hold, {a 31 =0, a 32 =0, a 33 =0 and a 34 =0} should not hold and {a 41 =0, a 42 =0, a 43 =0 and a 44 =0} should not hold. Also, {a 11 =0, a 21 =0, a 31 =0 and a 41 =0} should not hold, {a 12 =0, a 22 =0, a 32 =0 and a 42 =0} should not hold, {a 13 =0, a 23 =0, a 33 =0 and a 43 =0} should not hold and {a 14 =0, a 24 =0, a 34 =0 and a 44 =0} should not hold. 
     The “scheme of hopping between different precoding matrices” as an application of the precoding scheme of the present invention, such as the symbol arranging scheme described in Embodiments A1 through A5 and Embodiments 1 and 7, may also naturally be implemented as the precoding scheme of regularly hopping between precoding matrices using the precoding matrices represented by a plurality of different real numbers described as the “precoding scheme represented by real numbers”. The usefulness of hopping between precoding matrices in the present invention is the same as that in a case where the precoding matrices are represented by a plurality of different complex numbers. Note that the “plurality of different precoding matrices” are as described above. 
     The above describes that “scheme of regularly hopping between different precoding matrices” as an application of the precoding scheme of the present invention, such as the symbol arranging scheme described in Embodiments A1 through A5 and Embodiments 1 and 7, may also naturally be implemented as the precoding scheme of regularly hopping between precoding matrices using the precoding matrices represented by a plurality of different real numbers described as the “precoding scheme represented by real numbers”. As the “precoding scheme of regularly hopping between precoding matrices using the precoding matrices represented by a plurality of different real numbers”, a scheme of preparing N different precoding matrices (represented by real numbers), and hopping between precoding matrices using the N different precoding matrices (represented by real numbers) with an H-slot period (cycle) (H being a natural number larger than N) may be used (as an example, there is a scheme described in Embodiment C2). 
     With the symbol arranging scheme described in Embodiment 1, the present invention may be similarly implemented using the precoding scheme of regularly hopping between precoding matrices described in Embodiments C1 through C5. Similarly, the present invention may be similarly implemented using the precoding scheme of regularly hopping between precoding matrices described in Embodiments C1 through C5 as the precoding scheme of regularly hopping between precoding matrices described in Embodiments A1 through A5. 
     Embodiment F1 
     The precoding scheme of regularly hopping between precoding matrices described in Embodiments 1 through 26 and Embodiments C1 through C5 is applicable to any baseband signals s 1  and s 2  mapped in the I-Q plane. Therefore, in Embodiments 1 through 26 and Embodiments C1 through C5, the baseband signals s 1  and s 2  have not been described in detail. On the other hand, when the precoding scheme of regularly hopping between precoding matrices is applied to the baseband signals s 1  and s 2  generated from the error correction coded data, excellent reception quality can be achieved by controlling average power of the baseband signals s 1  and s 2 . In the present embodiment, the following describes a scheme of setting the average power of s 1  and s 2  when the precoding scheme of regularly hopping between precoding matrices is applied to the baseband signals s 1  and s 2  generated from the error correction coded data. 
     As an example, the modulation schemes for s 1  and s 2  are described as QPSK and 16QAM, respectively. 
     Since the modulation scheme for s 1  is QPSK, s 1  transmits two bits per symbol. Let the two bits to be transmitted be referred to as b 0  and b 1 . Since the modulation scheme for s 2  is 16QAM, s 2  transmits four bits per symbol. Let the four bits to be transmitted be referred to as b 2 , b 3 , b 4  and b 5 . The transmission device transmits one slot composed of one symbol for s 1  and one symbol for s 2 , i.e. six bits b 0 , b 1 , b 2 , b 3 , b 4  and b 5  per slot. 
     For example, in  FIG.  94    as an example of signal point layout in the I-Q plane for 16QAM, (b 2 , b 3 , b 4 , b 5 )=(0, 0, 0, 0) is mapped onto (I, Q)=(3×g, 3×g), (b 2 , b 3 , b 4 , b 5 )=(0, 0, 0, 1) is mapped onto (I, Q)=(3×g, 1×g), (b 2 , b 3 , b 4 , b 5 )=(0, 0, 1, 0) is mapped onto (I, Q)=(1×g, 3×g), (b 2 , b 3 , b 4 , b 5 )=(0, 0, 1, 1) is mapped onto (I, Q)=(1×g, 1×g), (b 2 , b 3 , b 4 , b 5 )=(0, 1, 0, 0) is mapped onto (I, Q)=(3×g, −3×g), . . . , (b 2 , b 3 , b 4 , b 5 )=(1, 1, 1, 0) is mapped onto (I, Q)=(−1×g, −3×g), and (b 2 , b 3 , b 4 , b 5 )=(1, 1, 1, 1) is mapped onto (I, Q)=(−1×g, 1×g). 
     Also, in  FIG.  95    as an example of signal point layout in the I-Q plane for QPSK, (b 0 , b 1 )=(0, 0) is mapped onto (I, Q)=(1×h, 1×h), (b 0 , b 1 )=(0, 1) is mapped onto (I, Q)=(1×h, −1×h), (b 0 , b 1 )=(1, 0) is mapped onto (I, Q)=(−1×h, 1×h), and (b 0 , b 1 )=(1, 1) is mapped onto (I, Q)=(−1×h, −1×h). 
     Here, assume that the average power (average value) of s 1  is equal to the average power (average value) of s 2 , i.e. h is represented by Equation 273 and g is represented by Equation 272.  FIG.  105    shows absolute values of the log-likelihood ratio for b 0  through b 5  described above when the reception device obtains the log-likelihood ratio. 
     In  FIG.  105 ,  10500    is the absolute value of the log-likelihood ratio for b 0 ,  10501  is the absolute value of the log-likelihood ratio for b 1 ,  10502  is the absolute value of the log-likelihood ratio for b 2 ,  10503  is the absolute value of the log-likelihood ratio for b 3 ,  10504  is the absolute value of the log-likelihood ratio for b 4 , and  10505  is the absolute value of the log-likelihood ratio for b 5 . In this case, when the absolute values of the log-likelihood ratio for b 0  and b 1  transmitted in QPSK are compared with the absolute values of the log-likelihood ratio for b 2  through b 5  transmitted in 16QAM, the absolute values of the log-likelihood ratio for b 0  and b 1  are higher than the absolute values of the log-likelihood ratio for b 2  through b 5 , i.e., reliability of b 0  and b 1  in the reception device is higher than the reliability of b 2  through b 5  in the reception device. This is because of the following reason. When h is represented by Equation 273 in  FIG.  95   , a minimum Euclidian distance between signal points in the I-Q plane for QPSK is as follows.
 
Math 599
 
√{square root over (2)} z   Equation 476
 
     On the other hand, when g is represented by Equation 272 in  FIG.  94   , 
                   Math   ⁢         600                        2     10       ⁢   z           Equation   ⁢         477               
represents a minimum Euclidian distance between signal points in the I-Q plane for 16QAM.
 
     If the reception device performs error correction decoding (e.g. belief propagation decoding such as a sum-product decoding in a case where the communication system uses LDPC coding) under this situation, due to a difference in reliability that “the absolute values of the log-likelihood ratio for b 0  and b 1  are higher than the absolute values of the log-likelihood ratio for b 2  through b 5 ”, a problem that the data reception quality degrades in the reception device by being affected by the absolute values of the log-likelihood ratio for b 2  through b 5  arises. 
     In order to overcome the problem, the difference between the absolute values of the log-likelihood ratio for b 0  and b 1  and the absolute values of the log-likelihood ratio for b 2  through b 5  should be reduced compared with  FIG.  105   , as shown in  FIG.  106   . 
     It is considered that the average power of s 1  is made to be different from the average power of s 2 .  FIGS.  107  and  108    each show an example of the structure of the signal processing unit relating to a power change unit (although being referred to as the power change unit here, the power change unit may be referred to as an amplitude change unit or a weighting unit) and the weighting combination unit. Note that, in  FIG.  107   , elements that operate in a similar way to  FIGS.  3  and  6    bear the same reference signs. Also, in  FIG.  108   , elements that operate in a similar way to  FIGS.  3 ,  6  and  107    bear the same reference signs. 
     Example 1 
     First, an example of the operation is described using  FIG.  107   . Let s 1 ( t ) be the (mapped) baseband signal for the modulation scheme QPSK. The mapping scheme is as shown in  FIG.  95   , and h is as represented by Equation 273. Also, let s 2 ( t ) be the (mapped) baseband signal for the modulation scheme 16QAM. The mapping scheme is as shown in  FIG.  94   , and g is as represented by Equation 272. Note that t is time. In the present embodiment, description is made taking the time domain as an example. 
     The power change unit ( 10701 B) receives a (mapped) baseband signal  307 B for the modulation scheme 16QAM and a control signal ( 10700 ) as input. Letting a value for power change set based on the control signal ( 10700 ) be u, the power change unit outputs a signal ( 10702 B) obtained by multiplying the (mapped) baseband signal  307 B for the modulation scheme 16QAM by u. Let u be a real number, and u&gt;1.0. Letting the precoding matrix in the precoding scheme of regularly hopping between precoding matrices be F[t] (represented as the function of t, as the precoding matrices are hopped by the time domain t), the following equation is satisfied. 
     
       
         
           
             
               
                 
                   Math 
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                   601 
                 
               
               
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     Therefore, a ratio of the average power for QPSK to the average power for 16QAM is set to 1:u 2 . With this structure, the reception device is in a reception condition in which the absolute value of the log-likelihood ratio shown in  FIG.  106    is obtained. Therefore, data reception quality is improved in the reception device. 
     The following describes a case where u in the ratio of the average power for QPSK to the average power for 16QAM 1:u 2  is set as shown in the following equation.
 
Math 602
 
 u =√{square root over (5)}  Equation 479
 
     In this case, the minimum Euclidian distance between signal points in the I-Q plane for QPSK and the minimum Euclidian distance between signal points in the I-Q plane for 16QAM can be the same. Therefore, excellent reception quality can be achieved. 
     The condition that the minimum Euclidian distances between signal points in the I-Q plane for two different modulation schemes are equalized, however, is a mere example of the scheme of setting the ratio of the average power for QPSK to the average power for 16QAM. For example, according to other conditions such as a code length and a code ratio of an error correction code used for error correction coding, excellent reception quality may be achieved when the value u for power change is set to a value (higher value or lower value) different from the value at which the minimum Euclidian distances between signal points in the I-Q plane for two different modulation schemes are equalized. 
     In order to increase the minimum distance between candidate signal points obtained at the time of reception, a scheme of setting the value u as shown in the following equation is considered, for example.
 
Math 603
 
 u =√{square root over (2)}  Equation 480
 
     The value, however, is set appropriately according to conditions required as a system. In the conventional technology, transmission power control is generally performed based on feedback information from a communication partner. The present invention is characterized in that the transmission power is controlled regardless of the feedback information from the communication partner in the present embodiment. Detailed description is made on this point. 
     The above describes that the value u for power change is set based on the control signal ( 10700 ). The following describes setting of the value u for power change based on the control signal ( 10700 ) in order to improve data reception quality in the reception device in detail. 
     Example 1-1 
     The following describes a scheme of setting the average power (average values) of s 1  and s 2  according to a block length (the number of bits constituting one coded block, and is also referred to as the code length) for the error correction coding used to generate s 1  and s 2  when the transmission device supports a plurality of block lengths for the error correction coding. 
     Examples of the error correction coding include block coding such as turbo coding or duo-binary turbo coding using tail-biting, LDPC coding, or the like. In many communication systems and broadcasting systems, a plurality of block lengths are supported. Encoded data for which error correction coding whose block length is selected from among the plurality of supported block lengths has been performed is distributed to two systems. The encoded data having been distributed to the two systems is modulated in the modulation scheme for s 1  and in the modulation scheme for s 2  to generate the (mapped) baseband signals s 1 ( t ) and s 2 ( t ). 
     The control signal ( 10700 ) is a signal indicating the selected block length for the error correction coding described above. The power change unit ( 10701 B) sets the value u for power change according to the control signal ( 10700 ). 
     The example 1-1 is characterized in that the power change unit ( 10701 B) sets the value u for power change according to the selected block length indicated by the control signal ( 10700 ). 
     Here, a value for power change set according to a block length X is referred to as u LX . 
     For example, when 1000 is selected as the block length, the power change unit ( 10701 B) sets a value for power change to u L1000 . When 1500 is selected as the block length, the power change unit ( 10701 B) sets a value for power change to u L1500 . When 3000 is selected as the block length, the power change unit ( 10701 B) sets a value for power change to u L3000 . In this case, for example, by setting u Ll000 , u L1500  and u L3000  so as to be different from one another, a high error correction capability can be achieved for each code length. Depending on the set code length, however, the effect might not be obtained even if the value for power change is changed. In such a case, even when the code length is changed, it is unnecessary to change the value for power change (for example, u L1000 =u L1500  may be satisfied. What is important is that two or more values exist in u L1500 , and u L3000 ). Although the case of three code lengths is taken as an example in the above description, the present invention is not limited to this. The important point is that two or more values for power change exist when there are two or more code lengths that can be set, and the transmission device selects any of the values for power change from among the two or more values for power change when the code length is set, and performs power change. 
     Example 1-2 
     The following describes a scheme of setting the average power (average values) of s 1  and s 2  according to a coding rate for the error correction coding used to generate s 1  and s 2  when the transmission device supports a plurality of coding rates for the error correction coding. 
     Examples of the error correction coding include block coding such as turbo coding or duo-binary turbo coding using tail-biting, LDPC coding, or the like. In many communication systems and broadcasting systems, a plurality of coding rates are supported. Encoded data for which error correction coding whose coding rate is selected from among the plurality of supported coding rates has been performed is distributed to two systems. The encoded data having been distributed to the two systems is modulated in the modulation scheme for s 1  and in the modulation scheme for s 2  to generate the (mapped) baseband signals s 1 ( t ) and s 2 ( t ). 
     The control signal ( 10700 ) is a signal indicating the selected coding rate for the error correction coding described above. The power change unit ( 10701 B) sets the value u for power change according to the control signal ( 10700 ). 
     The example 1-2 is characterized in that the power change unit ( 10701 B) sets the value u for power change according to the selected coding rate indicated by the control signal ( 10700 ). 
     Here, a value for power change set according to a coding rate rx is referred to as u rX . 
     For example, when r 1  is selected as the coding rate, the power change unit ( 10701 B) sets a value for power change to u r1 . When r 2  is selected as the coding rate, the power change unit ( 10701 B) sets a value for power change to u r2 . When r 3  is selected as the coding rate, the power change unit ( 10701 B) sets a value for power change to u r3 . In this case, for example, by setting u r1 , u r2  and u r3  so as to be different from one another, a high error correction capability can be achieved for each coding rate. Depending on the set coding rate, however, the effect might not be obtained even if the value for power change is changed. In such a case, even when the coding rate is changed, it is unnecessary to change the value for power change (for example, u r1 =u r2  may be satisfied. What is important is that two or more values exist in u r1 , u r2  and u r3 ). 
     Note that, as examples of r 1 , r 2  and r 3  described above, coding rates 1/2, 2/3 and 3/4 are considered when the error correction code is the LDPC code. 
     Although the case of three coding rates is taken as an example in the above description, the present invention is not limited to this. The important point is that two or more values for power change exist when there are two or more coding rates that can be set, and the transmission device selects any of the values for power change from among the two or more values for power change when the coding rate is set, and performs power change. 
     Example 1-3 
     In order for the reception device to achieve excellent data reception quality, it is important to implement the following. 
     The following describes a scheme of setting the average power (average values) of s 1  and s 2  according to a modulation scheme used to generate s 1  and s 2  when the transmission device supports a plurality of modulation schemes. 
     Here, as an example, a case where the modulation scheme for s 1  is fixed to QPSK and the modulation scheme for s 2  is changed from 16QAM to 64QAM by the control signal (or can be set to either 16QAM or 64QAM) is considered. Note that, in a case where the modulation scheme for s 2 ( t ) is 64QAM, the mapping scheme for s 2 ( t ) is as shown in  FIG.  109   , and k is represented by the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   604 
                 
               
               
                  
               
             
             
               
                 
                   k 
                   = 
                   
                     z 
                     
                       42 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   481 
                 
               
             
           
         
       
     
     By performing mapping in this way, the average power (average value) obtained when h is represented by Equation 273 in  FIG.  95    in QPSK becomes equal to the average power (average value) obtained when g is represented by Equation 272 in  FIG.  94    in 16QAM. In the mapping in 64QAM, the values I and Q are determined from an input of six bits. In this regard, the mapping 64QAM may be performed similarly to the mapping in QPSK and 16QAM. 
     That is to say, in  FIG.  109    as an example of signal point layout in the I-Q plane for 64QAM, (b 0 , b 1 , b 2 , b 3 , b 4 , b 5 )=(0, 0, 0, 0, 0, 0) is mapped onto (I, Q)=(7×k, 7×k), (b 0 , b 1 , b 2 , b 3 , b 4 , b 5 )=(0, 0, 0, 0, 0, 1) is mapped onto (I, Q)=(7×k, 5×k), (b 0 , b 1 , b 2 , b 3 , b 4 , b 5 )=(0, 0, 0, 0, 1, 0) is mapped onto (I, Q)=(5×k, 7×k), (b 0 , b 1 , b 2 , b 3 , b 4 , b 5 )=(0, 0, 0, 0, 1, 1) is mapped onto (I, Q)=(5×k, 5×k), (b 0 , b 1 , b 2 , b 3 , b 4 , b 5 )=(0, 0, 0, 1, 0, 0) is mapped onto (I, Q)=(7×k, 1×k), (b 0 , b 1 , b 2 , b 3 , b 4 , b 5 )=(1, 1, 1, 1, 1, 0) is mapped onto (I, Q)=(−3×k, −1×k), and (b 0 , b 1 , b 2 , b 3 , b 4 , b 5 )=(1, 1, 1, 1, 1, 1) is mapped onto (I, Q)=(−3×k, −3×k). 
     In  FIG.  107   , the power change unit  10701 B sets such that u=u 16  when the modulation scheme for s 2  is 16QAM, and sets such that u=u 64  when the modulation scheme for s 2  is 64QAM. In this case, due to the relationship between minimum Euclidian distances, by setting such that u 16 &lt;u 64 , excellent data reception quality is obtained in the reception device when the modulation scheme for s 2  is either 16QAM or 64QAM. 
     Note that, in the above description, the “modulation scheme for s 1  is fixed to QPSK”. It is also considered that the modulation scheme for s 2  is fixed to QPSK. In this case, power change is assumed to be not performed for the fixed modulation scheme (here, QPSK), and to be performed for a plurality of modulation schemes that can be set (here, 16QAM and 64QAM). That is to say, in this case, the transmission device does not have the structure shown in  FIG.  107   , but has a structure in which the power change unit  10701 B is eliminated from the structure in  FIG.  107    and a power change unit is provided to a s 1 ( t )-side. When the fixed modulation scheme (here, QPSK) is set to s 2 , the following equation is satisfied. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   605 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         
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                   Equation 
                   ⁢ 
                       
                   482 
                 
               
             
           
         
       
     
     When the modulation scheme for s 2  is fixed to QPSK and the modulation scheme for s 1  is changed from 16QAM to 64QAM (is set to either 16QAM or 64QAM), the relationship u 16 &lt;u 64  should be satisfied (note that a multiplied value for power change in 16QAM is u 16 , a multiplied value for power change in 64QAM is u 64 , and power change is not performed in QPSK). 
     Also, when a set of the modulation scheme for s 1  and the modulation scheme for s 2  can be set to any one of a set of QPSK and 16QAM, a set of 16QAM and QPSK, a set of QPSK and 64QAM and a set of 64QAM and QPSK, the relationship u 16 &lt;u 64  should be satisfied. 
     The following describes a case where the above-mentioned description is generalized. 
     Let the modulation scheme for s 1  be fixed to a modulation scheme C in which the number of signal points in the I-Q plane is c. Let the modulation scheme for s 2  be set to either a modulation scheme A in which the number of signal points in the I-Q plane is a or a modulation scheme B in which the number of signal points in the I-Q plane is b (a&gt;b&gt;c) (however, let the average power (average value) for s 2  in the modulation scheme A be equal to the average power (average value) for s 2  in the modulation scheme B). In this case, a value for power change set when the modulation scheme A is set to the modulation scheme for s 2  is u a . Also, a value for power change set when the modulation scheme B is set to the modulation scheme for s 2  is u b . In this case, when the relationship u b &lt;u a  is satisfied, excellent data reception quality is obtained in the reception device. 
     Power change is assumed to be not performed for the fixed modulation scheme (here, modulation scheme C), and to be performed for a plurality of modulation schemes that can be set (here, modulation schemes A and B). When the modulation scheme for s 2  is fixed to the modulation scheme C and the modulation scheme for s 1  is changed from the modulation scheme A to the modulation scheme B (is set to either the modulation schemes A or B), the relationship u b &lt;u a  should be satisfied. Also, when a set of the modulation scheme for s 1  and the modulation scheme for s 2  can be set to any one of a set of the modulation scheme C and the modulation scheme A, a set of the modulation scheme A and the modulation scheme C, a set of the modulation scheme C and the modulation scheme B and a set of the modulation scheme B and the modulation scheme C, the relationship u b &lt;u a  should be satisfied. 
     Example 2 
     The following describes an example of the operation different from that described in Example 1, using  FIG.  107   . Let s 1 ( t ) be the (mapped) baseband signal for the modulation scheme 64QAM. The mapping scheme is as shown in  FIG.  109   , and k is as represented by Equation 481. Also, let s 2 ( t ) be the (mapped) baseband signal for the modulation scheme 16QAM. The mapping scheme is as shown in  FIG.  94   , and g is as represented by Equation 272. Note that t is time. In the present embodiment, description is made taking the time domain as an example. 
     The power change unit ( 10701 B) receives a (mapped) baseband signal  307 B for the modulation scheme 16QAM and a control signal ( 10700 ) as input. Letting a value for power change set based on the control signal ( 10700 ) be u, the power change unit outputs a signal ( 10702 B) obtained by multiplying the (mapped) baseband signal  307 B for the modulation scheme 16QAM by u. Let u be a real number, and u&lt;1.0. Letting the precoding matrix in the precoding scheme of regularly hopping between precoding matrices be F[t], the following equation is satisfied. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   606 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         
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                                   z 
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                         = 
                           
                         
                           
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                   Equation 
                   ⁢ 
                       
                   483 
                 
               
             
           
         
       
     
     Therefore, a ratio of the average power for 64QAM to the average power for 16QAM is set to 1:u 2 . With this structure, the reception device is in a reception condition as shown in  FIG.  106   . Therefore, data reception quality is improved in the reception device. 
     In the conventional technology, transmission power control is generally performed based on feedback information from a communication partner. The present invention is characterized in that the transmission power is controlled regardless of the feedback information from the communication partner in the present embodiment. Detailed description is made on this point. 
     The above describes that the value u for power change is set based on the control signal ( 10700 ). The following describes setting of the value u for power change based on the control signal ( 10700 ) in order to improve data reception quality in the reception device in detail. 
     Example 2-1 
     The following describes a scheme of setting the average power (average values) of s 1  and s 2  according to a block length (the number of bits constituting one coded block, and is also referred to as the code length) for the error correction coding used to generate s 1  and s 2  when the transmission device supports a plurality of block lengths for the error correction coding. 
     Examples of the error correction coding include block coding such as turbo coding or duo-binary turbo coding using tail-biting, LDPC coding, or the like. In many communication systems and broadcasting systems, a plurality of block lengths are supported. Encoded data for which error correction coding whose block length is selected from among the plurality of supported block lengths has been performed is distributed to two systems. The encoded data having been distributed to the two systems is modulated in the modulation scheme for s 1  and in the modulation scheme for s 2  to generate the (mapped) baseband signals s 1 ( t ) and s 2 ( t ). 
     The control signal ( 10700 ) is a signal indicating the selected block length for the error correction coding described above. The power change unit ( 10701 B) sets the value u for power change according to the control signal ( 10700 ). 
     The present invention is characterized in that the power change unit ( 10701 B) sets the value u for power change according to the selected block length indicated by the control signal ( 10700 ). Here, a value for power change set according to the block length X is referred to as u LX . 
     For example, when 1000 is selected as the block length, the power change unit ( 10701 B) sets a value for power change to u L1000 . When 1500 is selected as the block length, the power change unit ( 10701 B) sets a value for power change to u L1500 . When 3000 is selected as the block length, the power change unit ( 10701 B) sets a value for power change to u L3000 . In this case, for example, by setting u L1000 , u L1500  and u L3000  so as to be different from one another, a high error correction capability can be achieved for each code length. Depending on the set code length, however, the effect might not be obtained even if the value for power change is changed. In such a case, even when the code length is changed, it is unnecessary to change the value for power change (for example, u L1000 =u L1500  may be satisfied. What is important is that two or more values exist in u L1000 , u L1500  and u L3000 ). Although the case of three code lengths is taken as an example in the above description, the present invention is not limited to this. The important point is that two or more values for power change exist when there are two or more code lengths that can be set, and the transmission device selects any of the values for power change from among the two or more values for power change when the code length is set, and performs power change. 
     Example 2-2 
     The following describes a scheme of setting the average power (average values) of s 1  and s 2  according to a coding rate for the error correction coding used to generate s 1  and s 2  when the transmission device supports a plurality of coding rates for the error correction coding. 
     Examples of the error correction coding include block coding such as turbo coding or duo-binary turbo coding using tail-biting, LDPC coding, or the like. In many communication systems and broadcasting systems, a plurality of coding rates are supported. Encoded data for which error correction coding whose coding rate is selected from among the plurality of supported coding rates has been performed is distributed to two systems. The encoded data having been distributed to the two systems is modulated in the modulation scheme for s 1  and in the modulation scheme for s 2  to generate the (mapped) baseband signals s 1 ( t ) and s 2 ( t ). 
     The control signal ( 10700 ) is a signal indicating the selected coding rate for the error correction coding described above. The power change unit ( 10701 B) sets the value u for power change according to the control signal ( 10700 ). 
     The present invention is characterized in that the power change unit ( 10701 B) sets the value u for power change according to the selected coding rate indicated by the control signal ( 10700 ). Here, a value for power change set according to the coding rate rx is referred to as u rx . 
     For example, when r 1  is selected as the coding rate, the power change unit ( 10701 B) sets a value for power change to u r1 . When r 2  is selected as the coding rate, the power change unit ( 10701 B) sets a value for power change to u r2 . When r 3  is selected as the coding rate, the power change unit ( 10701 B) sets a value for power change to u r3 . In this case, for example, by setting u r1 , u r2  and u r3  so as to be different from one another, a high error correction capability can be achieved for each coding rate. Depending on the set coding rate, however, the effect might not be obtained even if the value for power change is changed. In such a case, even when the coding rate is changed, it is unnecessary to change the value for power change (for example, u r1 =u r2  may be satisfied. What is important is that two or more values exist in u r1 , u r2  and u r3 ). 
     Note that, as examples of r 1 , r 2  and r 3  described above, coding rates 1/2, 2/3 and 3/4 are considered when the error correction code is the LDPC code. Although the case of three coding rates is taken as an example in the above description, the present invention is not limited to this. The important point is that two or more values for power change exist when there are two or more coding rates that can be set, and the transmission device selects any of the values for power change from among the two or more values for power change when the coding rate is set, and performs power change. 
     Example 2-3 
     In order for the reception device to achieve excellent data reception quality, it is important to implement the following. 
     The following describes a scheme of setting the average power (average values) of s 1  and s 2  according to a modulation scheme used to generate s 1  and s 2  when the transmission device supports a plurality of modulation schemes. 
     Here, as an example, a case where the modulation scheme for s 1  is fixed to 64QAM and the modulation scheme for s 2  is changed from 16QAM to QPSK by the control signal (or can be set to either 16QAM or QPSK) is considered. 
     In a case where the modulation scheme for s 1  is 64QAM, the mapping scheme for s 1 ( t ) is as shown in  FIG.  109   , and k is represented by Equation 481 in  FIG.  109   . In a case where the modulation scheme for s 2  is 16QAM, the mapping scheme for s 2 ( t ) is as shown in  FIG.  94   , and g is represented by Equation 272 in  FIG.  94   . Also, in a case where the modulation scheme for s 2 ( t ) is QPSK, the mapping scheme for s 2 ( t ) is as shown in  FIG.  95   , and h is represented by Equation 273 in  FIG.  95   . 
     By performing mapping in this way, the average power in 16QAM becomes equal to the average power in QPSK. 
     In  FIG.  107   , the power change unit  10701 B sets such that u=u 16  when the modulation scheme for s 2  is 16QAM, and sets such that u=u 4  when the modulation scheme for s 2  is QPSK. In this case, due to the relationship between minimum Euclidian distances, by setting such that u 4 &lt;u 16 , excellent data reception quality is obtained in the reception device when the modulation scheme for s 2  is either 16QAM or QPSK. 
     Note that, in the above description, the modulation scheme for s 1  is fixed to 64QAM. When the modulation scheme for s 2  is fixed to 64QAM and the modulation scheme for s 1  is changed from 16QAM to QPSK (is set to either 16QAM or QPSK), the relationship u 4 &lt;u 16  should be satisfied (the same considerations should be made as the example 1-3) (note that a multiplied value for power change in 16QAM is u 16 , a multiplied value for power change in QPSK is u 4 , and power change is not performed in 64QAM). Also, when a set of the modulation scheme for s 1  and the modulation scheme for s 2  can be set to any one of a set of 64QAM and 16QAM, a set of 16QAM and 64QAM, a set of 64QAM and QPSK and a set of QPSK and 64QAM, the relationship u 4 &lt;u 16  should be satisfied. 
     The following describes a case where the above-mentioned description is generalized. 
     Let the modulation scheme for s 1  be fixed to a modulation scheme C in which the number of signal points in the I-Q plane is c. Let the modulation scheme for s 2  be set to either a modulation scheme A in which the number of signal points in the I-Q plane is a or a modulation scheme B in which the number of signal points in the I-Q plane is b (c&gt;b&gt;a) (however, let the average power (average value) for s 2  in the modulation scheme A be equal to the average power (average value) for s 2  in the modulation scheme B). 
     In this case, a value for power change set when the modulation scheme A is set as the modulation scheme for s 2  is u a . Also, a value for power change set when the modulation scheme B is set to the modulation scheme for s 2  is u b . In this case, when the relationship u a &lt;u b  is satisfied, excellent data reception quality is obtained in the reception device. 
     Power change is assumed to be not performed for the fixed modulation scheme (here, modulation scheme C), and to be performed for a plurality of modulation schemes that can be set (here, modulation schemes A and B). When the modulation scheme for s 2  is fixed to the modulation scheme C and the modulation scheme for s 1  is changed from the modulation scheme A to the modulation scheme B (is set to either the modulation schemes A or B), the relationship u a &lt;u b  should be satisfied. Also, when a set of the modulation scheme for s 1  and the modulation scheme for s 2  can be set to any one of a set of the modulation scheme C and the modulation scheme A, a set of the modulation scheme A and the modulation scheme C, a set of the modulation scheme C and the modulation scheme B and a set of the modulation scheme B and the modulation scheme C, the relationship u a &lt;u b  should be satisfied. 
     Example 3 
     The following describes an example of the operation different from that described in Example 1, using  FIG.  107   . Let s 1 ( t ) be the (mapped) baseband signal for the modulation scheme 16QAM. The mapping scheme is as shown in  FIG.  94   , and g is as represented by Equation 272. Let s 2 ( t ) be the (mapped) baseband signal for the modulation scheme 64QAM. The mapping scheme is as shown in  FIG.  109   , and k is as represented by Equation 481. Note that t is time. In the present embodiment, description is made taking the time domain as an example. 
     The power change unit ( 10701 B) receives a (mapped) baseband signal  307 B for the modulation scheme 64QAM and a control signal ( 10700 ) as input. Letting a value for power change set based on the control signal ( 10700 ) be u, the power change unit outputs a signal ( 10702 B) obtained by multiplying the (mapped) baseband signal  307 B for the modulation scheme 64QAM by u. Let u be a real number, and u&gt;1.0. Letting the precoding matrix in the precoding scheme of regularly hopping between precoding matrices be F[t], the following equation is satisfied. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   607 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         
                           ( 
                           
                             
                               
                                 
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                                   2 
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                         = 
                           
                         
                           
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                             [ 
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                   Equation 
                   ⁢ 
                       
                   484 
                 
               
             
           
         
       
     
     Therefore, a ratio of the average power for 16QAM to the average power for 64QAM is set to 1:u 2 . With this structure, the reception device is in a reception condition as shown in  FIG.  106   . Therefore, data reception quality is improved in the reception device. 
     In the conventional technology, transmission power control is generally performed based on feedback information from a communication partner. The present invention is characterized in that the transmission power is controlled regardless of the feedback information from the communication partner in the present embodiment. Detailed description is made on this point. 
     The above describes that the value u for power change is set based on the control signal ( 10700 ). The following describes setting of the value u for power change based on the control signal ( 10700 ) in order to improve data reception quality in the reception device in detail. 
     Example 3-1 
     The following describes a scheme of setting the average power (average values) of s 1  and s 2  according to a block length (the number of bits constituting one coded block, and is also referred to as the code length) for the error correction coding used to generate s 1  and s 2  when the transmission device supports a plurality of block lengths for the error correction coding. 
     Examples of the error correction coding include block coding such as turbo coding or duo-binary turbo coding using tail-biting, LDPC coding, or the like. In many communication systems and broadcasting systems, a plurality of block lengths are supported. Encoded data for which error correction coding whose block length is selected from among the plurality of supported block lengths has been performed is distributed to two systems. The encoded data having been distributed to the two systems is modulated in the modulation scheme for s 1  and in the modulation scheme for s 2  to generate the (mapped) baseband signals s 1 ( t ) and s 2 ( t ). 
     The control signal ( 10700 ) is a signal indicating the selected block length for the error correction coding described above. The power change unit ( 10701 B) sets the value u for power change according to the control signal ( 10700 ). 
     The present invention is characterized in that the power change unit ( 10701 B) sets the value u for power change according to the selected block length indicated by the control signal ( 10700 ). Here, a value for power change set according to the block length X is referred to as u LX . 
     For example, when 1000 is selected as the block length, the power change unit ( 10701 B) sets a value for power change to u L1000 . When 1500 is selected as the block length, the power change unit ( 10701 B) sets a value for power change to u L1500 . When 3000 is selected as the block length, the power change unit ( 10701 B) sets a value for power change to u L3000 . In this case, for example, by setting u L1000 , u L1500  and u L3000  so as to be different from one another, a high error correction capability can be achieved for each code length. Depending on the set code length, however, the effect might not be obtained even if the value for power change is changed. In such a case, even when the code length is changed, it is unnecessary to change the value for power change (for example, u L1000 =u L1500  may be satisfied. What is important is that two or more values exist in u L1000 , u L1500  and u L3000 ). Although the case of three code lengths is taken as an example in the above description, the present invention is not limited to this. The important point is that two or more values for power change exist when there are two or more code lengths that can be set, and the transmission device selects any of the values for power change from among the two or more values for power change when the code length is set, and performs power change. 
     Example 3-2 
     The following describes a scheme of setting the average power (average values) of s 1  and s 2  according to a coding rate for the error correction coding used to generate s 1  and s 2  when the transmission device supports a plurality of coding rates for the error correction coding. 
     Examples of the error correction coding include block coding such as turbo coding or duo-binary turbo coding using tail-biting, LDPC coding, or the like. In many communication systems and broadcasting systems, a plurality of coding rates are supported. Encoded data for which error correction coding whose coding rate is selected from among the plurality of supported coding rates has been performed is distributed to two systems. The encoded data having been distributed to the two systems is modulated in the modulation scheme for s 1  and in the modulation scheme for s 2  to generate the (mapped) baseband signals s 1 ( t ) and s 2 ( t ). 
     The control signal ( 10700 ) is a signal indicating the selected coding rate for the error correction coding described above. The power change unit ( 10701 B) sets the value u for power change according to the control signal ( 10700 ). 
     The present invention is characterized in that the power change unit ( 10701 B) sets the value u for power change according to the selected coding rate indicated by the control signal ( 10700 ). Here, a value for power change set according to the coding rate rx is referred to as u rx . 
     For example, when r 1  is selected as the coding rate, the power change unit ( 10701 B) sets a value for power change to u r1 . When r 2  is selected as the coding rate, the power change unit ( 10701 B) sets a value for power change to u r2 . When r 3  is selected as the coding rate, the power change unit ( 10701 B) sets a value for power change to u r3 . In this case, for example, by setting u r1 , u r2  and u r3  so as to be different from one another, a high error correction capability can be achieved for each coding rate. Depending on the set coding rate, however, the effect might not be obtained even if the value for power change is changed. In such a case, even when the coding rate is changed, it is unnecessary to change the value for power change (for example, u r1 =u r2  may be satisfied. What is important is that two or more values exist in u r1 , u r2  and u r3 ). 
     Note that, as examples of r 1 , r 2  and r 3  described above, coding rates 1/2, 2/3 and 3/4 are considered when the error correction code is the LDPC code. Although the case of three coding rates is taken as an example in the above description, the present invention is not limited to this. The important point is that two or more values for power change exist when there are two or more coding rates that can be set, and the transmission device selects any of the values for power change from among the two or more values for power change when the coding rate is set, and performs power change. 
     Example 3-3 
     In order for the reception device to achieve excellent data reception quality, it is important to implement the following. 
     The following describes a scheme of setting the average power (average values) of s 1  and s 2  according to a modulation scheme used to generate s 1  and s 2  when the transmission device supports a plurality of modulation schemes. 
     Here, as an example, a case where the modulation scheme for s 1  is fixed to 16QAM and the modulation scheme for s 2  is changed from 64QAM to QPSK by the control signal (or can be set to either 64QAM or QPSK) is considered. 
     In a case where the modulation scheme for s 1  is 16QAM, the mapping scheme for s 2 ( t ) is as shown in  FIG.  94   , and g is represented by Equation 272 in  FIG.  94   . In a case where the modulation scheme for s 2  is 64QAM, the mapping scheme for s 1 ( t ) is as shown in  FIG.  109   , and k is represented by Equation 481 in  FIG.  109   . Also, in a case where the modulation scheme for s 2 ( t ) is QPSK, the mapping scheme for s 2 ( t ) is as shown in  FIG.  95   , and h is represented by Equation 273 in  FIG.  95   . 
     By performing mapping in this way, the average power in 16QAM becomes equal to the average power in QPSK. 
     In  FIG.  107   , the power change unit  10701 B sets such that u=u 64  when the modulation scheme for s 2  is 64QAM, and sets such that u=u 4  when the modulation scheme for s 2  is QPSK. In this case, due to the relationship between minimum Euclidian distances, by setting such that u 4 &lt;u 64 , excellent data reception quality is obtained in the reception device when the modulation scheme for s 2  is either 16QAM or 64QAM. 
     Note that, in the above description, the modulation scheme for s 1  is fixed to 16QAM. When the modulation scheme for s 2  is fixed to 16QAM and the modulation scheme for s 1  is changed from 64QAM to QPSK (is set to either 64QAM or QPSK), the relationship u 4 &lt;u 64  should be satisfied (the same considerations should be made as the example 1-3) (note that a multiplied value for power change in 64QAM is u 64 , a multiplied value for power change in QPSK is u 4 , and power change is not performed in 16QAM). Also, when a set of the modulation scheme for s 1  and the modulation scheme for s 2  can be set to any one of a set of 16QAM and 64QAM, a set of 64QAM and 16QAM, a set of 16QAM and QPSK and a set of QPSK and 16QAM, the relationship u 4 &lt;u 64  should be satisfied. 
     The following describes a case where the above-mentioned description is generalized. 
     Let the modulation scheme for s 1  be fixed to a modulation scheme C in which the number of signal points in the I-Q plane is c. Let the modulation scheme for s 2  be set to either a modulation scheme A in which the number of signal points in the I-Q plane is a or a modulation scheme B in which the number of signal points in the I-Q plane is b (c&gt;b&gt;a) (however, let the average power (average value) for s 2  in the modulation scheme A be equal to the average power (average value) for s 2  in the modulation scheme B). 
     In this case, a value for power change set when the modulation scheme A is set as the modulation scheme for s 2  is u a . Also, a value for power change set when the modulation scheme B is set to the modulation scheme for s 2  is u b . In this case, when the relationship u a &lt;u b  is satisfied, excellent data reception quality is obtained in the reception device. 
     Power change is assumed to be not performed for the fixed modulation scheme (here, modulation scheme C), and to be performed for a plurality of modulation schemes that can be set (here, modulation schemes A and B). When the modulation scheme for s 2  is fixed to the modulation scheme C and the modulation scheme for s 1  is changed from the modulation scheme A to the modulation scheme B (is set to either the modulation schemes A or B), the relationship u a &lt;u b  should be satisfied. Also, when a set of the modulation scheme for s 1  and the modulation scheme for s 2  can be set to any one of a set of the modulation scheme C and the modulation scheme A, a set of the modulation scheme A and the modulation scheme C, a set of the modulation scheme C and the modulation scheme B and a set of the modulation scheme B and the modulation scheme C, the relationship u a &lt;u b  should be satisfied. 
     Example 4 
     The case where power change is performed for one of the modulation schemes for s 1  and s 2  has been described above. The following describes a case where power change is performed for both of the modulation schemes for s 1  and s 2 . 
     An example of the operation is described using  FIG.  108   . Let s 1 ( t ) be the (mapped) baseband signal for the modulation scheme QPSK. The mapping scheme is as shown in  FIG.  95   , and h is as represented by Equation 273. Also, let s 2 ( t ) be the (mapped) baseband signal for the modulation scheme 16QAM. The mapping scheme is as shown in  FIG.  94   , and g is as represented by Equation 272. Note that t is time. In the present embodiment, description is made taking the time domain as an example. 
     The power change unit ( 10701 A) receives a (mapped) baseband signal  307 A for the modulation scheme QPSK and the control signal ( 10700 ) as input. Letting a value for power change set based on the control signal ( 10700 ) be v, the power change unit outputs a signal ( 10702 A) obtained by multiplying the (mapped) baseband signal  307 A for the modulation scheme QPSK by v. 
     The power change unit ( 10701 B) receives the (mapped) baseband signal  307 B for the modulation scheme 16QAM and the control signal ( 10700 ) as input. Letting a value for power change set based on the control signal ( 10700 ) be u, the power change unit outputs the signal ( 10702 B) obtained by multiplying the (mapped) baseband signal  307 B for the modulation scheme 16QAM by u. Then, let u=v×w (w&gt;1.0). 
     Letting the precoding matrix in the precoding scheme of regularly hopping between precoding matrices be F[t], the following Equation 485 is satisfied. 
     
