Patent Publication Number: US-7903753-B2

Title: Structured space-time code achieving the full diversity and full rate and generating method thereof, and multi-input multi-output system

Description:
TECHNICAL FIELD 
     The present invention relates to a multi-input multi-output (MIMO) system, and particularly to a structured space-time code designed to simultaneously achieve full diversity even under full spatial multiplexing rate by using multiples antennas at both the transmitter and receiver sides, and a method for generating the same, and a MIMO system capable of enhancing reliability and/or increasing the transmission capacity by using the space-time code in a wireless communication environment. 
     BACKGROUND ART 
     Recently, the generalization of telecommunication services, and the emergence of various multimedia and high-quality services have resulted in the increase of demands to communication services. To actively copy with these trends, the capacity of a communication system should be increased in a wireless communication environment rather than in a wired communication environment. This is because in the wireless environment, available frequency spectrum is extremely limited and should be shared, and the need for wireless communication services gets increasing fastly by its inherent unthetheredness. 
     The capacity of wireless communication systems can be increased by allocating a greater bandwidth and enhancing the efficiency of a given radio resource. 
     Various methods to increase the efficiency of the given radio resource have been developed, Among them, a space-time coding method has attracted considerable attention in the wireless communication environment since it can improve the reliability of data transmission in a wireless communication system by using additionally the spatial dimension for resource utilization without bandwidth expansion and/or increase transmission capacity through parallel transmission using spatial multiplexing. 
     In a like manner, transmission capacity of wireless communication systems may be remarkably increased by employing MIMO techniques. 
     A space-time block coding method proposed by Alamouti (entitled “A simple transmit diversity technique for wireless communications”, IEEE JSAC, vol. 16, no. 8, October 1998) is a representative transmit diversity technique that overcomes multipath fading over wireless channels by using multiple antennas both at the transmitter and receiver. The above space-time block coding method uses only two transmit antennas and can achieve the full diversity by providing the diversity order corresponding to a product of the number of transmit antennas and the number of receive antennas. However, the above methods can transmit only two data symbols during two time slots through two transmit antennas, thus resulting in a transmission rate of 1, and no spatial multiplexing gain is achieved irrespective of the number of receive antennas. Furthermore, this method cannot be applied to the case of more than three transmit antennas. 
     Bell Lab&#39;s V-BLAST (Vertical Bell Laboratories Layered Space-Time) system (entitled “Detection algorithm and initial laboratory results using V-BLAST space-time communication architecture”, IEEE, Vol. 35, No. 1, pp. 14-16, 1999) is a representative method for achieving a spatial multiplexing gain. In the V-BLAST system, each transmit antenna transmits a different signal with the same transmission power and data rate, and a receiver performs the three consecutive processes of detection ordering, interference nulling, and interference cancellation to remove undesired interference signals, thereby to increase a signal-to-noise ratio (SNR) when the receiver detects the transmitted signal. In the V-BLAST system, the full spatial multiplexing gain is maintained since independent data signals corresponding to the number of transmit antennas can be simultaneously transmitted if the number of transmit antennas is equal to or greater than the number of receive antennas. However, this method requires the number of receive antennas to be equal to or greater than the number of transmit antennas and achieves the full multiplexing gain with no diversity gain. Moreover, once a data symbol is restored with error, the erroneous data is propagated to the following signal detection processes thereby resulting in severe performance degradation. 
     Meanwhile, a tilted Quadrature Amplitude Modulation (QAM) code proposed by Yao and Wornell (entitled “Structured space-time block codes with optimal diversity-multiplexing tradeoff and minimum delay,” Globecom, pp. 1941-1945, 2003) is a space-time code for providing full diversity and full rate (FDFR) that achieves an optimal diversity-multiplexing tradeoff proposed by Zhang and Tse. The tilted QAM code is a short space-time block code with code length of two for a system with two transmit antennas and two receive antennas, and the rotation of QAM constellations is used to obtain the full diversity gain while preserving the full multiplexing gain. However, this algorithm cannot obtain a full coding gain because it uses simple rotation of a signal, and may be exploited only with a two transmit antenna and two receive antenna system. The information disclosed in this Background of the Invention section is only for enhancement of understanding of the background of the invention, and therefore, unless explicitly described to the contrary, it should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art that is already known in this country to a person of ordinary skill in the art. 
     DISCLOSURE 
     Technical Problem 
     The present invention has been made in an effort to provide a structured space-time code and a method for generating the structured space-time code, and a multi-input multi-output system having advantages of achieving full diversity and full rate (FDFR) transmissions using the space-time code. 
     Technical Solution 
     In one aspect of the present invention, a space-time code is used for a transmitter to transmit a plurality of data symbols from a transmitter to a receiver in a multi-input multi-output (MIMO) system having multiple transmit antennas and multiple receive antennas. The space-time code includes a square code word matrix for transmitting an amount of data symbols corresponding to a product of the number of transmit antennas and a spatial multiplexing rate during one code block period, a row index of the code word matrix indicating combined signals transmitted through different transmit antennas and a column index of the code word matrix indicating time slots. 
     In a code block, an average number of data symbols allocated to each transmit antenna at every time slot is equal to the spatial multiplexing rate and at every time slot, the data symbols allocated for each transmit antenna are combined together and simultaneously transmitted through the corresponding transmit antenna, and each transmit antenna transmits a different set of data symbols from a time slot to another. 
     In addition, when setting a code word matrix to transmit a plurality of data symbols that correspond to a product of the number of transmit antennas and the spatial multiplexing rate during one code block period, every data symbols to be transmitted in the code block period is allocated at least once to all transmit antennas. 
     When the average number of data symbols that corresponds to the spatial multiplexing rate is allocated to each transmit antenna at every time slot of the code word matrix, different sets of data symbols are allocated to the respective transmit antennas for transmission. 
     When the data symbols allocated to each transmit antenna are combined together and simultaneously transmitted through the corresponding transmit antenna, the data symbols allocated to each transmit antenna are combined together with a set of combining coefficients from a transmit antenna to another. 
     In addition, the code word matrix is determined to control the time slot when allocating a set of data symbols to each transmit antenna, the data symbols are controlled to be rotationally moved from one transmit antenna to another and allocated to an adjacent transmit antenna. 
     In another aspect of the present invention, a method for generating a space-time code used for transmitting a plurality of data symbols from a transmitting unit of a multi-input multi-output (MIMO) system to a receiver is provided. The method includes a) setting columns and rows of a codeword matrix determining the space-time code to match with the number of antennas at the transmitting unit, the row corresponding to the number of antennas of the receiving unit and the column corresponding to the number of time slots for one code block period; b) determining an average number of data symbols to be transmitted during the code block period by a product of the number of antennas at the transmitting side and a spatial multiplexing rate; c) selecting a given row in the code word matrix, and allocating the average number of data symbols that corresponds to the spatial multiplexing rate among the data symbols determined in b); d) allocating a combining coefficient corresponding to the average number of data symbols allocated in c) to each data symbol and combining each by using the combining coefficient; and e) iteratively performing c) and d) on other rows, excluding the row selected in c) and d) while allocating different data symbols in the respective rows and columns of the code word matrix and, at the same time, allocating a different combining coefficient to each symbol allocated to the respective rows. 
     In e), when allocating a data symbol to each column of a row that is adjacent to the selected row, data symbols allocated to columns of the selected row are controlled to be rotationally moved with respect to the selected row and allocated to the adjacent row. 
     In addition, after e), the method further includes selecting combining coefficients allocated to the respective symbols to equalize mean powers of the data symbols allocated to the respective columns of the selected row of the code word matrix, average transmit power of the selected row, or average transmit power allocated to the respective data symbols. 
     In another aspect of the present invention, a multi-input multi-output (MIMO) system includes a transmitting unit and a receiving unit. The transmitting unit generates space-time codes for data symbols that correspond to a product of the number of transmit antennas and a spatial multiplexing rate within one code block period, and transmits the space-time codes through a plurality of transmit antennas. The receiving unit receives signals transmitted to the transmitting unit using a plurality of receive antennas, decodes the signals, and restoring data symbols corresponding to the signals. The space-time codes are formed in a code word matrix that corresponding to the number of the transmit antennas, rows of the code matrix indicating time slots that correspond to the number of transmit antennas and columns of the codeword matrix representing the number of time slots corresponding to the number of receive antennas. In the codeword matrix, an average number of data symbols allocated to the respective receive antennas for transmission corresponds to the spatial multiplexing rate. The data symbols are combined together by different combining coefficients, respectively, and synchronously transmitted to the corresponding transmit antenna, and the respective antennas in each time slot are allocated with different sets of data symbols. 
     Advantageous Effects 
     Accordingly, the present invention is proposed to provide a space-time code and a method of generating the same, and a multi-input multi-output (MIMO) system using the space-time code. The space-time code has a minimum delay while simultaneously achieving the full diversity gain and the full multiplexing gain, and the multi-input multi-output (MIMO) system transmits simultaneously data symbols through a plurality of transmit antennas by using the space-time code. 
    