       
         
           
             
               
                 
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                   608 
                 
               
               
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                   Equation 
                   ⁢ 
                       
                   485 
                 
               
             
           
         
       
     
     Therefore, a ratio of the average power for QPSK to the average power for 16QAM is set to v 2 :u 2 =v 2 :v 2 ×w 2 =1:w 2 . With this structure, the reception device is in a reception condition as shown in  FIG.  106   . Therefore, data reception quality is improved in the reception device. 
     Note that, in view of Equations 479 and 480, effective examples of the ratio of the average power for QPSK to the average power for 16QAM are considered to be v 2 :u 2 =v 2 :v 2 ×w 2 =1:w 2 =1:5 or v 2 :u 2 =v 2 :v 2 ×w 2 =1:w 2 =1:2. The ratio, however, is set appropriately according to conditions required as a system. 
     In the conventional technology, transmission power control is generally performed based on feedback information from a communication partner. The present invention is characterized in that the transmission power is controlled regardless of the feedback information from the communication partner in the present embodiment. Detailed description is made on this point. 
     The above describes that the values v and u for power change are set based on the control signal ( 10700 ). The following describes setting of the values v and u for power change based on the control signal ( 10700 ) in order to improve data reception quality in the reception device in detail. 
     Example 4-1 
     The following describes a scheme of setting the average power (average values) of s 1  and s 2  according to a block length (the number of bits constituting one coded block, and is also referred to as the code length) for the error correction coding used to generate s 1  and s 2  when the transmission device supports a plurality of block lengths for the error correction coding. 
     Examples of the error correction coding include block coding such as turbo coding or duo-binary turbo coding using tail-biting, LDPC coding, or the like. In many communication systems and broadcasting systems, a plurality of block lengths are supported. Encoded data for which error correction coding whose block length is selected from among the plurality of supported block lengths has been performed is distributed to two systems. The encoded data having been distributed to the two systems is modulated in the modulation scheme for s 1  and in the modulation scheme for s 2  to generate the (mapped) baseband signals s 1 ( t ) and s 2 ( t ). 
     The control signal ( 10700 ) is a signal indicating the selected block length for the error correction coding described above. The power change unit ( 10701 A) sets the value v for power change according to the control signal ( 10700 ). Similarly, the power change unit ( 10701 B) sets the value u for power change according to the control signal ( 10700 ). 
     The present invention is characterized in that the power change units ( 10701 A and  10701 B) respectively set the values v and u for power change according to the selected block length indicated by the control signal ( 10700 ). Here, values for power change set according to the block length X are referred to as v LX  and u LX . 
     For example, when 1000 is selected as the block length, the power change unit ( 10701 A) sets a value for power change to v L1000 . When 1500 is selected as the block length, the power change unit ( 10701 A) sets a value for power change to v L1500 . When 3000 is selected as the block length, the power change unit ( 10701 A) sets a value for power change to V L3000 . 
     On the other hand, when 1000 is selected as the block length, the power change unit ( 10701 B) sets the value for power change to u L1000 . When 1500 is selected as the block length, the power change unit ( 10701 B) sets the value for power change to u L1500 . When 3000 is selected as the block length, the power change unit ( 10701 B) sets the value for power change to u L3000 . 
     In this case, for example, by setting v L1000 , v L1500  and V L3000  so as to be different from one another, a high error correction capability can be achieved for each code length. Similarly, by setting u L1000 , u L1500  and u L3000  so as to be different from one another, a high error correction capability can be achieved for each code length. Depending on the set code length, however, the effect might not be obtained even if the value for power change is changed. In such a case, even when the code length is changed, it is unnecessary to change the value for power change (for example, u L1000 =u L1500  may be satisfied, and v L1000 =v L1500  may be satisfied. What is important is that two or more values exist in a set of v L1000 , v L1500  and V L3000 , and that two or more values exist in a set of u L1000 , u L1500  and u L1000 ). Note that, as described above, v LX  and u LX  are set so as to satisfy the ratio of the average power 1:w 2 . 
     Although the case of three code lengths is taken as an example in the above description, the present invention is not limited to this. One important point is that two or more values u LX  for power change exist when there are two or more code lengths that can be set, and the transmission device selects any of the values for power change from among the two or more values u LX  for power change when the code length is set, and performs power change. Another important point is that two or more values v LX  for power change exist when there are two or more code lengths that can be set, and the transmission device selects any of the values for power change from among the two or more values v LX  for power change when the code length is set, and performs power change. 
     Example 4-2 
     The following describes a scheme of setting the average power (average values) of s 1  and s 2  according to a coding rate for the error correction coding used to generate s 1  and s 2  when the transmission device supports a plurality of coding rates for the error correction coding. 
     Examples of the error correction coding include block coding such as turbo coding or duo-binary turbo coding using tail-biting, LDPC coding, or the like. In many communication systems and broadcasting systems, a plurality of coding rates are supported. Encoded data for which error correction coding whose coding rate is selected from among the plurality of supported coding rates has been performed is distributed to two systems. The encoded data having been distributed to the two systems is modulated in the modulation scheme for s 1  and in the modulation scheme for s 2  to generate the (mapped) baseband signals s 1 ( t ) and s 2 ( t ). 
     The control signal ( 10700 ) is a signal indicating the selected coding rate for the error correction coding described above. The power change unit ( 10701 A) sets the value v for power change according to the control signal ( 10700 ). Also, the power change unit ( 10701 B) sets the value u for power change according to the control signal ( 10700 ). 
     The present invention is characterized in that the power change units ( 10701 A and  10701 B) respectively set the values v and u for power change according to the selected coding rate indicated by the control signal ( 10700 ). Here, values for power change set according to the coding rate rx are referred to as v rx  and u rx . 
     For example, when r 1  is selected as the coding rate, the power change unit ( 10701 A) sets a value for power change to v r1 . When r 2  is selected as the coding rate, the power change unit ( 10701 A) sets a value for power change to v r2 . When r 3  is selected as the coding rate, the power change unit ( 10701 A) sets a value for power change to v r3 . 
     Also, when r 1  is selected as the coding rate, the power change unit ( 10701 B) sets a value for power change to u r1 . When r 2  is selected as the coding rate, the power change unit ( 10701 B) sets a value for power change to u r2 . When r 3  is selected as the coding rate, the power change unit ( 10701 B) sets a value for power change to u r3 . 
     In this case, for example, by setting v r1 , v r2  and v r3  so as to be different from one another, a high error correction capability can be achieved for each code length. Similarly, by setting u r1 , u r2  and u r3  so as to be different from one another, a high error correction capability can be achieved for each coding rate. Depending on the set coding rate, however, the effect might not be obtained even if the value for power change is changed. In such a case, even when the coding rate is changed, it is unnecessary to change the value for power change (for example, v r1 =v r2  may be satisfied, and u r1 =u r2  may be satisfied. What is important is that two or more values exist in a set of v r1 , v r2  and v r3 , and that two or more values exist in a set of u r1 , u r2  and u r3 ). Note that, as described above, v rx  and u rx  are set so as to satisfy the ratio of the average power 1:w 2 . 
     As examples of r 1 , r 2  and r 3  described above, coding rates 1/2, 2/3 and 3/4 are considered when the error correction code is the LDPC code. 
     Although the case of three coding rates is taken as an example in the above description, the present invention is not limited to this. One important point is that two or more values u rx  for power change exist when there are two or more coding rates that can be set, and the transmission device selects any of the values for power change from among the two or more values u rx  for power change when the coding rate is set, and performs power change. Another important point is that two or more values v rx  for power change exist when there are two or more coding rates that can be set, and the transmission device selects any of the values for power change from among the two or more values v rx  for power change when the coding rate is set, and performs power change. 
     Example 4-3 
     In order for the reception device to achieve excellent data reception quality, it is important to implement the following. 
     The following describes, with respect to the case where the transmission device supports a plurality of modulation schemes, how to set the average powers (average values) of s 1  and s 2  according to the modulation schemes that are to be used for generating s 1  and s 2 . 
     For example, the following describes the case in which the modulation scheme for s 1  is fixed to QPSK, and the modulation scheme for s 2  is changed from 16QAM to 64QAM (or either 16QAM or 64QAM is applicable). When modulation scheme for s 1  is QPSK, the mapping scheme for s 1 ( t ) is as shown in  FIG.  95   . In  FIG.  95   , h is represented by Equation 273. When the modulation scheme for s 2  is 16QAM, the mapping scheme for s 2 ( t ) is as shown in  FIG.  94   . In  FIG.  94   , g is represented by Equation 272. When the modulation scheme for s 2 ( t ) is 64QAM, the mapping scheme for s 2 ( t ) is as shown in  FIG.  109   . In  FIG.  109   , k is represented by Equation 481. 
     In  FIG.  108   , when the modulation scheme for s 1  is QPSK and the modulation scheme for s 2  is 16QAM, assume that v=α and u=α×w 16 . In this case, the ratio between the average power of QPSK and the average power of 16QAM is v 2 :u 2 =α 2 :α 2 ×w 16   2 =1:w 16   2 . 
     In  FIG.  108   , when the modulation scheme for s 1  is QPSK and the modulation scheme for s 2  is 64QAM, assume that v=β and u=β×w 64 . In this case, the ratio between the average power of QPSK and the average power of 64QAM is v:u=β 2 :β 2 ×w 64   2 =1:w 64   2 . In this case, according to the minimum Euclidean distance relationship, the reception device achieves high data reception quality when 1.0&lt;w 16 &lt;w 64 , regardless of whether the modulation scheme for s 2  is 16QAM or 64QAM. 
     Note that although “the modulation scheme for s 1  is fixed to QPSK” in the description above, it is possible that “the modulation scheme for s 2  is fixed to QPSK”. If this is the case, assume that the power change is not performed with respect to the fixed modulation scheme (QPSK in this example), but is performed with respect to the selectable modulation schemes (16QAM and 64QAM in this example). Consequently, when the fixed modulation scheme (QPSK in this example) is set to s 2 , the following Equation 486 is fulfilled. 
     
       
         
           
             
               
                 
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                   Equation 
                   ⁢ 
                       
                   486 
                 
               
             
           
         
       
     
     Given that, even when “the modulation scheme for s 2  is fixed to QPSK and the modulation scheme for s 1  is changed from 16QAM to 64QAM (set to either 16QAM or 64QAM)”, 1.0&lt;w 16 &lt;w64 should be fulfilled. (Note that the value used for the multiplication for the power change in the case of 16QAM is u=α×w 16 , the value used for the multiplication for the power change in the case of 64QAM is u=β×w 64 , the value used for the power change in the case of QPSK is v=α when the selectable modulation scheme is 16QAM and v=β when the selectable modulation scheme is 64QAM.) Also, when the set of (the modulation scheme for s 1 , the modulation scheme for s 2 ) is selectable from the sets of (QPSK, 16QAM), (16QAM, QPSK), (QPSK, 64QAM) and (64QAM, QPSK), 1.0&lt;w 16 &lt;w 64  should be fulfilled. 
     The following generalizes the description above. 
     For generalization, assume that the modulation scheme for s 1  is fixed to a modulation scheme C with which the number of signal points in the I-Q plane is c. Also assume that the modulation scheme for s 2  is selectable from a modulation scheme A with which the number of signal points in the I-Q plane is a and a modulation scheme B with which the number of signal points in the I-Q plane is b (a&gt;b&gt;c). In this case, when the modulation scheme for s 2  is set to the modulation scheme A, assume that ratio between the average power of the modulation scheme for s 1 , which is the modulation scheme C, and the average power of the modulation scheme for s 2 , which is the modulation scheme A, is 1:w a   2 . Also, when the modulation scheme for s 2  is set to the modulation scheme B, assume that ratio between the average power of the modulation scheme for s 1 , which is the modulation scheme C, and the average power of the modulation scheme for s 2 , which is the modulation scheme B, is 1:w b   2 . If this is the case, the reception device achieves a high data reception quality when w b &lt;w a  is fulfilled. 
     Note that although “the modulation scheme for s 1  is fixed to C” in the description above, even when “the modulation scheme for s 2  is fixed to the modulation scheme C and the modulation scheme for s 1  is changed from the modulation scheme A to the modulation scheme B (set to either the modulation scheme A or the modulation scheme B), the average powers should fulfill w b &lt;w a . (If this is the case, as with the description above, when the average power of the modulation scheme C is 1, the average power of the modulation scheme A is w a   2 , and the average power of the modulation scheme B is w b   2 .) Also, when the set of (the modulation scheme for s 1 , the modulation scheme for s 2 ) is selectable from the sets of (the modulation scheme C, the modulation scheme A), (the modulation scheme A, the modulation scheme C), (the modulation scheme C, the modulation scheme B) and (the modulation scheme B, the modulation scheme C), the average powers should fulfill w b &lt;w a . 
     Example 5 
     The following explains another operation example that is different form Example 4, with reference to  FIG.  108   . Note that s 1 ( t ) denotes a baseband signal (mapped signal) of the modulation scheme 64QAM, and the mapping scheme is as shown in  FIG.  109   , and k is as represented by Equation 481. s 2 ( t ) denotes a baseband signal (mapped signal) of the modulation scheme 16QAM, and the mapping scheme is as shown in  FIG.  94   , and g is as represented by Equation 272. The sign t denotes time. In the present embodiment, hopping in the time domain is explained as an example. 
     The inputs to the power change unit ( 10701 A) are the baseband signal  307 A (mapped signal) of the modulation scheme 64QAM and the control signal ( 10700 ). When the value that has been set for the power change is v, the power change unit outputs a signal ( 10702 A) generated by multiplying the baseband signal  307 A (mapped signal) of the modulation scheme 64QAM by v, according to the control signal ( 10700 ). 
     The inputs to the power change unit ( 10701 B) are the baseband signal  307 B (mapped signal) of the modulation scheme 16QAM and the control signal ( 10700 ). When the value that has been set for the power change is u, the power change unit outputs a signal ( 10702 B) generated by multiplying the baseband signal  307 B (mapped signal) of the modulation scheme 16QAM by u, according to the control signal ( 10700 ). Then, u=v×w (w&lt;1.0) is fulfilled. 
     When the precoding matrices for the precoding scheme that regularly hops between precoding matrices are represented by F[t], the Equation 86 above is fulfilled. 
     In this case, the ratio between the average power of 64QAM and the average power of 16QAM is set to fulfill v 2 :u 2 =v 2 :v 2 ×w 2 =1:w 2 . Consequently, the reception state will be that shown in  FIG.  106   , which shows that the data reception quality of the reception device is improved. 
     Conventionally, transmission power control is generally performed based on the feedback information received from the communication party. This Embodiment of the present invention is characterized by that the transmission power is controlled regardless of the feedback information from the communication party. The following explains this point in detail. 
     In the above, it is described that the values v and u for the power change are determined based on the control signal ( 10700 ). In the following, the determination, based on the control signal ( 10700 ), of the values v and u for the power change is described in detail, particularly with respect to the setting for further improving the data reception quality in the reception device. 
     Example 5-1 
     The following explains how to determine the average power (average value) for s 1  and s 2  according to the block length of the error correction coding applied to the data used for generating s 1  and s 2 , assuming that the transmission device supports error correction coding for a plurality of block lengths (the number of bits constituting one block after coding, which is also referred to as a code length). 
     Examples of the error correction coding include block coding such as turbo coding or duo-binary turbo coding using tail-biting, LDPC coding, or the like. Many communications systems and broadcast systems support a plurality of block lengths. The data after the error correction coding with the block length selected from a plurality of block lengths supported thereby is distributed via two routes. The pieces of data distributed via two routes are respectively modulated by the modulation scheme for s 1  and the modulation scheme for s 2 , and the baseband signals (mapped signals) s 1 ( t ) and s 2 ( t ) are generated. 
     The control signal ( 10700 ) is a signal indicating the block length of the selected error correction coding. The power change unit ( 10701 A) sets the value v for the power change according to the control signal ( 10700 ). Similarly, the power change unit ( 10701 B) sets the value u for the power change according to the control signal ( 10700 ). 
     The present invention is characterized by that the power change units ( 10701 A,  10701 B) set the values v and u for the power change according to the block length indicated by the control signal ( 10700 ). Here, the values for the power change according to a block length X are denoted as v LX  and u LX . 
     For example, when 1000 is selected as the block length, the power change unit ( 10701 A) sets the value v L1000  for the power change, and when 1500 is selected as the block length, the power change unit ( 10701 A) sets the value v L1500  for the power change, and when 3000 is selected as the block length, the power change unit ( 10701 A) sets the value v L3000  for the power change. 
     On the other hand, when 1000 is selected as the block length, the power change unit ( 10701 B) sets the value u L1000  for the power change, and when 1500 is selected as the block length, the power change unit ( 10701 B) sets the value u L1500  for the power change, and when 3000 is selected as the block length, the power change unit ( 10701 B) sets the value u L3000  for the power change. 
     In some cases, setting the values v L1000 , v L1500  and v L1000  to be different from each other may achieve a high error correction capability with respect to each coding length. Similarly, in some cases, setting the values u L1000 , u L1500  and u L3000  to be different from each other may achieve a high error correction capability with respect to each coding length. However, there is a possibility that changing the value for the power change is not effective, depending on the code length that has been set. In such cases, it is unnecessary to change the values for the power change even when the code length is changed. (For example, u L1000 =u L1500  or v L1000 =v L1500  may be fulfilled. The important point is that two or more values exist in the set of (v L1000 , v L1500 , v L1000 ), and two or more values exist in the set of (u L1000 , u L1500 , u L1000 )). Note that the values v LX  and u LX  are set to fulfill the average power ratio 1:w 2 , as described above. 
     Although description is given to an example case where there are three code lengths, this is not essential. One important point is that there are two or more selectable values u LX  for the power change when two or more code lengths are selectable, and when a code length is selected, the transmission device selects one from the values u LX  for the power change and performs the power change. It is also important that there are two or more selectable values v LX  for the power change when two or more code lengths are selectable, and when a code length is selected, the transmission device selects one from the values v LX  for the power change and performs the power change. 
     Example 5-2 
     The following describes, with respect to the case where the transmission device supports error correction coding with a plurality of coding rates, how to set the average power (average value) of s 1  and s 2  according to the coding rate of the error correction coding that is to be used for generating s 1  and s 2 . 
     Examples of the error correction coding include block coding such as turbo coding or duo-binary turbo coding using tail-biting, LDPC coding, or the like. Many communications systems and broadcast systems support a plurality of coding rates. The data after the error correction coding with the coding rate selected from a plurality of coding rates supported thereby is distributed via two routes. The pieces of data distributed via two routes are respectively modulated by the modulation scheme for s 1  and the modulation scheme for s 2 , and the baseband signals (mapped signals) s 1 ( t ) and s 2 ( t ) are generated. 
     The control signal ( 10700 ) is a signal indicating the coding rate of the selected error correction coding. The power change unit ( 10701 A) sets the value v for the power change according to the control signal ( 10700 ). Similarly, the power change unit ( 10701 B) sets the value u for the power change according to the control signal ( 10700 ). 
     The present invention is characterized by that the power change units ( 10701 A,  10701 B) set the values v and u for the power change according to the coding rate indicated by the control signal ( 10700 ). Here, the values for the power change according to a coding rate rx are denoted as v rx  and u rx . 
     For example, when r 1  is selected as the coding rate, the power change unit ( 10701 A) sets the value v r1  for the power change, and when r 2  is selected as the coding rate, the power change unit ( 10701 A) sets the value v r2  for the power change, and when r 3  is selected as the coding rate, the power change unit ( 10701 A) sets the value v r3  for the power change. 
     Similarly, when r 1  is selected as the coding rate, the power change unit ( 10701 B) sets the value u r1  for the power change, and when r 2  is selected as the coding rate, the power change unit ( 10701 B) sets the value u r2  for the power change, and when r 3  is selected as the coding rate, the power change unit ( 10701 B) sets the value u r3  for the power change. 
     In some cases, setting the values v r1 , v r2  and v r3  to be different from each other may achieve a high error correction capability with respect to each coding rate. Similarly, in some cases, setting the values u r1 , u r2  and u r3  to be different from each other may achieve a high error correction capability with respect to each coding rate. However, there is a possibility that changing the value for the power change is not effective, depending on the coding rate that has been set. In such cases, it is unnecessary to change the values for the power change even when the coding rate is changed. (For example, v r1 =v r2  or u r1 =u r2  may be fulfilled. The important point is that two or more values exist in the set of (v r1 , v r2 , v r3 ), and two or more values exist in the set of (u r1 , u r2 , u r3 )). Note that the values v rx  and u rx  are set to fulfill the average power ratio 1:w 2 , as described above. 
     For example, the coding rates r 1 , r 2  and r 3  may be 1/2, 2/3 and 3/4 when the error correction coding is LDPC coding. 
     Although description is given to an example case where there are three coding rates, this is not essential. One important point is that there are two or more selectable values u rx  for the power change when two or more coding rates are selectable, and when a coding rate is selected, the transmission device selects one from the values u rx  for the power change and performs the power change. It is also important that there are two or more selectable values v rx  for the power change when two or more code lengths are selectable, and when a code length is selected, the transmission device selects one from the values v rx  for the power change and performs the power change. 
     Example 5-3 
     To achieve a higher data reception quality in the reception device, the following points are important. 
     The following describes, with respect to the case where the transmission device supports a plurality of modulation schemes, how to set the average power (average value) of s 1  and s 2  according to the modulation scheme that is to be used for generating s 1  and s 2 . 
     For example, the following describes the case in which the modulation scheme for s 1  is fixed to 64QAM, and the modulation scheme for s 2  is changed from 16QAM to 64QAM (or either 16QAM or 64QAM is applicable). When modulation scheme for s 1  is 64QAM, the mapping scheme for s 1 ( t ) is as shown in  FIG.  109   . In  FIG.  109   , k is represented by Equation 481. When the modulation scheme for s 2  is 16QAM, the mapping scheme for s 2 ( t ) is as shown in  FIG.  94   . In  FIG.  94   , g is represented by Equation 272. When the modulation scheme for s 2 ( t ) is QPSK, the mapping scheme for s 2 ( t ) is as shown in  FIG.  95   . In  FIG.  95   , h is represented by Equation 273. 
     In  FIG.  108   , when the modulation scheme for s 1  is 64QAM and the modulation scheme for s 2  is 16QAM, assume that v=α and u=α×w 16 . In this case, the ratio between the average power of 64QAM and the average power of 16QAM is V 2 :u 2 =α 2 :α 2 ×w 16   2 =1:w 16   2 . 
     In  FIG.  108   , when the modulation scheme for s 1  is 64QAM and the modulation scheme for s 2  is QPSK, assume that v=β and u=β×w 4 . In this case, the ratio between the average power of 64QAM and the average power of QPSK is v 2 :u 2 =β 2 :β 2 ×w 4   2 =1:w 4   2 . In this case, according to the minimum Euclidean distance relationship, the reception device achieves a high data reception quality when w 4 &lt;w 16 &lt;1.0, regardless of whether the modulation scheme for s 2  is 16QAM or QPSK. 
     Note that although “the modulation scheme for s 1  is fixed to 64QAM” in the description above, it is possible that “the modulation scheme for s 2  is fixed to 64QAM and the modulation scheme for s 1  is changed from 16QAM to QPSK (set to either 16QAM or QPSK)”, w 4 &lt;w 16 &lt;1.0 should be fulfilled. (The same as described in Example 4-3.) (Note that the value used for the multiplication for the power change in the case of 16QAM is u=α×w 16 , the value used for the multiplication for the power change in the case of QPSK is u=β×w 4 , the value used for the power change in the case of 64QAM is v=α when the selectable modulation scheme is 16QAM and v=β when the selectable modulation scheme is QPSK.) Also, when the set of (the modulation scheme for s 1 , the modulation scheme for s 2 ) is selectable from the sets of (64QAM, 16QAM), (16QAM, 64QAM), (64QAM, QPSK) and (QPSK, 64QAM), w 4 &lt;w 16 &lt;1.0 should be fulfilled. 
     The following generalizes the description above. 
     For generalization, assume that the modulation scheme for s 1  is fixed, and the modulation scheme therefor is a modulation scheme C with which the number of signal points on the I-Q plane is c. Also assume that the modulation scheme for s 2  is selectable from the modulation scheme A with which the number of signal points on the I-Q plane is a and a modulation scheme B with which the number of signal points on the I-Q plane is b (c&gt;b&gt;a). In this case, when the modulation scheme for s 2  is set to the modulation scheme A, assume that ratio between the average power of the modulation scheme for s 1 , which is the modulation scheme C, and the average power of the modulation scheme for s 2 , which is the modulation scheme A, is 1:w a   2 . Also, when the modulation scheme for s 2  is set to the modulation scheme B, assume that ratio between the average power of the modulation scheme for s 1 , which is the modulation scheme C, and the average power of the modulation scheme for s 2 , which is the modulation scheme B is 1:w b   2 . If this is the case, the reception device achieves a high data reception quality when w a &lt;w b  is fulfilled. 
     Note that although “the modulation scheme for s 1  is fixed to C” in the description above, even when “the modulation scheme for s 2  is fixed to the modulation scheme C and the modulation scheme for s 1  is changed from the modulation scheme A to the modulation scheme B (set to either the modulation scheme A or the modulation scheme B), the average powers should fulfill w a &lt;w b . (If this is the case, as with the description above, when the average power of the modulation scheme is C, the average power of the modulation scheme A is w a   2 , and the average power of the modulation scheme B is w b   2 .) Also, when the set of (the modulation scheme for s 1 , the modulation scheme for s 2 ) is selectable from the sets of (the modulation scheme C, the modulation scheme A), (the modulation scheme A, the modulation scheme C), (the modulation scheme C, the modulation scheme B) and (the modulation scheme B, the modulation scheme C), the average powers should fulfill w a &lt;w b . 
     Example 6 
     The following explains another operation example that is different form Example 4, with reference to  FIG.  108   . s 1 ( t ) denotes a baseband signal (mapped signal) of the modulation scheme 16QAM, and the mapping scheme is as shown in  FIG.  94   , and g is as represented by Equation 272. s 2 ( t ) denotes a baseband signal (mapped signal) of the modulation scheme 64QAM, and the mapping scheme is as shown in  FIG.  109   , and k is as represented by Equation 481. The sign t denotes time. In the present embodiment, the time domain is taken as an example. 
     The inputs to the power change unit ( 10701 A) are the baseband signal  307 A (mapped signal) of the modulation scheme 16QAM and the control signal  10700 . When the value that has been set for the power change is v, the power change unit outputs a signal ( 10702 A) generated by multiplying the baseband signal  307 A (mapped signal) of the modulation scheme 16QAM by v, according to the control signal ( 10700 ). 
     The inputs to the power change unit ( 10701 B) are the baseband signal  307 B (mapped signal) of the modulation scheme 64QAM and the control signal ( 10700 ). When the value that has been set for the power change is u, the power change unit outputs a signal ( 10702 B) generated by multiplying the baseband signal  307 B (mapped signal) of the modulation scheme 64QAM by u, according to the control signal ( 10700 ). Then, u=v×w (w&lt;1.0) is fulfilled. 
     When the precoding matrices for the precoding scheme that regularly hops between precoding matrices are represented by F[t], the Equation 86 above is fulfilled. 
     In this case, the ratio between the average power of 64QAM and the average power of 16QAM is set to fulfill v 2 :u 2 =v 2 :v 2 ×w 2 =1:w 2 . Consequently, the reception state will be that shown in  FIG.  106   , which shows that the data reception quality of the reception device is improved. 
     Conventionally, transmission power control is generally performed based on the feedback information received from the communication party. This Embodiment of the present invention is characterized by that the transmission power is controlled regardless of the feedback information from the communication party. The following explains this point in detail. 
     In the above, it is described that the values v and u for the power change are determined based on the control signal ( 10700 ). In the following, the determination, based on the control signal ( 10700 ), of the values v and u for the power change is described in detail, particularly with respect to the setting for further improving the data reception quality in the reception device. 
     Example 6-1 
     The following explains how to determine the average power (average value) for s 1  and s 2  according to the block length of the error correction coding applied to the data used for generating s 1  and s 2 , assuming that the transmission device supports error correction coding for a plurality of block lengths (the number of bits constituting one block after coding, which is also referred to as a code length). 
     Examples of the error correction coding include block coding such as turbo coding or duo-binary turbo coding using tail-biting, LDPC coding, or the like. Many communications systems and broadcast systems support a plurality of block lengths. The data after the error correction coding with the block length selected from a plurality of block lengths supported thereby is distributed via two routes. The pieces of data distributed via two routes are respectively modulated by the modulation scheme for s 1  and the modulation scheme for s 2 , and the baseband signals (mapped signals) s 1 ( t ) and s 2 ( t ) are generated. 
     The control signal ( 10700 ) is a signal indicating the block length of the selected error correction coding. The power change unit ( 10701 A) sets the value v for the power change according to the control signal ( 10700 ). Similarly, the power change unit ( 10701 B) sets the value u for the power change according to the control signal ( 10700 ). 
     The present invention is characterized by that the power change units ( 10701 A,  10701 B) set the values v and u for the power change according to the block length indicated by the control signal ( 10700 ). Here, the values for the power change according to a block length X are denoted as v LX  and u LX . 
     For example, when 1000 is selected as the block length, the power change unit ( 10701 A) sets the value v L1000  for the power change, and when 1500 is selected as the block length, the power change unit ( 10701 A) sets the value v L1500  for the power change, and when 3000 is selected as the block length, the power change unit ( 10701 A) sets the value v L1000  for the power change. 
     On the other hand, when 1000 is selected as the block length, the power change unit ( 10701 B) sets the value u L1000  for the power change, and when 1500 is selected as the block length, the power change unit ( 10701 B) sets the value u L1500  for the power change, and when 3000 is selected as the block length, the power change unit ( 10701 B) sets the value u L3000  for the power change. 
     In some cases, setting the values v L1000 , v L1500  and v L1000  to be different from each other may achieve a high error correction capability with respect to each coding length. Similarly, in some cases, setting the values u L1000 , u L1500  and u L3000  to be different from each other may achieve a high error correction capability with respect to each coding length. However, there is a possibility that changing the value for the power change is not effective, depending on the code length that has been set. In such cases, it is unnecessary to change the values for the power change even when the code length is changed. (For example, u L1000 =u L1500  or v L1000 =v L1500  may be fulfilled. The important point is that two or more values exist in the set of (v L1000 , v L1500 , v L3000 ), and two or more values exist in the set of (u L1000 , u L1500 , u L3000 )). Note that the values v LX  and u LX  are set to fulfill the average power ratio 1:w 2 , as described above. 
     Although description is given to an example case where there are three code lengths, this is not essential. One important point is that there are two or more selectable values u LX  for the power change when two or more code lengths are selectable, and when a code length is selected, the transmission device selects one from the values u LX  for the power change and performs the power change. It is also important that there are two or more selectable values v LX  for the power change when two or more code lengths are selectable, and when a code length is selected, the transmission device selects one from the values v LX  for the power change and performs the power change. 
     Example 6-2 
     The following describes, with respect to the case where the transmission device supports error correction coding with a plurality of coding rates, how to set the average power of s 1  and s 2  according to the coding rate of the error correction coding that is to be used for generating s 1  and s 2 . 
     Examples of the error correction coding include block coding such as turbo coding or duo-binary turbo coding using tail-biting, LDPC coding, or the like. Many communications systems and broadcast systems support a plurality of coding rates. The data after the error correction coding with the coding rate selected from a plurality of coding rates supported thereby is distributed via two routes. The pieces of data distributed via two routes are respectively modulated by the modulation scheme for s 1  and the modulation scheme for s 2 , and the baseband signals (mapped signals) s 1 ( t ) and s 2 ( t ) are generated. 
     The control signal ( 10700 ) is a signal indicating the coding rate of the selected error correction coding. The power change unit ( 10701 A) sets the value v for the power change according to the control signal ( 10700 ). Similarly, the power change unit ( 10701 B) sets the value u for the power change according to the control signal ( 10700 ). 
     The present invention is characterized by that the power change units ( 10701 A,  10701 B) set the values v and u for the power change according to the coding rate indicated by the control signal ( 10700 ). Here, the values for the power change according to a coding rate rx are denoted as v rx  and u rx . 
     For example, when r 1  is selected as the coding rate, the power change unit ( 10701 A) sets the value v r1  for the power change, and when r 2  is selected as the coding rate, the power change unit ( 10701 A) sets the value v r2  for the power change, and when r 3  is selected as the coding rate, the power change unit ( 10701 A) sets the value v r3  for the power change. 
     Similarly, when r 1  is selected as the coding rate, the power change unit ( 10701 B) sets the value u r1  for the power change, and when r 2  is selected as the coding rate, the power change unit ( 10701 B) sets the value u r2  for the power change, and when r 3  is selected as the coding rate, the power change unit ( 10701 B) sets the value u r3  for the power change. 
     In some cases, setting the values v r1 , v r2  and v r3  to be different from each other may achieve a high error correction capability with respect to each coding rate. Similarly, in some cases, setting the values u r1 , u r2  and u r3  to be different from each other may achieve a high error correction capability with respect to each coding rate. However, there is a possibility that changing the value for the power change is not effective, depending on the coding rate that has been set. In such cases, it is unnecessary to change the values for the power change even when the coding rate is changed. (For example, v r1 =v r2  or u r1 =u r2  may be fulfilled. The important point is that two or more values exist in the set of (v r1 , v r2 , v r3 ), and two or more values exist in the set of (u r1 , u r2 , u r3 )). Note that the values v rx  and u rx  are set to fulfill the average power ratio 1:w 2 , as described above. 
     For example, the coding rates r 1 , r 2  and r 3  may be 1/2, 2/3 and 3/4 when the error correction coding is LDPC coding. 
     Although description is given to an example case where there are three coding rates, this is not essential. One important point is that there are two or more selectable values u rx  for the power change when two or more coding rates are selectable, and when a coding rate is selected, the transmission device selects one from the values u rx  for the power change and performs the power change. It is also important that there are two or more selectable values v rx  for the power change when two or more code lengths are selectable, and when a code length is selected, the transmission device selects one from the values v rx  for the power change and performs the power change. 
     Example 6-3 
     To achieve a higher data reception quality in the reception device, the following points are important. 
     The following describes, with respect to the case where the transmission device supports a plurality of modulation schemes, how to set the average power (average value) of s 1  and s 2  according to the modulation scheme that is to be used for generating s 1  and s 2 . 
     For example, the following describes the case in which the modulation scheme for s 1  is fixed to 16QAM, and the modulation scheme for s 2  is changed from 64QAM to QPSK (or either 16QAM or QPSK is applicable). When modulation scheme for s 1  is 16QAM, the mapping scheme for s 1 ( t ) is as shown in  FIG.  94   . In  FIG.  94   , g is represented by Equation 272. When the modulation scheme for s 2  is 64QAM, the mapping scheme for s 2 ( t ) is as shown in  FIG.  109   . In  FIG.  109   , k is represented by Equation 481. When the modulation scheme for s 2 ( t ) is QPSK, the mapping scheme for s 2 ( t ) is as shown in  FIG.  95   . In  FIG.  95   , h is represented by Equation 273. 
     In  FIG.  108   , when the modulation scheme for s 1  is 16QAM and the modulation scheme for s 2  is 64QAM, assume that v=α and u=α×w 64 . In this case, the ratio between the average power of 64QAM and the average power of 16QAM is v 2 :u 2 =α 2 :α 2 ×w 64   2 =1:w 64   2 . 
     In  FIG.  108   , when the modulation scheme for s 1  is 16QAM and the modulation scheme for s 2  is QPSK, assume that v=β and u=β×w 4 . In this case, the ratio between the average power of 64QAM and the average power of QPSK is v 2 :u 2 =β 2 :β 2 ×w 4   2 =1:w 4   2 . In this case, according to the minimum Euclidean distance relationship, the reception device achieves a high data reception quality when w 4 &lt;w 64 , regardless of whether the modulation scheme for s 2  is 64QAM or QPSK. 
     Note that although “the modulation scheme for s 1  is fixed to 16QAM” in the description above, it is possible that “the modulation scheme for s 2  is fixed to 16QAM and the modulation scheme for s 1  is changed from 64QAM to QPSK (set to either 16QAM or QPSK)”, w 4 &lt;w 64  should be fulfilled. (The same as described in Example 4-3.) (Note that the value used for the multiplication for the power change in the case of 16QAM is u=α×w 16 , the value used for the multiplication for the power change in the case of QPSK is u=β×w 4 , the value used for the power change in the case of 64QAM is v=α when the selectable modulation scheme is 16QAM and v=β when the selectable modulation scheme is QPSK.) Also, when the set of (the modulation scheme for s 1 , the modulation scheme for s 2 ) is selectable from the sets of (16QAM, 64QAM), (64QAM, 16QAM), (16QAM, QPSK) and (QPSK, 16QAM), w 4 &lt;w 64  should be fulfilled. 
     The following generalizes the description above. 
     For generalization, assume that the modulation scheme for s 1  is fixed, and the modulation scheme therefor is a modulation scheme C with which the number of signal points on the I-Q plane is c. Also assume that the modulation scheme for s 2  is selectable from the modulation scheme A with which the number of signal points on the I-Q plane is a and a modulation scheme B with which the number of signal points on the I-Q plane is b (c&gt;b&gt;a). In this case, when the modulation scheme for s 2  is set to the modulation scheme A, assume that ratio between the average power of the modulation scheme for s 1 , which is the modulation scheme C, and the average power of the modulation scheme for s 2 , which is the modulation scheme A, is 1:w a   2 . Also, when the modulation scheme for s 2  is set to the modulation scheme B, assume that ratio between the average power of the modulation scheme for s 1 , which is the modulation scheme C, and the average power of the modulation scheme for s 2 , which is the modulation scheme B is 1:w b   2 . If this is the case, the reception device achieves a high data reception quality when w a &lt;w b  is fulfilled. 
     Note that although “the modulation scheme for s 1  is fixed to C” in the description above, even when “the modulation scheme for s 2  is fixed to the modulation scheme C and the modulation scheme for s 1  is changed from the modulation scheme A to the modulation scheme B (set to either the modulation scheme A or the modulation scheme B), the average powers should fulfill w a &lt;w b . (If this is the case, as with the description above, when the average power of the modulation scheme is C, the average power of the modulation scheme A is w a   2 , and the average power of the modulation scheme B is w b   2 .) Also, when the set of (the modulation scheme for s 1  and the modulation scheme for s 2 ) is selectable from the sets of (the modulation scheme C and the modulation scheme A), (the modulation scheme A and the modulation scheme C), (the modulation scheme C and the modulation scheme B) and (the modulation scheme B and the modulation scheme C), the average powers should fulfill w a &lt;w b . 
     Electrical Power 
     In the present description including “Embodiment 8”, “Embodiment 9”, “Embodiment 10”, “Embodiment 18”, “Embodiment 19”, “Embodiment C1” and “Embodiment C2”, the power consumption by the transmission device can be reduced by setting a=1 in the equation of precoding matrix used for the precoding scheme that regularly hops between precoding matrices. This is because the average power of z 1  and the average power of z 2  are the same even when “the average power (average value) of s 1  and the average power (average value) of s 2  are set to be different when the modulation scheme for s 1  and the modulation scheme for s 2  are different”, and setting a=1 does not result in increasing the PAPR (Peak-to-Average Power Ratio) of the transmission power amplifier provided in the transmission device. For example, the precoding matrices used with the precoding scheme that regularly hops between precoding matrices may be set according to Equation #3, Equation #14, Equation #15 and Equation #16 in Embodiment C1 or Equation #20, Equation #24, Equation #25 and Equation #26 in Embodiment C2. Also, a=1 is to be fulfilled when, for example, the precoding matrices used with the precoding scheme that regularly hops between precoding matrices are generalized as shown in to Equation 268 and Equation 269 in Embodiment 18, or in Equation #1, Equation #2, Equation #9, Equation #10, Equation #12 and Equation #13 in Embodiment C1, or in Equation #18, Equation #19, Equation #21, Equation #22 and Equation #23 in Embodiment C2. The same applies to the other embodiments. (Note that the number of the slots in the period (cycle) is not limited to an odd number.) 
     However, even when α≠1, there are some precoding matrices that can be used with the precoding scheme that regularly hops between precoding matrices and have limited influence to PAPR. For example, when the precoding matrices represented by Equation 279 and Equation 280 in Embodiment 19 are used, the precoding scheme that regularly hops precoding matrices, the precoding matrices have limited influence to PAPR even when α≠1. (Note that the precoding scheme relating to Embodiment 19 that regularly hops between precoding matrices is described in Embodiment 10 as well. Also, in Embodiment 13 and Embodiment 20, the precoding matrices have only limited influence to PAPR even when α≠1.) Reception Device 
     In the case of Example 1, Example 2 and Example 3, the following relationship is derived from  FIG.  5   . 
     
       
         
           
             
               
                 
                   Math 
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                   Equation 
                   ⁢ 
                       
                   487 
                 
               
             
           
         
       
     
     Also, as explained in Example 1, Example 2, and Example 3, the relationship may be as follows: 
     
       
         
           
             
               
                 
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                   611 
                 
               
               
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                   Equation 
                   ⁢ 
                       
                   488 
                 
               
             
           
         
       
     
     The reception device performs demodulation (detection) (i.e. estimates the bits transmitted by the transmission device) by using the relationships described above (in the same manner as described in Embodiment 1, Embodiments A1 to A5, and so on). 
     In the case of Example 4, Example 5 and Example 6, the following relationship is derived from  FIG.  5   . 
     
       
         
           
             
               
                 
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                   Equation 
                   ⁢ 
                       
                   489 
                 
               
             
           
         
       
     
     Also, as explained in Example 4, Example 5, and Example 6, the relationship may be as follows: 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   613 
                 
               
               
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                                       12 
                                     
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                                       22 
                                     
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                             [ 
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                             ] 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
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                           ⁢ 
                           
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                         = 
                           
                         
                           
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                                     ) 
                                   
                                 
                               
                             
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                           ⁢ 
                           
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                             [ 
                             t 
                             ] 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   
                                     v 
                                     × 
                                     w 
                                   
                                 
                                 
                                   0 
                                 
                               
                               
                                 
                                   0 
                                 
                                 
                                   v 
                                 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   
                                     s 
                                     ⁢ 
                                     1 
                                     ⁢ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
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                                     ⁢ 
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                                     ⁢ 
                                     
                                       ( 
                                       t 
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                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   490 
                 
               
             
           
         
       
     
     The reception device performs demodulation (detection) (i.e. estimates the bits transmitted by the transmission device) by using the relationships described above (in the same manner as described in Embodiment 1, Embodiments A1 to A5, and so on). 
     Relationship Between Power Change and Mapping 
     As described in Example 1, Example 2, and Example 3, and as particularly shown in Equation 487, the mapping unit  306 B in  FIG.  4    may output u×s 2 ( t ), and the power change unit may be omitted in such cases. If this is the case, it can be said that the precoding scheme for regularly hopping between precoding matrices is applied to the signal s 1 ( t ) after the mapping and the signal u×s 2 ( t ) after the mapping. 
     As described in Example 1, Example 2, and Example 3, and as particularly shown in Equation 488, the mapping unit  306 A in  FIG.  3    and  FIG.  4    may output u×s 1 ( t ), and the power change unit may be omitted in such cases. If this is the case, it can be said that the precoding scheme for regularly hopping between precoding matrices is applied to the signal u×s 1 ( t ) after the mapping and the signal s 2 ( t ) after the mapping. 
     In Example 4, Example 5, and Example 6, as particularly shown in Equation 489, the mapping unit  306 A in  FIG.  3    and  FIG.  4    may output v×s 1 ( t ), and the mapping unit  306 B may output u×s 2 ( t ), and the power change unit may be omitted in such cases. If this is the case, it can be said that the precoding scheme for regularly hopping between precoding matrices is applied to the signal v×s 1 ( t ) after the mapping and the signal u×s 2 ( t ) after the mapping. 
     In Example 4, Example 5, and Example 6, as particularly shown in Equation 490, the mapping unit  306 A in  FIG.  3    and  FIG.  4    may output u×s 1 ( t ), and the mapping unit  306 B may output v×s 2 ( t ), and the power change unit may be omitted in such cases. If this is the case, it can be said that the precoding scheme for regularly hopping between precoding matrices is applied to the signal u×s 1 ( t ) after the mapping and the signal v×s 2 ( t ) after the mapping. 
     That is, F[t] in the present embodiment denotes precoding matrices used by the precoding scheme that regularly hops between precoding matrices, and examples of F[t] are in conformity with one of Equation #3, Equation #14, Equation #15 and Equation #16 in Embodiment C1 and Equation #20, Equation #24, Equation #25 and Equation #26 in Embodiment C2. Alternatively, examples of F[t] are in conformity with one of Equation 268 and Equation 269 in Embodiment 18, Equation #1, Equation #2, Equation #9, Equation #10, Equation #12 and Equation #13 in Embodiment C1, and Equation #18, Equation #19, Equation #21, Equation #22 and Equation #23 in Embodiment C2. (Note that the number of the slots in the period (cycle) is not limited to an odd number.) 
     Alternatively, F[t] may be a precoding scheme that uses precoding matrices represented by Equation 279 and Equation 280 in Embodiment 19 and regularly hops between the precoding matrices. (Note that the precoding scheme relating to Embodiment 19 that regularly hops between precoding matrices is described in Embodiment 10, Embodiment 13, and Embodiment 20 as well. Also, F[t] may be a precoding scheme that regularly hops between precoding matrices described in Embodiment 10, Embodiment 13, and Embodiment 20.) 
     Note that F[t] denotes a precoding matrices used at time t when the precoding scheme that regularly hops between precoding matrices is adopted. The reception device performs demodulation (detection) by using the relationships between r 1 ( t ), r 2 ( t ) and s 1 ( t ), s 2 ( t ) described above (in the same manner as described in Embodiment 1, Embodiments A1 to A5, and so on). However, distortion components, such as noise components, frequency offset, channel estimation error, and the likes are not considered in the equations described above. Hence, demodulation (detection) is performed with them. Regarding the values u and v that the transmission device uses for performing the power change, the transmission device transmits information about these values, or transmits information of the transmission mode (such as the transmission scheme, the modulation scheme and the error correction scheme) to be used. The reception device detects the values used by the transmission device by acquiring the information, obtains the relationships described above, and performs the demodulation (detection). 
     In the present embodiment, the hopping between the precoding matrices is performed in the time domain. However, when a multi-carrier transmission scheme such as an OFDM scheme is used, the present invention is applicable to the case where the hopping between the precoding matrices is performed in the frequency domain, as described in other embodiments. If this is the case, t used in the present embodiment is to be replaced with f (frequency ((sub) carrier)). 
     Accordingly, in the case of performing the hopping between the precoding matrices in the time domain, z 1 ( t ) and z 2 ( t ) at the same time point is transmitted from different antennas by using the same frequency. On the other hand, in the case of performing the hopping between the precoding matrices in the frequency domain, z 1 ( f ) and z 2 ( f ) at the same frequency is transmitted from different antennas at the same time point. 
     Also, even in the case of performing the hopping between the precoding matrices in the time and frequency domains, the present invention is applicable as described in other embodiments. The precoding scheme pertaining to the present embodiment, which regularly hops between precoding matrices, is not limited the precoding scheme which regularly hops between precoding matrices as described in the present Description. Even when the precoding matrices are fixed (according to a scheme in which the precoding matrices are not represented by F(t) (i.e. not a function oft (or f)), adopting the average power of s 1 ( t ) and the average power of s 2 ( t ) as described in the present embodiment advantageously improves the data reception quality in the reception device. 
     Embodiment G1 
     The present embodiment describes the case where, when the modulation schemes used for generating s 1  and s 2  are different, the setting scheme for making the average powers of s 1  and s 2  different from each other is adopted in combination with the precoding scheme that regularly hops between precoding matrices that use the unitary matrix which is based on Embodiment 9 and is described in Embodiment 18. In the scheme of regularly hopping between precoding matrices over a period (cycle) with N slots as described in Embodiment 8, the precoding matrices prepared for the N slots with reference to Equations (82)-(85) are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   614 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   268 
                   ) 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). (α&gt;0.) Since a unitary matrix is used in the present embodiment, the precoding matrices in Equation 268 may be represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   615 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   269 
                   ) 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). (α&gt;0.) From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment 3, the following condition is important for achieving high data reception quality.
 
Math 616
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #53
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; and x≠y.)
 
Math 617
 
 e   j(θ     11     (x)−θ     21     (x)−π)   ≠e   j(θ     11     (y)−θ     21     (y)−π)  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #54
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; and x≠y.)
 
     Precoding matrices F[0]-F[N−1] are generated based on Equation 269 (the precoding matrices F[0]-F[N−1] may be in any order for the N slots in the period (cycle). Symbol number Ni may be precoded using F[0], symbol number Ni+1 may be precoded using F[1], . . . , and symbol number N×i+h may be precoded using F[h], for example (h=0, 1, 2, . . . , N−2, N−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) 
     When N=5, precoding matrices prepared for the N slots, based on Equation 269 are represented as follows, for example. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   618 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       0 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
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                                 ⁢ 
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                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
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                                   ⁢ 
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                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   274 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   619 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       1 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
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                     ⁢ 
                     
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                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   275 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   620 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       2 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
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                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
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                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
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                                 e 
                                 
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                                   ⁢ 
                                   
                                     4 
                                     5 
                                   
                                   ⁢ 
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                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       4 
                                       5 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   276 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   621 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       3 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
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                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
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                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
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                                 e 
                                 
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                                   ⁢ 
                                   
                                     6 
                                     5 
                                   
                                   ⁢ 
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                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       6 
                                       5 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   277 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   622 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       4 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     8 
                                     5 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     
                                       8 
                                       5 
                                     
                                     ⁢ 
                                     π 
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   278 
                   ) 
                 
               
             
           
         
       
     
     As described above, in order to reduce the calculation scale of the precoding by the transmission device, θ 11 (i)=0 radians and λ=0 radians should be fulfilled in Equation 269. Note that λ in Equation 269 may be varied according to i, or be fixed. That is, in Equation 269, λ in F[i=x] and λ in F[i=y] (x≠y) may be the same or different. 
     Regarding the value to be set to α, although using the value described above is effective, this is not essential. For example, α may be determined according to the value of i in the matrices F[i], as described in Embodiment 17. (That is, α in F[i] is not necessarily a fixed value when i is changed). 
     In the present embodiment, the scheme of structuring N different precoding matrices for a precoding hopping scheme with an N-slot time period (cycle) has been described. In this case, as the N different precoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] are prepared. When a single carrier transmission scheme is adopted, symbols are arranged in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1] in the time domain (Alternatively, it can be arranged in the frequency domain when a multicarrier transmission scheme is adopted). The present invention is not, however, limited in this way, and the N different precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1] generated in the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaption in this case, precoding weights may be changed by arranging symbols in the frequency domain and in the frequency-time domain. Note that a precoding hopping scheme with a N-slot time period (cycle) has been described, but the same advantageous effects may be obtained by randomly using N different precoding matrices. In other words, the N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots N in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the N different precoding matrices of the present embodiment are included, the probability of high reception quality increases. In this case, Condition #55 and Condition #56 can be replaced by the following conditions. (The number of slots in the period (cycle) is considered to be N.)
 
Math 623
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∃ x,∃y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #55′
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; and x≠y.)
 
Math 624
 
 e   j(θ     11     (x)−θ     21     (x)−π)   ≠e   j(θ     11     (y)−θ     21     (y)−π)  for ∃ x,∃y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #56′
 
(x is 0, 1, 2, . . . , N−2, N−1; y is 0, 1, 2, . . . , N−2, N−1; and x≠y.)
 
     In the present embodiment, the case where λ=0 radians is explained as an example of precoding matrices when λ is a fixed value. Considering the mapping of the modulation scheme, λ may be fixed to be λ=π/2 radians, λ=π radians, or λ=(3π)/2 radians. (It is assumed, for example, that λ=π radians in the precoding matrices for the precoding scheme that regularly hops between precoding matrices). This setting reduces the circuit scale as with the case where λ=0 radians. 
     The following describes the setting scheme for the average powers of s 1  and s 2  to be set to the precoding scheme that regularly hops between precoding matrices as described in Embodiment 18 for example when the modulation schemes used for generating s 1  and s 2  are different (For details, see Embodiment F1). 
     “The setting scheme for the average powers of s 1  and s 2  when the modulation schemes for s 1  and s 2  are different” is applicable to all the precoding schemes described in the present Description, which regularly hops between precoding matrices. The important points are:
         As an error correction coded block coding such as turbo coding or duo-binary turbo coding using tail-biting, LDPC coding, or the like is used, and a plurality of block lengths (the number of bits that constitute one block)(code length) are supported, and when the transmission device selects one of the plurality of block lengths and performs error correction coding with the selected block length, the transmission device changes the setting scheme for the average powers (average values) of s 1  and s 2  according to the selected block length when the modulation scheme for s 1  and the modulation scheme for s 2  are different.   With an error correction coding, a plurality of coding rates are supported, and when the transmission device selects one of the plurality of coding rates and performs error correction coding with the selected coding rate, the transmission device changes the setting scheme for the average powers (average values) of s 1  and s 2  according to the selected coding rate when the modulation scheme for s 1  and the modulation scheme for s 2  are different.   When the modulation scheme for s 1  and the modulation scheme for s 2  are different, a plurality of selectable modulation schemes for s 2  are supported, and the schemes for setting the average powers (average values) for s 1  and s 2  are switched according to the modulation scheme that the transmission device uses for generating s 2 .   When the modulation scheme for s 1  and the modulation scheme for s 2  are different, a plurality of selectable modulation schemes for s 1  are supported, and the schemes for setting the average powers (average values) for s 1  and s 2  are switched according to the modulation scheme that the transmission device uses for generating s 1 .       

     “The setting scheme for the average powers of s 1  and s 2  when the modulation scheme for s 1  and the modulation scheme for s 2  are different” described in the present embodiment is not necessarily the precoding scheme regularly hopping between precoding matrices as explained in the present Description. Any precoding schemes that regularly hop between precoding matrices are applicable. 
     In the present embodiment, the hopping between the precoding matrices is performed in the time domain. However, when a multi-carrier transmission scheme such as an OFDM scheme is used, the present invention is applicable to the case where the hopping between the precoding matrices is performed in the frequency domain, as described in other embodiments. If this is the case, t used in the present embodiment is to be replaced with f (frequency ((sub) carrier)). Also, even in the case of performing the hopping between the precoding matrices in the time and frequency domains, the present invention is applicable. 
     Embodiment G2 
     The present embodiment describes the case where, when the modulation schemes used for generating s 1  and s 2  are different, the setting scheme for making the average powers of s 1  and s 2  different from each other is adopted in combination with the precoding scheme that regularly hops between precoding matrices that use the unitary matrix which is based on Embodiment 10 and is described in Embodiment 19. 
     In the scheme of regularly hopping between precoding matrices over a period (cycle) with 2N slots, the precoding matrices prepared for the 2N slots are represented as follows. 
             Math   ⁢         625                         for   ⁢         i     =     0   ,   1   ,   2       ,              …         ,   N     -     2   ,   N     -     1   :     F   [   i   ]         =       1         α   2     +   1         ⁢     (           e     j   ⁢       θ   11     (   i   )               α   ⨯     e     j   ⁢     (         θ   11     (   i   )         +   λ     )                         α   ⨯     e     j   ⁢       θ   21     (   i   )                      e     j   ⁢     (         θ   21     (   i   )         +   λ   +   π     )                   )                 Equation   ⁢         279               
Let α be a fixed value (not depending on i), where α&gt;0.
 
             Math   ⁢         626                         for   ⁢         i     =   N     ,     N   +   1     ,     N   +   2     ,        …         ,       2   ⁢   N     -   2     ,         2   ⁢   N     -     1   :     F   [   i   ]         =       1         α   2     +   1         ⁢     (           α   ⨯     e     j   ⁢       θ   11     (   i   )                 e     j   ⁢     (         θ   11     (   i   )         +   λ     )                       e     j   ⁢       θ   21     (   i   )                    α   ⨯     e     j   ⁢     (         θ   21     (   i   )         +   λ   +   π     )                     )                 Equation   ⁢         280               
Let α be a fixed value (not depending on i), where α&gt;0.
 
(Let the α in Equation 279 and the α in Equation 280 be the same value.) (α&lt;0 may be fulfilled.)
 
     From Condition #5 (Math 106) and Condition #6 (Math 107) in Embodiment 3, the following condition is important for achieving high data reception quality.
 
Math 627
 
 e   j(θ     11     (x)−θ     21     (x))   ≠e   j(θ     11     (y)−θ     21     (y))  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #57
 
(x is 0, 1, 2, . . . , N−2, N−1;
 
y is 0, 1, 2, . . . , N−2, N−1; and x≠y.)
 
Math 628
 
 e   j(θ     11     (x)−θ     21     (x)−π)   ≠e   j(θ     11     (y)−θ     21     (y)−π)  for ∀ x,∀y  ( x≠y;x,y= 0,1,2 , . . . ,N− 2 ,N− 1)  Condition #58
 
(x is 0, 1, 2, . . . , N−2, N−1;
 
y is 0, 1, 2, . . . , N−2, N−1; and x≠y.)
 
     Addition of the following condition is considered.
 
Math 629
 
θ 11 ( x )=θ 11 ( x+N ) for ∀ x  ( x= 0,1,2, . . . , N− 2, N− 1)
 
and
 
θ 21 ( y )=θ 21 ( y+N ) for ∀ y  ( y= 0,1,2, . . . , N− 2, N− 1)  Condition #59
 
     Precoding matrices F[0]-F[2N−1] are generated based on Equation 279 and Equation 280 (the precoding matrices F[0]-F[2N−1] may be in any order for the 2N slots in the period (cycle). Symbol number 2Ni may be precoded using F[0], symbol number 2Ni+1 may be precoded using F[1], . . . , and symbol number 2N×+h may be precoded using F[h], for example (h=0, 1, 2, . . . , 2N−2, 2N−1). (In this case, as described in previous embodiments, precoding matrices need not be hopped between regularly.) 
     When N=15, precoding matrices prepared for the 2N slots, based on Equation 279 and Equation 280 are represented as follows, for example. 
     
       
         
           
             Math 
             ⁢ 
                 
             630 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       0 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                                    
                               
                             
                           
                           
                             
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                                 ⁢ 
                                 π 
                                   
                               
                             
                           
                         
                       
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                   ( 
                   281 
                   ) 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             631 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       1 
                     
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                   = 
                   
                     
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                   ( 
                   282 
                   ) 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             632 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
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                   = 
                   
                     
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                   ( 
                   283 
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             Math 
             ⁢ 
                 
             633 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
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                   ( 
                   284 
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             Math 
             ⁢ 
                 
             634 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
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                   = 
                   
                     
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                   ( 
                   285 
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             Math 
             ⁢ 
                 
             635 
           
         
       
       
         
           
             
               
                 
                   
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                   ( 
                   286 
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             Math 
             ⁢ 
                 
             636 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
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                       6 
                     
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                   = 
                   
                     
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                   ( 
                   287 
                   ) 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             637 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
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                       7 
                     
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                   ( 
                   288 
                   ) 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             638 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       8 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
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                     ⁢ 
                     
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                                       16 
                                         
                                     
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                   ( 
                   289 
                   ) 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             639 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       9 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
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                     ⁢ 
                     
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                   ( 
                   290 
                   ) 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             640 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       10 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
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                     ⁢ 
                     
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                   ( 
                   291 
                   ) 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             641 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       11 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
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                   ( 
                   292 
                   ) 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             642 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       12 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
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                           1 
                         
                       
                     
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                       ( 
                       
                         
                           
                             
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                                       24 
                                         
                                     
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                   ( 
                   293 
                   ) 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             643 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       13 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
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                                       26 
                                         
                                     
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                                         26 
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                                       ⁢ 
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                                   ) 
                                 
                                   
                               
                             
                           
                         
                       
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                   ( 
                   294 
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             ⁢ 
                 
             644 
           
         
       
       
         
           
             
               
                 
                   
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                     [ 
                     
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                       = 
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                   ( 
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             Math 
             ⁢ 
                 
             645 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
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                       = 
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             ⁢ 
                 
             646 
           
         
       
       
         
           
             
               
                 
                   
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                   ( 
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             ⁢ 
                 
             647 
           
         
       
       
         
           
             
               
                 
                   
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             ⁢ 
                 
             648 
           
         
       
       
         
           
             
               
                 
                   
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             ⁢ 
                 
             649 
           
         
       
       
         
           
             
               
                 
                   
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                   ( 
                   300 
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             Math 
             ⁢ 
                 
             650 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       20 
                     
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                   ( 
                   301 
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             Math 
             ⁢ 
                 
             651 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
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                       = 
                       21 
                     
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                   302 
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             Math 
             ⁢ 
                 
             652 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       22 
                     
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                                     14 
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                   ( 
                   303 
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             Math 
             ⁢ 
                 
             653 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       23 
                     
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                   = 
                   
                     
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                       ( 
                       
                         
                           
                             
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                                   ⁢ 
                                   
                                     16 
                                     15 
                                   
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                   ( 
                   304 
                   ) 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             654 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       24 
                     
                     ] 
                   
                   = 
                   
                     
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                             α 
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                           + 
                           1 
                         
                       
                     
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                       ( 
                       
                         
                           
                             
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                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     18 
                                     15 
                                   
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                                         18 
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                                   ⁢ 
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                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   305 
                   ) 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             655 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       25 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
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                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     20 
                                     15 
                                   
                                   ⁢ 
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                               e 
                               
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                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         20 
                                         15 
                                       
                                       ⁢ 
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                                     π 
                                   
                                   ) 
                                 
                                   
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
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                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
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                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   306 
                   ) 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             656 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       26 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     22 
                                     15 
                                   
                                   ⁢ 
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                                   ( 
                                   
                                     
                                       
                                         22 
                                         15 
                                       
                                       ⁢ 
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                                     π 
                                   
                                   ) 
                                 
                                   
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
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                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   307 
                   ) 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             657 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       27 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
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                                   ⁢ 
                                   
                                     24 
                                     15 
                                   
                                   ⁢ 
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                                   ( 
                                   
                                     
                                       
                                         24 
                                         15 
                                       
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                                     π 
                                   
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                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
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                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   308 
                   ) 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             658 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       28 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
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                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     26 
                                     15 
                                   
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                                   π 
                                 
                               
                             
                           
                           
                             
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                                   ( 
                                   
                                     
                                       
                                         26 
                                         15 
                                       
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                               e 
                               
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                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
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                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   309 
                   ) 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             659 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     
                       i 
                       = 
                       29 
                     
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               α 
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                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     28 
                                     15 
                                   
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                                   π 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         28 
                                         15 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                                   
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
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                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   310 
                   ) 
                 
               
             
           
         
       
     
     As described above, in order to reduce the calculation scale of the precoding by the transmission device, θ 11 (i)=0 radians and λ=0 radians should be fulfilled in Equation 279, and θ 21 (i)=0 radians and λ=0 should be fulfilled in Equation 280. 
     Note that λ in Equation 279 and Equation 280 may be varied according to i, or be fixed. That is, in Equation 279 and Equation 280, λ in F[i=x] and λ in F[i=y] (x≠y) may be the same or different. Alternatively, λ may be a fixed value in Equation 279 and in Equation 280, and the fixed value λ in Equation 279 and the fixed value λ in Equation 280 may be different. (Alternatively, it may be the fixed value λ in Equation 279 and the fixed value λ in Equation 280). 
     Regarding the value to be set to α, although using the value described above is effective, this is not essential. For example, α may be determined according to the value of i in the matrices F[i], as described in Embodiment 17. (That is, α in F[i] is not necessarily a fixed value when i is changed). 
     In the present embodiment, the scheme of structuring 2N different precoding matrices for a precoding hopping scheme with a 2N-slot time period (cycle) has been described. In this case, as the 2N different precoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] are prepared. When a single carrier transmission scheme is adopted, symbols are arranged in the order F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] in the time domain (Alternatively, it can be arranged in the frequency domain when a multicarrier transmission scheme is adopted). The present invention is not, however, limited in this way, and the 2N different precoding matrices F[0], F[1], F[2], . . . , F[2N−2], F[2N−1] generated in the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaption in this case, precoding weights may be changed by arranging symbols in the frequency domain and in the frequency-time domain. Note that a precoding hopping scheme with a 2N-slot time period (cycle) has been described, but the same advantageous effects may be obtained by randomly using 2N different precoding matrices. In other words, the 2N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots 2N in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the 2N different precoding matrices of the present embodiment are included, the probability of high reception quality increases. 
     In the present embodiment, the case where λ=0 radians is explained as an example of precoding matrices when λ is a fixed value. Considering the mapping of the modulation scheme, λ may be fixed to be λ=π/2 radians, λ=π radians, or λ=(3π)/2 radians. (It is assumed, for example, that λ=π radians in the precoding matrices for the precoding scheme that regularly hops between precoding matrices). This setting reduces the circuit scale as with the case where λ=0 radians. 
     The following describes the setting scheme for the average powers of s 1  and s 2  to be set to the precoding scheme that regularly hops between precoding matrices as described in Embodiment 19 for example when the modulation schemes used for generating s 1  and s 2  are different (For details, see Embodiment F1). 
     “The setting scheme for the average powers of s 1  and s 2  when the modulation schemes for s 1  and s 2  are different” is applicable to all the precoding schemes described in the present Description, which regularly hops between precoding matrices. The important points are:
         As an error correction coded block coding such as turbo coding or duo-binary turbo coding using tail-biting, LDPC coding, or the like is used, and a plurality of block lengths (the number of bits that constitute one block)(code length) are supported, and when the transmission device selects one of the plurality of block lengths and performs error correction coding with the selected block length, the transmission device changes the setting scheme for the average powers (average values) of s 1  and s 2  according to the block length when the modulation scheme for s 1  and the modulation scheme for s 2  are different.   With an error correction coding, a plurality of coding rates are supported, and when the transmission device selects one of the plurality of coding rates and performs error correction coding with the selected coding rate, the transmission device changes the setting scheme for the average powers (average values) of s 1  and s 2  according to the selected coding rate when the modulation scheme for s 1  and the modulation scheme for s 2  are different.   When the modulation scheme for s 1  and the modulation scheme for s 2  are different, a plurality of selectable modulation schemes for s 2  are supported, and the schemes for setting the average powers (average values) for s 1  and s 2  are switched according to the modulation scheme that the transmission device uses for generating s 2 .   When the modulation scheme for s 1  and the modulation scheme for s 2  are different, a plurality of selectable modulation schemes for s 1  are supported, and the schemes for setting the average powers (average values) for s 1  and s 2  are switched according to the modulation scheme that the transmission device uses for generating s 2 .       

     “The setting scheme for the average powers of s 1  and s 2  when the modulation scheme for s 1  and the modulation scheme for s 2  are different” described in the present embodiment is not necessarily the precoding scheme regularly hopping between precoding matrices as explained in the present Description. Any precoding schemes that regularly hop between precoding matrices are applicable. 
     In the present embodiment, the hopping between the precoding matrices is performed in the time domain. However, when a multi-carrier transmission scheme such as an OFDM scheme is used, the present invention is applicable to the case where the hopping between the precoding matrices is performed in the frequency domain, as described in other embodiments. If this is the case, t used in the present embodiment is to be replaced with f (frequency ((sub) carrier)). Also, even in the case of performing the hopping between the precoding matrices in the time and frequency domains, the present invention is applicable. 
     Embodiment G3 
     The present embodiment describes the case where, when the modulation schemes used for generating s 1  and s 2  are different, the setting scheme for making the average powers of s 1  and s 2  different from each other is applied to Embodiment C1. Embodiment C1 is a generalization of Example 1 and Example 2 of Embodiment 2. 
     In the scheme of regularly hopping between precoding matrices over a period (cycle) with N slots, the precoding matrices prepared for the N slots are represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             660 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                    
                               
                             
                           
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         i 
                                         ) 
                                       
                                         
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                     
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                      
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                       
                                     + 
                                     λ 
                                     + 
                                     δ 
                                   
                                   ) 
                                 
                                   
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #1 
                   ) 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). (α&gt;0.) A unitary matrix is used in the present embodiment, and the precoding matrices in Equation #1 are represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             661 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                    
                               
                             
                           
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         i 
                                         ) 
                                       
                                         
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                     
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                      
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                       
                                     + 
                                     λ 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                                   
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #2 
                   ) 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). (α&gt;0.) For the simplification of mapping performed in the transmission device and the reception device, λ may be 0 radians, π/2 radians or (3π)/2 radians, and be fixed to one of these three values. In particular, α=1 is fulfilled in Embodiment 2, and Equation #2 is represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             662 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                    
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                                   
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                    
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                                   
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #3 
                   ) 
                 
               
             
           
         
       
     
     In order to distribute the poor reception points evenly with regards to phase in the complex plane, as described in Embodiment 2, Condition #101 and Condition #102 are provided to Equation #1 and Equation #2. 
     
       
         
           
             Math 
             ⁢ 
                 
             663 
           
         
       
       
         
           
             
               
                 
                   
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             
                               x 
                               + 
                               1 
                             
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             
                               x 
                               + 
                               1 
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             x 
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             x 
                             ) 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         e 
                         j 
                       
                       ( 
                       
                         π 
                         N 
                       
                       ) 
                     
                     ⁢ 
                         
                     for 
                        
                     ∀ 
                     
                       x 
                       ⁡ 
                       ( 
                       
                         x 
                         = 
                         
                           
                             0 
                             , 
                             1 
                             , 
                             2 
                             , 
                                
                             … 
                                 
                             , 
                             N 
                           
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #101 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             664 
           
         
       
       
         
           
             
               
                 
                   
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             
                               x 
                               + 
                               1 
                             
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             
                               x 
                               + 
                               1 
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     
                       e 
                       
                         j 
                         ⁡ 
                         ( 
                         
                           
                             
                               θ 
                               11 
                             
                             ( 
                             x 
                             ) 
                           
                           - 
                           
                             
                               θ 
                               21 
                             
                             ( 
                             x 
                             ) 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         e 
                         j 
                       
                       ( 
                       
                         - 
                         
                           π 
                           N 
                         
                       
                       ) 
                     
                     ⁢ 
                         
                     for 
                        
                     ∀ 
                     
                       x 
                       ⁡ 
                       ( 
                       
                         x 
                         = 
                         
                           
                             0 
                             , 
                             1 
                             , 
                             2 
                             , 
                                
                             … 
                                 
                             , 
                             N 
                           
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #102 
                 
               
             
           
         
       
     
     In particular, when θ 11 (i) is a fixed value not depending on i, Condition #103 or Condition #104 can be provided. 
     
       
         
           
             Math 
             ⁢ 
                 
             665 
           
         
       
       
         
           
             
               
                 
                   
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           
                             θ 
                             21 
                           
                           ( 
                           
                             x 
                             + 
                             1 
                           
                           ) 
                         
                       
                     
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           
                             θ 
                             21 
                           
                           ( 
                           x 
                           ) 
                         
                       
                     
                   
                   = 
                   
                     
                       
                         e 
                         j 
                       
                       ( 
                       
                         π 
                         N 
                       
                       ) 
                     
                     ⁢ 
                         
                     for 
                        
                     ∀ 
                     
                       x 
                       ⁡ 
                       ( 
                       
                         x 
                         = 
                         
                           
                             0 
                             , 
                             1 
                             , 
                             2 
                             , 
                                
                             … 
                                 
                             , 
                             N 
                           
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #103 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             666 
           
         
       
       
         
           
             
               
                 
                   
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           
                             θ 
                             21 
                           
                           ( 
                           
                             x 
                             + 
                             1 
                           
                           ) 
                         
                       
                     
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           
                             θ 
                             21 
                           
                           ( 
                           x 
                           ) 
                         
                       
                     
                   
                   = 
                   
                     
                       
                         e 
                         j 
                       
                       ( 
                       
                         - 
                         
                           π 
                           N 
                         
                       
                       ) 
                     
                     ⁢ 
                         
                     for 
                        
                     ∀ 
                     x 
                     ⁢ 
                     
                       ( 
                       
                         x 
                         = 
                         
                           
                             0 
                             , 
                             1 
                             , 
                             2 
                             , 
                                
                             … 
                               
                             , 
                             N 
                           
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #104 
                 
               
             
           
         
       
     
     Similarly, when θ 21 (i) is a fixed value not depending on i, Condition #105 or Condition #106 can be provided. 
     
       
         
           
             Math 
             ⁢ 
                 
             667 
           
         
       
       
         
           
             
               
                 
                   
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           
                             θ 
                             11 
                           
                           ( 
                           
                             x 
                             + 
                             1 
                           
                           ) 
                         
                       
                     
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           
                             θ 
                             11 
                           
                           ( 
                           x 
                           ) 
                         
                       
                     
                   
                   = 
                   
                     
                       
                         e 
                         j 
                       
                       ( 
                       
                         π 
                         N 
                       
                       ) 
                     
                     ⁢ 
                         
                     for 
                        
                     ∀ 
                     
                       x 
                       ⁡ 
                       ( 
                       
                         x 
                         = 
                         
                           
                             0 
                             , 
                             1 
                             , 
                             2 
                             , 
                                
                             … 
                                 
                             , 
                             N 
                           
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #105 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             668 
           
         
       
       
         
           
             
               
                 
                   
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           
                             θ 
                             11 
                           
                           ( 
                           
                             x 
                             + 
                             1 
                           
                           ) 
                         
                       
                     
                     
                       e 
                       
                         j 
                         ⁢ 
                         
                           
                             θ 
                             11 
                           
                           ( 
                           x 
                           ) 
                         
                       
                     
                   
                   = 
                   
                     
                       
                         e 
                         j 
                       
                       ( 
                       
                         - 
                         
                           π 
                           N 
                         
                       
                       ) 
                     
                     ⁢ 
                         
                     for 
                        
                     ∀ 
                     
                       x 
                       ⁡ 
                       ( 
                       
                         x 
                         = 
                         
                           
                             0 
                             , 
                             1 
                             , 
                             2 
                             , 
                                
                             … 
                                 
                             , 
                             N 
                           
                           - 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Condition 
                   ⁢ 
                       
                   #106 
                 
               
             
           
         
       
     
     Next, with respect to the scheme of regularly hopping between precoding matrices over a period (cycle) with N slots, the following shows example precoding matrices using the unitary matrix described above. The precoding matrices prepared for the N slots based on Equation #2 are represented as follows. (In Equation #2, λ is set to zero radians and θ 11 (i) is set to zero radians.) 
     
       
         
           
             Math 
             ⁢ 
                 
             669 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                                    
                               
                             
                           
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                     
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                     
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                                    
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #10 
                   ) 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1) (α&gt;0), and Condition #103 or Condition #104 is fulfilled. Also, θ 21  (i=0) may be set to any value, such as 0 radians. 
     As an alternative, in the scheme of regularly hopping between precoding matrices over a period (cycle) with N slots, the precoding matrices prepared for the N slots are represented as follows. (In Equation #2, λ is set to zero radians and θ 11 (i) is set to zero radians.) 
     
       
         
           
             Math 
             ⁢ 
                 
             670 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                                    
                               
                             
                           
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   π 
                                     
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                     
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                    
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #9 
                   ) 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1) (α&gt;0), and Condition #103 or Condition #104 is fulfilled. Also, θ 21  (i=0) may be set to any value, such as 0 radians. 
     As an alternative, the precoding matrices prepared for the N slots are represented as follows. (In Equation #2, λ is set to zero radians and θ 21 (i) is set to zero radians.) 
     
       
         
           
             Math 
             ⁢ 
                 
             671 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                    
                               
                             
                           
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     ) 
                                   
                                     
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                     
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                                    
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #12 
                   ) 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1) (α&gt;0), and Condition #105 or Condition #106 is fulfilled. Also, θ 11  (i=0) may be set to any value, such as 0 radians. 
     As an alternative, the precoding matrices prepared for the N slots are represented as follows. (In Equation #2, λ is set to π radians and θ 21 (i) is set to zero radians.) 
     
       
         
           
             Math 
             ⁢ 
                 
             672 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                    
                               
                             
                           
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         i 
                                         ) 
                                       
                                         
                                       + 
                                       π 
                                     
                                     ) 
                                   
                                     
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                     
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                                    
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #13 
                   ) 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1) (α&gt;0), and Condition #105 or Condition #106 is fulfilled. Also, θ 11  (i=0) may be set to any value, such as 0 radians. 
     In the example case according to Embodiment 2, as an alternative, the precoding matrices prepared for the N slots are represented as follows. (In Equation #3, λ is set to zero radians and θ 11  (i) is set to zero radians.) 
     
       
         
           
             Math 
             ⁢ 
                 
             673 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #14 
                   ) 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and Condition #103 or Condition #104 is fulfilled. Also, θ 21  (i=0) may be set to any value, such as 0 radians. 
     As an alternative, in the scheme of regularly hopping between precoding matrices over a period (cycle) with N slots, the precoding matrices prepared for the N slots are represented as follows. (In Equation #3, λ is set to π radians and θ 11 (i) is set to zero radians.) 
     
       
         
           
             Math 
             ⁢ 
                 
             674 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #15 
                   ) 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and Condition #103 or Condition #104 is fulfilled. Also, θ 21  (i=0) may be set to any value, such as 0 radians. 
     As an alternative, the precoding matrices prepared for the N slots are represented as follows. (In Equation #3, λ is set to zero radians and θ 21 (i) is set to zero radians.) 
     
       
         
           
             Math 
             ⁢ 
                 
             675 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 π 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #16 
                   ) 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and Condition #105 or Condition #106 is fulfilled. Also, θ 11  (i=0) may be set to any value, such as 0 radians. 
     As an alternative, the precoding matrices prepared for the N slots are represented as follows. (In Equation #3, λ is set to π radians and θ 21 (i) is set to zero radians.) 
     
       
         
           
             Math 
             ⁢ 
                 
             676 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #17 
                   ) 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1), and Condition #105 or Condition #106 is fulfilled. Also, θ 11  (i=0) may be set to any value, such as 0 radians. 
     When compared with the precoding scheme described in Embodiment 9 of regularly hopping between precoding matrices, the precoding scheme of the present embodiment has a possibility of achieving high data reception quality even when the period (cycle) is approximately a half of the period (cycle) in Embodiment 9, and needs a fewer precoding matrices to be prepared. Thus, the present embodiment achieves an advantageous effect of reducing the circuit scale in the transmission device and the reception device. To enhance the advantageous effect described above, the transmission device or the reception device may be configured to have one encoder and have a function to distribute coded data, as shown in  FIG.  4   . 
     As a preferable example of a in the example above, the scheme described in Embodiment 18 may be adopted. However, the present invention is not limited in this way. 
     In the present embodiment, the scheme of structuring N different precoding matrices for a precoding hopping scheme with an N-slot time period (cycle) has been described. In this case, as the N different precoding matrices, F[0], F[1], F[2], . . . , F[N−2], F[N−1] are prepared. In the present embodiment, an example of a single carrier transmission scheme has been described, and therefore the case of arranging symbols in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1] in the time domain (or the frequency domain) has been described. The present invention is not, however, limited in this way, and the N different precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1] generated in the present embodiment may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaption in this case, precoding weights may be changed by arranging symbols in the frequency domain and in the frequency-time domain. Note that a precoding hopping scheme with a N-slot time period (cycle) has been described, but the same advantageous effects may be obtained by randomly using N different precoding matrices. In other words, the N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots N in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the N different precoding matrices of the present embodiment are included, the probability of high reception quality increases. 
     The following describes the setting scheme for the average powers of s 1  and s 2  to be set to the precoding scheme that regularly hops between precoding matrices as described in Embodiment C1 for example when the modulation schemes used for generating s 1  and s 2  are different (For details, see Embodiment F1). 
     “The setting scheme for the average powers of s 1  and s 2  when the modulation schemes for s 1  and s 2  are different” is applicable to all the precoding schemes described in the present Description, which regularly hops between precoding matrices. The important points are:
         As an error correction coded block coding such as turbo coding or duo-binary turbo coding using tail-biting, LDPC coding, or the like is used, and a plurality of block lengths (the number of bits that constitute one block)(code length) are supported, and when the transmission device selects one of the plurality of block lengths and performs error correction coding with the selected block length, the transmission device changes the setting scheme for the average powers (average values) of s 1  and s 2  according to the block length when the modulation scheme for s 1  and the modulation scheme for s 2  are different.   With an error correction coding, a plurality of coding rates are supported, and when the transmission device selects one of the plurality of coding rates and performs error correction coding with the selected coding rate, the transmission device changes the setting scheme for the average powers (average values) of s 1  and s 2  according to the selected coding rate when the modulation scheme for s 1  and the modulation scheme for s 2  are different.   When the modulation scheme for s 1  and the modulation scheme for s 2  are different, a plurality of selectable modulation schemes for s 2  are supported, and the schemes for setting the average powers (average values) for s 1  and s 2  are switched according to the modulation scheme that the transmission device uses for generating s 2 .   When the modulation scheme for s 1  and the modulation scheme for s 2  are different, a plurality of selectable modulation schemes for s 1  are supported, and the schemes for setting the average powers (average values) for s 1  and s 1  are switched according to the modulation scheme that the transmission device uses for generating s 2 .       

     “The setting scheme for the average powers of s 1  and s 2  when the modulation scheme for s 1  and the modulation scheme for s 2  are different” described in the present embodiment is not necessarily the precoding scheme regularly hopping between precoding matrices as explained in the present Description. Any precoding schemes that regularly hop between precoding matrices are applicable. 
     In the present embodiment, the hopping between the precoding matrices is performed in the time domain. However, when a multi-carrier transmission scheme such as an OFDM scheme is used, the present invention is applicable to the case where the hopping between the precoding matrices is performed in the frequency domain, as described in other embodiments. If this is the case, t used in the present embodiment is to be replaced with f (frequency ((sub) carrier)). Also, even in the case of performing the hopping between the precoding matrices in the time and frequency domains, the present invention is applicable. 
     Embodiment G4 
     The present embodiment describes the case where, when the modulation schemes used for generating s 1  and s 2  are different, the setting scheme for making the average powers of s 1  and s 2  different from each other is applied to Embodiment C2. Embodiment C2 is a precoding scheme of regularly hopping precoding matrices that is the combination of Embodiment C1 and Embodiment 9 and is different from Embodiment C1. That is, the present invention is a scheme of realizing Embodiment C1 applying the case where the number of slots in the period (cycle) in Embodiment 9 is an odd number. 
     In the scheme of regularly hopping between precoding matrices over a period (cycle) with N slots, the precoding matrices prepared for the N slots are represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             677 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #18 
                   ) 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). (α&gt;0.) A unitary matrix is used in the present embodiment, and the precoding matrices in Equation #1 are represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             678 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #19 
                   ) 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). (α&gt;0.) For the simplification of mapping performed in the transmission device and the reception device, λ may be 0 radians, π/2 radians or (3π)/2 radians, and be fixed to one of these three values. In particular, a=1 is fulfilled, and Equation #19 is represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             679 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     21 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #20 
                   ) 
                 
               
             
           
         
       
     
     The precoding matrices used in the precoding scheme of the present embodiment, which regularly hops between precoding matrices, are as described above. The characteristic feature thereof is that N, which represents the number of slots in the period (cycle) of the precoding scheme of the present embodiment regularly hopping between precoding matrices, is an odd number (N=2n+1). The number of different precoding matrices prepared for achieving the N=2n+1 slots is n+1. Among n+1 different precoding matrices, n precoding matrices are used twice in one period (cycle), and one precoding matrix is used once. N=2n+1 is thus achieved. The following describes in detail the precoding matrices used in this case. 
     The n+1 different precoding matrices required for achieving the precoding scheme with the period (cycle) of N=2n+1 slots, which regularly hops between precoding matrices, can be represented as F[0], F[1], . . . , F[i], . . . , F[n−1], F[n](i=0, 1, 2, . . . , n−2, n−1, n (i being an integer in a range of 0 to n)). If this is the case, n+1 different precoding matrices, F[0], F[1], . . . , F[i], . . . , F[n−1], F[n], based on Equation #19 are represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             680 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   θ 
                                   11 
                                 
                               
                             
                           
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   
                                     j 
                                     ⁡ 
                                     ( 
                                     
                                       
                                         θ 
                                         11 
                                       
                                       + 
                                       
                                         
                                           2 
                                           ⁢ 
                                           i 
                                           ⁢ 
                                           π 
                                         
                                         
                                           
                                             2 
                                             ⁢ 
                                             n 
                                           
                                           + 
                                           1 
                                         
                                       
                                     
                                     ) 
                                   
                                     
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     θ 
                                     11 
                                   
                                   + 
                                   
                                     
                                       2 
                                       ⁢ 
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     
                                       
                                         2 
                                         ⁢ 
                                         n 
                                       
                                       + 
                                       1 
                                     
                                   
                                   + 
                                   λ 
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #21 
                   ) 
                 
               
             
           
         
       
     
     Note that i=0, 1, 2, . . . , n−2, n−1, n (i being an integer in a range of 0 to n). Among n+1 different precoding matrices in Equation #21, namely F[0], F[1], . . . F[i], . . . , F[n−1] and F[n], F[0] is used once, and F[1]-F[n] are each used twice (F[1] is used twice, F[2] is used twice, . . . , F[n−1] is used twice, and F[n] is used twice). The precoding scheme thus regularly hops between precoding matrices with the period (cycle) of N=2n+1 slots. As a result, as with the precoding scheme in Embodiment 9 which regularly hops between precoding matrices when the number of slots in the period (cycle) is an odd number, the reception device achieves high data reception quality. If this is the case, the precoding scheme described above has a possibility of achieving high data reception quality even when the period (cycle) is approximately a half of the period (cycle) in Embodiment 9, and needs a fewer precoding matrices to be prepared. Thus, the present embodiment achieves an advantageous effect of reducing the circuit scale in the transmission device and the reception device. To enhance the advantageous effect described above, the transmission device or the reception device may be configured to have one encoder and have a function to distribute coded data, as shown in  FIG.  4   . 
     In particular, when λ=0 radians and θ 11 =0 radians, the equation above can be represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             681 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   
                                     j 
                                     ⁡ 
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       
                                         
                                           2 
                                           ⁢ 
                                           n 
                                         
                                         + 
                                         1 
                                       
                                     
                                     ) 
                                   
                                     
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       2 
                                       ⁢ 
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     
                                       
                                         2 
                                         ⁢ 
                                         n 
                                       
                                       + 
                                       1 
                                     
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #22 
                   ) 
                 
               
             
           
         
       
     
     Note that i=0, 1, 2, . . . , n−2, n−1, n (i being an integer in a range of 0 to n). Among n+1 different precoding matrices in Equation #22, namely F[0], F[1], . . . F[i], . . . , F[n−1] and F[n], F[0] is used once, and F[1]-F[n] are each used twice (F[1] is used twice, F[2] is used twice, . . . , F[n−1] is used twice, and F[n] is used twice). The precoding scheme thus regularly hops between precoding matrices with the period (cycle) of N=2n+1 slots. As a result, as with the precoding scheme in Embodiment 9 which regularly hops between precoding matrices when the number of slots in the period (cycle) is an odd number, the reception device achieves high data reception quality. If this is the case, the precoding scheme described above has a possibility of achieving high data reception quality even when the period (cycle) is approximately a half of the period (cycle) in Embodiment 9, and needs a fewer precoding matrices to be prepared. Thus, the present embodiment achieves an advantageous effect of reducing the circuit scale in the transmission device and the reception device. When λ=0 radians and θ 11 =0 radians, the equation above can be represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             682 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   π 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   
                                     j 
                                     ⁡ 
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       
                                         
                                           2 
                                           ⁢ 
                                           n 
                                         
                                         + 
                                         1 
                                       
                                     
                                     ) 
                                   
                                     
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     2 
                                     ⁢ 
                                     i 
                                     ⁢ 
                                     π 
                                   
                                   
                                     
                                       2 
                                       ⁢ 
                                       n 
                                     
                                     + 
                                     1 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #23 
                   ) 
                 
               
             
           
         
       
     
     Note that i=0, 1, 2, . . . , n−2, n−1, n (i being an integer in a range of 0 to n). Among n+1 different precoding matrices in Equation #23, namely F[0], F[1], . . . F[i], . . . , F[n−1] and F[n], F[0] is used once, and F[1]-F[n] are each used twice (F[1] is used twice, F[2] is used twice, . . . , F[n−1] is used twice, and F[n] is used twice). The precoding scheme thus regularly hops between precoding matrices with the period (cycle) of N=2n+1 slots. As a result, as with the precoding scheme in Embodiment 9 which regularly hops between precoding matrices when the number of slots in the period (cycle) is an odd number, the reception device achieves high data reception quality. If this is the case, the precoding scheme described above has a possibility of achieving high data reception quality even when the period (cycle) is approximately a half of the period (cycle) in Embodiment 9, and needs a fewer precoding matrices to be prepared. Thus, the present embodiment achieves an advantageous effect of reducing the circuit scale in the transmission device and the reception device. 
     When α=1, Equation #21 can be represented as follows, as with the relationship between Equation #19 and Equation #20, 
     
       
         
           
             Math 
             ⁢ 
                 
             683 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   θ 
                                   11 
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 e 
                                 
                                   
                                     j 
                                     ⁡ 
                                     ( 
                                     
                                       
                                         θ 
                                         11 
                                       
                                       + 
                                       
                                         
                                           2 
                                           ⁢ 
                                           i 
                                           ⁢ 
                                           π 
                                         
                                         
                                           
                                             2 
                                             ⁢ 
                                             n 
                                           
                                           + 
                                           1 
                                         
                                       
                                     
                                     ) 
                                   
                                     
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁡ 
                                 ( 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   + 
                                     
                                   
                                     
                                       2 
                                       ⁢ 
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     
                                       
                                         2 
                                         ⁢ 
                                         n 
                                       
                                       + 
                                       1 
                                     
                                   
                                   + 
                                   λ 
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #24 
                   ) 
                 
               
             
           
         
       
     
     Note that i=0, 1, 2, . . . , n−2, n−1, n (i being an integer in a range of 0 to n). Among n+1 different precoding matrices in Equation #24, namely F[0], F[1], . . . F[i], . . . , F[n−1] and F[n], F[0] is used once, and F[1]-F[n] are each used twice (F[1] is used twice, F[2] is used twice, . . . , F[n−1] is used twice, and F[n] is used twice). The precoding scheme thus regularly hops between precoding matrices with the period (cycle) of N=2n+1 slots. As a result, as with the precoding scheme in Embodiment 9 which regularly hops between precoding matrices when the number of slots in the period (cycle) is an odd number, the reception device achieves high data reception quality. If this is the case, the precoding scheme described above has a possibility of achieving high data reception quality even when the period (cycle) is approximately a half of the period (cycle) in Embodiment 9, and needs a fewer precoding matrices to be prepared. Thus, the present embodiment achieves an advantageous effect of reducing the circuit scale in the transmission device and the reception device. 
     Similarly, when α=1, Equation #22 can be represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             684 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               
                                 e 
                                 
                                   
                                     j 
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                                         2 
                                         ⁢ 
                                         i 
                                         ⁢ 
                                         π 
                                       
                                       
                                         
                                           2 
                                           ⁢ 
                                           n 
                                         
                                         + 
                                         1 
                                       
                                     
                                     ) 
                                   
                                     
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       2 
                                       ⁢ 
                                       i 
                                       ⁢ 
                                       π 
                                     
                                     
                                       
                                         2 
                                         ⁢ 
                                         n 
                                       
                                       + 
                                       1 
                                     
                                   
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #25 
                   ) 
                 
               
             
           
         
       
     
     Note that i=0, 1, 2, . . . , n−2, n−1, n (i being an integer in a range of 0 to n). Among n+1 different precoding matrices in Equation #25, namely F[0], F[1], . . . F[i], . . . , F[n−1] and F[n], F[0] is used once, and F[1]-F[n] are each used twice (F[1] is used twice, F[2] is used twice, . . . , F[n−1] is used twice, and F[n] is used twice). The precoding scheme thus regularly hops between precoding matrices with the period (cycle) of N=2n+1 slots. As a result, as with the precoding scheme in Embodiment 9 which regularly hops between precoding matrices when the number of slots in the period (cycle) is an odd number, the reception device achieves high data reception quality. If this is the case, the precoding scheme described above has a possibility of achieving high data reception quality even when the period (cycle) is approximately a half of the period (cycle) in Embodiment 9, and needs a fewer precoding matrices to be prepared. Thus, the present embodiment achieves an advantageous effect of reducing the circuit scale in the transmission device and the reception device. 
     Similarly, when α=1, Equation #23 can be represented as follows. 
     
       
         
           
             Math 
             ⁢ 
                 
             685 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                       
                     
                     ⁢ 
                     
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                               e 
                               
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                                 0 
                               
                             
                           
                           
                             
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                                 π 
                               
                             
                           
                         
                         
                           
                             
                               
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                                     j 
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                                     ( 
                                     
                                       
                                         2 
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                                     ) 
                                   
                                     
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     2 
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                                       n 
                                     
                                     + 
                                     1 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   #26 
                   ) 
                 
               
             
           
         
       
     
     Note that i=0, 1, 2, . . . , n−2, n−1, n (i being an integer in a range of 0 to n). Among n+1 different precoding matrices in Equation #26, namely F[0], F[1], . . . F[i], . . . , F[n−1] and F[n], F[0] is used once, and F[1]-F[n] are each used twice (F[1] is used twice, F[2] is used twice, . . . , F[n−1] is used twice, and F[n] is used twice). The precoding scheme thus regularly hops between precoding matrices with the period (cycle) of N=2n+1 slots. As a result, as with the precoding scheme in Embodiment 9 which regularly hops between precoding matrices when the number of slots in the period (cycle) is an odd number, the reception device achieves high data reception quality. If this is the case, the precoding scheme described above has a possibility of achieving high data reception quality even when the period (cycle) is approximately a half of the period (cycle) in Embodiment 9, and needs a fewer precoding matrices to be prepared. Thus, the present embodiment achieves an advantageous effect of reducing the circuit scale in the transmission device and the reception device. 
     As a preferable example of a in the example above, the scheme described in Embodiment 18 may be adopted. However, the present invention is not limited in this way. 
     In this embodiment, when a single carrier transmission scheme is adopted, the precoding matrices W[0], W[1], . . . , W[2n−1] and W[2n] (note that W[0], W[1], . . . , W[2n−1] and W[2n] are constituted of F[0], F[1], F[2], . . . , F[n−1] and F[n]) for the precoding hopping scheme with the period (cycle) of N=2n+1 slots (i.e., precoding scheme regularly hopping between precoding matrices with the period (cycle) of N=2n+1 slots) are arranged in the order W[0], W[1], . . . , W[2n−1] and W[2n] in the time domain (or the frequency domain). The present invention is not, however, limited in this way, and the precoding matrices W[0], W[1], . . . , W[2n−1] and W[2n] may be adapted to a multi-carrier transmission scheme such as an OFDM transmission scheme or the like. As in Embodiment 1, as a scheme of adaption in this case, precoding weights may be changed by arranging symbols in the frequency domain and in the frequency-time domain. Note that a precoding hopping scheme with a N-slot time period (cycle) (N=2n+1) has been described, but the same advantageous effects may be obtained by randomly using precoding matrices W[0], W[1], . . . , W[2n−1], W[2n]. In other words, the precoding matrices W[0], W[1], . . . , W[2n−1], W[2n] do not necessarily need to be used in a regular period (cycle). 
     Furthermore, in the precoding matrix hopping scheme over an H-slot period (cycle) (H being a natural number larger than the number of slots N=2n+1 in the period (cycle) of the above scheme of regularly hopping between precoding matrices), when the n+1 different precoding matrices of the present embodiment are included, the probability of high reception quality increases. 
     The following describes the setting scheme for the average powers of s 1  and s 2  to be set to the precoding scheme that regularly hops between precoding matrices as described in Embodiment C2 for example when the modulation schemes used for generating s 1  and s 2  are different (For details, see Embodiment F1). 
     “The setting scheme for the average powers of s 1  and s 2  when the modulation schemes for s 1  and s 2  are different” is applicable to all the precoding schemes described in the present Description, which regularly hops between precoding matrices. The important points are:
         As an error correction coded block coding such as turbo coding or duo-binary turbo coding using tail-biting, LDPC coding, or the like is used, and a plurality of block lengths (the number of bits that constitute one block)(code length) are supported, and when the transmission device selects one of the plurality of block lengths and performs error correction coding with the selected block length, the transmission device changes the setting scheme for the average powers (average values) of s 1  and s 2  according to the block length when the modulation scheme for s 1  and the modulation scheme for s 2  are different.   With an error correction coding, a plurality of coding rates are supported, and when the transmission device selects one of the plurality of coding rates and performs error correction coding with the selected coding rate, the transmission device changes the setting scheme for the average powers (average values) of s 1  and s 2  according to the selected coding rate when the modulation scheme for s 1  and the modulation scheme for s 2  are different.   When the modulation scheme for s 1  and the modulation scheme for s 2  are different, a plurality of selectable modulation schemes for s 2  are supported, and the schemes for setting the average powers (average values) for s 1  and s 2  are switched according to the modulation scheme that the transmission device uses for generating s 2 .   When the modulation scheme for s 1  and the modulation scheme for s 2  are different, a plurality of selectable modulation schemes for s 1  are supported, and the schemes for setting the average powers (average values) for s 1  and s 2  are switched according to the modulation scheme that the transmission device uses for generating s 1 .       