    
     
       DESCRIPTION OF DRAWINGS 
         FIG. 1  is a block diagram of a MIMO system that uses a structured space-time code to obtain the full diversity gain and the full multiplexing gain according to an embodiment of the present invention. 
         FIG. 2  exemplarily illustrates an example of a space-time codeword matrix in the MIMO system with two transmit antennas and the spatial multiplexing rate 2 of  FIG. 1 . 
         FIG. 3  exemplarily illustrates an example of a space-time codeword matrix in the MIMO system with three transmit antennas and the spatial multiplexing rate 1 of  FIG. 1 . 
         FIG. 4  exemplarily illustrates an example of a space-time codeword matrix in the MIMO system with three transmit antennas and the spatial multiplexing rate 2 of  FIG. 1 . 
         FIG. 5  exemplarily illustrates an example of a space-time codeword matrix in the MIMO system with four transmit antennas and the spatial multiplexing rate 1 of  FIG. 1 . 
         FIG. 6  exemplarily illustrates an example of a space-time codeword matrix in the MIMO system with four transmit antennas and the spatial multiplexing rate 2 of  FIG. 1 . 
     
    
    
     BEST MODE 
     In the following detailed description, only the preferred embodiment of the invention has been shown and described, simply by way of illustration of the best mode contemplated by the inventor(s) of carrying out the invention. As will be realized, the invention is capable of modification in various obvious respects, all without departing from the invention. Accordingly, the drawings and description are to be regarded as illustrative in nature, and not restrictive. A method for generating a structured space-time code for the full diversity gain and the full multiplexing gain according to an embodiment of the present invention will hereinafter be described with reference to the accompanying drawings. 
       FIG. 1  is a block diagram of a MIMO system that employs structured space-time coding designed for achieving the full diversity gain and the full multiplexing gain according to an embodiment of the present invention. 
     As shown in  FIG. 1 , the MIMO system includes a transmitter  100  that encodes input data symbols according to the structured space-time code and transmits the encoded data input through N t  transmit antennas, and a receiver  200  that receives signals through N r  receive antennas and decodes the signals by using some decoding rule based on the structured time-space code. 
     The transmitter  100  includes a space-time encoder  110  and a plurality of transmit antennas  120 _ 1 - 120 _N t . 
     The space-time encoder  110  generates encoded symbols using the proposed space-time code (to be described later) from input data symbols, and transmits the space-time coded symbols to the receiver  200  through a plurality of transmit antennas  120 _ 1 - 120 _N t . 
     The receiver  200  includes a plurality of receive antennas  210 _ 1 - 210 _N r  and a space-time decoder  220 . 
     The space-time decoder  220  restores the data symbol transmitted from the transmitter  100  by decoding signals received through the plurality of receive antennas  210 _ 1 - 210 _N r  using some decoding rule based on the space-time code. 
     The space-time encoder  110  of the transmitter  100  and the space-time decoder  220  of the receiver  200  respectively encode data symbols and decode the received signals using some decoding rule based on the space-time code according to the embodiment of the present invention. Throughout the specification, a structure of the space-time code and an encoding algorithm will be described, but a decoding algorithm will not be further described since it is well-known to those skilled in the art. 
     A space-time code is a block code that is defined by a square matrix corresponding to a product of the number of transmit antennas and the number of time slots for a code block. Rows of the matrix indicate combined signals respectively transmitted through different transmit antennas and columns of the matrix indicate time slots indicates the time slots according to an embodiment of the present invention. 
     When the number of transmit antennas is set to be N t , the number of receive antennas is set to be N r , and a spatial multiplexing rate is set to be r, the combined signal that is actually transmitted through N t  transmit antennas during N t  time slots may be defined by [Math Figure 1]. Herein, basically min(N t , N r ) should be set to be equal to or greater than r to obtain the spatial multiplexing rate r, and the signals transmitted through the corresponding transmit antennas at every time slot are determined by combining all data symbols transmitted in a code block period with different sets of complex weights. 
     
       
         
           
             
               
                 
                   
                     
                       
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     where S n  is an n-th data symbol, and y m  is a combined signal actually transmitted through the transmit antenna. Herein, c i,j  is a combining coefficient given as a complex number. 
     A space-time codeword matrix C can be defined by [Math Figure 2]. 
     
       
         
           
             
               
                 
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     The number of rows in matrix C set to be equal to the number of transmit antennas N t , for minimum delay. 
     The space-time code is designed to simultaneously transmit N t ×r data symbols during one code block period. Thus, the number of data symbols corresponding to the spatial multiplexing rate γ is allocated to each transmit antenna at a time slot within the code block period. The data symbols allocated to each antenna are combined with different complex weights and simultaneously transmitted. 
     The same set of data symbols corresponding to the spatial multiplexing rate r is repeated at every time slot in the code block period, but transmitted through different transmit antennas with different sets of complex weights. 
     When allocating the data symbols to each transmit antennas, a random data symbol is allocated only once to a specific transmit antenna, and is allocated to each transmit antenna at least once to all transmit antennas during one code block period according to an embodiment of the present invention. 
     A set of data symbols allocated to each transmit antenna may be variously formatted at every time slot, and the data symbols are transmitted through the corresponding transmit antenna with a different set of complex weights at every time slot. A combining coefficient C i,j  that combines data symbols of the respective rows is preferably set to be “0,” excluding r number of combining coefficients allocated to each transmit antennas. Further, it is preferred to set a value of the combining coefficient C i,j  to be appropriate such that each data symbol is transmitted at least once and only once through all transmit antennas during one code block period when allocating data symbols per antenna at every time slot during the code block period. 
     For simplicity in concept and design as shown in [Math Figure 3], sets of data symbols allocated to each transmit antenna at every time slot are rotationally shifted by one transmit antenna to another and allocated to adjacent antennas, respectively. The data symbols allocated to the adjacent antennas are combined together with different complex weights and then transmitted. 
     
       
         
           
             
               
                 
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                                   · 
                                   r 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 c 
                                 
                                   1 
                                   , 
                                   1 
                                 
                                 2 
                               
                               ⁢ 
                               
                                 s 
                                 1 
                               
                             
                             + 
                             … 
                             + 
                             
                               
                                 c 
                                 
                                   1 
                                   , 
                                   r 
                                 
                                 2 
                               
                               ⁢ 
                               
                                 s 
                                 r 
                               
                             
                           
                         
                         
                           ⋯ 
                         
                         
                           
                             
                               
                                 c 
                                 
                                   
                                     N 
                                     t 
                                   
                                   , 
                                   1 
                                 
                                 T 
                               
                               ⁢ 
                               
                                 s 
                                 
                                   
                                     r 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         
                                           N 
                                           t 
                                         
                                         - 
                                         2 
                                       
                                       ) 
                                     
                                   
                                   + 
                                   1 
                                 
                               
                             
                             + 
                             … 
                             + 
                             
                               
                                 c 
                                 
                                   
                                     N 
                                     t 
                                   
                                   , 
                                   r 
                                 
                                 T 
                               
                               ⁢ 
                               
                                 s 
                                 
                                   
                                     ( 
                                     
                                       
                                         N 
                                         t 
                                       
                                       - 
                                       1 
                                     
                                     ) 
                                   
                                   · 
                                   r 
                                 
                               
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ] 
                 
               
             
           
         
       
     
     In [Math Figure 3], a combining coefficient c i,j   t  denotes a complex weight for combining a j-th data symbol transmitted through an i-th antenna at a t-th time slot. The definition of a complex weight will hereinafter be varied for simple description as necessary. 
     According to a first exemplarily embodiment of the present invention, if N t =2 and r=2, a space-time codeword is realized as a combination of data symbols defined by [Math Figure 4]. 
     
       
         
           
             
               
                 
                   
                     
                       
                         y 
                         1 
                       
                       = 
                       
                         
                           
                             c 
                             1 
                           
                           ⁢ 
                           
                             s 
                             1 
                           
                         
                         + 
                         
                           
                             c 
                             2 
                           
                           ⁢ 
                           
                             s 
                             2 
                           
                         
                       
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         y 
                         3 
                       
                       = 
                       
                         
                           
                             c 
                             5 
                           
                           ⁢ 
                           
                             s 
                             3 
                           
                         
                         + 
                         
                           
                             c 
                             6 
                           
                           ⁢ 
                           
                             s 
                             4 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         y 
                         2 
                       
                       = 
                       
                         
                           
                             c 
                             3 
                           
                           ⁢ 
                           
                             s 
                             3 
                           
                         
                         + 
                         
                           
                             c 
                             4 
                           
                           ⁢ 
                           
                             s 
                             4 
                           
                         
                       
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         y 
                         4 
                       