     “The setting scheme for the average powers of s 1  and s 2  when the modulation scheme for s 1  and the modulation scheme for s 2  are different” described in the present embodiment is not necessarily the precoding scheme regularly hopping between precoding matrices as explained in the present Description. Any precoding schemes that regularly hop between precoding matrices are applicable. 
     In the present embodiment, the hopping between the precoding matrices is performed in the time domain. However, when a multi-carrier transmission scheme such as an OFDM scheme is used, the present invention is applicable to the case where the hopping between the precoding matrices is performed in the frequency domain, as described in other embodiments. If this is the case, t used in the present embodiment is to be replaced with f (frequency ((sub) carrier)). Also, even in the case of performing the hopping between the precoding matrices in the time and frequency domains, the present invention is applicable. 
     Embodiment H1 
     The present embodiment describes a scheme that is used when the modulation signal subject to the QPSK mapping and the modulation signal subject to the 16QAM mapping are transmitted, for example, and is used for setting the average power of the modulation signal subject to the QPSK mapping and the average power of the modulation signal subject to the 16QAM mapping such that the average powers will be different from each other. This scheme is different from Embodiment F1. 
     As explained in Embodiment F1, when the modulation scheme for the modulation signal of s 1  is QPSK and the modulation scheme for the modulation signal of s 2  is 16QAM (or the modulation scheme for the modulation signal s 1  is 16QAM and the modulation scheme for the modulation signal s 2  is QPSK), if the average power of the modulation signal subject to the QPSK mapping and the average power of the modulation signal subject to the 16QAM mapping are set to be different from each other, the PAPR (Peak-to-Average Power Ratio) of the transmission power amplifier provided in the transmission device may increase, depending on the precoding scheme used by the transmission device, which regularly hops between precoding matrices. The increase of the PAPR may lead to the increase in power consumption by the transmission device. 
     More specifically, in the present description, which includes “Embodiment 8”, “Embodiment 9”, “Embodiment 18”, “Embodiment 19”, “Embodiment C1” and “Embodiment C2”, when α≠1 in the equation of the precoding matrix to be used in the precoding scheme for regularly hopping between precoding matrices, the following influences are brought about. That is, the average power of the modulated signal z 1  and the modulated signal z 2  are caused to differ from each other, which influences the PAPR of the transmission power amplifier included in the transmission device. As a result, the problem arises of the power consumption of the transmission device being increased (however, as already mentioned in the above, certain precoding matrices in the scheme for regularly hopping between precoding matrices influence the PAPR to only a minimal extent even when α≠1). 
     Thus, in the present embodiment, description is provided on a precoding scheme for regularly hopping between precoding matrices, where, when α≠1 in the equation of the precoding matrix to be used in the precoding scheme, the influence to the PAPR is suppressed to a minimal extent. As already mentioned in the above, description has been made on the precoding scheme for regularly hopping between precoding matrices in the present description, more specifically, in “Embodiment 8”, “Embodiment 9”, “Embodiment 18”, “Embodiment 19”, “Embodiment C1” and “Embodiment C2”. 
     In the present embodiment, description is provided taking as an example a case where the modulation scheme applied to the streams s 1  and s 2  is either QPSK or 16QAM. 
     Firstly, explanation is provided of the mapping scheme for QPSK modulation and the mapping scheme for 16QAM modulation. Note that, in the present embodiment, the symbols s 1  and s 2  refer to signals which are either in accordance with the mapping for QPSK modulation or the mapping for 16QAM modulation. 
     First of all, description is provided concerning mapping for 16QAM with reference to the accompanying  FIG.  94   .  FIG.  94    illustrates an example of a signal point layout in the in-phase component I—quadrature component Q plane for 16QAM. Concerning the signal point  9400  in  FIG.  94   , when the bits transferred (input bits) are b 0 -b 3 , that is, when the bits transferred are indicated by (b 0 , b 1 , b 2 , b 3 )=(1, 0, 0, 0) (this value being illustrated in  FIG.  94   ), the coordinates in the in-phase component I-quadrature component Q plane corresponding thereto is denoted as (I, Q)=(−3×g, 3×g). The values of coordinates I and Q in this set of coordinates indicates the mapped signals. Note that, when the bits transferred (b 0 , b 1 , b 2 , b 3 ) take other values than in the above, the set of values I and Q is determined according to the values of the bits transferred (b 0 , b 1 , b 2 , b 3 ) and according to  FIG.  94   . Further, similar as in the above, the values of coordinates I and Q in this set indicates the mapped signals (s 1  and s 2 ). 
     Subsequently, description is provided concerning mapping for QPSK modulation with reference to the accompanying  FIG.  95   .  FIG.  95    illustrates an example of a signal point layout in the in-phase component I—quadrature component Q plane for QPSK. Concerning the signal point  9500  in  FIG.  95   , when the bits transferred (input bits) are b 0  and b 1 , that is, when the bits transferred are indicated by (b 0 , b 1 )=(1, 0) (this value being illustrated in  FIG.  95   ), the coordinates in the in-phase component I—quadrature component Q plane corresponding thereto is denoted as (I, Q)=(−1×h, 1×h). Further, the values of coordinates I and Q in this set of coordinates indicates the mapped signals. Note that, when the bits transferred (b 0 , b 1 ) take other values than in the above, the set of coordinates (I, Q) is determined according to the values of the bits transferred (b 0 , b 1 ) and according to  FIG.  95   . Further, similar as in the above, the values of coordinates I and Q in this set indicates the mapped signals (s 1  and s 2 ). 
     Further, when the modulation scheme applied to s 1  and s 2  is either QPSK or 16QAM, and when equalizing the average power of the modulated signal z 1  and the modulated signal z 2 , h represents equation (273), and g represents equation (272). 
       FIGS.  110  and  111    illustrate an example of the scheme of changing the modulation scheme, the power change value, and the precoding matrix in the time domain (or in the frequency domain, or in the time domain and the frequency domain) when using a precoding-related signal processing unit illustrated in  FIG.  108   . 
     In  FIG.  110   , a chart is provided indicating the modulation scheme, the power change value, and the precoding scheme to be set at each of times t=0 through t=11. Note that, concerning the modulated signals z 1 ( t ) and z 2 ( t ), the modulated signals z 1 ( t ) and z 2 ( t ) at the same time point are to be simultaneously transmitted from different transmit antennas at the same frequency. (Although the chart in  FIG.  110    is based on the time domain, when using a multi-carrier transmission scheme as the OFDM scheme, switching between schemes may be performed according to the frequency (subcarrier) domain, rather than according to the time domain. In such a case, replacement should be made of t=0 with f=f 0 , t=1 with f=f 1 , . . . , as is shown in  FIG.  110   . (Note that here, f denotes frequencies (subcarriers), and thus, f 0 , f 1 , . . . , indicate different frequencies (subcarriers) to be used.) Further, note that concerning the modulated signals z 1 ( f ) and z 2 ( f ) in such a case, the modulated signals z 1 ( f ) and z 2 ( f ) having the same frequency are to be simultaneously transmitted from different transmit antennas. 
     As illustrated in  FIG.  110   , when the modulation scheme applied is QPSK, the power change unit (although referred to as the power change unit herein, may also be referred to as an amplification change unit or a weighting unit) multiplies a (a being a real number) with respect to a signal modulated in accordance with QPSK. Similarly, when the modulation scheme applied is 16QAM, the power change unit (although referred to as the power change unit herein, may also be referred to as the amplification change unit or the weighting unit) multiplies b (b being a real number) with respect to a signal modulated in accordance with 16QAM. 
     In the example illustrated in  FIG.  110   , three precoding matrices, namely F[0], F[1], and F[2] are prepared as precoding matrices used in the precoding scheme for regularly hopping between precoding matrices. Additionally, the period (cycle) for hopping in the scheme of regularly hopping between precoding matrices is 3 (thus, each of t 0 -t 2 , t 3 -t 5 , . . . composes one period (cycle)). 
     Further, in  FIG.  110   , the modulation scheme applied to s 1 ( t ) is QPSK in period (cycle) t 0 -t 2 , 16QAM in period (cycle) t 3 -t 5  and so on, whereas the modulation scheme applied to s 2 ( t ) is 16QAM in period (cycle) t 0 -t 2 , QPSK in period (cycle) t 3 -t 5  and so on. Thus, the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) is either (QPSK, 16QAM) or (16QAM, QPSK). 
     Here, it is important that: 
     when performing precoding according to matrix F[0], both (QPSK, 16QAM) and (16QAM, QPSK) can be the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )), when performing precoding according to matrix F[1], both (QPSK, 16QAM) and (16QAM, QPSK) can be the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )), and similarly, when performing precoding according to matrix F[2], both (QPSK, 16QAM) and (16QAM, QPSK) can be the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )). 
     In addition, when the modulation scheme applied to s 1 ( t ) is QPSK, the power change unit ( 10701 A) multiples s 1 ( t ) with a and thereby outputs a×s 1 ( t ). On the other hand, when the modulation scheme applied to s 2 ( t ) is 16QAM, the power change unit ( 10701 A) multiples s 1 ( t ) with b and thereby outputs b× s 1 ( t ). 
     Further, when the modulation scheme applied to s 2 ( t ) is QPSK, the power change unit ( 10701 B) multiples s 2 ( t ) with a and thereby outputs a×s 2 ( t ). On the other hand, when the modulation scheme applied to s 2 ( t ) is 16QAM, the power change unit ( 10701 B) multiples s 2 ( t ) with b and thereby outputs b×s 2 ( t ). 
     Note that, regarding the scheme for differently setting the average power of signals in accordance with mapping for QPSK modulation and the average power of signals in accordance with mapping for 16QAM modulation, description has already been made in Embodiment F1. 
     Thus, when taking the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) into consideration, the period (cycle) for the hopping between precoding matrices and the switching between modulation schemes is 6=3×2 (where 3: the number of precoding matrices prepared as precoding matrices used in the precoding scheme for regularly hopping between precoding matrices, and 2: both (QPSK, 16QAM) and (16QAM, QPSK) can be the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) for each of the precoding matrices). 
     As description has been made in the above, by making an arrangement such that both (QPSK, 16QAM) and (16QAM, QPSK) exist as the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )), and such that both (QPSK, 16QAM) and (16QAM, QPSK) exist as the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) with respect to each of the precoding matrices prepared as precoding matrices used in the precoding scheme for regularly hopping between precoding matrices, the following advantageous effects are to be yielded. That is, even when differently setting the average power of signals in accordance with mapping for QPSK modulation and the average power of signals in accordance with mapping for 16QAM modulation, the influence with respect to the PAPR of the transmission power amplifier included in the transmission device is suppressed to a minimal extent, and thus the influence with respect to the power consumption of the transmission device is suppressed to a minimal extent, while the reception quality of data received by the reception device in the LOS environment is improved, as explanation has already been provided in the present description. 
     Note that, although description has been provided in the above, taking as an example a case where the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) is (QPSK, 16QAM) and (16QAM, QPSK), the possible sets of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) are not limited to this. More specifically, the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) may be one of: (QPSK, 64QAM), (64QAM, QPSK); (16QAM, 64QAM), (64QAM, 16QAM); (128QAM, 64QAM), (64QAM, 128QAM); (256QAM, 64QAM), (64QAM, 256QAM), and the like. That is, the present invention is to be similarly implemented provided that two different modulation schemes are prepared, and a different one of the modulation schemes is applied to each of s 1 ( t ) and s 2 ( t ). 
     In  FIG.  111   , a chart is provided indicating the modulation scheme, the power change value, and the precoding matrix to be set at each of times t=0 through t=11. Note that, concerning the modulated signals z 1 ( t ) and z 2 ( t ), the modulated signals z 1 ( t ) and z 2 ( t ) at the same time point are to be simultaneously transmitted from different transmit antennas at the same frequency. (Although the chart in  FIG.  111    is based on the time domain, when using a multi-carrier transmission scheme as the OFDM scheme, switching between schemes may be performed according to the frequency (subcarrier) domain, rather than according to the time domain. In such a case, replacement should be made of t=0 with f=f 0 , t=1 with f=f 1 , . . . , as is shown in  FIG.  111   . (Note that here, f denotes frequencies (subcarriers), and thus, f 0 , f 1 , . . . , indicate different frequencies (subcarriers) to be used.) Further, note that concerning the modulated signals z 1 ( f ) and z 2 ( f ) in such a case, the modulated signals z 1 ( f ) and z 2 ( f ) having the same frequency are to be simultaneously transmitted from different transmit antennas. Note that the example illustrated in  FIG.  111    is an example that differs from the example illustrated in  FIG.  110   , but satisfies the requirements explained with reference to  FIG.  110   . 
     As illustrated in  FIG.  111   , when the modulation scheme applied is QPSK, the power change unit (although referred to as the power change unit herein, may also be referred to as the amplification change unit, or the weighting unit) multiplies a (a being a real number) with respect to a signal modulated in accordance with QPSK. Similarly, when the modulation scheme applied is 16QAM, the power change unit (although referred to as the power change unit herein, may also be referred to as the amplification change unit or the weighting unit) multiplies b (b being a real number) with respect to a signal modulated in accordance with 16QAM. 
     In the example illustrated in  FIG.  111   , three precoding matrices, namely F[0], F[1], and F[2] are prepared as precoding matrices used in the precoding scheme for regularly hopping between precoding matrices. Additionally, the period (cycle) for hopping in the scheme of regularly hopping between precoding matrices is 3 (thus, each of t 0 -t 2 , t 3 -t 5 , . . . composes one period (cycle)). 
     Further, QPSK and 16QAM are alternately set as the modulation scheme applied to s 1 ( t ) in the time domain, and the same applies to the modulation scheme set to s 2 ( t ). Thus, the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) is either (QPSK, 16QAM) or (16QAM, QPSK). 
     Here, it is important that: 
     when performing precoding according to matrix F[0], both (QPSK, 16QAM) and (16QAM, QPSK) can be the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )), when performing precoding according to matrix F[1], both (QPSK, 16QAM) and (16QAM, QPSK) can be the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )), and similarly, when performing precoding according to matrix F[2], both (QPSK, 16QAM) and (16QAM, QPSK) can be the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )). 
     In addition, when the modulation scheme applied to s 1 ( t ) is QPSK, the power change unit ( 10701 A) multiples s 1 ( t ) with a and thereby outputs a×s 1 ( t ). On the other hand, when the modulation scheme applied to s 2 ( t ) is 16QAM, the power change unit ( 10701 A) multiples s 1 ( t ) with b and thereby outputs b× s 1 ( t ). 
     Further, when the modulation scheme applied to s 2 ( t ) is QPSK, the power change unit ( 10701 B) multiples s 2 ( t ) with a and thereby outputs a×s 2 ( t ). On the other hand, when the modulation scheme applied to s 2 ( t ) is 16QAM, the power change unit ( 10701 B) multiples s 2 ( t ) with b and thereby outputs b×s 2 ( t ). 
     Thus, when taking the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) into consideration, the period (cycle) for the hopping between precoding matrices and the switching between modulation schemes is 6=3×2 (where 3: the number of precoding matrices prepared as precoding matrices used in the precoding scheme for regularly hopping between precoding matrices, and 2: both (QPSK, 16QAM) and (16QAM, QPSK) can be the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) for each of the precoding matrices). 
     As description has been made in the above, by making an arrangement such that both (QPSK, 16QAM) and (16QAM, QPSK) exist as the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )), and such that both (QPSK, 16QAM) and (16QAM, QPSK) exist as the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) for each of the precoding matrices prepared as precoding matrices used in the precoding scheme for regularly hopping between precoding matrices, the following advantageous effects are to be yielded. That is, even when differently setting the average power of signals in accordance with mapping for QPSK modulation and the average power of signals in accordance with mapping for 16QAM modulation, the influence with respect to the PAPR of the transmission power amplifier included in the transmission device is suppressed to a minimal extent, and thus the influence with respect to the power consumption of the transmission device is suppressed to a minimal extent, while the reception quality of data received by the reception device in the LOS environment is improved, as explanation has already been provided in the present description. 
     Note that, although description has been provided in the above, taking as an example a case where the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) is (QPSK, 16QAM) and (16QAM, QPSK), the possible sets of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) are not limited to this. More specifically, the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) may be one of: (QPSK, 64QAM), (64QAM, QPSK); (16QAM, 64QAM), (64QAM, 16QAM); (128QAM, 64QAM), (64QAM, 128QAM); (256QAM, 64QAM), (64QAM, 256QAM), and the like. That is, the present invention is to be similarly implemented provided that two different modulation schemes are prepared, and a different one of the modulation schemes is applied to each of s 1 ( t ) and s 2 ( t ). 
     Additionally, the relation between the modulation scheme, the power change value, and the precoding matrix set at each of times (or for each of frequencies) is not limited to those described in the above with reference to  FIGS.  110  and  111   . 
     To summarize the explanation provided in the above, the following points are essential. 
     Arrangements are to be made such that the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) can be either (modulation scheme A, modulation scheme B) or (modulation scheme B, modulation scheme A), and such that the average power of signals in accordance with mapping for QPSK modulation and the average power of signals in accordance with mapping for 16QAM modulation are differently set. 
     Further, when the modulation scheme applied to s 1 ( t ) is modulation scheme A, the power change unit ( 10701 A) multiples s 1 ( t ) with a and thereby outputs a×s 1 ( t ). On the other hand, when the modulation scheme applied to s 2 ( t ) is modulation scheme B, the power change unit ( 10701 A) multiples s 1 ( t ) with b and thereby outputs b× s 1 ( t ). Similarly, when the modulation scheme applied to s 2 ( t ) is modulation scheme A, the power change unit ( 10701 B) multiples s 2 ( t ) with a and thereby outputs a×s 2 ( t ). On the other hand, when the modulation scheme applied to s 2 ( t ) is modulation scheme B, the power change unit ( 10701 A) multiples s 2 ( t ) with b and thereby outputs b× s 2 ( t ). 
     Further, an arrangement is to be made such that precoding matrices F[0], F[1], . . . , F[n−2], and F[n−1] (or F[k], where k satisfies 0≤k≤n−1) exist as precoding matrices prepared for use in the precoding scheme for regularly hopping between precoding matrices. Further, an arrangement is to be made such that both (modulation scheme A, modulation scheme B) and (modulation scheme B, modulation scheme A) exist as the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) for F[k]. (Here, the arrangement may be made such that both (modulation scheme A, modulation scheme B) and (modulation scheme B, modulation scheme A) exist as the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) for F[k] for all values of k, or such that a value k exists where both (modulation scheme A, modulation scheme B) and (modulation scheme B, modulation scheme A) exist as the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) for F[k].) 
     As description has been made in the above, by making an arrangement such that both (modulation scheme A, modulation scheme B) and (modulation scheme B, modulation scheme A) exist as the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )), and such that both (modulation scheme A, modulation scheme B) and (modulation scheme B, modulation scheme A) exist as the set of (modulation scheme of s 1 ( t ), modulation scheme of s 2 ( t )) for each of the precoding matrices prepared as precoding matrices used in the precoding scheme for regularly hopping between precoding matrices, the following advantageous effects are yielded. That is, even when differently setting the average power of signals in accordance with mapping for modulation scheme A and the average power of signals in accordance with mapping for modulation scheme B, the influence with respect to the PAPR of the transmission power amplifier included in the transmission device is suppressed to a minimal extent, and thus the influence with respect to the power consumption of the transmission device is suppressed to a minimal extent, while the reception quality of data received by the reception device in the LOS environment is improved, as explanation has already been provided in the present description. 
     In connection with the above, explanation is provided of a scheme for generating baseband signals s 1 ( t ) and s 2 ( t ) in the following. As illustrated in  FIGS.  3    and  4 , the baseband signal s 1 ( t ) is generated by the mapping unit  306   a  and the baseband signal s 2 ( t ) is generated by the mapping unit  306   b . As such, in the examples provided in the above with reference to  FIGS.  110  and  111   , the mapping units  306   a  and  306   b  switch between mapping according to QPSK and mapping according to 16QAM by referring to the charts illustrated in  FIGS.  110  and  110   . 
     Here, note that, although separate mapping units for generating each of the baseband signal s 1 ( t ) and the baseband signal s 2 ( t ) are provided in the illustrations in  FIGS.  3  and  4   , the present invention is not limited to this. For instance, the mapping unit ( 11202 ) may receive input of digital data ( 11201 ), generate s 1 ( t ) and s 2 ( t ) according to  FIGS.  110  and  111   , and respectively output s 1 ( t ) as the mapped signal  307 A and s 2 ( t ) as the mapped signal  307 B. 
       FIG.  113    illustrates one structural example of the periphery of the weighting combination unit (precoding unit), which differs from the structures illustrated in  FIGS.  108  and  112   . In  FIG.  113   , elements that operate in a similar way to  FIGS.  3  and  107    bear the same reference signs. In  FIG.  114   , a chart is provided indicating the modulation scheme, the power change value, and the precoding matrix to be set at each of times t=0 through t=11 with respect to the structural example illustrated in  FIG.  113   . Note that, concerning the modulated signals z 1 ( t ) and z 2 ( t ), the modulated signals z 1 ( t ) and z 2 ( t ) at the same time point are to be simultaneously transmitted from different transmit antennas at the same frequency. (Although the chart in  FIG.  114    is based on the time domain, when using a multi-carrier transmission scheme as the OFDM scheme, switching between schemes may be performed according to the frequency (subcarrier) domain, rather than according to the time domain. In such a case, replacement should be made of t=0 with f=f 0 , t=1 with f=f 1 , . . . , as is shown in  FIG.  114   . (Note that here, f denotes frequencies (subcarriers), and thus, f 0 , f 1 , . . . , indicate different frequencies (subcarriers) to be used.) Further, note that concerning the modulated signals z 1 ( f ) and z 2 ( f ) in such a case, the modulated signals z 1 ( f ) and z 2 ( f ) having the same frequency are to be simultaneously transmitted from different transmit antennas. 
     As illustrated in  FIG.  114   , when the modulation scheme applied is QPSK, the power change unit (although referred to as the power change unit herein, may also be referred to as the amplification change unit, or the weighting unit) multiplies a (a being a real number) with respect to a signal modulated in accordance with QPSK. Similarly, when the modulation scheme applied is 16QAM, the power change unit (although referred to as the power change unit herein, may also be referred to as the amplification change unit or the weighting unit) multiplies b (b being a real number) with respect to a signal modulated in accordance with 16QAM. 
     In the example illustrated in  FIG.  114   , three precoding matrices, namely F[0], F[1], and F[2] are prepared as precoding matrices used in the precoding scheme for regularly hopping between precoding matrices. Additionally, the period (cycle) for hopping in the scheme of regularly hopping between precoding matrices is 3 (thus, each of t 0 -t 2 , t 3 -t 5 , . . . composes one period (cycle)). 
     Further, the modulation scheme applied to s 1 ( t ) is fixed to QPSK, and the modulation scheme to be applied to s 2 ( t ) is fixed to 16QAM. Additionally, the signal switching unit ( 11301 ) illustrated in  FIG.  113    receives the mapped signals  307 A and  307 B and the control signal ( 10700 ) as input thereto. The signal switching unit ( 11301 ) performs switching with respect to the mapped signals  307 A and  307 B according to the control signal ( 10700 ) (there are also cases where the switching is not performed), and outputs switched signals ( 11302 A: Ω 1 ( t ), and  11302 B: Ω 2 ( t )). 
     Here, it is important that: 
     when performing precoding according to matrix F[0], both (QPSK, 16QAM) and (16QAM, QPSK) can be the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )), when performing precoding according to matrix F[1], both (QPSK, 16QAM) and (16QAM, QPSK) can be the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )), and similarly, when performing precoding according to matrix F[2], both (QPSK, 16QAM) and (16QAM, QPSK) can be the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )). 
     Further, when the modulation scheme applied to Ω 1 ( t ) is QPSK, the power change unit ( 10701 A) multiples Ω 1 ( t ) with a and thereby outputs a×Ω 1 ( t ). On the other hand, when the modulation scheme applied to Ω 1 ( t ) is 16QAM, the power change unit ( 10701 A) multiples Ω 1 ( t ) with b and thereby outputs b×Ω 1 ( t ). 
     Further, when the modulation scheme applied to Ω 2 ( t ) is QPSK, the power change unit ( 10701 B) multiples Ω 2 ( t ) with a and thereby outputs a×Ω 2 ( t ). On the other hand, when the modulation scheme applied to Ω 2 ( t ) is 16QAM, the power change unit ( 10701 B) multiples Ω 2 ( t ) with b and thereby outputs b×Ω 2 ( t ). 
     Note that, regarding the scheme for differently setting the average power of signals in accordance with mapping for QPSK modulation and the average power of signals in accordance with mapping for 16QAM modulation, description has already been made in Embodiment F1. 
     Thus, when taking the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )) into consideration, the period (cycle) for the hopping between precoding matrices and the switching between modulation schemes is 6=3×2 (where 3: the number of precoding matrices prepared as precoding matrices used in the precoding scheme for regularly hopping between precoding matrices, and 2: both (QPSK, 16QAM) and (16QAM, QPSK) can be the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )) for each of the precoding matrices). 
     As description has been made in the above, by making an arrangement such that both (QPSK, 16QAM) and (16QAM, QPSK) exist as the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )), and such that both (QPSK, 16QAM) and (16QAM, QPSK) exist as the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )) for each of the precoding matrices prepared as precoding matrices used in the precoding scheme for regularly hopping between precoding matrices, the following advantageous effects are to be yielded. That is, even when differently setting the average power of signals in accordance with mapping for QPSK modulation and the average power of signals in accordance with mapping for 16QAM modulation, the influence with respect to the PAPR of the transmission power amplifier included in the transmission device is suppressed to a minimal extent, and thus the influence with respect to the power consumption of the transmission device is suppressed to a minimal extent, while the reception quality of data of received by the reception device in the LOS environment is improved. 
     Note that, although description has been provided in the above, taking as an example a case where the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )) is (QPSK, 16QAM) and (16QAM, QPSK), the possible sets of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )) are not limited to this. More specifically, the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )) may be one of: (QPSK, 64QAM), (64QAM, QPSK); (16QAM, 64QAM), (64QAM, 16QAM); (128QAM, 64QAM), (64QAM, 128QAM); (256QAM, 64QAM), (64QAM, 256QAM), and the like. That is, the present invention is to be similarly implemented provided that two different modulation schemes are prepared, and a different one of the modulation schemes is applied to each of Ω 1 ( t ) and Ω 2 ( t ). 
     In  FIG.  115   , a chart is provided indicating the modulation scheme, the power change value, and the precoding matrix to be set at each of times t=0 through t=11 with respect to the structural example illustrated in  FIG.  113   . Note that the chart in  FIG.  115    differs from the chart in  FIG.  114   . Further, concerning the modulated signals z 1 ( t ) and z 2 ( t ), the modulated signals z 1 ( t ) and z 2 ( t ) at the same time point are to be simultaneously transmitted from different transmit antennas at the same frequency. (Although the chart in  FIG.  115    is based on the time domain, when using a multi-carrier transmission scheme as the OFDM scheme, switching between schemes may be performed according to the frequency (subcarrier) domain, rather than according to the time domain. In such a case, replacement should be made of t=0 with f=f 0 , t=1 with f=f 1 , . . . , as is shown in  FIG.  115   . (Note that here, f denotes frequencies (subcarriers), and thus, f 0 , f 1 , . . . , indicate different frequencies (subcarriers) to be used.) Further, note that concerning the modulated signals z 1 ( f ) and z 2 ( f ) in such a case, the modulated signals z 1 ( f ) and z 2 ( f ) having the same frequency are to be simultaneously transmitted from different transmit antennas. 
     As illustrated in  FIG.  115   , when the modulation scheme applied is QPSK, the power change unit (although referred to as the power change unit herein, may also be referred to as the amplification change unit, or the weighting unit) multiplies a (a being a real number) with respect to a signal modulated in accordance with QPSK. Similarly, when the modulation scheme applied is 16QAM, the power change unit (although referred to as the power change unit herein, may also be referred to as the amplification change unit or the weighting unit) multiplies b (b being a real number) with respect to a signal modulated in accordance with 16QAM. 
     In the example illustrated in  FIG.  115   , three precoding matrices, namely F[0], F[1], and F[2] are prepared as precoding matrices used in the precoding scheme for regularly hopping between precoding matrices. Additionally, the period (cycle) for hopping in the scheme of regularly hopping between precoding matrices is 3 (thus, each of t 0 -t 2 , t 3 -t 5 , . . . composes one period (cycle)). 
     Further, the modulation scheme applied to s 1 ( t ) is fixed to QPSK, and the modulation scheme to be applied to s 2 ( t ) is fixed to 16QAM. Additionally, the signal switching unit ( 11301 ) illustrated in  FIG.  113    receives as the mapped signals  307 A and  307 A and a control signal ( 10700 ) as input thereto. The signal switching unit ( 11301 ) performs switching with respect to the mapped signals  307 A and  307 B according to the control signal ( 10700 ) (there are also cases where the switching is not performed), and outputs switched signals ( 11302 A: Ω 1 ( t ), and  11302 B: Ω 2 ( t )). 
     Here, it is important that: 
     when performing precoding according to matrix F[0], both (QPSK, 16QAM) and (16QAM, QPSK) can be the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )), when performing precoding according to matrix F[1], both (QPSK, 16QAM) and (16QAM, QPSK) can be the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )), and similarly, when performing precoding according to matrix F[2], both (QPSK, 16QAM) and (16QAM, QPSK) can be the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )). 
     Further, when the modulation scheme applied to Ω 1 ( t ) is QPSK, the power change unit ( 10701 A) multiples Ω 1 ( t ) with a and thereby outputs a×Ω 1 ( t ). On the other hand, when the modulation scheme applied to Ω 1 ( t ) is 16QAM, the power change unit ( 10701 A) multiples Ω 1 ( t ) with b and thereby outputs b×Ω 1 ( t ). 
     Further, when the modulation scheme applied to Ω 2 ( t ) is QPSK, the power change unit ( 10701 B) multiples Ω 2 ( t ) with a and thereby outputs a×Ω 2 ( t ). On the other hand, when the modulation scheme applied to Ω 2 ( t ) is 16QAM, the power change unit ( 10701 B) multiples Ω 2 ( t ) with b and thereby outputs b×Ω 2 ( t ). 
     Note that, regarding the scheme for differently setting the average power of signals in accordance with mapping for QPSK modulation and the average power of signals in accordance with mapping for 16QAM modulation, description has already been made in Embodiment F1. 
     Thus, when taking the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )) into consideration, the period (cycle) for the hopping between precoding matrices and the switching between modulation schemes is 6=3×2 (where 3: the number of precoding matrices prepared as precoding matrices used in the precoding scheme for regularly hopping between precoding matrices, and 2: both (QPSK, 16QAM) and (16QAM, QPSK) can be the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )) for each of the precoding matrices). 
     As description has been made in the above, by making an arrangement such that both (QPSK, 16QAM) and (16QAM, QPSK) exist as the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )), and such that both (QPSK, 16QAM) and (16QAM, QPSK) exist as the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )) for each of the precoding matrices prepared as precoding matrices used in the precoding scheme for regularly hopping between precoding matrices, the following advantageous effects are to be yielded. That is, even when differently setting the average power of signals in accordance with mapping for QPSK modulation and the average power of signals in accordance with mapping for 16QAM modulation, the influence with respect to the PAPR of the transmission power amplifier included in the transmission device is suppressed to a minimal extent, and thus the influence with respect to the power consumption of the transmission device is suppressed to a minimal extent, while the reception quality of data of received by the reception device in the LOS environment is improved. 
     Note that, although description has been provided in the above, taking as an example a case where the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )) is (QPSK, 16QAM) and (16QAM, QPSK), the possible sets of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )) are not limited to this. More specifically, the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )) may be one of: (QPSK, 64QAM), (64QAM, QPSK); (16QAM, 64QAM), (64QAM, 16QAM); (128QAM, 64QAM), (64QAM, 128QAM); (256QAM, 64QAM), (64QAM, 256QAM), and the like. That is, the present invention is to be similarly implemented provided that two different modulation schemes are prepared, and a different one of the modulation schemes is applied to each of Ω 1 ( t ) and Ω 2 ( t ). 
     Additionally, the relation between the modulation scheme, the power change value, and the precoding matrix set at each of times (or for each of frequencies) is not limited to those described in the above with reference to  FIGS.  114  and  115   . 
     To summarize the explanation provided in the above, the following points are essential. 
     Arrangements are to be made such that the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )) can be either (modulation scheme A, modulation scheme B) or (modulation scheme B, modulation scheme A), and such that the average power of signals in accordance with mapping for QPSK modulation and the average power of signals in accordance with mapping for 16QAM modulation are differently set. 
     Further, when the modulation scheme applied to Ω 1 ( t ) is modulation scheme A, the power change unit ( 10701 A) multiples Ω 1 ( t ) with a and thereby outputs a×Ω 1 ( t ). On the other hand, when the modulation scheme applied to Ω 1 ( t ) is modulation scheme B, the power change unit ( 10701 A) multiples Ω 1 ( t ) with b and thereby outputs b×Ω 1 ( t ). Further, when the modulation scheme applied to Ω 2 ( t ) is modulation scheme A, the power change unit ( 10701 B) multiples Ω 2 ( t ) with a and thereby outputs a×Ω 2 ( t ). On the other hand, when the modulation scheme applied to Ω 2 ( t ) is modulation scheme B, the power change unit ( 10701 B) multiples Ω 2 ( t ) with b and thereby outputs b×Ω 2 ( t ). 
     Further, an arrangement is to be made such that precoding matrices F[0], F[1], . . . , F[n−2], and F[n−1] (or F[k], where k satisfies 0≤k≤n−1) exist as precoding matrices prepared for use in the precoding scheme for regularly hopping between precoding matrices. Further, an arrangement is to be made such that both (modulation scheme A, modulation scheme B) and (modulation scheme B, modulation scheme A) exist as the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t ) for F[k]. (Here, the arrangement may be made such that both (modulation scheme A, modulation scheme B) and (modulation scheme B, modulation scheme A) exist as the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t ) for F[k] for all values of k, or such that a value k exists where both (modulation scheme A, modulation scheme B) and (modulation scheme B, modulation scheme A) exist as the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t ) for F[k].) 
     As description has been made in the above, by making an arrangement such that both (modulation scheme A, modulation scheme B) and (modulation scheme B, modulation scheme A) exist as the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t )), and such that both (modulation scheme A, modulation scheme B) and (modulation scheme B, modulation scheme A) exist as the set of (modulation scheme of Ω 1 ( t ), modulation scheme of Ω 2 ( t ) for each of the precoding matrices prepared as precoding matrices used in the precoding scheme for regularly hopping between precoding matrices, the following advantageous effects are to be yielded. That is, even when differently setting the average power of signals in accordance with mapping for modulation scheme A and the average power of signals in accordance with mapping for modulation scheme B, the influence with respect to the PAPR of the transmission power amplifier included in the transmission device is suppressed to a minimal extent, and thus the influence with respect to the power consumption of the transmission device is suppressed to a minimal extent, while the reception quality of data received by the reception device in the LOS environment is improved, as explanation has already been provided in the present description. 
     Subsequently, explanation is provided of the operations of the reception unit. Explanation of the reception device has already been provided in Embodiment 1, Embodiments A1-A5 and the like, and the structure of the reception unit is illustrated in  FIGS.  7 ,  8 ,  9 ,  56 ,  73 ,  74 , and  75   , for instance. 
     According to the relation illustrated in  FIG.  5   , when the transmission device transmits modulation signals as introduced in  FIGS.  110 ,  111 ,  114 , and  115   , one relation among the two relations denoted by the two equations below is satisfied. Note that in the two equations below, r 1 ( t ) and r 2 ( t ) indicate reception signals, whereas h 11 (t), h 12 (t), h 21 (t), and h 22 (t) indicate channel fluctuation values. 
     
       
         
           
             Math 
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             686 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         
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                             [ 
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                         = 
                           
                         
                           
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                                       ( 
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                             [ 
                             t 
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                             ( 
                             
                               
                                 
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                                       ( 
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                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   H1 
                   ) 
                 
               
             
           
         
       
       
         
           
             Math 
             ⁢ 
                 
             687 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         
                           ( 
                           
                             
                               
                                 
                                   r 
                                   ⁢ 
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                         = 
                           
                         
                           
                             ( 
                             
                               
                                 
                                   
                                     
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                             [ 
                             t 
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                             ( 
                             
                               
                                 
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                             ( 
                             
                               
                                 
                                   
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                                       ( 
                                       t 
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                   ( 
                   H2 
                   ) 
                 
               
             
           
         
       
     
     Here, it should be noted that F[t] is a precoding matrix utilizing a parameter time t when applied for the precoding scheme for regularly hopping between precoding matrices. The reception device performs demodulation (detection) of signals by utilizing the relation defined in the two equations above (that is, demodulation is to be performed in the same manner as explanation has been provided in Embodiment 1 and Embodiments A1 though A5). However, the two equations above do not take into consideration such distortion components as noise components, frequency offsets, and channel estimation errors, and thus, the demodulation (detection) is performed with such distortion components included in the signals. As for the values u and v used by the transmission device in performing power change, the transmission device may transmit information concerning such information or otherwise, the transmission device may transmit information concerning the transmission mode applied (such as transmission scheme, modulation scheme, and error correction scheme). By obtaining such information, the reception device is capable of acknowledging the values u and v used by the transmission device. As such, the reception device derives the two equations above, and performs demodulation (detection). 
     Although description is provided in the present invention taking as an example a case where hopping between precoding matrices is performed in the time domain, the present invention may be similarly embodied when using a multi-carrier transmission scheme such as OFDM or the like and when hopping between precoding matrices in the frequency domain, as description has been made in other embodiments. In such a case, the parameter t used in the present embodiment is to be replaced with a parameter f (frequency ((sub) carrier)). Further, the present invention may be similarly embodied in a case where hopping between precoding matrices is performed in the time-frequency domain. In addition, in the present embodiment, the precoding scheme for regularly hopping between precoding matrices is not limited to the precoding scheme for regularly hopping between precoding matrices, explanation of which has been provided in the other sections of the present description. Further in addition, the same effect of minimalizing the influence with respect to the PAPR is to be obtained when applying the present embodiment with respect to a precoding scheme where a fixed precoding matrix is used. 
     Embodiment H2 
     In the present embodiment, description is provided on the precoding scheme for regularly hopping between precoding matrices, the application of which realizes an advantageous effect of reducing circuit size when the broadcast (or communications) system supports both of a case where the modulation scheme applied to s 1  is QPSK and the modulation scheme applied to s 2  is 16QAM, and a case where the modulation scheme applied to s 1  is 16QAM and the modulation scheme applied to s 2  is 16QAM. 
     Firstly, explanation is made of the precoding scheme for regularly hopping between precoding matrices in a case where 16QAM is applied as the modulation scheme to both s 1  and s 2 . 
     As an example, the precoding schemes for regularly hopping between precoding matrices which have been described in embodiments 9, 10, 18, 19 and the like of the present description are applied as an example of the precoding scheme for regularly hopping between precoding matrices in a case where 16QAM is applied as the modulation scheme to both s 1  and s 2 . (However, the precoding schemes for regularly hopping between precoding matrices are not necessarily limited to those described in embodiments 9, 10, 18, and 19.) Here, taking for example the precoding schemes for regularly hopping between precoding matrices as described in embodiments 8 and 18, a precoding matrix (F[i]) with an N-slot time period (cycle) is expressed by the following equation. 
     
       
         
           
             Math 
             ⁢ 
                 
             688 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         11 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     θ 
                                     21 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   H3 
                   ) 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). Here, note that θ 11 (i), θ 21 (i), α, λ, and δ are similar as in the description provided in embodiments 8 and 18. (Further, the conditions described in embodiments 8 and 18 which are to be satisfied by θ 11 (i), θ 21 (i), α, λ, and δ provide a good example.) Further, a unitary matrix is used as the precoding matrix with an N-slot time period (cycle). Accordingly, the following equation expresses the precoding matrix (F[i]) with an N-slot time period (cycle). 
     
       
         
           
             Math 
             ⁢ 
                 
             689 
           
         
       
       
         
           
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁡ 
                                   ( 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     + 
                                     λ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               ⨯ 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     θ 
                                     21 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   H4 
                   ) 
                 
               
             
           
         
       
     
     In the following, description is provided on an example where the equation (H4) is used as the precoding scheme for regularly hopping between precoding matrices in a case where 16QAM is applied as the modulation scheme to both s 1  and s 2 . Note that, although description is provided in the following taking the equation (H4) as an example, a more specific example is a precoding scheme for regularly hopping between precoding matrices where one of the equations (#1), (#2), (#9), (#10), (#12), (#13), and (#17), all of which are described in Embodiment C1, is applied. Alternatively, the precoding scheme for regularly hopping between precoding matrices may be the precoding scheme defined by the two equations (279) and (280) in Embodiment 19. 
     Firstly,  FIG.  116    illustrates a structural example of the periphery of the weighting combination unit (precoding unit) which supports both of a case where the modulation scheme applied to s 1  is QPSK and the modulation scheme applied to s 2  is 16QAM, and a case where the modulation scheme applied to s 1  is 16QAM and the modulation scheme applied to s 2  is 16QAM. In  FIG.  116   , elements that operate in a similar way to  FIGS.  3 ,  6 , and  107    bear the same reference signs and explanation thereof is to be omitted in the following. 
     In  FIG.  116   , the baseband signal switching unit  11601  receives the precoded signal  309 A(z 1 ( t )), the precoded signal  309 B(z 2 ( t )), and the control signal  10700  as input. When the control signal  10700  indicates “do not perform switching of signals”, the precoded signal  309 A(z 1 ( t )) is output as the signal  11602 A(z 1 ′( t )), and the precoded signal  309 B(z 2 ( t )) is output as the signal  11602 B(z 2 ′( t )). 
     In contrast, when the control signal  10700  indicates “perform switching of signals”, the baseband signal switching unit  11601  performs the following: 
     when time=2k (k being an integer), 
     outputs the precoded signal  309 A(z 1 (2k)) as the signal  11602 A(z 1 ′(2k)), and 
     outputs the precoded signal  309 B(z 2 (2k)) as the signal  11602 B(z 2 ′(2k)), 
     when time=2k+1 (k being an integer), 
     outputs the precoded signal  309 B(z 2 (2k+1)) as the signal  11602 A(z 1 ′(2k+1)), and 
     outputs the precoded signal  309 A(z 1 (2k+1)) as the signal  11602 B(z 2 ′(2k+1)), and further, 
     when time=2k (k being an integer), 
     outputs the precoded signal  309 B(z 2 (2k)) as the signal  11602 A(z 1 ′(2k)), and 
     outputs the precoded signal  309 A(z 1 (2k)) as the signal  11602 B(z 2 ′(2k)), and 
     when time=2k+1 (k being an integer), 
     outputs the precoded signal  309 A(z 1 (2k+1)) as the signal  11602 A(z 1 ′(2k+1)), and outputs the precoded signal  309 B(z 2 (2k+1)) as the signal  11602 B(z 2 ′(2k+1)). (Although the above description provides an example of the switching between signals, the switching between signals to be performed in accordance with the present embodiment is not limited to this. It is to be noted that importance lies in that switching between signals is performed when the control signal indicates “perform switching of signals”.) 
     Here, it should be noted that the present embodiment is a modification of Embodiment H1, and further, that the switching of signals as described in the above is performed with respect to only precoded symbols. That is, the switching of signals is not performed with respect to other inserted symbols such as pilot symbols and symbols for transmitting un-precoded information (e.g. control information symbols), for example. Further, although the description is provided in the above of a case where the precoding scheme for regularly hopping between precoding matrices is applied in the time domain, the present invention is not limited to this. The present embodiment may be similarly applied also in cases where the precoding scheme for regularly hopping between precoding matrices is applied in the frequency domain and in the time-frequency domain. Similarly, the switching of signals may be performed in the frequency domain or the time-frequency domain, even though description is provided in the above where switching of signals is performed in the time domain. 
     Subsequently, explanation is provided concerning the operation of each of the units in  FIG.  116    in a case where 16QAM is applied as the modulation scheme for both s 1  and s 2 . 
     Since s 1 ( t ) and s 2 ( t ) are baseband signals (mapped signals) mapped with the modulation scheme 16QAM, the mapping scheme applied thereto is as illustrated in  FIG.  94   , and g represents equation (272). 
     The power change unit ( 10701 A) receives the baseband signal (mapped signal)  307 A mapped according to the modulation scheme 16QAM, and the control signal ( 10700 ) as input. Further, the power change unit ( 10701 A) multiplies the baseband signal (mapped signal)  307 A mapped according to the modulation scheme 16QAM by a factor v, and outputs the signal obtained as a result of the multiplication (the power-changed signal:  10702 A). The factor v is a value for performing power change and is set according to the control signal ( 10700 ). 
     The power change unit ( 10701 B) receives the baseband signal (mapped signal)  307 B mapped according to the modulation scheme 16QAM, and the control signal ( 10700 ) as input. Further, the power change unit ( 10701 B) multiplies the baseband signal (mapped signal)  307 B mapped according to the modulation scheme 16QAM by a factor u, and outputs the signal obtained as a result of the multiplication (the power-changed signal:  10702 B). The factor u is a value for performing power change and is set according to the control signal ( 10700 ). 
     Here, the factors v and u satisfy: v=u=Ω, v 2 :u 2 =1:1. By making such an arrangement, data is received at an excellent reception quality by the reception device. 
     The weighting combination unit  600  receives the power-changed signal  10702 A (the signal obtained by multiplying the baseband signal (mapped signal)  307 A mapped with the modulation scheme 16QAM by the factor v), the power-changed signal  10702 B (the signal obtained by multiplying the baseband signal (mapped signal)  307 B mapped with the modulation scheme 16QAM by the factor u) and the information  315  regarding the weighting scheme as input. Further, the weighting combination unit  600  performs precoding according to the precoding scheme for regularly hopping between precoding matrices based on the information  315  regarding the weighting scheme, and outputs the precoded signal  309 A(z 1 ( t )) and the precoded signal  309 B(z 2 ( t )). Here, when F[t] represents a precoding matrix according to the precoding scheme for regularly hopping between precoding matrices, the following equation holds. 
     
       
         
           
             Math 
             ⁢ 
                 
             690 
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         
                           ( 
                           
                             
                               
                                 
                                   z 
                                   ⁢ 
                                   1 
                                   ⁢ 
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   z 
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                           
                           ) 
                         
                         = 
                           
                         
                           
                             F 
                             [ 
                             t 
                             ] 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   
                                     ve 
                                     
                                       j 
                                       ⁢ 
                                       0 
                                     
                                   
                                 
                                 
                                   0 
                                 
                               
                               
                                 
                                   0 
                                 
                                 
                                   
                                     ue 
                                     
                                       j 
                                       ⁢ 
                                       0 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   
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                                     ⁢ 
                                     1 
                                     ⁢ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     s 
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                             
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                         = 
                           
                         
                           
                             F 
                             [ 
                             t 
                             ] 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   v 
                                 
                                 
                                   0 
                                 
                               
                               
                                 
                                   0 
                                 
                                 
                                   u 
                                 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   
                                     s 
                                     ⁢ 
                                     1 
                                     ⁢ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     s 
                                     ⁢ 
                                     2 
                                     ⁢ 
                                     
                                       ( 
                                       t 
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                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         
                           
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                             [ 
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                           ⁢ 
                           
                             ( 
                             
                               
                                 
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                                   Ω 
                                 
                               
                             
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                           ⁢ 
                           
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                                     ⁢ 
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                                     ⁢ 
                                     
                                       ( 
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                                     ⁢ 
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                                     ⁢ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   H5 
                   ) 
                 
               
             
           
         
       
     
     When the precoding matrix F[t], which is a precoding matrix according to the precoding scheme for regularly hopping between precoding matrices, is represented by equation (H4) and when 16QAM is applied as the modulation scheme of both s 1  and s 2 , equation (270) is suitable as the value of a, as is described in Embodiment 18. When a is represented by equation (270), z 1 ( t ) and z 2 ( t ) each are baseband signals corresponding to one of the 256 signal points in the I-Q plane, as illustrated in  FIG.  117   . Note that  FIG.  117    illustrates an example of the layout of the 256 signal points, and the layout may be a phase-rotated layout of the 256 signal components. 
     Here, since the modulation scheme applied to s 1  is 16QAM and the modulation scheme applied to s 2  is also 16QAM, the weighted and combined signals z 1 ( t ) and z 2 ( t ) are each transmitted as 4 bits according to 16QAM. Therefore a total of 8 bits are transferred as is indicated by the 256 signals points illustrated in  FIG.  117   . In such a case, since the minimum Euclidian distance between the signal points is comparatively large, the reception quality of data received by the reception unit is improved. 
     The baseband signal switching unit  11601  receives the precoded signal  309 A(z 1 ( t )), the precoded signal  309 B(z 2 ( t )), and the control signal  10700  as input. Since 16QAM is applied as the modulation scheme of both s 1  and s 2 , the control signal  10700  indicates “do not perform switching of signals”. Thus, the precoded signal  309 A(z 1 ( t )) is output as the signal  11602 A(z 1 ′(0) and the precoded signal  309 B(z 2 ( t )) is output as the signal  11602 B(z 2 ′( t )). 
     Subsequently, explanation is provided concerning the operation of each of the units in  FIG.  12    in a case where QPSK is applied as the modulation scheme for s 1  and 16QAM is applied as the modulation scheme for s 2 . 
     Here, s 1 ( t ) is a baseband signal (mapped signal) mapped with the modulation scheme QPSK, and the mapping scheme applied thereto is as illustrated in  FIG.  95   . Additionally, h represents equation (273). Further, s 2 ( t ) is a baseband signal (mapped signal) mapped with the modulation scheme 16QAM, and the mapping scheme applied thereto is as illustrated in  FIG.  94   . Additionally, g represents equation (272). 
     The power change unit ( 10701 A) receives the baseband signal (mapped signal)  307 A mapped according to the modulation scheme QPSK, and the control signal ( 10700 ) as input. Further, the power change unit ( 10701 A) multiplies the baseband signal (mapped signal)  307 A mapped according to the modulation scheme QPSK by a factor v, and outputs the signal obtained as a result of the multiplication (the power-changed signal:  10702 A). The factor v is a value for performing power change and is set according to the control signal ( 10700 ). 
     The power change unit ( 10701 B) receives the baseband signal (mapped signal)  307 B mapped according to the modulation scheme 16QAM, and the control signal ( 10700 ) as input. Further, the power change unit ( 10701 B) multiplies the baseband signal (mapped signal)  307 B mapped according to the modulation scheme 16QAM by a factor u, and outputs the signal obtained as a result of the multiplication (the power-changed signal:  10702 B). The factor u is a value for performing power change and is set according to the control signal ( 10700 ). 
     In Embodiment H1, description is provided that one exemplary example is where “the ratio between the average power of QPSK and the average power of 16QAM is set so as to satisfy the equation v 2 :u 2 =1:5”. By making such an arrangement, data is received at an excellent reception quality by the reception device. In the following, explanation is provided of the precoding scheme for regularly hopping between precoding matrices when such an arrangement is made. 
     The weighting combination unit  600  receives the power-changed signal  10702 A (the signal obtained by multiplying the baseband signal (mapped signal)  307 A mapped with the modulation scheme QPSK by the factor v), the power-changed signal  10702 B (the signal obtained by multiplying the baseband signal (mapped signal)  307 B mapped with the modulation scheme 16QAM by the factor u) and the information  315  regarding the weighting scheme as input. Further, the weighting combination unit  600  performs precoding according to the precoding scheme for regularly hopping between precoding matrices based on the information  315  regarding the weighting scheme, and outputs the precoded signal  309 A(z 1 ( t )) and the precoded signal  309 B(z 2 ( t )). Here, when F[t] represents a precoding matrix according to the precoding scheme for regularly hopping between precoding matrices, the following equation holds. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   691 
                 
               
               
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                   H6 
                   ) 
                 
               
             
           
         
       
     
     When the precoding matrix F[t], which is a precoding matrix according to the precoding scheme for regularly hopping between precoding matrices, is represented by equation (H4) and when 16QAM is applied as the modulation scheme of both s 1  and s 2 , equation (270) is suitable as the value of a, as is described in Embodiment 18. The reason for this is explained in the following. 
       FIG.  118    illustrates the relationship between the 16 signal points of 16QAM and the 4 signal points of QPSK on the I-Q plane when the transmission state is as described in the above. In  FIG.  118   , each ◯ indicates a signal point of 16QAM, whereas each ● indicates a signal point of QPSK. As can be seen in  FIG.  118   , four signal points among the 16 signal points of the 16QAM coincide with the 4 signal points of the QPSK. Under such circumstances, when the precoding matrix F[t], which is a precoding matrix according to the precoding scheme for regularly hopping between precoding matrices, is represented by equation (H4) and when equation (270) is the value of a, each of z 1 ( t ) and z 2 ( t ) is a baseband signal corresponding to 64 signal points extracted from the 256 signal points illustrated in  FIG.  117    of a case where the modulation scheme applied to s 1  is 16QAM and the modulation scheme applied to s 2  is 16QAM. Note that  FIG.  117    illustrates an example of the layout of the 256 signal points, and the layout may be a phase-rotated layout of the 256 signal components. 
     Since QPSK is the modulation scheme applied to s 1  and 16QAM is the modulation scheme applied to s 2 , the weighted and combined signals z 1 ( t ) and z 2 ( t ) are respectively transmitted as 2 bits according to QPSK, and 4 bits according to 16QAM. Therefore a total of 6 bits are transferred as is indicated by the 64 signals points. Since the minimum Euclidian distance between the 64 signal points as described in the above is comparatively large, the reception quality of the data received by the reception device is improved. 
     The baseband signal switching unit  11601  receives the precoded signal  309 A(z 1 ( t )), the precoded signal  309 B(z 2 ( t )), and the control signal  10700  as input. Since QPSK is the modulation scheme for s 1  and 16QAM is the modulation scheme for s 2  and thus, the control signal  10700  indicates “perform switching of signals”, the baseband signal switching unit  11601  performs, for instance, the following: 
     when time=2k (k being an integer), 
     outputs the precoded signal  309 A(z 1 (2k)) as the signal  11602 A(z 1 ′(2k)), and 
     outputs the precoded signal  309 B(z 2 (2k)) as the signal  11602 B(z 2 ′(2k)), 
     when time=2k+1 (k being an integer), 
     outputs the precoded signal  309 B(z 2 (2k+1)) as the signal  11602 A(z 1 ′(2k+1)), and 
     outputs the precoded signal  309 A(z 1 (2k+1)) as the signal  11602 B(z 2 ′(2k+1)), and further, 
     when time=2k (k being an integer), 
     outputs the precoded signal  309 B(z 2 (2k)) as the signal  11602 A(z 1 ′(2k)), and 
     outputs the precoded signal  309 A(z 1 (2k)) as the signal  11602 B(z 2 ′(2k)), and 
     when time=2k+1 (k being an integer), 
     outputs the precoded signal  309 A(z 1 (2k+1)) as the signal  11602 A(z 1 ′(2k+1)), 
     and outputs the precoded signal  309 B(z 2 (2k+1)) as the signal  11602 B(z 2 ′(2k+1)). 
     Note that, in the above, description is made that switching of signals is performed when QPSK is the modulation scheme applied to s 1  and 16QAM is the modulation scheme applied to s 2 . By making such an arrangement, the reduction of PAPR is realized and further, the electric consumption by the transmission unit is suppressed, as description has been provided in Embodiment F1. However, when the electric consumption by the transmission device need not be taken into account, an arrangement may be made such that switching of signals is not performed similar to the case where 16QAM is applied as the modulation scheme for both s 1  and s 2 . 
     Additionally, description has been provided in the above on a case where QPSK is the modulation scheme applied to s 1  and 16QAM is the modulation scheme applied to s 2 , and further, the condition v 2 :u 2 =1:5 is satisfied, since such a case is considered to be exemplary. However, there exists a case where excellent reception quality is realized when (i) the precoding scheme for regularly hopping between precoding matrices when QPSK is the modulation scheme applied to s 1  and 16QAM is the modulation scheme applied to s 2  and (ii) the precoding scheme for regularly hopping between precoding matrices when 16QAM is the modulation scheme applied to s 1  and 16QAM is the modulation scheme applied to s 2  are considered as being identical under the condition v 2 &lt;u 2 . Thus, the condition to be satisfied by values v and u is not limited to v 2 :u 2 =1:5. 
     By considering (i) the precoding scheme for regularly hopping between precoding matrices when QPSK is the modulation scheme applied to s 1  and 16QAM is the modulation scheme applied to s 2  and (ii) the precoding scheme for regularly hopping between precoding matrices when 16QAM is the modulation scheme applied to s 1  and 16QAM is the modulation scheme applied to s 2  to be identical as explained in the above, the reduction of circuit size is realized. Further, in such a case, the reception device performs demodulation according to equations (H5) and (H6), and to the scheme of switching between signals, and since signal points coincide as explained in the above, the sharing of a single arithmetic unit computing reception candidate signal points is possible, and thus, the circuit size of the reception device can be realized to a further extent. 
     Note that, although description has been provided in the present invention taking the equation (H4) as an example of the precoding scheme for regularly hopping between precoding matrices, the precoding scheme for regularly hopping between precoding matrices is not limited to this. 
     The essential aspects of the present invention are as described in the following:
         When both the case where QPSK is the modulation scheme applied to s 1  and 16QAM is the modulation scheme applied to s 2  and the case where 16QAM is the modulation scheme applied for both s 1  and s 2  are supported, the same precoding scheme for regularly hopping between precoding matrices is applied in both cases.   The condition v 2 =u 2  holds when 16QAM is the modulation scheme applied for both s 1  and s 2 , and the condition v 2 &lt;u 2  holds when QPSK is the modulation scheme applied to s 1  and 16QAM is the modulation scheme applied to s 2 .       

     Further, exemplary examples where excellent reception quality of the reception device is realized are described in the following. 
     Example 1 (the Two Following Conditions are to be Satisfied) 
     
         
         
           
             the condition v 2 =u 2  holds when 16QAM is the modulation scheme applied for both s 1  and s 2 , and the condition v 2 :u 2 =1:5 holds when QPSK is the modulation scheme applied to s 1  and 16QAM is the modulation scheme applied to s 2 , and 
             the same precoding scheme for regularly hopping between precoding matrices is applied in both of cases where 16QAM is the modulation scheme applied for both s 1  and s 2  and QPSK is the modulation scheme applied to s 1  and 16QAM is the modulation scheme applied to s 2 . 
           
         
       
    
     Example 2 (the Two Following Conditions are to be Satisfied) 
     
         
         
           
             the condition v 2 =u 2  holds when 16QAM is the modulation scheme applied for both s 1  and s 2 , and the condition v 2 &lt;u 2  holds when QPSK is the modulation scheme applied to s 1  and 16QAM is the modulation scheme applied to s 2 , and 
             when both the case where QPSK is the modulation scheme applied to s 1  and 16QAM is the modulation scheme applied to s 2  and the case where 16QAM is the modulation scheme applied for both s 1  and s 2  are supported, the same precoding scheme represented by equation (H4) for regularly hopping between precoding matrices is applied in both cases. Note that, although description has been provided in the above taking an example where the precoding scheme for regularly hopping between precoding matrices is represented by the equation (H4), the precoding scheme may be a precoding scheme for regularly hopping between precoding matrices applying one of the equations (#1), (#2), (#9), (#10), (#12), (#13), and (#17), all of which are described in Embodiment C1. Alternatively, the precoding scheme for regularly hopping between precoding matrices may be the precoding scheme defined by the two equations (279) and (280) described in Embodiment 19. (detailed description is provided in Embodiments 9, 10, 18, 19, and etc.) 
           
         
       
    
     Example 3 (the Two Following Conditions are to be Satisfied) 
     
         
         
           
             the condition v 2 =u 2  holds when 16QAM is the modulation scheme applied for both s 1  and s 2 , and the condition v 2 &lt;u 2  holds when QPSK is the modulation scheme applied to s 1  and 16QAM is the modulation scheme applied to s 2 , and 
             when both the case where QPSK is the modulation scheme applied to s 1  and 16QAM is the modulation scheme applied to s 2  and the case where 16QAM is the modulation scheme applied for both s 1  and s 2  are supported, the same precoding scheme represented by equation (H4) for regularly hopping between precoding matrices is applied in both cases and the equation (270) is the value of α. Note that, although description has been provided in the above taking an example where the precoding scheme for regularly hopping between precoding matrices is represented by the equation (H4), the precoding scheme may be a precoding scheme for regularly hopping between precoding matrices applying one of the equations (#1), (#2), (#9), (#10), (#12), (#13), and (#17), all of which are described in Embodiment C1. Alternatively, the precoding scheme for regularly hopping between precoding matrices may be the precoding scheme defined by the two equations (279) and (280) described in Embodiment 19 (detailed description is provided in embodiments 9, 10, 18, 19, and etc.). In either case, it is preferable that the equation (270) be the value of α. 
           
         
       
    
     Example 4 (the Two Following Conditions are to be Satisfied) 
     
         
         
           
             the condition v 2 =u 2  holds when 16QAM is the modulation scheme applied for both s 1  and s 2 , and the condition v 2 :u 2 =1:5 holds when QPSK is the modulation scheme applied to s 1  and 16QAM is the modulation scheme applied to s 2 , and 
             when both the case where QPSK is the modulation scheme applied to s 1  and 16QAM is the modulation scheme applied to s 2  and the case where 16QAM is the modulation scheme applied for both s 1  and s 2  are supported, the same precoding scheme represented by equation (H4) for regularly hopping between precoding matrices is applied in both cases and the equation (270) is the value of α. Note that, although description has been provided in the above taking an example where the precoding scheme for regularly hopping between precoding matrices is represented by the equation (H4), the precoding scheme may be a precoding scheme for regularly hopping between precoding matrices applying one of the equations (#1), (#2), (#9), (#10), (#12), (#13), and (#17), all of which are described in Embodiment C1. Alternatively, the precoding scheme for regularly hopping between precoding matrices may be the precoding scheme defined by the two equations (279) and (280) described in Embodiment 19 (detailed description is provided in Embodiments 9, 10, 18, 19, and etc.). In either case, it is preferable that the equation (270) be the value of α. 
           
         
       
    
     Note that, although the present embodiment has been described with an example where the modulation schemes are QPSK and 16QAM, the present embodiment is not limited to this example. The scope of the present embodiment may be expanded as described below. Consider a modulation scheme A and a modulation scheme B. Let a be the number of a signal point on the I-Q plane of the modulation scheme A, and let b be the number of signal points on the I-Q plane of the modulation scheme B, where a&lt;b. Then, the essential points of the present invention are described as follows. 
     The following two conditions are to be satisfied.
         If the case where the modulation scheme of s 1  is the modulation scheme A and the modulation scheme of s 2  is the modulation scheme B, and the case where the modulation scheme of s 1  is the modulation scheme B and the modulation scheme of s 2  is the modulation scheme B are both supported, the same precoding scheme is used in common in both the cases for regularly hopping between precoding matrices.   When the modulation scheme of s 1  is the modulation scheme B and the modulation scheme of s 2  is the modulation scheme B, the condition v 2 =u 2  is satisfied, and when the modulation scheme of s 1  is the modulation scheme A and the modulation scheme of s 2  is the modulation scheme B, the condition v 2 &lt;u 2  is satisfied.       

     Here, the baseband signal switching as described with reference to  FIG.  116    may be optionally executed. However, when the modulation scheme of s 1  is the modulation scheme A and the modulation scheme of s 2  is the modulation scheme B, it is preferable to perform the above-described baseband signal switching with the influence of the PAPR taken into account. 
     Alternatively, the following two conditions are to be satisfied.
         If the case where the modulation scheme of s 1  is the modulation scheme A and the modulation scheme of s 2  is the modulation scheme B, and the case where the modulation scheme of s 1  is the modulation scheme B and the modulation scheme of s 2  is the modulation scheme B are both supported, the same precoding scheme is used in common in both the cases for regularly hopping between precoding matrices, and the precoding scheme is represented by Equation H4. Note that, although in the present embodiment the description is given of the case where the precoding scheme for regularly hopping between precoding matrices is represented by Equation H4, the precoding scheme for regularly hopping between precoding matrices using any of Equations #1, #2, #9, #10, #12, #13, and #17 may also be employed. The precoding scheme for regularly hopping between precoding matrices defined by both Equations 279 and 280, as described in the Embodiment 19, may also be employed (the details are shown in the Embodiments 9, 10, 18, and 19).   When the modulation scheme of s 1  is the modulation scheme B and the modulation scheme of s 2  is the modulation scheme B, the condition θ=u 2  is satisfied, and when the modulation scheme of s 1  is the modulation scheme A and the modulation scheme of s 2  is the modulation scheme B, the condition v 2 &lt;u 2  is satisfied.       

     Here, the baseband signal switching as described with reference to  FIG.  116    may be optionally executed. However, when the modulation scheme of s 1  is the modulation scheme A and the modulation scheme of s 2  is the modulation scheme B, it is preferable to perform the above-described baseband signal switching with the influence of the PAPR taken into account. 
     As an exemplary set of the modulation scheme A and the modulation scheme B, (modulation scheme A, modulation scheme B) is one of (QPSK, 16QAM), (16QAM, 64QAM), (64QAM, 128QAM), and (64QAM, 256QAM). 
     In the present embodiment, the description is given of the case where the precoding matrices are switched in the time domain as an example. However, similarly to the description of other Embodiments, the case where a multi-carrier transmission scheme such as OFDM is used, and the case where the precoding matrices are switched in the time domain may be similarly implemented. In such cases, t, which is used in the present embodiment, is replaced with f (frequency ((sub) carrier)). Furthermore, the case where the precoding matrices are switched in the time-frequency domain may be similarly implemented. Note that, in the present embodiment, the precoding scheme for regularly hopping between precoding matrices is not limited to the precoding scheme that regularly hops between precoding matrices as described in the present specification. 
     Furthermore, in any one of the two patterns of setting the modulation scheme according to the present embodiment, the reception device performs demodulation and detection using the reception scheme described in the Embodiment F1. 
     Embodiment H3 
     In the present embodiment, a different scheme than that in the Embodiment H2 is described, as a precoding scheme for regularly hopping between precoding matrices that is capable of reducing the circuit size when the broadcasting (or communication) system supports both the case where the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, and the case where the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM. 
     Firstly, a description is given of the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM. 
     As the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM, the precoding scheme that regularly hops between precoding matrices as described in the Embodiments 8 and 18 is applied. Accordingly, in the precoding scheme for regularly hopping between precoding matrices, the precoding matrices F[i] over a period (cycle) of N slots are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                        
                   692 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
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                                       21 
                                     
                                     ( 
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                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
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                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   H7 
                   ) 
                 
               
             
           
         
       
     
     Here, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1). Note that θ 11 (i), θ 21 , α, λ, δ are the same as those described in the Embodiments 8 and 18 (as one preferable example, the requirements of θ 11 (i), θ 21 , α, λ, δ described in the Embodiments 8 and 18 are satisfied). Also, a unitary matrix is used as the precoding matrix for the period (cycle) of N slots. Accordingly, the precoding matrices F[i] for the period (cycle) of N slots are represented by the following Equation (i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1)). 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                        
                   693 
                 
               
               
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                                   + 
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                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   H8 
                   ) 
                 
               
             
           
         
       
     
       FIGS.  108  and  112    show a structure of the weighting (precoding) unit and its surroundings if the case where the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, and the case where the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM are both supported in the present embodiment (note that operations of  FIGS.  108  and  112    have been described in other Embodiments). 
     A description is given of s 1 ( t ) and s 2 ( t ) when the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM. 
     Since s 1 ( t ) and s 2 ( t ) are baseband signals (mapped signals) of the modulation scheme 16QAM, the mapping scheme is shown in  FIG.  94   , and g is represented by Equation 272. 
     Next, operations by components shown in  FIGS.  108  and  112    are described. 
     The power change unit ( 10701 A) receives, as inputs, the baseband signal (mapped signal)  307 A mapped according to the modulation scheme 16QAM and the control signal ( 10700 ), and outputs the signal (signal resulting from the power change:  10702 A) obtained by multiplying the baseband signal (mapped signal)  307 A mapped according to the modulation scheme 16QAM by v, where v denotes a value for performing power change and is set according to the control signal ( 10700 ). 
     The power change unit ( 10701 B) receives, as inputs, the baseband signal (mapped signal)  307 B mapped according to the modulation scheme 16QAM and the control signal ( 10700 ), and outputs the signal (power changed signal:  10702 B) obtained by multiplying the baseband signal (mapped signal)  307 B mapped according to the modulation scheme 16QAM by u, where u denotes a value for performing power change and is set according to the control signal ( 10700 ). 
     In this case, v=u=Ω, and v 2 :u 2 =1:1. As a result, data reception quality of data received by the reception device is improved. 
     The weighting unit  600  receives the signal  10702 A resulting from the power change (signal obtained by multiplying the baseband signal (mapped signal)  307 A mapped according to the modulation scheme 16QAM by v) and the signal  10702 B resulting from the power change (signal obtained by multiplying the baseband signal (mapped signal)  307 B mapped according to the modulation scheme 16QAM by u), and the information  315  regarding the weighting scheme, and based on the information  315  regarding the weighting scheme, performs precoding based on the precoding scheme that regularly hops between precoding matrices and outputs the signal  309 A (z 1 ( t )) and the signal  309 B(z 2 ( t )) resulting from the precoding. Here, letting F[t] be precoding matrices in the precoding scheme for regularly hopping between precoding matrices, the following Equation holds. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   694 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         
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                                   z 
                                   ⁢ 
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                                   z 
                                   ⁢ 
                                   2 
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                         = 
                           
                         
                           
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                                       t 
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                   ( 
                   H9 
                   ) 
                 
               
             
           
         
       
     
     If the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM, and the precoding matrices F[t] are represented by Equation H8 when the precoding scheme for regularly hopping between precoding matrices is applied, as shown in the Embodiment 18, Equation 270 is a suitable value as a. As shown in  FIG.  117   , when a is represented by Equation 270, each of z 1 ( t ) and z 2 ( t ) is a baseband signal corresponding to one of the 256 signal points on the I-Q plane. Note that  FIG.  117    only shows one example, and another arrangement of 256 signal points can be conceived in which the phase is rotated around the origin. 
     Since the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM, and since a total of 8 bits (16QAM: 4 bits and 16QAM: 4 bits) of each of z 1 ( t ) and z 2 ( t ) resulting from the weighing are transmitted, there are 256 signal points as shown in  FIG.  117   . Since the minimum Euclidian distance between the signal points is large, the reception quality of data received by the reception device is improved. 
     Next, a description is given of s 1 ( t ) and s 2 ( t ) in a case where the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM. 
     Note that s 1 ( t ) is a baseband signal (mapped signal) according to the modulation scheme QPSK, the mapping scheme is shown in  FIG.  95   , and h is represented by Equation 273. Since s 2 ( t ) is the baseband signal (mapped signal) according to the modulation scheme 16QAM, the mapping scheme is shown in  FIG.  94   , and g is represented by Equation 272. 
     Next, operations by components shown in  FIGS.  108  and  112    are described. 
     The power change unit ( 10701 A) receives, as inputs, the baseband signal (mapped signal)  307 A mapped according to the modulation scheme QPSK and the control signal ( 10700 ), and outputs the signal (signal resulting the power change:  10702 A) obtained by multiplying the baseband signal (mapped signal)  307 A mapped according to the modulation scheme QPSK by v, where v denotes a value for performing power change and is set according to the control signal ( 10700 ). 
     The power change unit ( 10701 B) receives, as inputs, the baseband signal (mapped signal)  307 B mapped according to the modulation scheme 16QAM and the control signal ( 10700 ), and outputs the signal (the signal resulting the power change:  10702 B) obtained by multiplying the baseband signal (mapped signal)  307 B mapped according to the modulation scheme 16QAM by u, where u denotes a value for performing power change and set according to the control signal ( 10700 ). 
     Here, as has been described in the Embodiment H1, it is one preferable example that a “ratio between an average QPSK power and an average 16QAM power is v 2 :u 2 =1:5 (as a result, the reception quality of data received by the reception device is improved). The following describes a precoding scheme for regularly hopping between precoding matrices here. 
     As the precoding scheme for regularly hopping between precoding matrices such that the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, the following N precoding matrices are added, in addition to the N precoding matrices of Equation H8 used when the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM. Thus, the scheme for regularly hopping between precoding matrices over a period (cycle) with 2N slots is formulated. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   695 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
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                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   H10 
                   ) 
                 
               
             
           
         
       
     
     In this case, i=N, N+1, N+2, . . . , 2N−2, 2N−1 (i being an integer in a range of N to 2N−1) (as one preferable example, the requirements of θ 11 (i), θ 21 , α, λ, and δ described in Embodiments 10 and 19 are satisfied). 
     As has been already mentioned, the precoding matrices for the precoding scheme for regularly hopping between precoding matrices over a period (cycle) with 2N slots when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM are represented by Equations H8 and 10. Equation H8 represents the precoding matrices for the precoding scheme that regularly hops between precoding matrices over a period (cycle) with N slots when the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM. Accordingly, the precoding matrices for the precoding scheme that regularly hops between precoding matrices over a period (cycle) with N slots when the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM can be used in the precoding scheme that regularly hops between precoding matrices when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM. 
     The weighting unit  600  receives the signal  10702 A resulting the power change (signal obtained by multiplying the baseband signal (mapped signal)  307 A mapped according to the modulation scheme QPSK by v) and the signal  10702 A resulting the power change (signal obtained by multiplying the baseband signal (mapped signal)  307 A mapped according to the modulation scheme by u), and the information  315  regarding the weighting scheme, and according to the information  315  regarding the weighting scheme, performs precoding based on the precoding scheme for regularly hopping between precoding matrices, and outputs the signal  309 A (z 1 ( t )) resulting from the precoding and the signal  309 B (z 2 ( t )) resulting from the precoding. Here, letting F[t] be precoding matrices in the precoding scheme for regularly hopping between precoding matrices, the following Equation holds. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   696 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         
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                   ( 
                   H11 
                   ) 
                 
               
             
           
         
       
     
     In the case where the precoding matrices F[t] are represented by Equations H8 and 10 if the precoding scheme for regularly hopping between precoding matrices is applied when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, as described in Embodiment 18, Equation 270 is a suitable value as a, similarly to the case where the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM. The reason is described below. 
       FIG.  118    shows an arrangement relation of 16 signal points of 16QAM and 4 signal points of QPSK on the I-Q plane when the transmission state is as described in the above. In  FIG.  118   , each ◯ indicates a signal point of 16QAM, and each ● indicates a signal point of QPSK. As can be seen from  FIG.  118   , 4 signal points among the 16 signal points of 16QAM coincide with the 4 signal points of QPSK. Under such circumstances, when the precoding matrices F[t] of the precoding scheme applied for regularly hopping between precoding matrices are represented by Equations H8 and 10, and when Equation 270 is α, each of z 1 ( t ) and z 2 ( t ) is a baseband signal corresponding to 64 signal points extracted from the 256 signal points illustrated in  FIG.  117    of a case where the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM. Note that  FIG.  117    only shows one example, and another arrangement of 256 signal points can be conceived in which the phase is rotated around the origin. 
     Since the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, and a total of 6 bits (QPSK: 2 bits and 16QAM: 4 bits) of each of z 1 ( t ) and z 2 ( t ) resulting from the weighing are transmitted, there are 64 signal points as above. Since the minimum Euclidian distance between these 64 signal points is large, the reception quality of data received by the reception device is improved. 
     Note that the description is given above of the case where v 2 :u 2 =1:5 when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM only as an example because this case is preferable. However, even if, under the condition v 2 &lt;u 2 , Equations H8 and 10 are used as the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, and Equation H8 is used as the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM, the reception quality might be improved in both cases. Accordingly, the present embodiment is not limited to the case where v 2 :u 2 =1:5. 
     As has been mentioned in the Embodiment F1, in the case where the above precoding scheme for regularly hopping between precoding matrices is used when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, v 2 &lt;u 2 . Here, an average power (value) of z 1 ( t ) and an average power (value) of z 2 ( t ) equal to each other, and the PAPR is reduced, whereby power consumption of the data transmission device is also reduced. 
     Furthermore, by sharing a part of the matrices in common in the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, and in the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM, the circuit size of the transmission device is reduced. Moreover, in such a case, the reception device performs demodulation based on Equations H8 and/or H10, while sharing the signal points as mentioned above. Accordingly, the sharing of a calculation unit seeking reception candidate signal points is possible, which provides an advantageous effect that the circuit size of the reception device is reduced. 
     Note that, although description has been given in the present embodiment taking Equations H8 and/or H10 as an example of the precoding scheme for regularly hopping between precoding matrices, the precoding scheme for regularly hopping between precoding matrices is not limited to the example. 
     The essential points of the present invention are described as follows.
         If the case where the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, and the case where the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM are both supported, a part of the matrices is shared in common in the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, and in the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM.   When the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM, the condition v 2 =u 2  is satisfied, and when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, the condition v 2 &lt;u 2  is satisfied.       

     Further, exemplary examples where excellent reception quality of the reception device is realized are described in the following. 
     Example 1 (the Following Two Conditions are to be Satisfied) 
     
         
         
           
             When the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM, the condition v 2 =u 2  is satisfied, and when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, the condition v 2 :u 2 =1:5 is satisfied. 
             If the case where the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, and the case where the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM are both supported, a part of the matrices is shared in common in the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, and in the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM. 
           
         
       
    
     Example 2 (the Following Two Conditions are to be Satisfied) 
     
         
         
           
             When the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM, the condition v 2 =u 2  is satisfied, and when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, the condition v 2 &lt;u 2  is satisfied. 
             As the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, Equations H8 and 10 are used, and as the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM, Equation H8 is used. 
           
         
       
    
     Example 3 (the Following Two Conditions are to be Satisfied) 
     
         
         
           
             When the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM, the condition v 2 =u 2  is satisfied, and when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, the condition v 2 :u 2 =1:5 is satisfied. 
             As the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, Equations H8 and 10 are used, and as the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM, Equation H8 is used. 
           
         
       
    
     Example 4 (the Following Two Conditions are to be Satisfied) 
     
         
         
           
             When the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM, the condition v 2 =u 2  is satisfied, and when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, the condition v 2 &lt;u 2  is satisfied. 
             As the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, Equations H8 and 10 are used, and as the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM, Equation H8 is used. Furthermore, a in Equations H8 and 10 is represented by Equation 270. 
           
         
       
    
     Example 5 (the Following Two Conditions are to be Satisfied) 
     
         
         
           
             When the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM, the condition v 2 =u 2  is satisfied, and when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, the condition v 2 :u 2 =1:5 is satisfied. 
             As the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is QPSK and the modulation scheme of s 2  is 16QAM, Equations H8 and 10 are used, and as the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is 16QAM and the modulation scheme of s 2  is 16QAM, Equation H8 is used. Furthermore, a in Equations H8 and 10 is represented by Equation 270. 
           
         
       
    
     Note that, although in the present embodiment the description is given with examples of QPSK and 16QAM as the modulation scheme, the present invention is not limited to the examples. The scope of the present embodiment may be expanded as described below. Consider the modulation scheme A and the modulation scheme B. Let a be the number of signal points on the I-Q plane of the modulation scheme A, and let b be the number of signal points on the I-Q plane of the modulation scheme B, where a&lt;b. Then, the essential points of the present invention are described as follows. 
     The following two conditions are to be satisfied. 
     If the case where the modulation scheme of s 1  is the modulation scheme A and the modulation scheme of s 2  is the modulation scheme B, and the case where the modulation scheme of s 1  is the modulation scheme B and the modulation scheme of s 2  is the modulation scheme B are both supported, a part of the precoding matrices is used in common in the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is the modulation scheme A and the modulation scheme of s 2  is the modulation scheme B, and in the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is the modulation scheme B and the modulation scheme of s 2  is the modulation scheme B.
         When the modulation scheme of s 1  is the modulation scheme B and the modulation scheme of s 2  is the modulation scheme B, the condition v 2 =u 2  is satisfied, and when the modulation scheme of s 1  is the modulation scheme A and the modulation scheme of s 2  is the modulation scheme B, the condition v 2 &lt;u 2  is satisfied.       

     Alternatively, the following two conditions are to be satisfied.
         As the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is the modulation scheme A and the modulation scheme of s 2  is the modulation scheme B, Equations H8 and 10 are used, and as the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is the modulation scheme B and the modulation scheme of s 2  is the modulation scheme B, Equation H8 is used.   When the modulation scheme of s 1  is the modulation scheme B and the modulation scheme of s 2  is the modulation scheme B, the condition v 2 =u 2  is satisfied, and when the modulation scheme of s 1  is the modulation scheme A and the modulation scheme of s 2  is the modulation scheme B, the condition v 2 &lt;u 2  is satisfied.       

     As an exemplary set of the modulation scheme A and the modulation scheme B, (modulation scheme A, modulation scheme B) is one of (QPSK, 16QAM), (16QAM, 64QAM), (64QAM, 128QAM), and (64QAM, 256QAM). 
     Meanwhile, if, in the precoding scheme for regularly hopping between precoding matrices, the following conditions are satisfied without sharing the precoding matrices, the reception quality of data received by the reception device can become even higher while priority is not placed on reducing the circuit size in the transmission and reception devices.
         As the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is the modulation scheme A and the modulation scheme of s 2  is the modulation scheme B, Equations H8 and 10 are used, and as the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is the modulation scheme B and the modulation scheme of s 2  is the modulation scheme B, Equation H8 is used. Note that, however, the value of α of the precoding matrix in Equations H8 and 10 in the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is the modulation scheme A and the modulation scheme of s 2  is the modulation scheme B is different from the value of α of the precoding matrix in Equation H8 in the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is the modulation scheme B and the modulation scheme of s 2  is the modulation scheme B.   The number of slots in the period (cycle) is N in the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is the modulation scheme B and the modulation scheme of s 2  is the modulation scheme B. On the other hand, the number of slots in the period (cycle) is 2N in the precoding scheme for regularly hopping between precoding matrices when the modulation scheme of s 1  is the modulation scheme A and the modulation scheme of s 2  is the modulation scheme B.   When the modulation scheme of s 1  is the modulation scheme B and the modulation scheme of s 2  is the modulation scheme B, the condition v 2 =u 2  is satisfied, and when the modulation scheme of s 1  is the modulation scheme A and the modulation scheme of s 2  is the modulation scheme B, the condition v 2 &lt;u 2  is satisfied.       