                       = 
                       
                         
                           
                             
                               c 
                               7 
                             
                             ⁢ 
                             
                               s 
                               1 
                             
                           
                           + 
                           
                             
                               c 
                               8 
                             
                             ⁢ 
                             
                               
                                 s 
                                 2 
                               
                               ⁢ 
                               
                                 
 
                               
                               ( 
                               
                                 
                                   
                                     
                                       y 
                                       1 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       
                                         2 
                                         ⁢ 
                                         
                                             
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       3 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       4 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                         = 
                         
                           
                             ( 
                             
                               
                                 
                                   
                                     c 
                                     1 
                                   
                                 
                                 
                                   
                                     c 
                                     2 
                                   
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                               
                               
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   
                                     c 
                                     3 
                                   
                                 
                                 
                                   
                                     c 
                                     4 
                                   
                                 
                               
                               
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   
                                     c 
                                     5 
                                   
                                 
                                 
                                   
                                     c 
                                     6 
                                   
                                 
                               
                               
                                 
                                   
                                     c 
                                     7 
                                   
                                 
                                 
                                   
                                     c 
                                     8 
                                   
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   
                                     s 
                                     1 
                                   
                                 
                               
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                 
                               
                               
                                 
                                   
                                     s 
                                     3 
                                   
                                 
                               
                               
                                 
                                   
                                     s 
                                     4 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ] 
                 
               
             
           
         
       
     
     In [Math Figure 4], a code matrix may be variously formatted depending on a combination of data symbols for the corresponding transmit antenna. However, a basic concept is that at one time slot, two data symbols in each transmit antenna are combined together with complex weights and transmitted, and during the other time slot, a different set of data symbols is allocated to the corresponding transmit antenna. 
     The space-time code of [Math Figure 4] may be realized as a space-time codeword matrix C of [Math Figure 5], and a MIMO system that uses such a codeword matrix is shown in  FIG. 2 . 
     
       
         
           
             
               
                 
                   C 
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               y 
                               1 
                             
                           
                           
                             
                               y 
                               3 
                             
                           
                         
                         
                           
                             
                               y 
                               2 
                             
                           
                           
                             
                               y 
                               4 
                             
                           
                         
                       
                       ) 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               
                                 
                                   c 
                                   1 
                                 
                                 ⁢ 
                                 
                                   s 
                                   1 
                                 
                               
                               + 
                               
                                 
                                   c 
                                   2 
                                 
                                 ⁢ 
                                 
                                   s 
                                   2 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   c 
                                   5 
                                 
                                 ⁢ 
                                 
                                   s 
                                   3 
                                 
                               
                               + 
                               
                                 
                                   c 
                                   6 
                                 
                                 ⁢ 
                                 
                                   s 
                                   4 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   c 
                                   3 
                                 
                                 ⁢ 
                                 
                                   s 
                                   3 
                                 
                               
                               + 
                               
                                 
                                   c 
                                   4 
                                 
                                 ⁢ 
                                 
                                   s 
                                   4 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   c 
                                   7 
                                 
                                 ⁢ 
                                 
                                   s 
                                   1 
                                 
                               
                               + 
                               
                                 
                                   c 
                                   8 
                                 
                                 ⁢ 
                                 
                                   s 
                                   2 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ] 
                 
               
             
           
         
       
     
     According to a second exemplarily embodiment of the present invention, if N t =3 and r=1, a space-time codeword is realized as a combination of data symbols defined by [Math Figure 6]. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 1 
                               
                               ⁢ 
                               
                                 s 
                                 1 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               4 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 4 
                               
                               ⁢ 
                               
                                 s 
                                 2 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               7 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 7 
                               
                               ⁢ 
                               
                                 s 
                                 3 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               2 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 2 
                               
                               ⁢ 
                               
                                 s 
                                 2 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               5 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 5 
                               
                               ⁢ 
                               
                                 s 
                                 3 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               8 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 8 
                               
                               ⁢ 
                               
                                 s 
                                 1 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               3 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 3 
                               
                               ⁢ 
                               
                                 s 
                                 3 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               6 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 6 
                               
                               ⁢ 
                               
                                 s 
                                 1 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             y 
                             9 
                           
                           = 
                             
                           ⁢ 
                           
                             
                               c 
                               9 
                             
                             ⁢ 
                             
                               
                                 s 
                                 2 
                               
                               . 
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       ( 
                       
                         
                           
                             
                               y 
                               1 
                             
                           
                         
                         
                           
                             
                               y 
                               2 
                             
                           
                         
                         
                           
                             
                               y 
                               3 
                             
                           
                         
                         
                           
                             
                               y 
                               4 
                             
                           
                         
                         
                           
                             
                               y 
                               5 
                             
                           
                         
                         
                           
                             
                               y 
                               6 
                             
                           
                         
                         
                           
                             
                               y 
                               7 
                             
                           
                         
                         
                           
                             
                               y 
                               8 
                             
                           
                         
                         
                           
                             
                               y 
                               9 
                             
                           
                         
                       
                       ) 
                     
                     = 
                     
                       
                         ( 
                         
                           
                             
                               
                                 c 
                                 1 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 c 
                                 2 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 c 
                                 3 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 c 
                                 4 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 c 
                                 5 
                               
                             
                           
                           
                             
                               
                                 c 
                                 6 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 c 
                                 7 
                               
                             
                           
                           
                             
                               
                                 c 
                                 8 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 c 
                                 9 
                               
                             
                             
                               0 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 s 
                                 1 
                               
                             
                           
                           
                             
                               
                                 s 
                                 2 
                               
                             
                           
                           
                             
                               
                                 s 
                                 3 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ] 
                 
               
             
           
         
       
     
     In [Math Figure 6], a code matrix may be variously formatted depending on a combination of signals for the corresponding antenna, and a space-time code of [Math Figure 6] may be realized as a codeword matrix C of [Math Figure 7].  FIG. 3  shows a MIMO system that uses such a codeword matrix. 
     