     As an exemplary set of the modulation scheme A and the modulation scheme B, (modulation scheme A, modulation scheme B) is one of (QPSK, 16QAM), (16QAM, 64QAM), (64QAM, 128QAM), and (64QAM, 256QAM). 
     In the present embodiment, the description is given of the case where the precoding matrices are hopped in the time domain as an example. However, as description has been given in other Embodiments, the case where a multi-carrier transmission scheme such as OFDM is used, and the case where the precoding matrices are hopped in the time domain may be similarly implemented. In such cases, t, which is used in the present embodiment, is replaced with f (frequency ((sub) carrier)). Furthermore, the case where the precoding matrices are hopped in the time-frequency domain may be similarly implemented. Note that, in the present embodiment, the precoding scheme for regularly hopping between precoding matrices is not limited to the precoding scheme for regularly hopping between precoding matrices as described in the present specification. 
     Furthermore, in any one of the two patterns of setting the modulation scheme according to the present embodiment, the reception device performs demodulation and detection using the reception scheme described in the Embodiment F1. 
     Embodiment I1 
     In the present embodiment, description is provided on the method of regularly switching between precoding matrices, which differs from that in Embodiment F1 and influences the PAPR to only a minimal extent, where the modulated signals s 1  and s 2  are each modulated with a different modulation scheme. 
     The following describes, as an example, a scheme of regularly hopping between precoding matrices that is used in the case where the average power of modulated signals subjected to QPSK mapping and the average power of modulated signals subjected to 16QAM mapping, which are to be transmitted, are set to be different from each other. 
     As explained in Embodiment F1, when the modulation scheme for the signal s 1  is QPSK and the modulation scheme for the signal s 2  is 16QAM (or the modulation scheme for the signal s 1  is 16QAM and the modulation scheme for the signal s 2  is QPSK) and the average power of the modulated signal subject to the QPSK mapping and the average power of the modulated signal subject to the 16QAM mapping are set to be different from each other, the PAPR (Peak-to-Average Power Ratio) of the transmission power amplifier provided in the transmission device may increase, depending on the precoding scheme for regularly hopping between precoding matrices used by the transmission device. The increase of the PAPR may lead to the increase in power consumption by the transmission device. 
     In response to this problem, Embodiment F1 has described that a=1 should be set in the equation of the precoding matrix to be used in the precoding scheme for regularly hopping between precoding matrices in the present specification including Embodiments 8, 9, 18, 19, C1, and C2. 
     In the present embodiment, description is provided on an example of a method of improving the data reception quality in the reception device where a=1 is set in the precoding matrix to be used in the scheme of regularly hopping between precoding matrices. 
     Here, as a precoding matrix to be used in the precoding scheme for regularly hopping between precoding matrice, a precoding matrix is used where the precoding scheme is used where α=1 is set in the equation of the precoding matrix to be used in the present specification including Embodiments 8, 9, 10, 18, 19, C1, and C2. 
     For example, the precoding matrices to be used in the precoding scheme for regularly hopping between precoding matrices should be set according to Equations #3, #14, #15, and #16 in Embodiment C1 or Equations #20, #24, #25, and #26 in Embodiment C2. Also, a=1 should be set when, for example, the precoding matrices to be used in the precoding scheme for regularly hopping between precoding matrices are generalized as shown in Equations 268 and 269 in Embodiment 18, Equations #1, #2, #9, #10, #12, and #13 in Embodiment C1, or Equations #18, #19, #21, #22, and #23 in Embodiment C2 (Note that the number of slots in the period (cycle) is not limited to an odd number). 
       FIG.  119    shows the structure of the weighting unit (precoding unit) and its surroundings in the present embodiment. In  FIG.  119   , elements that operate in a similar way to  FIGS.  3  and  107    bear the same reference signs. The following describes mapped signals  307 A and  307 B before describing  FIG.  119   . 
     In  FIG.  119   , a modulation scheme for a signal s 1 ( t ), which is the mapped signal  307 A, is QSPK, and a modulation scheme for a signal s 2 ( t ), which is the mapped signal  307 B, is 16QAM. The following describes the QPSK mapping scheme and the 16QAM mapping scheme. 
     Subsequently, description is provided on the QPSK mapping with reference to the accompanying  FIG.  95   .  FIG.  95    shows an example of a signal point layout in the I-Q plane for QPSK. Concerning the signal point  9500  in  FIG.  95   , when the bits transferred (input bits) are b 0  and b 1 , that is, when the bits transferred are indicated by (b 0 , b 1 )=(1, 0) (this value is shown in  FIG.  95   ), the coordinates in the I-Q plane corresponding thereto is denoted as (I, Q)=(−1×h, 1×h). Further, the values of coordinates I and Q in this set of coordinates indicate the mapped signals  307 A (s 1 ( t )). 
     Note that, when the bits transferred (b 0 , b 1 ) take other values than in the above, the set of coordinates (I, Q) is determined according to the values of the bits transferred (b 0 , b 1 ) and according to  FIG.  95   . Further, similar as in the above, the values of coordinates I and Q in this set indicates the mapped signals  307 A (s 1 ( t )). 
     Next, description is provided on the 16QAM mapping with reference to the accompanying  FIG.  94   .  FIG.  94    shows an example of a signal point layout in the I-Q plane for 16QAM. Concerning the signal point  9400  in  FIG.  94   , when the bits transferred (input bits) are b 0  to b 3 , that is, when the bits transferred are indicated by (b 0 , b 1 , b 2 , b 3 )=(1, 0, 0, 0) (this value is shown in  FIG.  94   ), the coordinates in the I-Q plane corresponding thereto is denoted as (I, Q)=(−3×g, 3×g). The values of coordinates I and Q in this set of coordinates indicate the mapped signals  307 B (s 2 ( t )). Note that, when the bits transferred (b 0 , b 1 , b 2 , b 3 ) take other values than in the above, the set of values I and Q is determined according to the values of the bits transferred (b 0 , b 1 , b 2 , b 3 ) and according to  FIG.  94   . Further, similar as in the above, the values of coordinates I and Q in this set indicates the mapped signals  307 B (s 2 ( t )). 
     Further, in order to equalize the average power of the signal modulated with the QPSK and the average power of the signal modulated with the 16QAM, h is represented by Equation (273), and g is represented by Equation (272). 
     In  FIG.  119   , a phase shift unit ( 11901 ) receives the mapped modulated signal  307 A (s 1 ( t ): modulated with the QPSK) and the control signal ( 10700 ) as inputs, performs phase shift on the mapped modulated signal  307 A according to the control signal ( 10700 ), and outputs a phase-shifted signal ( 11902 A). Here, when a value for phase shift is represented as e jθs , the phase-shifted signal ( 11902 A) is represented as s 1 ( t )×e jθs  (the units of θ s  are radians). 
     The power change unit ( 10701 A) receives the phase-shifted signal ( 11902 A) and the control signal ( 10700 ) as inputs, performs power change on the phase-shifted signal ( 11902 A), and outputs a power-changed signal ( 10702 A). Here, when a value for power change is set as v, the power-changed signal ( 10702 A) is represented as s 1 ( t )×e jθs ×v (where v is a real number greater than 0, and 0 radians≤θ s &lt;2π radians). 
     The power change unit ( 10701 B) receives the mapped modulated signal  307 B (s 2 ( t ): modulated with the 16QAM) and the control signal ( 10700 ) as inputs, performs power change on the mapped modulated signal  307 B, and outputs a power-changed signal ( 10702 B). Here, a value for power change is set as u, the power-changed signal ( 10702 B) is represented as s 2 ( t )×u (where u is a real number greater than 0). 
     The weighting unit  600  performs precoding on the input signals according to the precoding scheme for regularly hopping between precoding matrices based on the information  315  regarding the weighting scheme such as a scheme described in the present specification. Then, the weighting unit  600  outputs the precoded signals  309 A and  309 B. 
       FIG.  120    shows the relationship between the transmission bit (b 0 , b 1 ) and the signal point on the I-Q plane in the case where phase shift has been performed on the modulated signal  307 A subjected to QPSK mapping performed by the phase shift unit ( 11901 ) shown in  FIG.  119   . In  FIG.  120   , four white circles (◯) each represent a signal point before phase shift, and four black circles (●) each represent a signal point after phase shift, and the coordinates in the I-Q plane are such as shown in  FIG.  120   . 
     As shown in  FIG.  120   , an equation θ 5 =θ 4  holds, where, in the I-Q plane, θ 4  represents a phase formed by a line segment from a signal point of (b 0 , b 1 )=(0, 0) before phase shift to the origin and a line segment from a signal point of (b 0 , b 1 )=(0, 0) after phase shift to the origin. Here, the line segment from the signal point of (b 0 , b 1 )=(0, 0) before phase shift to the origin is set as the reference line segment, where 0 radians≤θ 4 &lt;2π radians. Also, the line segment from the signal point of (b 0 , b 1 )=(0, 0) before phase shift to the origin and the line segment from the signal point of (b 0 , b 1 )=(0, 0) after phase shift to the origin have the same length. 
     Similarly, an equation θ 5 =θ 4  holds, where θ 4  represents a phase formed by a line segment from a signal point of (b 0 , b 1 )=(0, 1) before phase shift to the origin and a line segment from a signal point of (b 0 , b 1 )=(0, 1) after phase shift to the origin. Here, the line segment from the signal point of (b 0 , b 1 )=(0, 1) before phase shift to the origin is set as the reference line segment, where 0 radians≤θ 4 &lt;2π radians. Also, the line segment from the signal point of (b 0 , b 1 )=(0, 1) before phase shift to the origin and the line segment from the signal point of (b 0 , b 1 )=(0, 1) after phase shift to the origin have the same length. 
     The same applies to the cases where (b 0 , b 1 )=(1, 0) and (1, 1). 
       FIG.  121    shows the structure of the weighting unit (precoding unit) and its surroundings, which differs from that shown in  FIG.  119   . In  FIG.  121   , elements that operate in a similar way to  FIGS.  3  and  107    bear the same reference signs. Firstly, mapped signals  307 A and  307 B are described. 
     A modulation scheme for a signal s 1 ( t ), which is the mapped signal  307 A, is QSPK, and a modulation scheme for a signal s 2 ( t ), which is the mapped signal  307 B, is 16QAM. The following describes the QPSK mapping scheme and the 16QAM mapping scheme. 
     Description is provided on the QPSK mapping with reference to the accompanying  FIG.  95   .  FIG.  95    shows an example of a signal point layout in the I-Q plane for QPSK. Concerning the signal point  9500  in  FIG.  95   , when the bits transferred (input bits) are b 0  and b 1 , that is, when the bits transferred are indicated by (b 0 , b 1 )=(1, 0) (this value is shown in  FIG.  95   ), the coordinates in the I-Q plane corresponding thereto is denoted as (I, Q)=(−1×h, 1×h). Further, the values of coordinates I and Q in this set of coordinates indicate the mapped signals  307 A (s 1 ( t )). Note that, when the bits transferred (b 0 , b 1 ) take other values than in the above, the set of coordinates (I, Q) is determined according to the values of the bits transferred (b 0 , b 1 ) and according to  FIG.  95   . Further, similar as in the above, the values of coordinates I and Q in this set indicates the mapped signals  307 A (s 1 ( t )). 
     Next, description is provided on the 16QAM mapping with reference to the accompanying  FIG.  94   .  FIG.  94    shows an example of a signal point layout in the I-Q plane for 16QAM. Concerning the signal point  9400  in  FIG.  94   , when the bits transferred (input bits) are b 0  to b 3 , that is, when the bits transferred are indicated by (b 0 , b 1 , b 2 , b 3 )=(1, 0, 0, 0) (this value is shown in  FIG.  94   ), the coordinates in the I-Q plane corresponding thereto is denoted as (I, Q)=(−3×g, 3×g). The values of coordinates I and Q in this set of coordinates indicate the mapped signals  307 B (s 2 ( t )). Note that, when the bits transferred (b 0 , b 1 , b 2 , b 3 ) take other values than in the above, the set of values I and Q is determined according to the values of the bits transferred (b 0 , b 1 , b 2 , b 3 ) and according to  FIG.  94   . Further, similar as in the above, the values of coordinates I and Q in this set indicates the mapped signals  307 B (s 2 ( t )). 
     Further, in order to equalize the average power of the signal modulated with the QPSK and the average power of the signal modulated with the 16QAM, h is represented by Equation (273), and g is represented by Equation (272). 
     The power change unit ( 10701 A) receives the mapped modulated signal  307 A (s 1 ( t ): modulated with the QPSK) and the control signal ( 10700 ) as inputs, performs power change on the mapped modulated signal  307 A (s 1 ( t )) according to the control signal ( 10700 ), and outputs a power-changed signal ( 10702 A). Here, a value for power change is set as v, the power-changed signal ( 10702 A) is represented as s 1 ( t )×v (where v is a real number greater than 0). 
     The power change unit ( 10701 B) receives the mapped modulated signal  307 B (s 2 ( t ): modulated with the 16QAM) and the control signal ( 10700 ) as inputs, performs power change on the mapped modulated signal  307 B, and outputs a power-changed signal ( 10702 B). Here, a value for power change is set as u, the power-changed signal ( 10702 B) is represented as s 2 ( t )×u (where u is a real number greater than 0). 
     The phase shift unit ( 12101 ) receives the power-changed signal ( 10702 A) (s 1 ( t )×v: modulated with the QPSK) and the control signal ( 10700 ) as inputs, performs phase shift on the power-changed signal ( 10702 A) according to the control signal ( 10700 ), and outputs a phase-shifted signal ( 12102 A). Here, when a value for phase shift is represented as e jθs , the phase-shifted signal ( 12102 A) is represented as s 1 ( t )×v×e jθs  (the units of θ s  are radians, and 0 radians≤0 s &lt;2π radians). 
     The weighting unit  600  performs precoding on the input signals according to the precoding scheme for regularly hopping between precoding matrices based on the information  315  regarding the weighting scheme such as a scheme described in the present specification. Then, the weighting unit  600  outputs the precoded signals  309 A and  309 B. 
       FIG.  122    shows the relationship between the transmission bit (b 0 , b 1 ) and the signal point on the plane in the case where phase shift has been performed on the power-changed signal ( 10702 A) (s 1 ( t )×v: modulated with the QPSK) performed by the phase shift unit ( 12101 ) shown in  FIG.  121   . In  FIG.  122   , four white circles (◯) each represent a signal point before phase shift, and four black circles (●) each represent a signal point after phase shift, and the coordinates in the plane are such as shown in  FIG.  122   . 
     As shown in  FIG.  122   , an equation θ s =θ 4  holds, where, in the plane, θ 4  represents a phase formed by a line segment from a signal point of (b 0 , b 1 )=(0, 0) before phase shift to the origin and a line segment from a signal point of (b 0 , 1)=(0, 0) after phase shift to the origin. Here, the line segment from the signal point of (b 0 , b 1 )=(0, 0) before phase shift to the origin is set as the reference line segment, where 0 radians≤θ 4 &lt;2π radians. Also, the line segment from the signal point of (b 0 , b 1 )=(0, 0) before phase shift to the origin and the line segment from the signal point of (b 0 , b 1 )=(0, 0) after phase shift to the origin have the same length. 
     Similarly, an equation θ s =θ 4  holds, where θ 4  represents a phase formed by a line segment from a signal point of (b 0 , b 1 )=(0, 1) before phase shift to the origin and a line segment from a signal point of (b 0 , b 1 )=(0, 1) after phase shift to the origin. Here, the line segment from the signal point of (b 0 , b 1 )=(0, 1) before phase shift to the origin is set as the reference line segment, where 0 radians≤θ 4 &lt;2π radians. Also, the line segment from the signal point of (b 0 , b 1 )=(0, 1) before phase shift to the origin and the line segment from the signal point of (b 0 , b 1 )=(0, 1) after phase shift to the origin have the same length. 
     The same applies to the cases where (b 0 , b 1 )=(1, 0) and (1, 1).  FIG.  120    and  FIG.  122    differ from each other in coordinates of the signal point in the I-Q plane. 
     The following describes how the phase shift unit  11901  shown in  FIG.  119    and the phase shift unit  12101  shown in  FIG.  121    perform phase shift on, that is, set θ 4  in, signals s 1 ( t ) and s 2 ( t ) in the case where the signal s 1 ( t ) that is the mapped signal  307 A is modulated with the QSPK and the signal s 2 ( t ) that is the mapped signal  307 A is modulated with the 16QAM. 
     In the operations such as described above in  FIG.  119    and  FIG.  121   , a value to be multiplied for power change on the QPSK modulated signal is v, and a value to be multiplied for power change on the 16QAM modulated signal is u. Embodiment F1 has described the scheme for satisfying v 2 :u 2 =1:5 in order to equalize the minimum Euclidian distance between signal points in the I-Q plane for the QPSK and the minimum Euclidian distance between signal points in the I-Q plane for the 16QAM. The following describes the scheme for setting  04  under the condition that v 2 :u 2 =1:5 is satisfied, as an example. 
     Here, assume that, in the present specification including Embodiments 8, 9, 10, 18, 19, C1, and C2, as a precoding matrix to be used in the precoding scheme for regularly hopping between precoding matrice, when α=1 is set in the equation of the precoding matrix to be used in the precoding scheme for regularly hopping between precoding matrices. In this case, when θ 4  is set as one of 0 radians, π/2 radians, π radians, and (3×π)/2 radians, the signals z 1 ( t ) and z 2 ( t ) are each a baseband signal corresponding to one of the 25 signal points in the I-Q plane such as shown in  FIG.  123   . 
     The signals z 1 ( t ) and z 2 ( t ) are each a signal obtained by weighting a signal modulated with the QPSK and a signal modulated with the 16QAM. The total of 6 bits are transferred since the weighted and combined signals z 1 ( t ) and z 2 ( t ) are transmitted as 2 bits according to the QPSK, and 4 bits according to the 16QAM, respectively. Therefore, in the case where there is no coincidence between signal points, the number of signal points is 64. However, in  FIG.  123   , since there is a coincidence between the signal points, the number of signal points reduces to 25. 
     The signals z 1 ( t ) and z 2 ( t ) are each transmitted from a different antenna as shown in  FIG.  5   . Here, the case is considered where the signals transmitted from one of the two transmit antennas are not transmitted to the reception device of the terminal. Under such circumstances, if the signal is transmitted in signal points in the I-Q plane such as shown in  FIG.  123   , the total 6 bits includes a bit whose an absolute value of log-likelihood ratio is zero (because the number of signal points reduces from 64 to 25). 
     As a result, the reception device sometimes cannot properly perform error correction decoding, and such a case deteriorates the reception quality of data in the reception device. In order to solve this problem, the number of each of the signals z 1 ( t ) and z 2 ( t ) in the I-Q plane needs to be 64 (=2 6 ), and needs to be a baseband signal corresponding to one of the 64 signal points in the I-Q plane. 
     In view of this, when θ 4  is set as one of π/6 radians, π/3 radians, (2×π)/3 radians, (5×π)/6 radians, (7×π)/6 radians, (4×π)/3 radians, (5×π)/3 radians, and (11×π)/6 radians, the signals z 1 ( t ) and z 2 ( t ) are each a baseband signal corresponding to one of the 64 signal points in the I-Q plane such as shown in  FIG.  124   . 
     Note that, when generalized, θ 4  is set as one of π/6+n×π radians, π/3+n×π radians, (2×π)/3+n×π radians, and (5×π)/6+n×π radians (n is an integer). 
     In this case, the minimum Euclidian distance between the 64 signal points in the I-Q plane is the maximum under the conditions that the average power (average value) of the signal z 1 ( t ) and the average power (average value) of the signal z 2 ( t ) are constant. 
     Accordingly, when θ 4  is set as such a value such as shown above, there is a high possibility of distinguishing between the 64 signal points even under the situation where the signals transmitted from one of the two transmit antennas are not transmitted to the reception device of the terminal. This increases a possibility of achieving an excellent data reception quality in the reception device. In the above description, an example is used under the condition that v 2 :u 2 =1:5 is satisfied. In the situation where the signals transmitted from one of the two transmit antennas are not transmitted to the reception device, there is a high possibility of achieving an excellent data reception quality in the reception device. However, in other radio wave propagation environment, there is sometimes a high possibility of achieving an excellent data reception quality in the reception device under the conditions that v 2 &lt;u 2  is satisfied but v 2 :u 2 =1:5 is not satisfied. Accordingly, in a plurality of radio wave propagation environments, there is a high possibility of achieving an excellent data reception quality in the reception device under the conditions that v 2 &lt;u 2  is satisfied and θ 4  is one of π/6 radians, π/3 radians, (2×π)/3 radians, (5×π)/6 radians, (7×π)/6 radians, (4×π)/3 radians, (5×π)/3 and (11×π)/6 radians (that is, θ 4  is one of π/6+n×π radians, π/3+n×π radians, (2×π)/3+n×π radians, and (5×π)/6+n×π radians (n is an integer)). However, there is a possibility of achieving an excellent data reception quality by setting θ 4  as a value other than four values of 0 radians, 3π/2 radians, π radians, and (3π)/2 radians. 
     Furthermore, in the present specification including Embodiments 8, 9, 10, 18, 19, C1, and C2, α≠1 is set and v 2 &lt;u 2  is satisfied, there is a possibility of achieving an excellent data reception quality by setting θ 16  as a value other than four values of 0 radians, 3π/2 radians, π radians, and (3π)/2 radians in the equation of the precoding matrix to be used in the precoding scheme for regularly hopping between precoding matrices. 
     The description has been made on the case where phase shift is performed on the QPSK modulated signal. Alternatively, phase shift may be performed on a 16QAM modulated signal. The following describes a case where phase shift is performed on a 16QAM modulated signal. 
       FIG.  125    shows the structure of a weighting unit (precoding unit) and its surroundings in the present embodiment. In  FIG.  125   , elements that operate in a similar way to  FIGS.  3  and  107    bear the same reference signs. 
     In  FIG.  125   , a modulation scheme for a signal s 1 ( t ), which is the mapped signal  307 A, is QSPK, and a modulation scheme for a signal s 2 ( t ), which is the mapped signal  307 B, is 16QAM. The signals s 1 ( t ) and s 2 ( t ) in this case are the same as those shown in  FIG.  119   , and accordingly explanation thereof is to be omitted in the following. 
     In  FIG.  125   , the phase shift unit ( 11901 ) receives the mapped modulated signal  307 B (s 2 ( t ): modulated with the 16QAM) and the control signal ( 10700 ) as inputs, performs phase shift on the mapped modulated signal  307 B according to the control signal ( 10700 ), and outputs a phase-shifted signal ( 11902 B). Here, when a value for phase shift is represented as e θs , the phase-shifted signal ( 11902 B) is represented as s 2 ( t )×e θs  (the units of θ s  are radians). 
     The power change unit ( 10701 A) receives the mapped modulated signal ( 307 A) and the control signal ( 10700 ) as inputs, performs power change on the mapped modulated signal ( 307 A), and outputs a power-changed signal ( 10702 A). Here, a value for power change is set as v, the power-changed signal ( 10702 A) is represented as s 1 ( t )×v (where v is a real number greater than 0). 
     The power change unit ( 10701 B) receives the phase-shifted signal ( 11902 B) and the control signal ( 10700 ) as inputs, performs power change on the phase-shifted signal ( 11902 B), and outputs a power-changed signal ( 10702 B). Here, a value for power change is set as u, the power-changed signal ( 10702 B) is represented as s 2 ( t )×e jθs ×u (where u is a real number greater than 0, and 0 radians≤e θs &lt;2π radians). 
     The weighting unit  600  performs precoding on the input signals according to the precoding scheme for regularly hopping between precoding matrices based on the information  315  regarding the weighting scheme such as a scheme described in the present specification. Then, the weighting unit  600  outputs the precoded signals  309 A and  309 B. 
       FIG.  126    shows the relationship between the transmission bit (b 0 , b 1 , b 2 , b 3 ) and the signal point on the I-Q plane in the case where phase shift has been performed on the modulated signal  307 B subjected to 16QAM mapping performed by the phase shift unit ( 11901 ) shown in  FIG.  125   . In  FIG.  126   , 16 white circles (◯) each represent a signal point before phase shift, and 16 black circles (●) each represent a signal point after phase shift, and the coordinates in the I-Q plane are such as shown in  FIG.  126   . 
     As shown in  FIG.  126   , an equation θ s =θ 16  holds, where, in the I-Q plane, θ 16  represents a phase formed by a line segment from a signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 0) before phase shift to the origin and a line segment from a signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 0) after phase shift to the origin. Here, the line segment from the signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 0) before phase shift to the origin is set as the reference line segment, where 0 radians≤θ 16 &lt;2π radians. Also, the line segment from the signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 0) before phase shift to the origin and the line segment from the signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 0) after phase shift to the origin have the same length. 
     Similarly, an equation θ s =θ 16  holds, where θ 16  represents a phase formed by a line segment from a signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 1) before phase shift to the origin and a line segment from a signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 1) after phase shift to the origin. Here, the line segment from the signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 1) before phase shift to the origin is set as the reference line segment, where 0 radians≤θ 16 &lt;2π radians. Also, the line segment from the signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 1) before phase shift to the origin and the line segment from the signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 1) after phase shift to the origin have the same length. 
     The same applies to the cases where (b 0 , b 1 , b 2 , b 3 )=(0, 0, 1, 0) to (1, 1, 1, 1). 
       FIG.  127    shows the structure of a weighting unit (precoding unit) and its surroundings, which differs from that shown in  FIG.  125   . In  FIG.  127   , elements that operate in a similar way to  FIGS.  3  and  107    bear the same reference signs. The mapped signals  307 A and  307 B are the same as those as described above, and accordingly explanation thereof is to be omitted in the following. 
     The power change unit ( 10701 A) receives the mapped modulated signal  307 A (s 1 ( t ): modulated with the QPSK) and the control signal ( 10700 ) as inputs, performs power change on the mapped modulated signal  307 A (s 1 ( t )) according to the control signal ( 10700 ), and outputs a power-changed signal ( 10702 A). Here, a value for power change is set as v, the power-changed signal ( 10702 A) is represented as s 1 ( t )×v (where v is a real number greater than 0). 
     The power change unit ( 10701 B) receives the mapped modulated signal  307 B (s 2 ( t ): modulated with the 16QAM) and the control signal ( 10700 ) as inputs, performs power change on the mapped modulated signal  307 B, and outputs a power-changed signal ( 10702 B). Here, a value for power change is set as u, the power-changed signal ( 10702 B) is represented as s 2 ( t )×u (where u is a real number greater than 0). 
     The phase shift unit ( 12101 ) receives the power-changed signal ( 10702 B) (s 2 ( t )xu: modulated with the 16QAM) and the control signal ( 10700 ) as inputs, performs phase shift on the power-changed signal ( 10702 B) according to the control signal ( 10700 ), and outputs a phase-shifted signal ( 12102 B). Here, when a value for phase shift is represented as ejθs, the phase-shifted signal ( 12102 A) is represented as s 1 ( t )×v×e jθs  (the units of θs are radians, and 0 radians≤θ s &lt;2π radians). 
     The weighting unit  600  performs precoding on the input signals according to the precoding scheme for regularly hopping between precoding matrices based on the information  315  regarding the weighting scheme such as a scheme described in the present specification. Then, the weighting unit  600  outputs the precoded signals  309 A and  309 B. 
       FIG.  128    shows the relationship between the transmission bit (b 0 , b 1 , b 2 , b 3 ) and the signal point on the I-Q plane in the case where phase shift has been performed on the power-changed signal ( 10702 B) (s 2 ( t )×u: modulated with the 16QAM) performed by the phase shift unit ( 12101 ) shown in  FIG.  125   . In  FIG.  128   , 16 white circles (◯) each represent a signal point before phase shift, and 16 black circles (●) each represent a signal point after phase shift, and the coordinates in the I-Q plane are such as shown in  FIG.  128   . 
     As shown in  FIG.  128   , an equation θ s =θ 16  holds, where, in the I-Q plane, θ 16  represents a phase formed by a line segment from a signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 0) before phase shift to the origin and a line segment from a signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 0) before phase shift to the origin. Here, the line segment from the signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 0) before phase shift to the origin is set as the reference line segment, where 0 radians≤θ 16 &lt;2π radians. Also, the line segment from the signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 0) before phase shift to the origin and the line segment from the signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 0) after phase shift to the origin have the same length. 
     Similarly, an equation θ s =θ 16  holds, where θ 16  represents a phase formed by a line segment from a signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 1) before phase shift to the origin and a line segment from a signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 1) after phase shift to the origin. Here, the line segment from the signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 1) before phase shift to the origin is set as the reference line segment, where 0 radians≤θ 16 &lt;2π radians. Also, the line segment from the signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 1) before phase shift to the origin and the line segment from the signal point of (b 0 , b 1 , b 2 , b 3 )=(0, 0, 0, 1) after phase shift to the origin have the same length. 
     The same applies to the cases where (b 0 , b 1 , b 2 , b 3 )=(0, 0, 1, 0) to (1, 1, 1, 1).  FIG.  126    and  FIG.  128    differ from each other in coordinates of the signal point in the I-Q plane. 
     The following describes how the phase shift unit  12501  shown in  FIG.  119    and the phase shift unit  12701  shown in  FIG.  121    perform phase shift on, that is, set θ 16  in, signals s 1 ( t ) and s 2 ( t ) in the case where the signal s 1 ( t ) that is the mapped signal  307 A is modulated with the QSPK and the signal s 2 ( t ) that is the mapped signal  307 A is modulated with the 16QAM. 
     In the operations such as described above in  FIG.  125    and  FIG.  127   , a value to be multiplied for power change on the QPSK modulated signal is v, and a value to be multiplied for power change on the 16QAM modulated signal is u. Embodiment F1 has described the scheme for satisfying v 2 :u 2 =1:5 in order to equalize the minimum Euclidian distance between signal points in the I-Q plane for the QPSK and the minimum Euclidian distance between signal points in the I-Q plane for the 16QAM. The following describes the scheme for setting θ 16  under the condition that v 2 :u 2 =1:5 is satisfied as an example. 
     Here, assume that, in the present specification including Embodiments 8, 9, 10, 18, 19, C1, and C2, as a precoding matrix to be used in the precoding scheme for regularly hopping between precoding matrice, when α=1 is set in the equation of the precoding matrix to be used in the precoding scheme for regularly hopping between precoding matrices. In this case, when θ 16  is set as one of 0 radians, π/2 radians, π radians, and (3×π)/2 radians, the signals z 1 ( t ) and z 2 ( t ) are each a baseband signal corresponding to one of the 25 signal points in the I-Q plane such as shown in  FIG.  123   . 
     The signals z 1 ( t ) and z 2 ( t ) are each a signal obtained by weighting a signal modulated with the QPSK and a signal modulated with the 16QAM. The total of 6 bits are transferred since the weighted and combined signals z 1 ( t ) and z 2 ( t ) are transmitted as 2 bits according to the QPSK, and 4 bits according to the 16QAM, respectively. Therefore, in the case where there is no coincidence between signal points, the number of signal points is 64. However, in  FIG.  123   , since there is a coincidence between the signal points, the number of signal points reduces to 25. 
     The signals z 1 ( t ) and z 2 ( t ) are each transmitted from a different antenna as shown in  FIG.  5   . Here, the case is considered where the signals transmitted from one of the two transmit antennas are not transmitted to the reception device of the terminal. Under such circumstances, if the signal is transmitted in signal points in the I-Q plane such as shown in  FIG.  123   , the total 6 bits includes a bit whose an absolute value of log-likelihood ratio is zero (because the number of signal points reduces from 64 to 25). 
     As a result, the reception device sometimes cannot properly perform error correction decoding, and such a case deteriorates the reception quality of data in the reception device. In order to solve this problem, the number of each of the signals z 1 ( t ) and z 2 ( t ) in the I-Q plane needs to be 64 (=2 6 ), and needs to be a baseband signal corresponding to one of the 64 signal points in the I-Q plane. 
     In view of this, when θ 16  is set as one of π/6 radians, π/3 radians, (2×π)/3 radians, (5×π)/6 radians, (7×π)/6 radians, (4×π)/3 radians, (5×π)/3 radians, and (11×π)/6 radians, the signals z 1 ( t ) and z 2 ( t ) are each a baseband signal corresponding to one of the 64 signal points in the I-Q plane such as shown in  FIG.  124   . 
     Note that, when generalized, θ 4  is set as one of π/6+n×π radians, π/3+n×π radians, (2×π)/3+n×π radians, and (5×π)/6+n×π radians (n is an integer). 
     In this case, the minimum Euclidian distance between the 64 signal points in the I-Q plane is the maximum under the conditions that the average power (average value) of the signal z 1 ( t ) and the average power (average value) of the signal z 2 ( t ) are constant. 
     Accordingly, when θ 16  is set as such a value such as shown above, there is a high possibility of distinguishing between the 64 signal points even under the situation where the signals transmitted from one of the two transmit antennas are not transmitted to the reception device. This increases a possibility of achieving an excellent data reception quality in the reception device. In the above description, an example is used under the condition that v 2 :u 2 =1:5 is satisfied. In the situation where the signals transmitted from one of the two transmit antennas are not transmitted to the reception device, there is a high possibility of achieving an excellent data reception quality in the reception device. However, in other radio wave propagation environment, there is sometimes a high possibility of achieving an excellent data reception quality in the reception device under the conditions that v 2 &lt;u 2  is satisfied but v 2 :u 2 =1:5 is not satisfied. Accordingly, in a plurality of radio wave propagation environments, there is a high possibility of achieving an excellent data reception quality in the reception device under the conditions that v 2 &lt;u 2  is satisfied and θ 16  is one of π/6 radians, π/3 radians, (2×π)/3 radians, (5×π)/6 radians, (7×π)/6 radians, (4×π)/3 radians, (5×π)/3 and (11×π)/6 radians (that is, θ4 is one of π/6+n×π radians, π/3+n×π radians, (2×π)/3+n×π radians, and (5×π)/6+n×π radians (n is an integer)). However, there is a possibility of achieving an excellent data reception quality by setting θ 16  as a value other than four values of 0 radians, 3π/2 radians, π radians, and (3π)/2 radians. 
     Furthermore, in the present specification including Embodiments 8, 9, 10, 18, 19, C1, and C2, α≠1 is set and v 2 &lt;u 2  is satisfied, there is a possibility of achieving an excellent data reception quality by setting θ 16  as a value other than four values of 0 radians, 3π/2 radians, π radians, and (3π)/2 radians in the equation of the precoding matrix to be used in the precoding scheme for regularly hopping between precoding matrices. 
     Next, operations of the reception device in the present embodiment are described. 
     In the case where the above-mentioned method for regularly hopping between precoding matrices shown in  FIG.  119    and  FIG.  121    is applied, the following relationship is derived from  FIG.  5   . 
     
       
         
           
             
               
                 
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     In the case where the above-mentioned method for regularly hopping between precoding matrices shown in  FIG.  125    and  FIG.  127    is applied, the following relationship is derived from  FIG.  5   . 
     
       
         
           
             
               
                 
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     Note that F[t] is a precoding matrix utilizing a parameter time t when applied for the precoding scheme for regularly hopping between precoding matrices. The reception device performs demodulation (detection) of signals by utilizing the relation between the signals r 1 ( t ) and r 2 ( t ) and the relation between the signals s 1 ( t ) and s 2 ( t ) mentioned above (that is, demodulation is to be performed in the same manner as explanation has been provided in Embodiments 1 and A1 to A5 and the like). However, the above equations do not take into consideration such distortion components as noise components, frequency offsets, and channel estimation errors, and thus, the demodulation (detection) is performed with such distortion components included in the signals. As for the values u and v used by the transmission device in performing power change, the transmission device may transmit information concerning such information or otherwise, the transmission device may transmit information concerning the transmission mode applied (such as transmission scheme, modulation scheme, and error correction scheme). 
     In the present embodiment, the hopping between the precoding matrices is performed in the time domain. However, when a multi-carrier transmission scheme such as an OFDM scheme is used, the present invention is applicable to the case where the hopping between the precoding matrices is performed in the frequency domain, as described in other embodiments. If this is the case, t used in the present embodiment is to be replaced with f (frequency ((sub) carrier)). 
     Accordingly, in the case of performing the hopping between the precoding matrices in the time domain, the signals z 1 ( t ) and z 2 ( t ) at the same time point are each transmitted from a different antenna by using the same frequency. On the other hand, in the case of performing the hopping between the precoding matrices in the frequency domain, the signals z 1 ( f ) and z 2 ( f ) at the same frequency (the same subcarrier) are each transmitted from a different antenna at the same time point. 
     Also, even in the case of performing the hopping between the precoding matrices in the time and frequency domains, the present invention is applicable as described in other embodiments. Note that, in the present embodiment, the precoding scheme for regularly hopping between precoding matrices is not limited to the precoding scheme for regularly hopping between precoding matrices as described in the present specification. Furthermore, even when the precoding matrices are fixed (according to a scheme in which the precoding matrices are not represented by F(t) (i.e. not a function of t (or f)), and settings of the average power of the signal s 1 ( t ) and the average power of the signal s 2 ( t ) and phase shift on mapped signals as described in the present embodiment are applied, there is a possibility of achieving an effect of improvement in the data reception quality in the reception device. 
     In the present embodiment, the phase shift unit is shown in  FIGS.  119  and  125   . Alternatively, the mapping unit shown in  FIGS.  3 ,  4 ,  13 ,  40   , and the like may output mapped signals on which phase shift has been performed in  FIGS.  119  and  125    instead of providing the phase shift unit. The description on this has already been made in Embodiment 1. 
     In the present embodiment, N-slot period (cycle) is used as a period (cycle) for the precoding hopping scheme (the method for regularly hopping between precoding matrices), F[0], F[1], F[2], . . . , F[N−2], F[N−1] are prepared as N different precoding matrices. The symbols are arranged in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1] in the time domain in the single carrier transmission scheme. However, this is not the only example, and N different precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1] generated in the present embodiment may be applied to a multi-carrier transmission scheme such as an OFDM transmission scheme. As in Embodiment 1, as a method of applying this, precoding weights can be changed by arranging symbols in the frequency domain or in the frequency-time domains. Note that a precoding hopping scheme with N-slot period (cycle) has been described, but the same advantageous effects may be obtained by randomly using N different precoding matrices. In other words, the N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     Embodiment 12 
     Embodiments F1 and I1 have described the method for regularly hopping between precoding matrices in the case where the signals s 1  and s 2  are modulated with the QPSK and the 16QAM, respectively (or the 16QAM and the QPSK, respectively). The present embodiment describes a method for regularly hopping between precoding matrices in the case the signals s 1  and s 2  are modulated with the 8QAM (8 Quadrature Amplitude Modulation) on the assumption that a data transmission speed equivalent to that in the case where the signals s 1  and s 2  are modulated with the QPSK and 16QAM modulation schemes, respectively. 
     In the present embodiment, the precoding scheme for regularly hopping between precoding matrices described in Embodiments 9 and 18 is applied. In the present embodiment, s 1  and s 2  are modulated with the 8QAM in the description in Embodiments 9 and 18.  FIG.  129    shows a signal point layout in the I-Q plane for 8QAM. In  FIG.  129   , when the average transmission power is set as z, a value of u is defined by the following Equation. 
     
       
         
           
             
               
                 
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                   ⁢ 
                       
                   #I3 
                 
               
             
           
         
       
     
     A coefficient for the average power of the QPSK modulated signal set as z is given in Equation 273. A coefficient for the average power of the 16QAM modulated signal set as z is given in Equation 272. A coefficient for the average power of the 64QAM modulated signal set as z is given in Equation 481. The transmission device can select the QPSK, the 16QAM, the 64QAM, or the 8QAM as a modulation scheme. Equation #I3 is important for equalizing the average power of the 8QAM modulated signal, the average power of the QPSK modulated signal, the 16QAM modulated signal, and the 64QAM modulated signal. 
     In  FIG.  129   , b 0 , b 1 , and b 2  that are 3 bits to be transmitted satisfy “b 0  b 1  b 2 ”=“000”, a point  12901  is selected as a signal point, and I, Q (I=1×u, Q=1×u) corresponding to the signal point  12901  are an in-phase component (I) and a quadrature component (Q) of an 8QAM signal, respectively. In the case where “b 0  b 1  b 2 ” satisfy “001” to “111”, an in-phase component (I) and a quadrature component (Q) of an 8QAM signal are generated, in the same way. 
     The following describes a method for regularly hopping between precoding matrices in the case where the signals s 1  and s 2  are modulated with the 8QAM (Note that the method for regularly hopping between precoding matrices in the present embodiment has been described in Embodiments 9 and 18). 
     As described in Embodiment 8, in the scheme for regularly hopping between precoding matrices in N-slot period (cycle) (N is a natural number), the precoding matrices F[i] (i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1)) prepared for N-slot period (cycle) with reference to Equations 82 to 85 are defined in the following equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   700 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         i 
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   δ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #I4 
                 
               
             
           
         
       
     
     In this case, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1) (let α&gt;0). Since a unitary matrix is used in the present embodiment, the precoding matrices in Equation I4 may be represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   701 
                 
               
               
                  
               
             
             
               
                 
                   
                     F 
                     [ 
                     i 
                     ] 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             α 
                             2 
                           
                           + 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     θ 
                                     11 
                                   
                                   ( 
                                   i 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         i 
                                         ) 
                                       
                                       + 
                                       λ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               α 
                               × 
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               e 
                               
                                 j 
                                 ( 
                                   
                                 
                                   
                                     
                                       θ 
                                       21 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                   + 
                                   λ 
                                   + 
                                   π 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #I5 
                 
               
             
           
         
       
     
     Here, i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1) (let a&gt;0). As described in Embodiment 18, the Conditions 53, 54, 55, and 56 should be satisfied for achieving excellent data reception quality (note that all these conditions do not necessarily need to be satisfied). 
     The following describes an example of an appropriate value of α in the case where the precoding matrix to be used in scheme of regularly hopping between precoding matrices is represented as Equation I5. 
     As described in Embodiment I1, precoded signals obtained by performing precoding are represented as the signals z 1 ( t ) and z 2 ( t ) (t: time). Here, the signals z 1 ( t ) and z 2 ( t ) are at the same frequency (the same (sub) carrier), and are each transmitted from a different antenna (Although signals in the time domain are described as an example here, the signals may be z 1 ( f ) and z 2 ( f ) (f: (sub) carrier) as described in Embodiment I1, which are the signals at the same time and are each transmitted from a different antenna). 
     The signals z 1 ( t ) and z 2 ( t ) are each a signal obtained by weighting signals modulated with the 8QAM. The total of 6 bits are transferred since the weighted signals z 1 ( t ) and z 2 ( t ) are transmitted as 3 bits in two parts according to the 8QAM. Therefore, in the case where there is no coincidence between signal points, the number of signal points is 64. 
       FIG.  130    shows an example of signal points of the precoded signals z 1 ( t ) and z 2 ( t ) in the I-Q plane for QPSK when a=3/2 (or  2 / 3 ) is satisfied, which is an example of an appropriate value of α, is used in Equation I5. As shown in  FIG.  130   , when α=3/2 (or 2/3) is satisfied, the distance between each adjacent signals is mostly equal. Accordingly, the 64 signal points are closely arranged in the I-Q plane. 
     The signals z 1 ( t ) and z 2 ( t ) are each transmitted from a different antenna as shown in  FIG.  5   . Here, the case is considered where the signals transmitted from one of the two transmit antennas are not transmitted to the reception device of the terminal. In  FIG.  130   , reduction of signal points such as described in Embodiment I1 does not occur, and the 64 signal points are closely arranged in the I-Q plane. Accordingly, the reception device achieves a high data reception quality as a result of detection and error correction decoding. 
     Next, the following describes the 8QAM for signals arranged in a different way from that shown in  FIG.  129   . Here, the precoding scheme for regularly hopping between precoding matrices described in Embodiments 9 and 18 is applied. The signals s 1  and s 2  are modulated with the 8QAM.  FIG.  131    shows a signal point layout in the I-Q plane for 8QAM which differs from that shown in  FIG.  129   . In  FIG.  131   , when the average transmission power is set as z, a value of v is defined by the following Equation. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   702 
                 
               
               
                  
               
             
             
               
                 
                   v 
                   = 
                   
                     z 
                     × 
                     
                       2 
                       
                         11 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #I6 
                 
               
             
           
         
       
     
     A coefficient for the average power of the QPSK modulated signal set as z is given in Equation 273. A coefficient for the average power of the 16QAM modulated signal set as z is given in Equation 272. A coefficient for the average power of the 64QAM modulated signal set as z is given in Equation 481. The transmission device can select the QPSK, the 16QAM, the 64QAM, or the 8QAM as a modulation scheme. Equation I6 is important for equalizing the average power of the 8QAM modulated signal, the average power of the QPSK modulated signal, the 16QAM modulated signal, and the 64QAM modulated signal. 
     In  FIG.  131   , b 0 , b 1 , b 2  that are 3 bits to be transmitted satisfy “b 0  b 1  b 2 ”=“000”, a point  13101  is selected as a signal point, and I, Q (I=2×v, Q=2×v) corresponding to the signal point  13101  are an in-phase component (I) and a quadrature component (Q) of an 8QAM signal, respectively. In the case where “b 0  b 1  b 2 ” satisfy “001” to “111”, an in-phase component (I) and a quadrature component (Q) of an 8QAM signal are generated, in the same way. 
     The following describes a method for regularly hopping between precoding matrices in the case where the signals s 1  and s 2  are modulated with the 8QAM (Note that the method for regularly hopping between precoding matrices in the present embodiment has been described in Embodiments 9 and 18). 
     As described in Embodiment 8, in the scheme for regularly hopping between precoding matrices in N-slot period (cycle) (N is a natural number), the precoding matrices F[i] (i=0, 1, 2, . . . , N−2, N−1 (i being an integer in a range of 0 to N−1)) prepared for N-slot period (cycle) with reference to Equations 82 to 85 are defined in the above Equation I4. 
     Since a unitary matrix is used in the present embodiment, the precoding matrices in Equation I4 may be represented by Equation I5. 
     As described in Embodiment 18, the Conditions 53, 54, 55, and 56 should be satisfied for achieving excellent data reception quality (note that all these conditions do not necessarily need to be satisfied). 
     The following describes an example of an appropriate value of α in the case where the precoding matrix to be used in scheme of regularly hopping between precoding matrices is represented as Equation I5. 
     As described in Embodiment I1, precoded signals obtained by performing precoding are represented as z 1 ( t ) and z 2 ( t ) (t: time). Here, the signals z 1 ( t ) and z 2 ( t ) are at the same frequency (the same (sub) carrier), and are each transmitted from a different antenna (Although signals in the time domain are described as an example here, the signals may be z 1 ( f ) and z 2 ( f ) (f: (sub) carrier) as described in Embodiment I1, which are the signals at the same time and are each transmitted from a different antenna). 
     The signals z 1 ( t ) and z 2 ( t ) are each a signal obtained by weighting signals modulated with the 8QAM. The total of 6 bits are transferred since the weighted signals z 1 ( t ) and z 2 ( t ) are transmitted as 3 bits in two parts according to the 8QAM. Therefore, in the case where there is no coincidence between signal points, the number of signal points is 64. 
       FIG.  132    shows an example of signal points of the precoded signals z 1 ( t ) and z 2 ( t ) in the I-Q plane for QPSK when α=3/2 (or 2/3) is satisfied, which is an example of an appropriate value of α, is used in Equation I5. As shown in  FIG.  132   , when α=3/2 (or 2/3), the distance between each adjacent signals is mostly equal. Accordingly, the 64 signal points are closely arranged in the I-Q plane. 
     The signals z 1 ( t ) and z 2 ( t ) are each transmitted from a different antenna as shown in  FIG.  5   . Here, the case is considered where the signals transmitted from one of the two transmit antennas are not transmitted to the reception device of the terminal. In  FIG.  132   , reduction of signal points such as described in Embodiment I1 does not occur, and the 64 signal points are closely arranged in the I-Q plane. Accordingly, the reception device achieves a high data reception quality as a result of detection and error correction decoding. 
     Next, operations of the reception device in the present embodiment are described. 
     In the case where the above-mentioned method for regularly hopping between precoding matrices is applied, the following relationship is derived from  FIG.  5   . 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   703 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         
                           ( 
                           
                             
                               
                                 
                                   r 
                                   ⁢ 
                                   1 
                                   ⁢ 
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   r 
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                           
                           ) 
                         
                         = 
                           
                         
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       h 
                                       11 
                                     
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                                 
                                   
                                     
                                       h 
                                       12 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       h 
                                       21 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                                 
                                   
                                     
                                       h 
                                       22 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       
                                         z 
                                           
                                       
                                       1 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         z 
                                           
                                       
                                       2 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       h 
                                       11 
                                     
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                                 
                                   
                                     
                                       h 
                                       12 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       h 
                                       21 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                                 
                                   
                                     
                                       h 
                                       22 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             F 
                             [ 
                             t 
                             ] 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       
                                         s 
                                           
                                       
                                       1 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         s 
                                           
                                       
                                       2 
                                     
                                     ⁢ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #I7 
                 
               
             
           
         
       
     
     Note that F[t] is a precoding matrix utilizing a parameter time t when applied for the precoding scheme for regularly hopping between precoding matrices. The reception device performs demodulation (detection) of signals by utilizing the relation between the signals r 1 ( t ) and r 2 ( t ) and the relation between the signals s 1 ( t ) and s 2 ( t ) mentioned above (that is, demodulation is to be performed in the same manner as explanation has been provided in Embodiments 1 and A1 to A5 and the like). However, the above equations do not take into consideration such distortion components as noise components, frequency offsets, and channel estimation errors, and thus, the demodulation (detection) is performed with such distortion components included in the signals. 
     Thus, the demodulation (detection) is performed based on the reception signals, values obtained from channel estimation, and the precoding matrices. The detection may result in either of a hard value (result of “0” or “1”) and a soft value (a log-likelihood or a log-likelihood ratio). Then, error correction decoding is performed based on the result of the detection. 
     In the present embodiment, the hopping between the precoding matrices is performed in the time domain. However, when a multi-carrier transmission scheme such as an OFDM scheme is used, the present invention is applicable to the case where the hopping between the precoding matrices is performed in the frequency domain, as described in other embodiments. If this is the case, t used in the present embodiment is to be replaced with f (frequency ((sub) carrier)). 
     Accordingly, in the case of performing the hopping between the precoding matrices in the time domain, the signals z 1 ( t ) and z 2 ( t ) at the same time point are each transmitted from a different antenna by using the same frequency. On the other hand, in the case of performing the hopping between the precoding matrices in the frequency domain, the signals z 1 ( f ) and z 2 ( f ) at the same frequency (the same subcarrier) are each transmitted from a different antenna at the same time point. Also, even in the case of performing the hopping between the precoding matrices in the time and frequency domains, the present invention is applicable as described in other embodiments. 
     In the present embodiment, N-slot period (cycle) is used as a period (cycle) for the precoding hopping scheme (the method for regularly hopping between precoding matrices), F[0], F[1], F[2], . . . , F[N−2], F[N−1] are prepared as N different precoding matrices. The symbols are arranged in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1] in the time domain in the single carrier transmission scheme. However, this is not the only example, and N different precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1] generated in the present embodiment may be applied to a multi-carrier transmission scheme such as an OFDM transmission scheme. As in Embodiment 1, as a method of applying this, precoding weights can be changed by arranging symbols in the frequency domain or in the frequency-time domains. Note that a precoding hopping scheme with N-slot period (cycle) has been described, but the same advantageous effects may be obtained by randomly using N different precoding matrices. In other words, the N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     That is, as described in Embodiments 1, 5, 15, and the like (see  FIGS.  14 ,  23   , and  54 ), the precoded signals z 1 ( t ) and z 2 ( t ) (or z 1 ( f ) and z 2 ( f ), or z 1  ( t,f ) and z 2 ( t,f )) may be reordered (in units of symbols, for example). 
     Embodiment 13 
     The present embodiment describes a method for regularly hopping between precoding matrices in the case the signals s 1  and s 2  are modulated with the 8QAM (8 Quadrature Amplitude Modulation), which differs from that described in Embodiment I2. 
     In the present embodiment, the precoding scheme for regularly hopping between precoding matrices described in Embodiments 10 and 19 is applied. In the present embodiment, the signals s 1  and s 2  are modulated with the 8QAM in the description in Embodiments 10 and 19.  FIG.  129    shows a signal point layout in the I-Q plane for 8QAM. In  FIG.  129   , when the average transmission power is set as z, a value of u is defined by Equation I3. An in-phase component (I) and a quadrature component (Q) for 8QAM are generated in the same way as that in Embodiment I2. 
     A coefficient for the average power of the QPSK modulated signal set as z is given in Equation 273. A coefficient for the average power of the 16QAM modulated signal set as z is given in Equation 272. A coefficient for the average power of the 64QAM modulated signal set as z is given in Equation 481. The transmission device can select the QPSK, the 16QAM, the 64QAM, or the 8QAM as a modulation scheme. Equation I3 is important for equalizing the average power of the 8QAM modulated signal, the average power of the QPSK modulated signal, the 16QAM modulated signal, and the 64QAM modulated signal. 
     The following describes a method for regularly hopping between precoding matrices in the case where the signals s 1  and s 2  are modulated with the 8QAM (Note that the method for regularly hopping between precoding matrices in the present embodiment has been described in Embodiments 10 and 19). 
     As described in Embodiment 10, the precoding matrices F[i] (i=0, 1, 2, . . . , 2N−2, 2N−1 (i being an integer in a range of 0 to N−1)) prepared for 2N-slot period (cycle) are represented as follows. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   704 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         When 
                         ⁢ 
                             
                         i 
                       
                       = 
                       0 
                     
                     , 
                     1 
                     , 
                     2 
                     , 
                     … 
                         
                     , 
                     N 
                     ⁢ 
                     ‐ 
                     ⁢ 
                     2 
                     , 
                     N 
                     ⁢ 
                     ‐ 
                     ⁢ 
                     
                       1 
                       : 
                     
                   
                   ⁢ 
                   
 
                   
                     
                       F 
                       [ 
                       i 
                       ] 
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               α 
                               2 
                             
                             + 
                             1 
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 e 
                                 
                                   j 
                                   ⁢ 
                                   
                                     
                                       θ 
                                       11 
                                     
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 α 
                                 × 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     
                                       ( 
                                       
                                         
                                           
                                             θ 
                                             11 
                                           
                                           ( 
                                           i 
                                           ) 
                                         
                                         + 
                                         λ 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 α 
                                 × 
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                 
                               
                             
                             
                               
                                 e 
                                 
                                   j 
                                   ( 
                                     
                                   
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                     + 
                                     λ 
                                     + 
                                     π 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #I8 
                 
               
             
           
         
       
     
     Let α be a fixed value (not depending on i), where α&gt;0. 
     