       
         
           
             
               
                 
                   C 
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               y 
                               1 
                             
                           
                           
                             
                               y 
                               4 
                             
                           
                           
                             
                               y 
                               7 
                             
                           
                         
                         
                           
                             
                               y 
                               2 
                             
                           
                           
                             
                               y 
                               5 
                             
                           
                           
                             
                               y 
                               8 
                             
                           
                         
                         
                           
                             
                               y 
                               3 
                             
                           
                           
                             
                               y 
                               6 
                             
                           
                           
                             
                               y 
                               9 
                             
                           
                         
                       
                       ) 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               
                                 c 
                                 1 
                               
                               ⁢ 
                               
                                 s 
                                 1 
                               
                             
                           
                           
                             
                               
                                 c 
                                 4 
                               
                               ⁢ 
                               
                                 s 
                                 2 
                               
                             
                           
                           
                             
                               
                                 c 
                                 7 
                               
                               ⁢ 
                               
                                 s 
                                 3 
                               
                             
                           
                         
                         
                           
                             
                               
                                 c 
                                 2 
                               
                               ⁢ 
                               
                                 s 
                                 2 
                               
                             
                           
                           
                             
                               
                                 c 
                                 5 
                               
                               ⁢ 
                               
                                 s 
                                 3 
                               
                             
                           
                           
                             
                               
                                 c 
                                 8 
                               
                               ⁢ 
                               
                                 s 
                                 1 
                               
                             
                           
                         
                         
                           
                             
                               
                                 c 
                                 3 
                               
                               ⁢ 
                               
                                 s 
                                 3 
                               
                             
                           
                           
                             
                               
                                 c 
                                 6 
                               
                               ⁢ 
                               
                                 s 
                                 1 
                               
                             
                           
                           
                             
                               
                                 c 
                                 9 
                               
                               ⁢ 
                               
                                 s 
                                 2 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     7 
                   
                   ] 
                 
               
             
           
         
       
     
     According to a third exemplarily embodiment of the present invention, if N t =3 and r=2, a space-time codeword is realized as a combination of data symbols defined by [Math Figure 8]. 
     
       
         
           
             
               
                 
                   
                     
                       
                         y 
                         1 
                       
                       = 
                       
                         
                           
                             c 
                             1 
                           
                           ⁢ 
                           
                             s 
                             1 
                           
                         
                         + 
                         
                           
                             c 
                             2 
                           
                           ⁢ 
                           
                             s 
                             2 
                           
                         
                       
                     
                     , 
                     
                         
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         y 
                         4 
                       
                       = 
                       
                         
                           
                             c 
                             7 
                           
                           ⁢ 
                           
                             s 
                             3 
                           
                         
                         + 
                         
                           
                             c 
                             8 
                           
                           ⁢ 
                           
                             s 
                             4 
                           
                         
                       
                     
                     , 
                     
                         
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         y 
                         7 
                       
                       = 
                       
                         
                           
                             c 
                             13 
                           
                           ⁢ 
                           
                             s 
                             5 
                           
                         
                         + 
                         
                           
                             c 
                             14 
                           
                           ⁢ 
                           
                             s 
                             6 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         y 
                         2 
                       
                       = 
                       
                         
                           
                             c 
                             3 
                           
                           ⁢ 
                           
                             s 
                             3 
                           
                         
                         + 
                         
                           
                             c 
                             4 
                           
                           ⁢ 
                           
                             s 
                             4 
                           
                         
                       
                     
                     , 
                     
                         
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         y 
                         5 
                       
                       = 
                       
                         
                           
                             c 
                             9 
                           
                           ⁢ 
                           
                             s 
                             5 
                           
                         
                         + 
                         
                           
                             c 
                             10 
                           
                           ⁢ 
                           
                             s 
                             6 
                           
                         
                       
                     
                     , 
                     
                         
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         y 
                         8 
                       
                       = 
                       
                         
                           
                             c 
                             15 
                           
                           ⁢ 
                           
                             s 
                             1 
                           
                         
                         + 
                         
                           
                             c 
                             16 
                           
                           ⁢ 
                           
                             s 
                             2 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         y 
                         3 
                       
                       = 
                       
                         
                           
                             c 
                             5 
                           
                           ⁢ 
                           
                             s 
                             5 
                           
                         
                         + 
                         
                           
                             c 
                             6 
                           
                           ⁢ 
                           
                             s 
                             6 
                           
                         
                       
                     
                     , 
                     
                         
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         y 
                         6 
                       
                       = 
                       
                         
                           
                             c 
                             11 
                           
                           ⁢ 
                           
                             s 
                             1 
                           
                         
                         + 
                         
                           
                             c 
                             12 
                           
                           ⁢ 
                           
                             s 
                             2 
                           
                         
                       
                     
                     , 
                     
                         
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         y 
                         9 
                       
                       = 
                       
                         
                           
                             
                               c 
                               17 
                             
                             ⁢ 
                             
                               s 
                               3 
                             
                           
                           + 
                           
                             
                               c 
                               18 
                             
                             ⁢ 
                             
                               
                                 s 
                                 4 
                               
                               ⁢ 
                               
                                 
 
                               
                               ( 
                               
                                 
                                   
                                     
                                       y 
                                       1 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       2 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       3 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       4 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       5 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       6 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       7 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       8 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       9 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                         = 
                         
                           
                             ( 
                             
                               
                                 
                                   
                                     c 
                                     1 
                                   
                                 
                                 
                                   
                                     c 
                                     2 
                                   
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                               
                               
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   
                                     c 
                                     3 
                                   
                                 
                                 
                                   
                                     c 
                                     4 
                                   
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                               
                               
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   
                                     c 
                                     5 
                                   
                                 
                                 
                                   
                                     c 
                                     6 
                                   
                                 
                               
                               
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   
                                     c 
                                     7 
                                   
                                 
                                 
                                   
                                     c 
                                     8 
                                   
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                               
                               
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   
                                     c 
                                     9 
                                   
                                 
                                 
                                   
                                     c 
                                     10 
                                   
                                 
                               
                               
                                 
                                   
                                     c 
                                     11 
                                   
                                 
                                 
                                   
                                     c 
                                     12 
                                   
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                               
                               
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   
                                     c 
                                     13 
                                   
                                 
                                 
                                   
                                     c 
                                     14 
                                   
                                 
                               
                               
                                 
                                   
                                     c 
                                     15 
                                   
                                 
                                 
                                   
                                     c 
                                     16 
                                   
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                               
                               
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                                 
                                   
                                     c 
                                     17 
                                   
                                 
                                 
                                   
                                     c 
                                     18 
                                   
                                 
                                 
                                   0 
                                 
                                 
                                   0 
                                 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   
                                     s 
                                     1 
                                   
                                 
                               
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                 
                               
                               
                                 
                                   
                                     s 
                                     3 
                                   
                                 
                               
                               
                                 
                                   
                                     s 
                                     4 
                                   
                                 
                               
                               
                                 
                                   
                                     s 
                                     5 
                                   
                                 
                               
                               
                                 
                                   
                                     s 
                                     6 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ] 
                 
               
             
           
         
       
     
     A code matrix of [Math Figure 8] may be variously formatted depending on a combination of data symbols for the corresponding antenna, and a space-time code of [Math Figure 8] may be realized as a codeword matrix C of [Math Figure 9].  FIG. 4  shows a MIMO system that uses such a codeword matrix. 
     
       
         
           
             
               
                 
                   C 
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               y 
                               1 
                             
                           
                           
                             
                               y 
                               4 
                             
                           
                           
                             
                               y 
                               7 
                             
                           
                         
                         
                           
                             
                               y 
                               2 
                             
                           
                           
                             
                               y 
                               5 
                             
                           
                           
                             
                               y 
                               8 
                             
                           
                         
                         
                           
                             
                               y 
                               3 
                             
                           
                           
                             
                               y 
                               6 
                             
                           
                           
                             
                               y 
                               9 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       
 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               
                                 
                                   c 
                                   1 
                                 
                                 ⁢ 
                                 
                                   s 
                                   1 
                                 
                               
                               + 
                               
                                 
                                   c 
                                   2 
                                 
                                 ⁢ 
                                 
                                   s 
                                   2 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   c 
                                   7 
                                 
                                 ⁢ 
                                 
                                   s 
                                   3 
                                 
                               
                               + 
                               
                                 
                                   c 
                                   8 
                                 
                                 ⁢ 
                                 
                                   s 
                                   4 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   c 
                                   13 
                                 
                                 ⁢ 
                                 
                                   s 
                                   5 
                                 
                               
                               + 
                               
                                 
                                   c 
                                   14 
                                 
                                 ⁢ 
                                 
                                   s 
                                   6 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   c 
                                   3 
                                 
                                 ⁢ 
                                 
                                   s 
                                   3 
                                 
                               
                               + 
                               
                                 
                                   c 
                                   4 
                                 
                                 ⁢ 
                                 
                                   s 
                                   4 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   c 
                                   9 
                                 
                                 ⁢ 
                                 
                                   s 
                                   5 
                                 
                               
                               + 
                               
                                 
                                   c 
                                   10 
                                 
                                 ⁢ 
                                 
                                   s 
                                   6 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   c 
                                   15 
                                 
                                 ⁢ 
                                 
                                   s 
                                   1 
                                 
                               
                               + 
                               
                                 
                                   c 
                                   16 
                                 
                                 ⁢ 
                                 
                                   s 
                                   2 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   c 
                                   5 
                                 
                                 ⁢ 
                                 
                                   s 
                                   5 
                                 
                               
                               + 
                               
                                 
                                   c 
                                   6 
                                 
                                 ⁢ 
                                 
                                   s 
                                   6 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   c 
                                   11 
                                 
                                 ⁢ 
                                 
                                   s 
                                   1 
                                 
                               
                               + 
                               
                                 
                                   c 
                                   12 
                                 
                                 ⁢ 
                                 
                                   s 
                                   2 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   c 
                                   17 
                                 
                                 ⁢ 
                                 
                                   s 
                                   3 
                                 
                               
                               + 
                               
                                 
                                   c 
                                   18 
                                 
                                 ⁢ 
                                 
                                   s 
                                   4 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ] 
                 
               
             
           
         
       
     
     According to a fourth exemplarily embodiment of the present invention, if N t =4 and r=1, a space-time codeword is realized as a combination of data symbols defined by [Math Figure 10]. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 1 
                               
                               ⁢ 
                               
                                 s 
                                 1 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               5 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 5 
                               
                               ⁢ 
                               
                                 s 
                                 2 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               9 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 9 
                               
                               ⁢ 
                               
                                 s 
                                 3 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               13 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 13 
                               
                               ⁢ 
                               
                                 s 
                                 4 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               2 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 2 
                               
                               ⁢ 
                               
                                 s 
                                 2 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               6 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 6 
                               
                               ⁢ 
                               
                                 s 
                                 3 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               10 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 10 
                               
                               ⁢ 
                               
                                 s 
                                 4 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               14 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 14 
                               
                               ⁢ 
                               
                                 s 
                                 1 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               3 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 3 
                               
                               ⁢ 
                               
                                 s 
                                 3 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               7 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 7 
                               
                               ⁢ 
                               
                                 s 
                                 4 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               11 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 11 
                               
                               ⁢ 
                               
                                 s 
                                 1 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               15 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 15 
                               
                               ⁢ 
                               
                                 s 
                                 2 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               4 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 4 
                               
                               ⁢ 
                               
                                 s 
                                 4 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               8 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 8 
                               
                               ⁢ 
                               
                                 s 
                                 1 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             
                               y 
                               12 
                             
                             = 
                               
                             ⁢ 
                             
                               
                                 c 
                                 12 
                               
                               ⁢ 
                               
                                 s 
                                 2 
                               
                             
                           