       
         
           
             
               
                 
                   Math 
                   ⁢ 
                       
                   705 
                 
               
               
                  
               
             
             
               
                 
                   
 
                   
                     
                       
                         
                           When 
                           ⁢ 
                               
                           i 
                         
                         = 
                         
                           N 
                           + 
                           1 
                         
                       
                       , 
                       
                         N 
                         + 
                         2 
                       
                       , 
                       … 
                           
                       , 
                       
                         2 
                         ⁢ 
                         N 
                       
                       ⁢ 
                       ‐ 
                       ⁢ 
                       2 
                       , 
                       
                         2 
                         ⁢ 
                         N 
                       
                       ⁢ 
                       ‐ 
                       ⁢ 
                       
                         1 
                         : 
                       
                     
                     ⁢ 
                     
 
                     
                       
                         F 
                         [ 
                         i 
                         ] 
                       
                       = 
                       
                         
                           1 
                           
                             
                               
                                 α 
                                 2 
                               
                               + 
                               1 
                             
                           
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 
                                   α 
                                   × 
                                   
                                     e 
                                     
                                       j 
                                       ⁢ 
                                       
                                         
                                           θ 
                                           11 
                                         
                                         ( 
                                         i 
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     
                                       ( 
                                       
                                         
                                           
                                             θ 
                                             11 
                                           
                                           ( 
                                           i 
                                           ) 
                                         
                                         + 
                                         λ 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   e 
                                   
                                     j 
                                     ⁢ 
                                     
                                       
                                         θ 
                                         21 
                                       
                                       ( 
                                       i 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   α 
                                   × 
                                   
                                     e 
                                     
                                       j 
                                       ( 
                                         
                                       
                                         
                                           
                                             θ 
                                             21 
                                           
                                           ( 
                                           i 
                                           ) 
                                         
                                         + 
                                         λ 
                                         + 
                                         π 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   #I9 
                 
               
             
           
         
       
     
     Let α be a fixed value (not depending on i), where α&gt;0. (Let α in Equation I8 and a in Equation I9 be equal.) (α&lt;0 may be satisfied). 
     As described in Embodiment I9, the Conditions 57, 58, 59, 60, 61, 62, and 63 should be satisfied for achieving excellent data reception quality (note that all these conditions do not necessarily need to be satisfied). 
     The following describes an example of an appropriate value of α in the case where the precoding matrix to be used in the scheme of regularly hopping between precoding matrices are represented as in Equations I8 or I9. 
     As described in Embodiments I1 and 12, precoded signals obtained by performing precoding are represented as z 1 ( t ) and z 2 ( t ) (t: time). Here, the signals z 1 ( t ) and z 2 ( t ) are at the same frequency (the same (sub) carrier), and are each transmitted from a different antenna (Although signals in the time domain are described as an example here, the signals may be z 1 ( f ) and z 2 ( f ) (f: (sub) carrier) as described in Embodiment I1, which are the signals at the same time and are each transmitted from a different antenna). 
     The signals z 1 ( t ) and z 2 ( t ) are each a signal obtained by weighting signals modulated with the 8QAM. The total of 6 bits are transferred since the weighted signals z 1 ( t ) and z 2 ( t ) are transmitted as 3 bits in two parts according to the 8QAM. Therefore, in the case where there is no coincidence between the signal points, the number of signal points is 64. 
       FIG.  130    shows an example of signal points of the precoded signals z 1 ( t ) and z 2 ( t ) in the I-Q plane for QPSK when α=3/2 (or 2/3) is satisfied, which is an example of an appropriate value of α, is used in Equations I8 and I9. As shown in  FIG.  130   , when α=3/2 (or 2/3) is satisfied, the distance between each adjacent signals is mostly equal. Accordingly, the 64 signal points are closely arranged in the I-Q plane. 
     The signals z 1 ( t ) and z 2 ( t ) are each transmitted from a different antenna as shown in  FIG.  5   . Here, the case is considered where the signals transmitted from one of the two transmit antennas are not transmitted to the reception device of the terminal. In  FIG.  130   , reduction of signal points such as described in Embodiment I1 does not occur, and the 64 signal points are closely arranged in the I-Q plane. Accordingly, the reception device achieves a high data reception quality as a result of detection and error correction decoding. 
     Next, the following describes the 8QAM for signals arranged in a different way from that shown in  FIG.  129   . Here, the precoding scheme for regularly hopping between precoding matrices described in Embodiments 10 and 19 is applied. The signals s 1  and s 2  are modulated with the 8QAM.  FIG.  131    shows a signal point layout in the I-Q plane for 8QAM which differs from that shown in  FIG.  129   . In  FIG.  131   , when the average transmission power is set as z, a value of v is defined by Equation I6. An in-phase component (I) and a quadrature component (Q) for 8QAM are generated in the same way as that in Embodiment I2. 
     A coefficient for the average power of the QPSK modulated signal set as z is given in Equation 273. A coefficient for the average power of the 16QAM modulated signal set as z is given in Equation 272. A coefficient for the average power of the 64QAM modulated signal set as z is given in Equation 481. The transmission device can select the QPSK, the 16QAM, the 64QAM, or the 8QAM as a modulation scheme. Equation I6 is important for equalizing the average power of the 8QAM modulated signal, the average power of the QPSK modulated signal, the 16QAM modulated signal, and the 64QAM modulated signal. 
     The following describes a method for regularly hopping between precoding matrices in the case where the signals s 1  and s 2  are modulated with the 8QAM (Note that the method for regularly hopping between precoding matrices in the present embodiment has been described in Embodiments 10 and 19). 
     As described in Embodiment 10, in the scheme for regularly hopping between precoding matrices in 2N-slot period (cycle) (N is a natural number), the precoding matrices F[i] (i=0, 1, 2, . . . , N−2, N−1) prepared for 2N-slot period (cycle) are defined in Equations I8 and I9. 
     As described in Embodiment 19, the Conditions 57, 58, 59, 60, 61, 62, and 63 should be satisfied for achieving excellent data reception quality (note that all these conditions do not necessarily need to be satisfied). 
     The following describes an example of an appropriate value of α in the case where the precoding matrix to be used in the scheme of regularly hopping between precoding matrices are represented as in Equations I8 or I9. 
     As described in Embodiments I1 and I2, precoded signals obtained by performing precoding are represented as the signals z 1 ( t ) and z 2 ( t ) (t: time). Here, the signals z 1 ( t ) and z 2 ( t ) are at the same frequency (the same (sub) carrier), and are each transmitted from a different antenna (Although signals in the time domain are described as an example here, the signals may be z 1 ( f ) and z 2 ( f ) (f: (sub) carrier) as described in Embodiment I1, which are the signals at the same time and are each transmitted from a different antenna). 
     The signals z 1 ( t ) and z 2 ( t ) are each a signal obtained by weighting signals modulated with the 8QAM. The total of 6 bits are transferred since the weighted signals z 1 ( t ) and z 2 ( t ) are transmitted as 3 bits in two parts according to the 8QAM. Therefore, in the case where there is no coincidence between signal points, the number of signal points is 64. 
       FIG.  132    shows an example of signal points of the precoded signals z 1 ( t ) and z 2 ( t ) in the I-Q plane for QPSK when α=3/2 (or 2/3) is satisfied, which is an example of an appropriate value of α, is used in Equations I8 and I9. As shown in  FIG.  132   , when α=3/2 (or 2/3) is satisfied, the distance between each adjacent signals is mostly equal. Accordingly, the 64 signal points are closely arranged in the I-Q plane. 
     The signals z 1 ( t ) and z 2 ( t ) are each transmitted from a different antenna as shown in  FIG.  5   . Here, the case is considered where the signals transmitted from one of the two transmit antennas are not transmitted to the reception device of the terminal. In  FIG.  132   , reduction of signal points such as described in Embodiment I 1  does not occur, and the 64 signal points are closely arranged in the I-Q plane. Accordingly, the reception device achieves a high data reception quality as a result of detection and error correction decoding. 
     Next, operations of the reception device in the present embodiment are described. 
     In the case where the above-mentioned method for regularly hopping between precoding matrices is applied, the following relationship (17) is derived from  FIG.  5   . Note that F[t] is a precoding matrix utilizing a parameter time t when applied for the precoding scheme for regularly hopping between precoding matrices. The reception device performs demodulation (detection) of signals by utilizing the relation between the signals r 1 ( t ) and r 2 ( t ) and the relation between the signals s 1 ( t ) and s 2 ( t ) mentioned above (that is, demodulation is to be performed in the same manner as explanation has been provided in Embodiments 1 and A1 to A5 and the like). However, the above equations do not take into consideration such distortion components as noise components, frequency offsets, and channel estimation errors, and thus, the demodulation (detection) is performed with such distortion components included in the signals. 
     Thus, the demodulation (detection) is performed based on the reception signals, values obtained from channel estimation, and the precoding matrices. The detection may result in either of a hard value (result of “0” or “1”) and a soft value (a log-likelihood or a log-likelihood ratio). Then, error correction decoding is performed based on the result of the detection. 
     In the present embodiment, the hopping between the precoding matrices is performed in the time domain. However, when a multi-carrier transmission scheme such as an OFDM scheme is used, the present invention is applicable to the case where the hopping between the precoding matrices is performed in the frequency domain, as described in other embodiments. If this is the case, t used in the present embodiment is to be replaced with f (frequency ((sub) carrier)). 
     Accordingly, in the case of performing the hopping between the precoding matrices in the time domain, the signals z 1 ( t ) and z 2 ( t ) at the same time point are each transmitted from a different antenna by using the same frequency. On the other hand, in the case of performing the hopping between the precoding matrices in the frequency domain, the signals z 1 ( f ) and z 2 ( f ) at the same frequency (the same subcarrier) are each transmitted from a different antenna at the same time point. Also, even in the case of performing the hopping between the precoding matrices in the time and frequency domains, the present invention is applicable as described in other embodiments. 
     In the present embodiment, 2N-slot period (cycle) is used as a period (cycle) for the precoding hopping scheme (the method for regularly hopping between precoding matrices), F[0], F[1], F[2], . . . , F[N−2], F[N−1] are prepared as 2N different precoding matrices. The symbols are arranged in the order F[0], F[1], F[2], . . . , F[N−2], F[N−1] in the time domain in the single carrier transmission scheme. However, this is not the only example, and 2N different precoding matrices F[0], F[1], F[2], . . . , F[N−2], F[N−1] generated in the present embodiment may be applied to a multi-carrier transmission scheme such as an OFDM transmission scheme. As in Embodiment 1, as a method of applying this, precoding weights can be changed by arranging symbols in the frequency domain or in the frequency-time domains. Note that a precoding hopping scheme with 2N-slot period (cycle) has been described, but the same advantageous effects may be obtained by randomly using 2N different precoding matrices. In other words, the N different precoding matrices do not necessarily need to be used in a regular period (cycle). 
     That is, as described in Embodiments 1, 5, 15, and the like (see  FIGS.  14 ,  23   , and  54 ), the precoded signals z 1 ( t ) and z 2 ( t ) (or z 1 ( f ) and z 2 ( f ), or z 1 ( t,f ) and z 2 ( t,f )) may be reordered (in units of symbols, for example). 
     In the present specification, the examples of the modulation schemes have been described such as BPSK, QPSK, 8QAM, 16QAM, and 64QAM. Alternatively, PAM (Pulse Amplitude Modulation) may be employed without limiting to these modulation schemes. Also, the scheme for arranging signal points whose number is 2, 4, 8, 16, 64, 128, 256, and 1024 in the I-Q plane (modulation scheme in signal points whose number is 2, 4, 8, 16, 64, 128, 256, and 1024) is not limited to the schemes described in the present specification (such as signal point layout for QPSK and signal point layout for 16QAM). Accordingly, the function of outputting an in-phase component and a quadrature component based on a plurality of bits is performed by the mapping unit. Therefore, execution of the method for regularly hopping between precoding matrices is one of efficient functions of the present invention. 
     (Regarding Cyclic Q Delay) 
     A description is given of application of Cyclic Q Delay described in the present specification. Non-Patent Literature 10 provides an overview of Cyclic Q Delay. The following describes specific examples of generating s 1  and s 2  when Cyclic Q Delay is used. 
       FIG.  133    shows one example of signal point layout on the in-phase components I-quadrature components Q plane. Let input bits be b 0 , b 1 , b 2 , b 3 . Then, b 0  b 1  b 2  b 3  is one of values from 0000 to 1111. For instance, when b 0  b 1  b 2  b 3  is represented as 0000, a signal point of  13301  illustrated in  FIG.  133    is selected, the value of the in-phase component based on  13301  is set as the in-phase component of the baseband signal, and the value of the quadrature component based on  13301  is set as the quadrature component of the baseband signal. Similarly, when b 0  b 1  b 2  b 3  is another value, the in-phase component and the quadrature component of a baseband signal are generated in the same manner. 
       FIG.  134    shows an example of the structure of the signal generating unit for generating the modulated signal s 1 ( t ) (t: time) (or s 1 ( f ), f: frequency) and the modulated signal s 2 ( t ) (t: time) (or s 2 ( f ), f: frequency) from (binary) data when Cyclic Q Delay is applied. 
     A mapping unit  13402  receives data  13401  and a control signal  13406  as inputs, and if the modulation scheme based on the control signal  13406 , such as 16QAM, is selected, performs mapping in accordance with the procedures in  FIG.  133   , and outputs the in-phase component  13403 _A and the quadrature component  13403 _B of the mapped baseband signal. Note that the modulation scheme is not limited to 16QAM, and the present invention is similarly embodied using other modulation schemes. 
     In this case, data at time  1  corresponding to b 0 , b 1 , b 2 , b 3  in  FIG.  133    is represented as b 01 , b 11 , b 21 , b 31 . Based on the data b 01 , b 11 , b 21 , b 31  at the time  1 , the mapping unit  13402  outputs the in-phase component I1 and the quadrature component Q1 of the baseband signal at the time  1 . The mapping unit  13402  also outputs the in-phase component I2, the quadrature component Q2, . . . of the baseband signal at time  2 . 
     A storing and signal switching unit  13404  receives, as inputs, the in-phase component  13403 _A and the quadrature component  13403 _B of the baseband signal, and the control signal  13406 . Then, according to the control signal  13406 , the storing and signal switching unit  13404  stores the in-phase component  13403 _A and the quadrature component  12003 _B of the baseband signal and switches signals, and then outputs the modulated signal s 1 ( t ) ( 13405 _A) and the modulated signal s 2 ( t ) ( 13405 _B). Note that the scheme for generating the modulated signals s 1 ( t ) and s 2 ( t ) is described below in the details. 
     As has been described in the specification, the precoding scheme for regularly hopping between precoding matrices is applied with respect to the modulated signals s 1 ( t ) and s 2 ( t ). In this case, as mentioned in the specification, signal processing such as phase change, power change, and signal switching may be performed in any stage. The modulated signals r 1 ( t ) and r 2 ( t ), which are obtained by applying the precoding scheme for regularly hopping between precoding matrices with respect to the modulated signals s 1 ( t ) and s 2 ( t ), are transmitted at the same (shared/common) time over the same frequency. 
     Meanwhile, although the above description is given using the time domain t, when a multi-carrier transmission scheme such as OFDM is used, s 1 ( t ) and s 2 ( t ) may be considered as s 1 ( f ) and s 2 ( f ) (f: (sub) carrier). The modulated signals r 1 ( f ) and r 2 ( f ), which are obtained by applying the precoding scheme for regularly hopping between precoding matrices with respect to the modulated signals s 1 ( t ) and s 2 ( t ), are transmitted at the same (shared/common) time (note that r 1 ( f ) and r 2 ( f ) are of course signals of the same frequency). Furthermore, as shown in the present specification, s 1 ( t ) and s 2 ( t ) may be considered as s 1 ( t, f ) and s 2 ( t, f ). 
     Next, a description is given of the scheme for generating the modulated signals s 1 ( t ) and s 2 ( t ).  FIG.  135    is a first example of the generation scheme of s 1 ( t ) and s 2 ( t ) when Cyclic Q Delay is used. 
     In  FIG.  135   , the portion (a) shows the in-phase components and the quadrature components of the baseband signals obtained by the mapping unit  13402  of  FIG.  134   . As shown in  FIG.  135 ( a )  and as description has been given of the mapping unit  13402  of  FIG.  134   , the mapping unit  13402  outputs the in-phase components and the quadrature components of the baseband signals in order starting from the in-phase component I1 and the quadrature component Q1 of the baseband signal at the time  1 , the in-phase component I2 and the quadrature component Q2 of the baseband signal at the time  2 , the in-phase component I3 and the quadrature component Q3 of the baseband signal at the time  3 , . . . . 
     In  FIG.  135   , the portion (b) shows exemplary sets of the in-phase and quadrature components of the baseband signals when the storing and signal switching unit  13404  of  FIG.  134    performs signal switching. In  FIG.  135 ( b ) , a set of the time  1  and the time  2 , a set of the time  3  and the time  4 , and a set of the time  5  and the time  6  are formed. In other words, a plurality of sets of time 2i+1 and time 2i+2 (i is an integer greater than or equal to zero) is formed. Within each set, e.g. at the time  1  and at the time  2 , the quadrature components of the baseband signals are switched. 
     Regarding the in-phase components of the baseband signals, signal switching is not performed, and accordingly, the in-phase component of the baseband signal at the time  1  is I1, the in-phase component of the baseband signal at the time  2  is I2, the in-phase component of the baseband signal at the time  3  is I3, . . . . 
     On the other hand, regarding the quadrature components of the baseband signals, signal switching is performed in each set, and accordingly, the quadrature component of the baseband signal at the time  1  is Q2, the quadrature component of the baseband signal at the time  2  is Q1, the quadrature component of the baseband signal at the time  3  is Q4, the quadrature component of the baseband signal at the time  4  is Q3, . . . . 
     In  FIG.  135   , the portion (c) shows one example of the structure of the modulated signals s 1 ( t ) and s 2 ( t ) before precoding when the precoding scheme for regularly hopping between precoding matrices is applied. For instance, as shown in  FIG.  135 ( c ) , the baseband signals generated as in  FIG.  135 ( b )  are alternately allocated to s 1 ( t ) and s 2 ( t ). Accordingly, the first slot of s 1 ( t ) is (I1, Q2), and the first slot of s 2 ( t ) is (I2, Q1). The second slot of s 1 ( t ) is (I3, Q4), the second slot of s 2 ( t ) is (I4, Q3), . . . . 
     Although the example of the time domain is illustrated in  FIG.  135   , the present embodiment may be similarly implemented in the frequency domain (as has been described above). In this case, s 1  ( f ) and s 2 ( f ) are described. 
     Precoding is performed according to the precoding scheme of regularly hopping precoding schemes with respect to s 1 ( t ) of an Nth slot and s 2 ( t ) of an Nth slot, and the signals r 1 ( t ) and r 2 ( t ) resulting from the precoding of the Nth slot are obtained. The above point has been described in the present specification. 
       FIG.  136    shows the structuring scheme for obtaining s 1 ( t ) and s 2 ( t ) of an Nth slot illustrated in  FIG.  135   , the scheme different from that of  FIG.  134   . The mapping unit  13602  receives the data  13601  and a control signal  13604  as inputs, and performs mapping according to the modulation scheme based on the control signal  13604 , e.g. mapping that takes the switching of  FIG.  135    into consideration, to generate a mapped signal (the in-phase component and the quadrature component of a baseband signal). Based on the mapped signal, the mapping unit  13602  also generates the modulated signal s 1 ( t ) ( 13603 _A) and the modulated signal s 2 ( t ) ( 13403 _B), and outputs the generated modulated signal s 1 ( t ) ( 13603 _A) and the generated modulated signal s 2 ( t ) ( 13403 _B). Note that the modulated signal s 1 ( t ) ( 13603 _A) is identical to the modulated signal  13405 _A of  FIG.  134   , and the modulated signal s 2 ( t ) ( 13403 _B) is identical to the modulated signal  13405 _B of  FIG.  134    and is shown in  FIG.  135 ( c ) . Accordingly, the first slot of the modulated signal s 1 ( t ) ( 13603 _A) is (I1, Q2), the first slot of the modulated signal s 2 ( t ) ( 13403 _B) is (I2, Q1), the second slot of the modulated signal s 1 ( t ) ( 13603 _A) is (I3, Q4), the second slot of the modulated signal s 2 ( t ) ( 13403 _B) is (I4, Q3), . . . . 
     In addition, a description is given of the scheme for generating the first slot (I1, Q2) of the modulated signal s 1 ( t ) ( 13603 _A), and the first slot (I2, Q1) of the modulated signal s 2 ( t ) ( 13403 _B). 
     In  FIG.  136   , data is represented as  13601 . Here, let the data at the time  1  be b 01 , b 11 , b 21 , b 31 , and let the data at the time  2  be b 02 , b 12 , b 22 , b 32 . The mapping unit  13602  of  FIG.  136    generates the above-described I1, Q1, I2, Q2 from b 01 , b 11 , b 21 , b 31  and b 02 , b 12 , b 22 , b 32 . Then, from I1, Q1, I2, Q2, the mapping unit  13602  of  FIG.  136    is able to generate the modulated signals s 1 ( t ) and s 2 ( t ). 
       FIG.  137    shows the structuring scheme for obtaining s 1 ( t ) and s 2 ( t ) of an Nth slot illustrated in  FIG.  135   , the scheme different from those of  FIGS.  134  and  136   . A mapping unit  12301 _A receives the data  13601  and the control signal  13604  as inputs, and performs mapping according to the modulation scheme based on the control signal  13604 , e.g. mapping that takes the switching of  FIG.  135    into consideration, to generate a mapped signal (the in-phase component and the quadrature component of a baseband signal). Based on the mapped signal, the mapping unit  13701 _A also generates the modulated signal s 1 ( t ) ( 13603 _A), and outputs the generated modulated signal s 1 ( t ) ( 13603 _A). A mapping unit  13701 _B receives the data  13601  and the control signal  13604  as inputs, and performs mapping according to the modulation scheme based on the control signal  13604 , e.g. mapping that takes the switching of  FIG.  135    into consideration, to generate a mapped signal (the in-phase component and the quadrature component of a baseband signal). Based on the mapped signal, the mapping unit  13701 _B also generates the modulated signal s 2 ( t ) ( 13403 _B), and outputs the generated modulated signal s 2 ( t ) ( 13403 _B). 
     Note that the data  13601  as the input to the mapping unit  13701 _A and the data  13601 _B as the input to the mapping unit  12301  is identical to each other. Furthermore, the modulated signal s 1 ( t ) ( 13603 _A) is identical to the modulated signal  13405 _A of  FIG.  134   , and the modulated signal s 2 ( t ) ( 13403 _B) is identical to the modulated signal  13405 _B of  FIG.  134    and is shown in  FIG.  135 ( c ) . 
     Accordingly, the first slot of the modulated signal s 1 ( t ) ( 13603 _A) is (I1, Q2), the first slot of the modulated signal s 2 ( t ) ( 13403 _B) is (I2, Q1), the second slot of the modulated signal s 1 ( t ) ( 13603 _A) is (I3, Q4), the second slot of the modulated signal s 2 ( t ) ( 13403 _B) is (I4, Q3), . . . . 
     In addition, a description is given of the scheme for generating the first slot (I1, Q2) of the modulated signal s 1 ( t ) ( 13603 _A) in the mapping unit  13701 _A of  FIG.  137   . In  FIG.  137   , data is represented as  13601 . Let the data at the time  1  be b 01 , b 11 , b 21 , b 31 , and let the data at the time  2  be b 02 , b 12 , b 22 , b 32 . The mapping unit  13701 _A of  FIG.  137    generates the above-described I1, Q2 from b 01 , b 11 , b 21 , b 31  and b 02 , b 12 , b 22 , b 32 . Then, from I1, Q2, the mapping unit  13701 _A of  FIG.  137    is able to generate the modulated signal s 1 ( t ). 
     A description is given of the scheme for generating the first slot (I2, Q1) of the modulated signal s 2 ( t ) ( 13403 _B) in the mapping unit  13701 _B of  FIG.  137   . In  FIG.  137   , data is represented as  13601 . Let the data at the time  1  be b 01 , b 11 , b 21 , b 31 , and let the data at the time  2  be b 02 , b 12 , b 22 , b 32 . The mapping unit  13701 _B of  FIG.  137    generates the above-described  12 , Q1 from b 01 , b 11 , b 21 , b 31  and b 02 , b 22 , b 22 , b 31 . Then, from I2, Q1, the mapping unit  13701 _B of  FIG.  137    is able to generate s 2 ( t ). 
     Next, referring to  FIG.  138   , a second example of the scheme for generating s 1 ( t ) and s 2 ( t ) using Cyclic Q Delay is shown, the scheme different from that of  FIG.  135   . Meanwhile, the same reference numerals are used in  FIG.  138    to refer to the same elements (e.g. the in-phase component and the quadrature component of a baseband signal) as  FIG.  135   . 
     In  FIG.  138   , the portion (a) shows the in-phase components and the quadrature components of the baseband signals obtained by the mapping unit  13402  of  FIG.  134   .  FIG.  138 ( a )  is the same as  FIG.  135 ( a )  and explanation thereof is omitted here. 
     In  FIG.  138   , the portion (b) shows the structure of the in-phase components and the quadrature components of the baseband signals s 1 ( t ) and s 2 ( t ) before signal switching. In  FIG.  138 ( b ) , the baseband signal at the time 2i+1 is assigned to s 1 ( t ), and the baseband signal at the time 2i+2 is assigned to s 2 ( t ) (where i is an integer greater than or equal to zero). 
     In  FIG.  138   , the portion (c) shows exemplary sets of the in-phase and quadrature components of the baseband signals when the storing and signal switching unit  13404  of  FIG.  134    performs signal switching.  FIG.  138 ( c )  is characterized (differs from  FIG.  135   ) in that signal switching is performed within s 1 ( t ) and within s 2 ( t ). 
     Specifically, in  FIG.  138 ( c ) , in comparison with  FIG.  138 ( b ) , Q1 and Q3 are switched in s 1 ( t ), and Q5 and Q7 are also switched in s 1 ( t ). Subsequently, the similar switching is performed. Furthermore, in  FIG.  138 ( c ) , in comparison with  FIG.  138 ( b ) , Q2 and Q4 are switched in s 2 ( t ), and Q6 and Q8 are also switched in s 2 ( t ). Subsequently, the similar switching is performed. 
     As a result, the in-phase component of the baseband signal s 1 ( t ) in the first slot is I1, the quadrature component of the baseband signal s 1 ( t ) in the first slot is Q3. The in-phase component of the baseband signal s 2 ( t ) in the first slot is I2, and the quadrature component of the baseband signal s 2 ( t ) in the first slot is Q4. Also, the in-phase component of the baseband signal s 1 ( t ) in the second slot is I3, the quadrature component of the baseband signal s 1 ( t ) in the second slot is Q1. The in-phase component of the baseband signal s 2 ( t ) in the second slot is I4, and the quadrature component of the baseband signal s 2 ( t ) in the second slot is Q2. Regarding the third slot and the fourth slot, an illustration is given in  FIG.  138 ( c ) . This applies to the subsequent slots as well. 
     Precoding is performed according to the precoding scheme for regularly hopping precoding schemes with respect to s 1 ( t ) of an Nth slot and s 2 ( t ) of an Nth slot, and the signals r 1 ( t ) and r 2 ( t ) resulting from the precoding of the Nth slot are obtained. The above point has been described in the present specification. 
       FIG.  139    shows the structuring scheme for obtaining s 1 ( t ) and s 2 ( t ) of an Nth slot illustrated in  FIG.  138   , the scheme different from that of  FIG.  134   . The mapping unit  13602  receives the data  13601  and the control signal  13604  as inputs, and performs mapping according to the modulation scheme based on the control signal  13604 , e.g. mapping that takes the switching of  FIG.  138    into consideration, to generate a mapped signal (the in-phase component and the quadrature component of a baseband signal). Based on the mapped signal, the mapping unit  13602  also generates the modulated signal s 1 ( t ) ( 13603 _A) and the modulated signal s 2 ( t ) ( 13403 _B), and outputs the generated modulated signal s 1 ( t ) ( 13603 _A) and the generated modulated signal s 2 ( t ) ( 13403 _B). Note that the modulated signal s 1 ( t ) ( 13603 _A) is identical to the modulated signal  13405 _A of  FIG.  134   , and the modulated signal s 2 ( t ) ( 13403 _B) is identical to the modulated signal  13405 _B of  FIG.  134    and is shown in  FIG.  138 ( c ) . Accordingly, the first slot of the modulated signal s 1 ( t ) ( 13603 _A) is (I1, Q3), the first slot of the modulated signal s 2 ( t ) ( 13403 _B) is (I2, Q4), the second slot of the modulated signal s 1 ( t ) ( 13603 _A) is (I3, Q1), the second slot of the modulated signal s 2 ( t ) ( 13403 _B) is (I4, Q2), . . . . 
     In addition, a description is given of the scheme for generating the first slot (I1, Q3) of the modulated signal s 1 ( t ) ( 13603 _A), the first slot (I2, Q4) of the modulated signal s 2 ( t ) ( 13403 _B), the second slot (I3, Q1) of the modulated signal s 1 ( t ) ( 13603 _A), and the first slot (I4, Q2) of the modulated signal s 2 ( t ) ( 13403 _B) in the mapping unit  13602  of  FIG.  139   . 
     In  FIG.  139   , data is represented as  13601 . Let the data at the time  1  be b 01 , b 11 , b 21 , b 31 , let the data at the time  2  be b 02 , b 12 , b 22 , b 32 , let the data at the time  3  be b 03 , b 13 , b 23 , b 33 , and let the data at the time  4  be b 04 , b 14 , b 24 , b 34 . The mapping unit  13602  of  FIG.  139    generates the above-described I1, Q1, I2, Q2, I3, Q3, 14, Q4 from b 01 , b 11 , b 21 , b 31 , and b 02 , b 12 , b 22 , b 32 , and b 03 , b 13 , b 23 , b 33 , and b 04 , b 14 , b 24 , b 34 . Then, from I1, Q1, I2, Q2, I3, Q3, 14, Q4, the mapping unit  13602  of  FIG.  139    is able to generate the modulated signals s 1 ( t ) and s 2 ( t ). 
       FIG.  140    shows the structuring scheme for obtaining s 1 ( t ) and s 2 ( t ) of an Nth slot illustrated in  FIG.  138   , the scheme different from those of  FIGS.  134  and  139   . The division unit  14001  receives the data  13601  and the control signal  13604  as inputs, and according to the control signal  13604 , divides the data, and outputs first data  14002 _A and second data  14002 _B. The mapping unit  13701 _A receives the first data  14002 _A and the control signal  13604  as inputs, and performs mapping according to the modulation scheme based on the control signal  13604 , e.g. mapping that takes the switching of  FIG.  138    into consideration, to generate a mapped signal (the in-phase component and the quadrature component of a baseband signal). Based on the mapped signal, the mapping unit  13701 _A also generates the modulated signal s 1 ( t ) ( 13603 _A), and outputs the generated modulated signal s 1 ( t ) ( 13603 _A). The mapping unit  13701 _B receives the second data  14002 _B and the control signal  13604  as inputs, and performs mapping according to the modulation scheme based on the control signal  13604 , e.g. mapping that takes the switching of  FIG.  138    into consideration, to generate a mapped signal (the in-phase component and the quadrature component of a baseband signal). Based on the mapped signal, the mapping unit  13701 _B also generates the modulated signal s 2 ( t ) ( 13403 _B), and outputs the generated modulated signal s 2 ( t ) ( 13403 _B). 
     Accordingly, the first slot of the modulated signal s 1 ( t ) ( 13603 _A) is (I1, Q3), the first slot of the modulated signal s 2 ( t ) ( 13403 _B) is (I2, Q4), the second slot of the modulated signal s 1 ( t ) ( 13603 _A) is (I3, Q1), the second slot of the modulated signal s 2 ( t ) ( 13403 _B) is (I4, Q2), . . . . 
     In addition, a description is given of the scheme for generating the first slot (I1, Q3) and the second slot (I3, Q1) of the modulated signal s 1 ( t ) ( 13603 _A) in the mapping unit  13701 _A of  FIG.  140   . In  FIG.  140   , data is represented as  13601 . Let the data at the time  1  be b 01 , b 11 , b 21 , b 31 , let the data at the time  2  be b 02 , b 12 , b 22 , b 32 , let the data at the time  3  be b 03 , b 13 , b 23 , b 33 , and let the data at the time  4  be b 04 , b 14 , b 24 , b 34 . The division unit  14001  outputs the data b 01 , b 11 , b 21 , b 31  at the time  1 , and the data b 03 , b 13 , b 23 , b 33  at the time  3 , as the first data  14002 _A. The division unit  14001  also outputs the data b 02 , b 12 , b 22 , b 32  at the time  2 , and the data b 04 , b 14 , b 24 , b 34  at the time  4 , as the second data  802 _B. The mapping unit  13701 _A of  FIG.  140    generates the first slot (I1, Q3) and the second slot (I3, Q1) from b 01 , b 11 , b 21 , b 31 , and b 03 , b 13 , b 23 , b 33 . The similar operations are performed for the third and subsequent slots. 
     A description is given of the scheme for generating the first slot (I2, Q4) of the modulated signal s 2 ( t ) ( 13403 _B) and the second slot (I4, Q2) in the mapping unit  13701 _B of  FIG.  140   . The mapping unit  13701 _B of  FIG.  140    generates the first slot (I2, Q4) and the second slot (I4, Q2) from both of the data b 02 , b 12 , b 22 , b 32  at the time  2 , and the data b 04 , b 14 , b 24 , b 34  at the time  4 . The similar operations are performed for the third and subsequent slots. 
     As above, the two Cyclic Q Delay schemes have been described. When signal switching is performed within slots as shown in  FIG.  135   , the number of the candidate signal points is reduced in the demodulation unit (detector) of the reception device. Consequently, an advantageous effect of reducing the calculation scale (circuit size) is obtained. On the other hand, as shown in  FIG.  138   , when signal switching is performed within the signal s 1 ( t ) and within the signal s 2 ( t ), the number of the candidate signal points is increased in the demodulation unit (detector) of the reception device. However, this type of scheme might yield an advantageous effect of obtaining time diversity gain (or frequency diversity gain, if switching is performed in the frequency domain), leading to the possibility of further improving the data reception quality. 
     Although the description is given above taking the example where the modulation scheme is 16QAM, the present invention may be similarly embodied even if the modulation scheme is for example one of QPSK, 8QAM, 32QAM, 64QAM, 128QAM, and 256QAM. 
     Furthermore, the scheme of Cyclic Q Delay is not limited to the above two types. For example, although switching is performed with respect to the quadrature components of the baseband signals in the above two examples, the in-phase components may be switched instead. Moreover, although switching is performed at two points of time (e.g. the quadrature components of the baseband signals are switched at the time  1  and the time  2 ), the in-phase components or (or possibly, and) the quadrature components of the baseband signals may be switched at a plurality of points of time. When Cyclic Q Delay is performed while the in-phase component and the quadrature component of a baseband signal is generated as shown in  FIG.  135 ( a ) , the following three possibilities hold. One is that “a symbol exists in which the in-phase component of the baseband signal after Cyclic Q Delay at time i is represented as Ii, and the quadrature component of the baseband signal after Cyclic Q Delay at time i is represented as Qj (i≠j)”. Another one is that “a symbol exists in which the in-phase component of the baseband signal after Cyclic Q Delay at time i is represented as Ij, and the quadrature component of the baseband signal after Cyclic Q Delay at time i is represented as Qi (i≠j)”. The other one is that “the in-phase component of the baseband signal after Cyclic Q Delay at time i is represented as Ij, and the quadrature component of the baseband signal after Cyclic Q Delay at time i is represented as Qk (i≠j, i≠k, j≠k). 
     Furthermore, the precoding scheme for regularly hopping between precoding matrices is applied with respect to the modulated signal s 1 ( t ) (or s 1 ( f ), or s 1 ( t, f )) and the modulated signal s 2 ( t ) (or s 2 ( f ), or s 2 ( t, f )) which are obtained by performing the aforementioned Cyclic Q Delay (Note that, as mentioned in the specification, signal processing, such as phase change, power change, and signal switching, may be performed in any stage). In this case, as the precoding scheme for regularly hopping between precoding matrices to be applied with respect to the modulated signals obtained by performing Cyclic Q Delay, any of the precoding schemes for regularly hopping between precoding matrices described in the present specification is applicable. 
     Embodiment M 
     In the present embodiment, description is given on an example of a scheme of leading signals to houses, for the case where a plurality of modulated signals, which are obtained using the precoding scheme of regularly hopping between precoding matrices, are transmitted from a broadcast station by a plurality of antennas (for example, in the same frequency band at the same time), and the modulated signals transmitted from the broadcast station are received, for example. (Note that precoding matrices to be used may be any of the precoding matrices described in the present specification. Also, even in the case where precoding matrices other than those described in the present specification are used, it is possible to execute the scheme of leading signals to houses described in the present embodiment. In addition, although the present specification gives description on the transmission scheme using the precoding scheme of regularly hopping between precoding matrices, it is possible to execute the scheme of leading signals to houses described in the present embodiment both in the case where precoding is performed without regularly hopping between precoding matrices and the case where no precoding is performed.) 
     A reception system  14101  shown in  FIG.  141    is composed of a relay device  14102 , and televisions  14103  and  14105  which are each provided in a house. Particularly, the relay device  14102  is a device for receiving a plurality of modulated signals transmitted from a broadcast station, and distributing the modulated signals to each of a plurality of houses. Note that although the description is given using an example of televisions, terminals included in the reception system  14101  are not limited to televisions, and the present embodiment may be similarly implemented for any terminal that requires information. 
     The relay device  14102  has a function of receiving broadcast waves (a plurality of modulated signals transmitted from the broadcast station). The relay device  14102  is characterized in having both a function of transmitting received signals to the television  14103  via a single cable  14104  and a function of transmitting received signals to the television  14105  via two cables  14106   a  and  14106   b.    
     Note that there has been used, for example, a scheme of providing the relay device  14102  on a rooftop of a tall building in consideration of overcrowded residential areas where radio wave reception is difficult due to influences by tall buildings. This achieves, in each house, excellent reception quality for modulated signals transmitted from the broadcast station. It is possible to acquire, in each house, a plurality of modulated signals transmitted from the broadcast station at the same frequency band, thereby achieving an effect of an increased data transmission speed. 
     As described in the present specification, the following describes detailed operations of the relay device, with reference to  FIG.  142   , for the case where when a broadcast station transmits a plurality of modulated signals at the same frequency band by different antennas, the relay device receives the modulated signals and relays the modulated signals to each house (residence) via a single signal line. 
     Description is given on the details of the case where signals are led to each house via a single signal line, with reference to  FIG.  142   . 
     As shown in  FIG.  142   , the relay device  14102  receives broadcast waves (a plurality of modulated signals transmitted from the broadcast station) by two antennas # 1  and # 2 . 
     A frequency converter  14211  converts a signal received by the antenna # 1  to an intermediate frequency (IF) # 1  (this signal is referred to as a signal of the IF # 1 ). 
     A frequency converter  14212  converts a signal received by the antenna # 2  to an IF # 2  that differs in frequency band from the IF # 1  (this signal is referred to as a signal of the IF # 2 ). 
     Then, an adder  14213  adds the signal of the IF # 1  and the signal of the IF # 2 . As a result, the relay device  14102  transmits the signal received by the antenna # 1  and the signal received by the antenna # 2  by performing frequency division multiplexing (FDM). 
     In the television  14103 , a brancher  14223  branches a signal transmitted via a single signal line to two signals. 
     A frequency converter  14221  performs frequency conversion relating to the IF # 1  to obtain a baseband signal # 1 . As a result, the baseband signal # 1  corresponds to the signal received by the antenna # 1 . 
     A frequency converter  14222  performs frequency conversion relating to the IF # 2  to obtain a baseband signal # 2 . As a result, the baseband signal # 2  corresponds to the signal received by the antenna # 2 . 
     Each of the intermediate frequencies # 1  and # 2  for use in leading signals to each house may be a frequency in a frequency band which is determined in advance between the relay device  14102  and the television  14103 . Alternatively, information regarding the intermediate frequencies # 1  and # 2  used by the relay device  14102  may be transmitted to the television  14103  via some sort of transport medium. Further alternatively, the television  14103  may transmit (or issue an instruction to use) the intermediate frequencies # 1  and # 2  which are desirable to be used to the relay device  14102  via some sort of transport medium. 
     A MIMO detector  14224  performs detection for MIMO such as MLD (Maximum Likelihood Detection) to obtain a log-likelihood ratio for each bit. (This point is such as described in other embodiments.) (Here, this unit is referred to as a MIMO detector because operations of signal processing for detection are the same as operations performed by a generally known MIMO detector. However, the scheme of leading signals to houses differs from a scheme of transmitting signals in a general MIMO system, and uses the FDM scheme in order to transmit the respective signals received by the antennas # 1  and # 2 . In the following description, although this unit is referred to as a MIMO detector even in this case, this unit may be regarded as a detector.) 
     As described in the present specification, in the case where a broadcast station transmits a plurality of modulated signals, which are obtained using the precoding scheme of regularly hopping between precoding matrices, by a plurality of antennas, the MIMO detector  14224  performs detection that reflects hopping between precoding matrices, and outputs a log-likelihood ratio for each bit, for example, as described in other embodiments. 
     Next, description is given on examples (schemes  1  and  2 ) of a case of leading signals to houses via two signal lines, with reference to  FIG.  143   . 
     (Scheme  1 : Leading at IF) 
     According to the scheme  1  as shown in  FIG.  143   , a signal received by the antenna # 1  is converted to a signal of the IF # 1 , a signal received by the antenna # 2  is converted to a signal of the IF # 2 . Then, the signal of the IF # 1  and the signal of the IF # 2  are led to the television  14105  provided in a house via separate signal lines  14106   a  and  1506   b , respectively. In this case, the IF # 1  and the IF # 2  may be the same, or may be different from each other. 
     (Scheme  2 : Leading at Radio Frequency (RF)) 
     According to the scheme  2 , a signal received by the antenna # 1  and a signal received by the antenna # 2  each having an RF at which the relay device has received the signal are led to houses without frequency conversion. In other words, in the relay device  14102 , as shown in  FIG.  144   , the signal received by the antenna # 1  and the signal received by the antenna # 2  are transmitted through relay units  14411  and  14412  which do not have a frequency conversion function, respectively, and then are transmitted through cables (signal lines)  14106   a  and  14106   b , respectively. Accordingly, the respective signals received by the antennas # 1  and # 2  each having an RF are led to the television  14105  provided in the house without frequency conversion. Note that the relay units  14411  and  14412  may perform waveform shaping such as band limiting and noise reduction. 
     Also, according to the scheme of transmitting signals to houses, there is also a structure where a television judges whether a relayed received signal uses an IF or an RF, and appropriately switches operations in accordance with the frequency which is used. 
     As shown in  FIG.  145   , a television  14501  includes a judgment unit  14531 . The judgment unit  14531  monitors a signal level of a received signal to judge whether the received signal uses an IF or an RF. 
     If judging that the received signal uses an IF, the judgment unit  14531  instructs the frequency converter  14221  to perform frequency conversion relating to the IF # 1  via a control signal  14532 , and instructs the frequency converter  14222  to perform frequency conversion relating to the IF # 2  via the control signal  14532 . 
     If judging that the received signal uses an RF, the judgment unit  14531  instructs each of the frequency converters  14221  and  14222  to perform frequency conversion relating to the RF via the control signal  14532 . 
     Then, the signals after frequency conversion are automatically detected by the MIMO detector  14224 . 
     Note that, instead of automatic judgment made by the judgment unit  14531 , the settings regarding the scheme of transmitting signals to houses may be designed via an input unit such a switch included in the television  14501 . The settings relate to “whether the number of signal lines is one or plural”, “whether an RF is used or an IF is used”, and so on. 
     The description has been given, with reference to  FIGS.  141  to  145   , on the scheme of transmitting signals to houses via a relay device for the case where a broadcast station transmits a plurality of modulated signals having the same frequency band by a plurality of antennas. Alternatively, as described in the present specification, the broadcast station may transmit a plurality of modulated signals by appropriately switching between “the transmission scheme of transmitting a plurality of modulated signals having the same frequency band by a plurality of antennas” and “the transmission scheme of transmitting a single modulated signal by a single antenna or a plurality of antennas”. Further alternatively, for a frequency band A, the broadcast station may transmit a plurality of modulated signals by performing FDM and using “the transmission scheme of transmitting a plurality of modulated signals having the same frequency band by a plurality of antennas”. In addition, for a frequency band B, the broadcast station may transmit a plurality of modulated signals by performing FDM and using “the transmission scheme of transmitting a single modulated signal by a single antenna or a plurality of antennas” for a frequency band B. 
     In the case where the broadcast station uses “the transmission scheme of transmitting a plurality of modulated signals having the same frequency band by a plurality of antennas” as a result of appropriately switching between “the transmission scheme of transmitting a plurality of modulated signals having the same frequency band by a plurality of antennas” and “the transmission scheme of transmitting a single modulated signal by a single antenna or a plurality of antennas”, the television can acquire data transmitted from the broadcast station using the scheme of “leading signals via a single signal line or a plurality of signal lines” to houses, as described above. 
     In the case where the broadcast station uses “the transmission scheme of transmitting a single modulated signal by a single antenna or a plurality of antennas”, the television can acquire data transmitted from the broadcast station using the scheme of “leading signals via a single signal line or a plurality of signal lines” to houses, in the similar way. In the case where a single signal line is used, signals may be received by both the antennas # 1  and # 2  shown in  FIG.  142   . (Here, the MIMO detector  14224  included in the television  14105  performs maximal ratio combining, thereby achieving excellent data reception quality.) Alternatively, only a signal received by one of the antennas # 1  and # 2  may be led to houses. In this case, the adder  14213  causes only the signal received by the one antenna to be transmitted through without performing addition operations. (Here, the MIMO detector  14224  included in the television  14105  performs not detection for MIMO but general detection (demodulation) for the case where a single modulated signal is transmitted and received.) 
     Also, in the case where the broadcast station transmits a plurality of modulated signals by performing FDM and using “the transmission scheme of transmitting a plurality of modulated signals having the same frequency band by a plurality of antennas” for the frequency band A and using “the transmission scheme of transmitting a single modulated signal by a single antenna or a plurality of antennas” for the frequency band B, the television performs detection (demodulation) such as described above for each frequency band. In other words, in order to demodulate a modulated signal having the frequency band A, the television performs detection (demodulation) such as described with reference to  FIGS.  142  to  145   . Also, in order to demodulate a modulated signal having the frequency band B, the television performs detection (demodulation) for use in “the transmission scheme of transmitting a single modulated signal by a single antenna or a plurality of antennas” as described above. Furthermore, in the case where there exists a frequency band other than the frequency bands A and B, detection (demodulation) may be performed in the similar way. 
     Note that  FIG.  141    shows, as an example, a relay system for the case where a common antenna is shared among a plurality of houses. Accordingly, signals received by antennas are distributed to a plurality of houses. Alternatively, a relay system corresponding to the relay system shown in  FIG.  141    may be provided in each house.  FIG.  141    represents an image that a signal line is wired to each house via the relay device. However, in the case where a relay system is provided in each house, a signal line is wired from the relay device to only a television device provided in the house. In this case, this number of signal lines to be wired may be one or plural. 
       FIG.  146    shows a relay device which has a new structure compared with the relay device included in the relay system shown in  FIG.  141   . 
     A relay device  14610  receives, as input, a signal  14601 _ 1  received by an antenna  14600 _ 1  for receiving radio waves of terrestrial digital television broadcast, a signal  14601 _ 2  received by an antenna  14600 _ 2  for receiving radio of terrestrial digital television broadcast, and a signal  14601 _ 3  received by a BS (Broadcasting Satellite) antenna  14600 _ 3  for receiving radio waves of satellite broadcast. Then, the relay device  14610  outputs a multiplexed signal  14608 . The relay device  14610  includes a filter  14603 , a plural modulated signal frequency converter  14604 , and a multiplexer  14607 . 
       FIG.  147    schematically shows, in portion (a), modulated signals transmitted from the broadcast station which correspond to the respective signals  14601 _ 1  and  14601 _ 2  received by the antennas  14601 _ 1  and  14601 _ 2 . In the portions (a) and (b) of  FIG.  147   , the horizontal axis represents frequency, and squares each represent a frequency band at which a transmission signal exists. 
     In the portion (a) of  FIG.  147   , in a frequency band of Channel  1  (CH_ 1 ), there exists no other transmission signal. This means that a broadcast station, which transmits terrestrial radio waves, transmits only a (single) modulated signal of the Channel  1  (CH_ 1 ) by an antenna. Similarly, in a frequency band of Channel L (CH_L), there exists no other transmission signal. This means that the broadcast station, which transmits terrestrial radio waves, transmits only a (single) modulated signal of the Channel L (CH_L) by an antenna. 
     On the other hand, in the portion (a) of  FIG.  147   , in a frequency band of Channel K (CH_K), there exist two modulated signals. (Accordingly, in the portion (a) of  FIG.  147 ( a ) , there are two squares expressed as Stream  1  and Stream  2  in the same frequency band.) The respective modulated signals of the Stream  1  and the Stream  2  are transmitted by different antennas at the same time. Note that, as described above, the Stream  1  and the Stream  2  each may be a modulated signal obtained using the precoding scheme of regularly hopping between precoding matrices, a modulated signal obtained by performing precoding without regularly hopping between precoding matrices, or a modulated signal obtained without performing precoding. Similarly, in a frequency band of Channel M (CH_M), there exist two modulated signals. (Accordingly, in the portion (a) of  FIG.  147 ( a ) , there are two squares expressed as the Stream  1  and the Stream  2  in the same frequency band.) The respective modulated signals of the Stream  1  and the Stream  2  are transmitted by different antennas at the same time. Note that, as described above, the Stream  1  and the Stream  2  each may be a modulated signal obtained using the precoding scheme of regularly hopping between precoding matrices, a modulated signal obtained by performing precoding without regularly hopping between precoding matrices, or a modulated signal obtained without performing precoding. 
     Also,  FIG.  147    schematically shows, in the portion (b), modulated signals transmitted from the broadcast station (BS) which correspond to the signal  14601 _ 3  received by the BS antenna  14600 _ 3 . 
     In the portion (b) of  FIG.  147   , in a frequency band of BS Channel  1  (CH 1 ), there exists no other transmission signal. This means that the broadcast station, which transmits BS radio waves, transmits only a (single) modulated signal of BS Channel  1  (CH 1 ) by an antenna. Similarly, in a frequency band of BS Channel  2  (CH 2 ), there exists no other transmission signal. This means that the broadcast station, which transmits BS radio waves, transmits only a (single) modulated signal of BS Channel  2  (CH 2 ) by an antenna. 
     In the portions (a) and (b) in  FIG.  147   , the same range of frequency band is allocated to the horizontal axis. 
     Although  FIG.  146    shows, as an example, the modulated signal transmitted by the terrestrial broadcast station and the modulated signal transmitted by the BS, modulated signals are not limited to be these. Alternatively, there may exist a modulated signal transmitted by CS (Communications Satellite) or a modulated signal transmitted by other different broadcasting system. In such a case, the relay device  14610  shown in  FIG.  146    includes a reception unit for receiving modulated signals transmitted from broadcasting systems. 
     Upon receiving the signal  14601 _ 1 , the filter  14603  eliminates a “signal having a frequency band of a plurality of modulated signals” included in the received signal  14601 _ 1 , and outputs a signal  14605  after filtering. 
     For example, in the case where frequency allocation for the received signal  14601 _ 1  is such as shown in the portion (a) of  FIG.  147   , the filter  14603  outputs the signal  14605  from which respective signals having the frequency bands of Channels K and Channel M have been eliminated, as shown in portion (b) of  FIG.  148   . 
     In the present embodiment, the plural modulated signal frequency converter  14604  has a function of the device described above as the relay devices  14102  and so on. Specifically, the plural modulated signal frequency converter  14604  detects a signal having a frequency band of a plurality of modulated signals, which have been transmitted from a broadcast station by different antennas in the same frequency band at the same time, and performs frequency conversion on the detected signal. In other words, the plural modulated signal frequency converter  14604  performs frequency conversion such that a “signal having a frequency band of a plurality of modulated signals” exists in each of two different frequency bands. 
     For example, the plural modulated signal frequency converter  14604  has the structure shown in  FIG.  142   , and converts a “signal having a frequency band of a plurality of modulated signals” included in signals received by two antennas to two intermediate frequencies, and as a result, the signal is converted to a frequency band that differs from a frequency band before conversion. 
     The plural modulated signal frequency converter  14604  shown in  FIG.  146    receives the signal  14601 _ 1  as input. As shown in  FIG.  149   , the plural modulated signal frequency converter  14604  extracts signals having frequency bands each where a plurality of modulated signals (a plurality of streams) exist, specifically, a signal of Channel K (CH_K)  14901  and a signal of Channel M (CH_M)  14902 , and converts each of the respective modulated signals having these two frequency bands to a different frequency band. As a result, the signal of Channel K (CH_K)  14901  is converted to a signal of a frequency band  14903  as shown in portion (b) of  FIG.  149   . Also, the signal of Channel M (CH_K)  14902  is converted to a signal of a frequency band  14904  as shown in portion (b) of  FIG.  149   . 
     Furthermore, the plural modulated signal frequency converter  14604  shown in  FIG.  146    receives the signal  14601 _ 2  as input. As shown in  FIG.  149   , the plural modulated signal frequency converter  14604  extracts signals having frequency bands each where a plurality of modulated signals (a plurality of streams) exist, specifically, a signal of the Channel K (CH_K)  14901  and a signal of Channel M (CH_M)  14902 , and converts each of the respective modulated signals having these two frequency bands to a different frequency band. As a result, the signal of the Channel K (CH_K)  14901  is converted to a signal of a frequency band  14905  as shown in portion (b) of  FIG.  149   . Also, the signal of the Channel K (CH_K)  14902  is converted to a signal of a frequency band  14906  as shown in portion (b) of  FIG.  149   . 
     Then, the plural modulated signal frequency converter  14604  shown in  FIG.  146    outputs a signal including components of the four frequency bands shown in the portion (b) of  FIG.  149   . 
     In the portions (a) and (b) of  FIG.  149   , the horizontal axis represents frequency, and the same range of frequency band is allocated to the horizontal axis. The frequency band of the signal shown in the portion (a) of  FIG.  149    does not overlap the frequency band of the signal shown in the portion (b) of  FIG.  149   . 
     The multiplexer  14607  shown in  FIG.  146    receives, as input, the signal  14605  output by the filter  14603 , the signal  14606  output by the plural modulated signal frequency converter  14604 , and the signal  14601 _ 3  input by the BS antenna  14600 _ 3 , and then multiplexes the received signals on the frequency domain. As a result, the multiplexer  14607  shown in  FIG.  146    obtains and outputs the signal  14608  including frequency components shown in  FIG.  151   . A television  14609  receives this signal  14608  as input. Therefore, it is possible to view television broadcast with a high data reception quality by leading signals via a single signal line. 
     Next, description is given, as another example, on respective schemes by the plural modulated signal frequency converter  14604 , which has the structure shown in  FIG.  142   , of setting a “signal having a frequency band of a plurality of modulated signals” included in signals received by two antennas to have a frequency band without frequency conversion and an IF band. 
     The plural modulated signal frequency converter  14604  shown in  FIG.  146    receives the signal  14601 _ 1  as input. As shown in  FIG.  150   , the plural modulated signal frequency converter  14604  extracts signals having frequency bands each where a plurality of modulated signals (a plurality of streams) exist, specifically, a signal of Channel K (CH_K)  15001  and a signal of Channel M (CH_M)  15002 , and converts each of the respective modulated signals having these two frequency bands to a different frequency band. As a result, the signal of the Channel K (CH_K)  15001  is converted to a signal of a frequency band  15003  as shown in portion (b) of  FIG.  150   . Also, the signal of the Channel M (CH_M)  15002  is converted to a signal of a frequency band  15004  as shown in the portion (b) of  FIG.  150   . 
     Furthermore, the plural modulated signal frequency converter  14604  shown in  FIG.  146    receives the signal  14601 _ 2  as input. As shown in  FIG.  150   , the plural modulated signal frequency converter  14604  extracts signals having frequency bands each where a plurality of modulated signals (a plurality of streams) exist, specifically, a signal of the Channel K (CH_K)  15001  and a signal of the Channel M (CH_M)  15002 , and arranges each of the respective modulated signals of these two frequency bands to the same frequency band before conversion. As a result, the signal of the Channel K (CH_K)  15001  is converted to a signal of the frequency band  15005  as shown in the portion (b) of  FIG.  150   . Also, the signal of the Channel M (CH_M)  15002  is converted to a signal of a frequency band  15006  as shown in the portion (b) of  FIG.  150   . 
     Then, the plural modulated signal frequency converter  14604  shown in  FIG.  146    outputs a signal including components of the four frequency bands shown in the portion (b) of  FIG.  150   . 
     In the portions (a) and (b) of  FIG.  150   , the horizontal axis represents frequency, and the same range of frequency band is allocated to the horizontal axis. The frequency bands  15001  and  15005  are the same frequency band. The frequency bands  15002  and  15006  are the same frequency band. 
     The multiplexer  14607  shown in  FIG.  146    receives, as input, the signal  14605  output from the filter  14603 , the signal output from the plural modulated signal frequency converter  14604 , and the signal  14601 _ 3  output from the BS antenna  14600 _ 3 , and then multiplexes the received signals on the frequency domain. As a result, the multiplexer  14607  shown in  FIG.  146    obtains and outputs the signal  14608  including frequency components shown in  FIG.  152   . The television  14609  receives this signal  14608  as input. Therefore, it is possible to view television broadcast with a high data reception quality by leading signals via a single signal line. 
     That is, signal leading to houses is performed such as described above, with respect to a signal, which is transmitted from the broadcast station in the frequency domain, having a frequency band which is used in the transmission scheme of transmitting a plurality of modulated signals by a plurality of antennas (for example, in the same frequency band at the same time). This exhibits advantageous effects that the television (terminal) achieves a high data reception quality and the number of signal lines to be wired to houses is reduced. Here, as described above, there may exist a frequency band where a transmission scheme is used of transmitting a single modulated signal from a broadcast station by one or more antennas. 
     In the present embodiment, the description has been given on the example where a relay device is provided on a rooftop of an apartment building or the like as shown in  FIG.  141    (portion (a) of  FIG.  153   ). However, the provision position of the relay device is not limited to this. Alternatively, as shown in portion (b) of  FIG.  153   , in the case where signals are led to a television or the like provided in each house, a relay device may be provided in each individual house, as described above. Further alternatively, as shown in portion (c) of  FIG.  153   , in the case where a cable television system operator receives broadcast waves (a plurality of modulated signals transmitted from a broadcast station), and re-distributes the received broadcast waves to each house and so on via a wire (cable), the relay device may be used as part of a relay system of the cable television system operator. 
     In other words, the respective relay devices described in the present embodiment shown in  FIGS.  142  to  146    each may be provided on a rooftop of an apartment building as shown in the portion (a) of  FIG.  153   . Alternatively, in the case where signals are led to a television or the like provided in each house, the relay device may be provided for each individual house as shown in the portion (b) of  FIG.  153   . Further alternatively, in the case where the cable television system operator receives broadcast waves (a plurality of modulated signals transmitted from the broadcast station), and re-distributes the received broadcast waves to each house and so on via a wire (cable), the relay device may be used as part of the relay system of the cable television system operator as shown in the portion (c) of  FIG.  153   . 
     Embodiment N 
     As described in the above embodiment of the present specification, the present embodiment describes a system of receiving a plurality of modulated signals transmitted by a plurality of antennas in the same frequency band at the same time using the precoding scheme of regularly hopping between precoding matrices, and re-distributing the received modulated signals via a cable television (wire). (Note that a precoding matrix hopping pattern for use in the precoding scheme of regularly hopping between precoding matrices may be any of the precoding matrix hopping patterns described in the present specification. Also, even in the case where a precoding matrix hopping pattern other than those described in the present specification are used, it is possible to implement the present embodiment. In addition, although the present specification provides description on the case where the precoding scheme of regularly hopping between precoding matrices is used, it is possible to execute the scheme described in the present embodiment even in the case where the precoding scheme of regularly hopping between precoding matrices is not used.) 
     A cable television system operator has a device for receiving radio waves of broadcast waves which are wirelessly transmitted, and re-distributes data such as video, audio, data information to each house and so on where reception of broadcast waves is difficult. In the general meaning, some cable television system operators provide Internet connection services and telephone connection services. 
     In the case where a broadcast station transmits a plurality of modulated signals by a plurality of antennas (for example, in the same frequency band at the same time), this cable television system operator might have a problem. The problem is explained in the following. 
     A transmission frequency for transmitting broadcast waves by the broadcast station is determined in advance. In  FIG.  154   , the horizontal axis represents frequency. As shown in  FIG.  154   , the broadcast station transmits a plurality of modulated signals of a certain channel (CH_K in  FIG.  154   ) from a plurality of antennas in the same frequency band at the same time. Note that Stream  1  and Stream  2  of the channel CH_K each contain different data, and accordingly a plurality of modulated signals are generated from the Stream  1  and the Stream  2 . 
     Here, the broadcast station wirelessly transmits, to the cable television system operator, the plurality of modulated signals of Channel K (CH_K) by the plurality of antennas in the same frequency band at the same time. Therefore, as described in the embodiment of the present specification, the cable television system operator receives, demodulates, and decodes signals which are transmitted from the broadcast station by the plurality of antennas in the frequency band of the Channel K (CH_K) at the same time. 
     As shown in  FIG.  154   , the plurality of modulated signals (two modulated signals in  FIG.  154   ) are transmitted at the frequency band of the Channel K (CH_K). Accordingly, if these modulated signals without conversion are distributed to a cable (a single wire) using the pass-through scheme, the data reception quality of data contained in the Channel K (CH_K) greatly degrades in each house to which the cable is wired. 
     In view of this, as described in the above Embodiment M, it is considered that the cable television system operator performs frequency conversion on each of a plurality of received signals of the Channel K (CH_K) to convert to two or more different frequency bands, and transmits a multiplexed signal. However, there is a case where other frequency band is difficult to use because of being occupied by other channel, satellite broadcast channel, and the like. 
     Therefore, the present embodiment discloses a scheme of, even in the case where frequency conversion is difficult to perform, re-distributing via a wire a plurality of modulated signals transmitted from the broadcast station in the same frequency band at the same time. 
       FIG.  155    shows the structure of a relay device for a cable television system operator.  FIG.  155    shows the case where the 2×2 MIMO communication system is used, in other words, the case where a broadcast station transmits two modulated signals in the same frequency band at the same time, and a relay device receives the modulated signals by two antennas. 
     The relay device for the cable television system operator includes a reception unit  15502  and a distribution data generating unit  15504 . 
     As described in the present specification, the reception unit  15502  performs reverse conversion processing of precoding and/or phase restoration processing is performed on each of a signal  15500 _ 1  and a signal  15500 _ 2  which are received by an antenna  15500 _ 1  and an antenna  15500 _ 2 , respectively. The reception unit  15502  obtains a data signal rs 1   15503 _ 1  and a data signal rs 2   15503 _ 2 , and outputs the obtained data signals rs 1   15503 _ 1  and rs 2   15503 _ 2  to the distribution data generating unit  15504 . Also, the reception unit  15502  outputs, as information  15503 _ 3  regarding a signal processing scheme, information regarding a signal processing scheme used for demodulating and decoding received signals and information regarding a transmission scheme used by the broadcast station for transmitting modulated signals, to the distribution data generating unit  15504 . 
     Note that although  FIG.  155    shows the case where the reception unit  15502  outputs data in two groups of the data signal rs 1   15503 _ 1  and the data signal rs 2   15503 _ 2 , this is just an example and the data output is not limited to this. Alternatively, the reception unit  15502  may output data in one group. 
     Specifically, the reception unit  15502  includes the wireless units  703 _X and  703 _Y, the channel fluctuation estimating unit  705 _ 1  for the modulated signal z 1 , the channel fluctuation estimating unit  705 _ 2  for the modulated signal z 2 , the channel fluctuation estimating unit  707 _ 1  for the modulated signal z 1 , the channel fluctuation estimating unit  707 _ 2  for the modulated signal z 2 , the control information decoding unit  709 , and the signal processing unit  711 , which are shown in  FIG.  7   . The antennas  15500 _ 1  and  15500 _ 2  shown in  FIG.  155    correspond to the antennas  701 _X and  701 _Y shown in  FIG.  7   , respectively. Note that the signal processing unit  711  relating to the present embodiment has the structure shown in  FIG.  156   , unlike the signal processing unit relating to Embodiment 1 shown in  FIG.  8   . 
     As shown in  FIG.  156   , the signal processing unit  711 , which is included in the reception unit  15502  relating to the present embodiment, includes an INNER MIMO detector  803 , a storage unit  815 , a log-likelihood calculating unit  15602 A, a log-likelihood calculating unit  15602 B, a hard-decision unit  15604 A, a hard-decision unit  15604 B, and a coefficient generating unit  15601 . 
     In  FIG.  156   , units that are common with those in  FIG.  8    have the same reference signs, and description thereof is omitted here. 
     The log-likelihood calculating unit  15602 A calculates a log-likelihood, and outputs a log-likelihood signal  15603 A to the hard-decision unit  15604 A, in a similar way to the log-likelihood calculating unit  805 A shown in  FIG.  8   . 
     Similarly, the log-likelihood calculating unit  15602 B calculates a log-likelihood, and outputs a log-likelihood signal  15603 B to the hard-decision unit  15604 B, in a similar way to the log-likelihood calculating unit  805 B shown in  FIG.  8   . 
     The hard-decision unit  15604 A makes hard decision on the log-likelihood signal  15603 A to obtain a bit value of the log-likelihood signal  15603 A, and outputs the bit value as the data signal rs 1   15503 _ 1  to the distribution data generating unit  15504 . 
     Similarly, the hard-decision unit  15604 B makes hard decision on the log-likelihood signal  15603 B to obtain a bit value of the log-likelihood signal  15603 B, and outputs the bit value as the data signal rs 2   15503 _ 2  to the distribution data generating unit  15504 . 
     In a similar way to the weighting coefficient generating unit  819 , the weighting coefficient generating unit  15601  generates a coefficient, and outputs the generated coefficient to the INNER MIMO detector  803 . In addition, the weighting coefficient generating unit  15601  extracts information regarding at least a modulation scheme used for two signals from a signal  818  regarding information on the transmission scheme indicated by the broadcast station (transmission device), such as information for specifying a precoding matrix hopping pattern used in the precoding scheme of regularly hopping between precoding matrices and a modulation scheme. Then, the weighting coefficient generating unit  15601  outputs a signal of the information  15503 _ 3  regarding the signal processing scheme including information regarding this modulation scheme to the distribution data generating unit  15504 . 
     As can be seen from the above description, the reception unit  15502  performs demodulation to a degree of performing calculation of a log-likelihood and hard decision. However, in this example, the reception unit  15502  does not perform error correction. 
       FIG.  156    shows the structure in which the reception unit  15502  includes the log-likelihood calculating unit and the hard-decision unit. Alternatively, the INNER MIMO detector  803  may make hard decision without making soft decision. In this case, the reception unit  15502  does not need to include the log-likelihood calculating unit and the hard-decision unit. Also, hard-decision results do not need to be rs 1  and rs 2 . Alternatively, soft-decision results for each bit may be rs 1  and rs 2 . 
     The distribution data generating unit  15504  shown in  FIG.  155    receives, as input, the data signal rs 1   15503 _ 1 , the data signal rs 2   15503 _ 2 , and the information  15503 _ 3  regarding the signal processing scheme, and generates a distribution signal  15505  for distribution to each contracted house and so on. 
     The following describes in detail the scheme of generating the distribution signal  15505  by the distribution data generating unit  15504  shown in  FIG.  155   , with reference to  FIGS.  157  to  159   . 
       FIG.  157    is a block diagram showing the structure of the distribution data generating unit  15504 . As shown in  FIG.  157   , the distribution data generating unit  15504  includes a combining unit  15701 , a modulation unit  15703 , a distribution unit  15705 . 
     The combining unit  15701  receives, as input, the data signal rs 1   15503 _ 1 , the data signal rs 2   15503 _ 2 , and the information  15503 _ 3  regarding the signal processing scheme and the transmission scheme used by the broadcast station for transmitting modulated signals. Then, the combining unit  15701  outputs, to the modulation unit  15703 , a combined data signal  15702  resulting from combining the data signals rs 1  and rs 2  defined by the information  15503 _ 3  regarding the signal processing scheme and the transmission scheme used by the broadcast station for transmitting modulated signals. In  FIG.  157   , the data signals rs 1   15503 _ 1  and rs 2   15503 _ 2  are shown. Alternatively, as described above, it is possible to employ the structure of outputting data in one group by combining the data signals rs 1  and rs 2  in  FIG.  156   . In this case, the combining unit  15701  shown in  FIG.  157    may be deleted. 
     The demodulation unit  15703  receives, as input, the combined data signal  15702  and the information  15503 _ 3  regarding the signal processing scheme and the transmission scheme used by the broadcast station for transmitting modulated signals, and performs mapping according to the set modulation scheme to generate a modulated signal  15704  for output. The scheme of setting the modulation scheme is described later in detail. 
     The distribution unit  15705  receives, as input, the modulated signal  15704  and the information  15503 _ 3  regarding the signal processing scheme and the transmission scheme used by the broadcast station for transmitting modulated signals. Then, the distribution unit  15705  distributes, to each contracted house and so on via a cable (wire), the modulated signal  15704 , the information of the modulation scheme used for the modulated signal  15704  as control information for demodulating and decoding in a television reception device provided in each house, and the distribution signal  15505  including control information indicating information of error correction coding such as information of coding and a coding rate for error correction coding. 
     The following describes in detail the processing performed by the combining unit  15701  and the demodulation unit  15703  shown in  FIG.  157   , with reference to  FIGS.  158  and  159   . 
       FIG.  158    is a conceptual diagram showing the data signal rs 1  and the data signal rs 2  that are input to the distribution data generating unit  15504 . In  FIG.  158   , the horizontal axis is the time domain. Squares shown in  FIG.  158    each represent a data block to be simultaneously distributed at each time. As the error correction coding, a systematic code may be used or a non-systematic code may be used. The data block is composed of data on which error correction coding has been performed. 
     Here, the respective modulation schemes used for transmitting the data signals rs 1  and rs 2  are each 16QAM. In other words, the modulation scheme used for transmitting the Stream  1  of the Channel K (CH_K) shown in  FIG.  154    is 16QAM, and the modulation scheme used for transmitting the Stream  2  of the Channel K (CH_K) shown in  FIG.  154    is 16QAM. 
     In this case, the number of bits constituting each symbol of the data signal rs 1  is four, and the number of bits constituting each symbol of the data signal rs 2  is four. Accordingly, the data blocks rs 1 _ 1 , rs 1 _ 2 , rs 1 _ 3 , rs 1 _ 4 , rs 2 _ 1 , rs 2 _ 2 , rs 2 _ 3 , and rs 2 _ 4  shown in  FIG.  158    are each 4-bit data. 
     As shown in  FIG.  158   , the data rs 1 _ 1  and the data rs 2 _ 1  are demodulated at a time t 1 , the data rs 1 _ 2  and the data rs 2 _ 2  are demodulated at a time t 2 , the data rs 1 _ 3  and the data rs 2 _ 3  are demodulated at a time t 3 , and the data rs 1 _ 4  and the data rs 2 _ 4  are demodulated at a time t 4 . 
     Note that an advantageous effect is exhibited that when the data rs 1 _ 1  and the data rs 1 _ 2  shown in  FIG.  158    are simultaneously distributed to each house and so on, there is a small delay in period when data is transmitted from the broadcast station to when the data reaches television (terminal). Similarly, the data rs 1 _ 2  and the data rs 2 _ 2  should be simultaneously distributed, the data rs 1 _ 3  and the data rs 2 _ 3  should be simultaneously distributed, and the data rs 1 _ 4  and the data rs 2 _ 4  should be simultaneously distributed. 
     Accordingly, the distribution data generating unit  15504  shown in  FIG.  155    combines data pieces (symbols) transmitted simultaneously included in the data signals rs 1  and rs 2  received from the reception unit  15502 , and performs processing so as to transmit the data signals in one symbol. 
     In other words, as shown in  FIG.  159   , one data symbol is composed of one symbol of the data signal rs 1 _ 1  and one symbol of the data signal rs 2 _ 1 . Specifically, in the case where the data signal rs 1 _ 1  and the data signal rs 1 _ 2  are judged to 4-bit data “0000” and 4-bit data “1111”, respectively as a result of hard decision, data pieces rs 1 _1+rs 2 _ 1  shown in  FIG.  158    corresponds to data “000θ1111”. The 8-bit data is defined as one data symbol. Similarly, data pieces rs 1 _ 2 +rs 2 _ 2  are defined as one data symbol composed of one symbol of the data signal rs 1 _ 2  and one symbol of the data signal rs 2 _ 2 , data pieces rs 1 _ 3 +rs 2 _ 3  are defined as one data symbol composed of one symbol of the data signal rs 1 _ 3  and one symbol of the data signal rs 2 _ 3 , and data pieces rs 1 _ 4 +rs 2 _ 4  are defined as one data symbol composed of one symbol of the data signal rs 1 _ 4  and one symbol of the data signal rs 2 _ 4 . In  FIG.  159   , the horizontal axis is the time domain, and squares each represent a data symbol to be transmitted at one time. Also, in  FIG.  159   , although the sign “+” is used for convenience, the sign “+” means not addition but data in a form where two data pieces are simply arranged. 
     By the way, the data pieces rs 1 _ 1 +rs 2 _ 1 , rs 1 _ 2 +rs 2 _ 2 , rs 1 _ 3 +rs 2 _ 3 , and rs 1 _ 4 +rs 2 _ 4  are each 8-bit data, and each are data that needs to be transmitted at one time. Although the 16QAM modulation scheme is used for transmitting the data signals rs 1  and rs 2 , it is impossible to transmit 8-bit data at one time in the 16QAM modulation scheme. 
     In view of this, the modulation unit  15703  modulates the input combined data signal  15702  in a modulation scheme enabling transmission of 8-bit data at one time, namely, the 256QAM modulation scheme. In other words, the modulation unit  15703  acquires information of a modulation scheme used for transmitting the two data signals from the information  15503 _ 3  regarding the signal processing scheme. Then, the modulation unit  15703  modulates the combined data signal  15702  in a modulation scheme whose number of constellation points is equal to a product of multiplication of the respective numbers of constellation points of the acquired two modulation schemes. Then, the modulation unit  15703  outputs a modulated signal  15704  resulting from modulation performed in the new modulation scheme (256QAM in this case) to the distribution unit  15705 . 
     Note that, in the case where the number of modulated signals transmitted from the broadcast station is one, the reception unit  15502  and the distribution data generating unit  15504  distribute the received modulated signal without conversion to a cable (wire) using the pass-through scheme. (Here, the description is given on the scheme of making hard decision and again performing modulation. Alternatively, a received signal may be amplified for transmission.) 
     In  FIG.  155   , the distribution signal  15505  distributed via a cable (wire) is received by a television reception device  16000  shown in  FIG.  160   . The television reception device  16000  shown in  FIG.  160    has substantially the same structure as that of the reception device  8500  shown in  FIG.  85   . Units in  FIG.  160    that are common with those in  FIG.  85    have the same reference signs, and description thereof is omitted here. 
     Upon receiving the distribution signal  15505  via a cable  16001 , a tuner  8501  extracts a signal of a designated channel, and outputs the extracted signal to a demodulation unit  16002 . 
     The demodulation unit  16002  has the following functions in addition to the functions of the demodulation unit  8500  shown in  FIG.  85   . Upon detecting that signals transmitted from the tuner  8501  are two or more signals which have been transmitted from a broadcast station in the same frequency band at the same time according to the control information included in the distribution signal  15505 , the demodulation unit  16002  divides each of the received modulated signals to two or more signals according to the control information. In other words, the demodulation unit  16002  performs processing of restoring the signal from the state shown in  FIG.  159    to the state shown in  FIG.  158   , and outputs a signal resulting from the processing to the stream input/output unit  8503 . The demodulation unit  16002  calculates a log-likelihood of each received signal, makes hard decision on the received signal, and divides data resulting from the calculation and the hard decision according to a mixing ratio of a plurality of signals. Then, the demodulation unit  16002  performs processing such as error correction on each of data pieces resulting from the division to obtain data. 
     In this way, the television reception device  16000  provided in each house can demodulate and decode broadcasts distributed via a cable (wire) even with respect to a channel at which a plurality of modulated signals are transmitted from a broadcast station to a cable television system operator in the same frequency band at the same time. 
     By the way, although the respective modulation schemes used for transmitting the two data signals rs 1  and rs 2  are each 16QAM in the present embodiment, combination of modulation schemes of transmitting a plurality of modulated signals is not limited to the combination of 16QAM and 16QAM. As an example, there are combinations shown in the following Table 8. 
     