                           , 
                         
                       
                     
                     
                       
                         
                           
                             y 
                             16 
                           
                           = 
                             
                           ⁢ 
                           
                             
                               c 
                               16 
                             
                             ⁢ 
                             
                               s 
                               3. 
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       ( 
                       
                         
                           
                             
                               y 
                               1 
                             
                           
                         
                         
                           
                             
                               y 
                               2 
                             
                           
                         
                         
                           
                             
                               y 
                               3 
                             
                           
                         
                         
                           
                             
                               y 
                               4 
                             
                           
                         
                         
                           
                             
                               y 
                               5 
                             
                           
                         
                         
                           
                             
                               y 
                               6 
                             
                           
                         
                         
                           
                             
                               y 
                               7 
                             
                           
                         
                         
                           
                             
                               y 
                               8 
                             
                           
                         
                         
                           
                             
                               y 
                               9 
                             
                           
                         
                         
                           
                             
                               y 
                               10 
                             
                           
                         
                         
                           
                             
                               y 
                               11 
                             
                           
                         
                         
                           
                             
                               y 
                               12 
                             
                           
                         
                         
                           
                             
                               y 
                               13 
                             
                           
                         
                         
                           
                             
                               y 
                               14 
                             
                           
                         
                         
                           
                             
                               y 
                               15 
                             
                           
                         
                         
                           
                             
                               y 
                               16 
                             
                           
                         
                       
                       ) 
                     
                     = 
                     
                       
                         ( 
                         
                           
                             
                               
                                 c 
                                 1 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 c 
                                 2 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 c 
                                 3 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 c 
                                 4 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 c 
                                 5 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 c 
                                 6 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 c 
                                 7 
                               
                             
                           
                           
                             
                               
                                 c 
                                 8 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 c 
                                 9 
                               
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 c 
                                 10 
                               
                             
                           
                           
                             
                               
                                 c 
                                 11 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 c 
                                 12 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 c 
                                 13 
                               
                             
                           
                           
                             
                               
                                 c 
                                 14 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               
                                 c 
                                 15 
                               
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               
                                 c 
                                 16 
                               
                             
                             
                               0 
                             
                           
                         
                         ) 
                       
                       · 
                       
                         ( 
                         
                           
                             
                               
                                 s 
                                 1 
                               
                             
                           
                           
                             
                               
                                 s 
                                 2 
                               
                             
                           
                           
                             
                               
                                 s 
                                 3 
                               
                             
                           
                           
                             
                               
                                 s 
                                 4 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     10 
                   
                   ] 
                 
               
             
           
         
       
     
     A code matrix of [Math Figure 10] may be variously formatted depending on a combination of data symbols for the corresponding antenna, and a space-time code may be represented as a codeword matrix C defined by [Math Figure 11].  FIG. 5  shows a MIMO system that uses such a codeword matrix. 
     
       
         
           
             
               
                 
                   C 
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               y 
                               1 
                             
                           
                           
                             
                               y 
                               5 
                             
                           
                           
                             
                               y 
                               9 
                             
                           
                           
                             
                               y 
                               13 
                             
                           
                         
                         
                           
                             
                               y 
                               2 
                             
                           
                           
                             
                               y 
                               6 
                             
                           
                           
                             
                               y 
                               10 
                             
                           
                           
                             
                               y 
                               14 
                             
                           
                         
                         
                           
                             
                               y 
                               3 
                             
                           
                           
                             
                               y 
                               7 
                             
                           
                           
                             
                               y 
                               11 
                             
                           
                           
                             
                               y 
                               15 
                             
                           
                         
                         
                           
                             
                               y 
                               4 
                             
                           
                           
                             
                               y 
                               8 
                             
                           
                           
                             
                               y 
                               12 
                             
                           
                           
                             
                               y 
                               16 
                             
                           
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       
 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               
                                 c 
                                 1 
                               
                               ⁢ 
                               
                                 s 
                                 1 
                               
                             
                           
                           
                             
                               
                                 c 
                                 5 
                               
                               ⁢ 
                               
                                 s 
                                 2 
                               
                             
                           
                           
                             
                               
                                 c 
                                 9 
                               
                               ⁢ 
                               
                                 s 
                                 3 
                               
                             
                           
                           
                             
                               
                                 c 
                                 13 
                               
                               ⁢ 
                               
                                 s 
                                 4 
                               
                             
                           
                         
                         
                           
                             
                               
                                 c 
                                 2 
                               
                               ⁢ 
                               
                                 s 
                                 2 
                               
                             
                           
                           
                             
                               
                                 c 
                                 6 
                               
                               ⁢ 
                               
                                 s 
                                 3 
                               
                             
                           
                           
                             
                               
                                 c 
                                 10 
                               
                               ⁢ 
                               
                                 s 
                                 4 
                               
                             
                           
                           
                             
                               
                                 c 
                                 14 
                               
                               ⁢ 
                               
                                 s 
                                 1 
                               
                             
                           
                         
                         
                           
                             
                               
                                 c 
                                 3 
                               
                               ⁢ 
                               
                                 s 
                                 3 
                               
                             
                           
                           
                             
                               
                                 c 
                                 7 
                               
                               ⁢ 
                               
                                 s 
                                 4 
                               
                             
                           
                           
                             
                               
                                 c 
                                 11 
                               
                               ⁢ 
                               
                                 s 
                                 1 
                               
                             
                           
                           
                             
                               
                                 c 
                                 15 
                               
                               ⁢ 
                               
                                 s 
                                 2 
                               
                             
                           
                         
                         
                           
                             
                               
                                 c 
                                 4 
                               
                               ⁢ 
                               
                                 s 
                                 4 
                               
                             
                           
                           
                             
                               
                                 c 
                                 8 
                               
                               ⁢ 
                               
                                 s 
                                 1 
                               
                             
                           
                           
                             
                               
                                 c 
                                 12 
                               
                               ⁢ 
                               
                                 s 
                                 2 
                               
                             
                           
                           
                             
                               
                                 c 
                                 16 
                               
                               ⁢ 
                               
                                 s 
                                 3 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     11 
                   
                   ] 
                 
               
             
           
         
       
     
     According to a fifth exemplarily embodiment of the present invention, if N t =4 and r=2, a space-time codeword is realized as a combination of data symbols defined by [Math Figure 12]. 
     