       
         
           
               
               
               
             
               
                 TABLE 8 
               
               
                   
               
               
                 Number of 
                   
                   
               
               
                 modulated 
                   
                   
               
               
                 transmission 
                   
                 Re-modulation 
               
               
                 signals 
                 Modulation scheme 
                 scheme 
               
               
                   
               
             
            
               
                 2 
                 #1: BPSK, #2: BPSK 
                 QPSK 
               
               
                 2 
                 #1: BPSK, #2: QPSK 
                 8QAM 
               
               
                 2 
                 #1: BPSK, #2: 16QAM 
                 32QAM 
               
               
                 2 
                 #1: BPSK, #2: 64QAM 
                 128QAM 
               
               
                 2 
                 #1: BPSK, #2: 256QAM 
                 512QAM 
               
               
                 2 
                 #1: QPSK, #2: 16QAM 
                 64QAM 
               
               
                 2 
                 #1: QPSK, #2: 64QAM 
                 256QAM 
               
               
                 2 
                 #l: QPSK, #2: 256QAM 
                 1024QAM 
               
               
                 2 
                 #1: 16QAM, #2: 16QAM 
                 256QAM 
               
               
                 2 
                 #1: 16QAM, #2: 64QAM 
                 1024QAM 
               
               
                 2 
                 #1: 16QAM, #2: 256QAM 
                 4096QAM 
               
               
                 . . . 
                 . . . 
                 . . . 
               
               
                   
               
            
           
         
       
     
     Table 8 shows the correspondence among the number of streams generated by the broadcast station (the number of modulated signals for transmission in Table 8), combination of modulation schemes used for generating the two streams (sign # 1  and sign # 2  in Table 8 represent modulation schemes for Stream  1  and Stream  2 , respectively), and a re-modulation scheme as a modulation scheme for use in re-modulation on each combination by the modulation unit  15703 . 
     In  FIG.  157   , a re-modulation scheme to be used by the modulation unit  15703  is included in a combination of modulation schemes, which is indicated by the information  15503 _ 3  regarding the signal processing scheme and the transmission scheme used by the broadcast station for transmitting modulated signals which is received by the demodulation unit  15703  as input. Combinations shown here are just examples. As can be seen from Table 8, the number of constellation points of each re-modulation scheme is equal to a product of multiplication of the respective numbers of constellation points of the respective modulation schemes for two streams. Specifically, the product is a product of multiplication of the number of signal points of the mapping scheme for the Stream # 1  on the I (in-phase)-Q (quadrature) plane and the number of signal points of the mapping scheme for the Stream # 2  on the I (in-phase)-Q (quadrature) plane. In the case where the number of constellation points of the re-modulation scheme (the number of signal points of the re-modulation scheme on the I (in-phase)-Q (quadrature) plane) exceeds this product, a modulation scheme other than the re-modulation schemes shown in Table 8 may be used. 
     Furthermore, also in the case where the number of streams transmitted from the broadcast station is at least three, a modulation scheme to be used by the modulation unit  15703  is determined based on a product of multiplication of the respective numbers of constellation points of the respective modulation schemes for the streams. 
     In the present embodiment, the description has been given on the case where the relay device makes hard decision to combine data pieces. Alternatively, soft decision may be made. In the case where soft decision is made, it is necessary to correct a baseband signal mapped according to a re-modulation scheme based on a soft-decision value. 
     Also, as described above, the data signals rs 1  and rs 2  are output in  FIG.  155   . The reception unit  15502  may output a single data signal by combining these data signals rs 1  and rs 2 . In this case, the number of data lines is one. In the case where the number of bits to be transmitted in one symbol of the Stream  1  is four and the number of bits to be transmitted in one symbol of the Stream  2  is four, the reception unit  15502  outputs the data signal via the single data line by defining 8-bit data as one data symbol. Here, a modulation scheme for re-modulation be used by the modulation unit  15703  shown in  FIG.  157    is the same as described above, and is for example 256QAM. That is, Table 8 is applicable. 
       FIG.  161    shows another structure of a relay device for the cable television system operator shown in  FIG.  155   . A reception unit  16102  and a distribution data generating unit  16104  included in the relay device shown in  FIG.  161    differ from those in  FIG.  155   , and perform processing on only a signal having a frequency band at which a plurality of modulated signals transmitted from a broadcast station in the same frequency band at the same time. The distribution data generating unit  16104  combines the signals as described above, and generates a signal  16105  by mapping, on the frequency band, a signal modulated in a modulation scheme that differs from the modulation scheme used at transmission from the broadcast station, and outputs the generated signal  16105 . 
     On the other hand, a signal  15501 _ 1  received by an antenna  15500 _ 1  is supplied to a filter  16106  in addition to the reception unit  16102 . 
     In the case where a plurality of modulated signals are transmitted from the broadcast station in the same frequency band at the same time, the filter  16106  eliminates only a signal having the frequency band from the received signal  15501 _ 1 , and outputs a signal  16107  after filtering to a multiplexer  16108 . 
     Then, the multiplexer  16108  multiplexes the signal  16107  after filtering and the signal  16105  output by the distribution data generating unit  16104  to generate a distribution signal  15505 , and distributes the generated distribution signal  15505  to each house via a cable (wire). 
     With this structure, the relay device for the cable television system operator does not need to perform processing on a signal having a frequency band other than the frequency band at which the plurality of modulated signals have been transmitted at the same time. 
     Although the present embodiment has described the relay device for the cable television system operator, the relay device is not limited to this. The relay device described in the present embodiment is in the form shown in the portion (c) of  FIG.  153   . Alternatively, as shown in the portions (a) and (b) of  FIG.  153   , a relay device for an apartment building, a relay device for individual house, and so on may be used. 
     Also, in the present embodiment, frequency conversion is not performed on a signal having a frequency band at which a plurality of modulated signals have been transmitted. Alternatively, frequency conversion such as described in Embodiment M may be performed on a signal having the frequency band at which the plurality of modulated signals have been transmitted. 
     Embodiment O 
     In other embodiments, the description has been given on the case where the precoding scheme of regularly hopping between precoding matrices is used in the broadcast system. In the present embodiment, description is given on the case where the precoding scheme of regularly hopping between precoding matrices is used in the communication system. In the case for use in the communication system, the following three sets of communication configurations and transmission schemes are employed as shown in  FIG.  162   . 
     (1) Multicast communication: Like in other embodiments, with use of the precoding scheme of regularly hopping between precoding matrices, a base station can transmit data to many terminals. 
     For example, the precoding scheme of regularly hopping between precoding matrices is used for multicast communication for simultaneous distribution of contents from a base station  16201  to mobile terminals  16202   a  to  16202   c  (portion (a) in  FIG.  162   ). 
     (2) Unicast communication and closed-loop (where feedback information is received from a communication terminal (specifically, CSI (Channel State Information) is fed back from the communication terminal or precoding matrices which are desirable to be used by the base station is designated by the communication terminal)): Based on the CSI transmitted from the communication terminal and/or information of the precoding matrices which are desirable to be used by the base station, the base station selects precoding matrices from among prepared precoding matrices. The base station performs precoding on a plurality of modulated signals using the selected precoding matrices, and transmits the plurality of modulated signals by a plurality of antennas in the same frequency band at the same time.  FIG.  162    shows an example in portion (b). 
     (3) Unicast communication and open-loop (where hopping between precoding matrices is performed independent from information transmitted from a communication terminal): The base station uses the precoding scheme of regularly hopping between precoding matrices.  FIG.  162    shows an example in portion (c). 
     Note that although  FIG.  162    shows examples of communication between a base station and communication terminals, communication may be performed between base stations or between communication terminals. 
     The following describes the structure of a base station (transmission device) and a mobile terminal (reception device) for realizing the above communication configuration. 
       FIG.  163    shows an example of the structure of a transmission and reception device of a base station relating to the present embodiment. Units included in the transmission and reception device of the base station shown in  FIG.  163    which have the same functions as the units included in the transmission device shown in  FIG.  4    have the same reference signs, and description thereof is omitted. Description is given on only the structure different from in  FIG.  4   . 
     As shown in  FIG.  163   , the transmission and reception device of the base station includes, in addition to the units shown in  FIG.  4   , an antenna  16301 , a wireless unit  16303 , and a feedback information analysis unit  16305 . Also, the transmission and reception device includes a weighting information generating unit  16314 , instead of the weighting information generating unit  314 . 
     The antenna  16301  is an antenna for receiving data transmitted from a communication partner of the transmission and reception device of the base station. Here, part of the reception device of the base station shown in  FIG.  163    receives feedback information transmitted from the communication partner. 
     The wireless unit  16303  demodulates and decodes a reception signal  16302  received by the antenna  16301 , and outputs a data signal  16304  resulting from demodulation and decoding to the feedback information analysis unit  16305 . 
     The feedback information analysis unit  16305  acquires, from the data signal  16304 , feedback information transmitted from the communication partner. The feedback information includes, for example, at least one of CSI, information of precoding matrices which are desirable to be used by the base station, a communication scheme to be requested to the base station (request information indicating whether multicast communication is to be used or unicast communication is to be used, and request information indicating whether open-loop is used or closed-loop is used). The feedback information analysis unit  16305  outputs the acquired feedback information as feedback information  16306 . 
     The weighting information generating unit  16314  receives, as input, a frame structure signal  16313  and the feedback information  16306 . The weighting information generating unit  16314  selects any one of the transmission schemes ( 1 ) to ( 3 ) described in the present embodiment, based on both the frame structure signal  16313  and the feedback information  16306  (a transmission scheme requested by a terminal may be prioritized or a transmission scheme desired by the base station may be prioritized). Then, the weighting information generating unit  16314  outputs control information  16315  including information of the selected transmission scheme. In the case where the transmission schemes ( 1 ) and ( 3 ) described in the present embodiment are each selected, the control information  16315  includes information regarding the precoding matrix hopping pattern used in the precoding scheme of regularly hopping between precoding matrices. Also, in the case where the transmission scheme ( 2 ) described in the present embodiment is selected, the control information  16315  includes information of precoding matrices to be used. The weighting units  308 A and  308 B each receive, as input, the control information  16315  including the information of the selected transmission scheme, performs precoding processing based on the designated precoding matrices, and outputs a signal  309 B resulting from the precoding processing. 
     This allows the transmission device to perform transmission suitable for each of the above three communication configurations. In order to notify a terminal that is a communication partner of information of the transmission scheme indicating which one of the transmission schemes ( 1 ) to ( 3 ) described in the present embodiment is selected and so on, the wireless unit  310 A receives, as input, the control information  16315  including the information of the selected transmission scheme. The wireless unit  310 A generates a symbol for transmitting the information of the selected transmission scheme, and inserts the generated symbol into a transmission frame. A transmission signal  311 A including this symbol is transmitted as a radio wave by the antenna  312 A. 
       FIG.  164    shows an example of the structure of a reception device of a terminal relating to the present embodiment. As shown in  FIG.  164   , the reception device includes a reception unit  16403 , a CSI generating unit  16405 , a feedback information generating unit  16407 , and a transmission unit  16409 . 
     The reception unit  16403  has the same structure as those shown in  FIGS.  7  and  8    in the above Embodiment 1. The reception unit  16403  receives, as input, a signal  16402 A received by an antenna  16401 A and a signal  16402 B received by an antenna  16401 B to acquire data transmitted from the transmission device. 
     Here, the reception unit  16403  outputs a signal  16404  of channel estimation information obtained in a process of acquiring the data to the CSI generating unit  16405 . The signal  16404  of the channel estimation information is output for example from each of the channel fluctuation estimating units  705 _ 1 ,  705 _ 2 ,  707 _ 1 , and  707 _ 2  shown in  FIG.  7   . 
     Based on the input signal  16404  of the channel estimation information, the CSI generating unit  16405  generates CQI (Channel Quality Information), RI (Rank Indication), and PMI (Precoding Matrix Indicator) which are basis for feedback information to be fed back to the transmission device (CSI (Channel State Information)), and outputs the generated CQI, RI, and PMI to the feedback information generating unit  16407 . The CQI, the RI, and the PMI are each generated by a conventional scheme. Particularly, the PMI is information for the reception device to designate precoding matrices for precoding which is desirable to be performed by the transmission device. 
     The feedback information generating unit  16407  generates the CSI based on the CQI, RI, and PMI generated by the CSI generating unit  16405 .  FIG.  165    shows an example of the frame structure of feedback information (CSI). 
     The transmission unit  16409  modulates the feedback information (CSI) transmitted from the feedback information generating unit  16407 , and transmits a modulated signal  16410  to the transmission device by an antenna  16411 . 
     Note that the terminal may feed all or part of the pieces of information shown in  FIG.  165    back to the base station. Also, information to be fed back is not limited to the pieces of information shown in  FIG.  165   . The base station selects one of the transmission schemes ( 1 ) to ( 3 ) described in the present embodiment, based on the feedback information transmitted from the terminal. Here, the base station does not necessarily need to select a transmission scheme of transmitting a plurality of modulated signals by a plurality of antennas. The base station may select other transmission scheme such as a transmission scheme of transmitting one modulated signal by at least one antenna, based on feedback information transmitted from the terminal. 
     With the above structure, it is possible to select a transmission scheme suitable for each of the communication configurations ( 1 ) to ( 3 ) described in the present embodiment. This allows the terminal to achieve excellent data reception quality in every communication configuration. 
     INDUSTRIAL APPLICABILITY 
     The present invention is widely applicable to wireless systems that transmit different modulated signals from a plurality of antennas, such as an OFDM-MIMO system. Furthermore, in a wired communication system with a plurality of transmission locations (such as a Power Line Communication (PLC) system, optical communication system, or Digital Subscriber Line (DSL) system), the present invention may be adapted to MIMO, in which case a plurality of transmission locations are used to transmit a plurality of modulated signals as described by the present invention. A modulated signal may also be transmitted from a plurality of transmission locations. 
     REFERENCE SIGNS LIST 
     
         
         
           
               302 A,  302 B encoder 
               304 A,  304 B interleaver 
               306 A,  306 B mapping unit 
               314  weighting information generating unit 
               308 A,  308 B weighting unit 
               310 A,  310 B wireless unit 
               312 A,  312 B antenna 
               402  encoder 
               404  distribution unit 
               504 # 1 ,  504 # 2  transmit antenna 
               505 # 1 ,  505 # 2  transmit antenna 
               600  weighting unit 
               703 _X wireless unit 
               701 _X antenna 
               705 _ 1  channel fluctuation estimating unit 
               705 _ 2  channel fluctuation estimating unit 
               707 _ 1  channel fluctuation estimating unit 
               707 _ 2  channel fluctuation estimating unit 
               709  control information decoding unit 
               711  signal processing unit 
               803  INNER MIMO detector 
               805 A,  805 B log-likelihood calculating unit 
               807 A,  807 B deinterleaver 
               809 A,  809 B log-likelihood ratio calculating unit 
               811 A,  811 B soft-in/soft-out decoder 
               813 A,  813 B interleaver 
               815  storage unit 
               819  weighting coefficient generating unit 
               901  soft-in/soft-out decoder 
               903  distribution unit 
               1301 A,  1301 B OFDM related processor 
               1402 A,  1402 A serial/parallel converter 
               1404 A,  1404 B reordering unit 
               1406 A,  1406 B inverse Fast Fourier transformer 
               1408 A,  1408 B wireless unit 
               2200  precoding weight generating unit 
               2300  reordering unit 
               4002  encoder group