       
         
           
             
               
                 
                   
                     
                       y 
                       1 
                     
                     = 
                     
                       
                         
                           c 
                           1 
                         
                         ⁢ 
                         
                           s 
                           1 
                         
                       
                       + 
                       
                         
                           c 
                           2 
                         
                         ⁢ 
                         
                           s 
                           2 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       5 
                     
                     = 
                     
                       
                         
                           c 
                           9 
                         
                         ⁢ 
                         
                           s 
                           3 
                         
                       
                       + 
                       
                         
                           c 
                           10 
                         
                         ⁢ 
                         
                           s 
                           4 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       9 
                     
                     = 
                     
                       
                         
                           c 
                           17 
                         
                         ⁢ 
                         
                           s 
                           5 
                         
                       
                       + 
                       
                         
                           c 
                           18 
                         
                         ⁢ 
                         
                           s 
                           6 
                         
                       
                     
                   
                   , 
                   
                       
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       13 
                     
                     = 
                     
                       
                         
                           c 
                           25 
                         
                         ⁢ 
                         
                           s 
                           7 
                         
                       
                       + 
                       
                         
                           c 
                           26 
                         
                         ⁢ 
                         
                           s 
                           8 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       2 
                     
                     = 
                     
                       
                         
                           c 
                           3 
                         
                         ⁢ 
                         
                           s 
                           3 
                         
                       
                       + 
                       
                         
                           c 
                           4 
                         
                         ⁢ 
                         
                           s 
                           4 
                         
                       
                     
                   
                   , 
                   
                       
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       6 
                     
                     = 
                     
                       
                         
                           c 
                           11 
                         
                         ⁢ 
                         
                           s 
                           5 
                         
                       
                       + 
                       
                         
                           c 
                           12 
                         
                         ⁢ 
                         
                           s 
                           6 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       10 
                     
                     = 
                     
                       
                         
                           c 
                           19 
                         
                         ⁢ 
                         
                           s 
                           7 
                         
                       
                       + 
                       
                         
                           c 
                           20 
                         
                         ⁢ 
                         
                           s 
                           8 
                         
                       
                     
                   
                   , 
                   
                       
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       14 
                     
                     = 
                     
                       
                         
                           c 
                           27 
                         
                         ⁢ 
                         
                           s 
                           1 
                         
                       
                       + 
                       
                         
                           c 
                           28 
                         
                         ⁢ 
                         
                           s 
                           2 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       3 
                     
                     = 
                     
                       
                         
                           c 
                           5 
                         
                         ⁢ 
                         
                           s 
                           5 
                         
                       
                       + 
                       
                         
                           c 
                           6 
                         
                         ⁢ 
                         
                           s 
                           6 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       7 
                     
                     = 
                     
                       
                         
                           c 
                           13 
                         
                         ⁢ 
                         
                           s 
                           7 
                         
                       
                       + 
                       
                         
                           c 
                           14 
                         
                         ⁢ 
                         
                           s 
                           8 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       11 
                     
                     = 
                     
                       
                         
                           c 
                           21 
                         
                         ⁢ 
                         
                           s 
                           1 
                         
                       
                       + 
                       
                         
                           c 
                           22 
                         
                         ⁢ 
                         
                           s 
                           2 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       15 
                     
                     = 
                     
                       
                         
                           c 
                           29 
                         
                         ⁢ 
                         
                           s 
                           3 
                         
                       
                       + 
                       
                         
                           c 
                           30 
                         
                         ⁢ 
                         
                           s 
                           4 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       4 
                     
                     = 
                     
                       
                         
                           c 
                           7 
                         
                         ⁢ 
                         
                           s 
                           7 
                         
                       
                       + 
                       
                         
                           c 
                           8 
                         
                         ⁢ 
                         
                           s 
                           8 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       8 
                     
                     = 
                     
                       
                         
                           c 
                           15 
                         
                         ⁢ 
                         
                           s 
                           1 
                         
                       
                       + 
                       
                         
                           c 
                           16 
                         
                         ⁢ 
                         
                           s 
                           2 
                         
                       
                     
                   
                   , 
                   
                       
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       12 
                     
                     = 
                     
                       
                         
                           c 
                           23 
                         
                         ⁢ 
                         
                           s 
                           3 
                         
                       
                       + 
                       
                         
                           c 
                           24 
                         
                         ⁢ 
                         
                           s 
                           4 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       y 
                       16 
                     
                     = 
                     
                       
                         
                           
                             c 
                             31 
                           
                           ⁢ 
                           
                             s 
                             5 
                           
                         
                         + 
                         
                           
                             c 
                             32 
                           
                           ⁢ 
                           
                             
                               s 
                               6 
                             
                             . 
                             
                               
 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     
                                       y 
                                       1 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       2 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       3 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       4 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       5 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       6 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       7 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       8 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       9 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       10 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       11 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       12 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       13 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       14 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       15 
                                     
                                   
                                 
                                 
                                   
                                     
                                       y 
                                       16 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                       = 
                       
                           
                       
                       ⁢ 
                       
                         
                           ( 
                           
                               
                           
                           ⁢ 
                           
                             
                               
                                 
                                   c 
                                   1 
                                 
                               
                               
                                 
                                   c 
                                   2 
                                 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 
                                   c 
                                   3 
                                 
                               
                               
                                 
                                   c 
                                   4 
                                 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 
                                   c 
                                   5 
                                 
                               
                               
                                 
                                   c 
                                   6 
                                 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 
                                   c 
                                   7 
                                 
                               
                               
                                 
                                   c 
                                   8 
                                 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 
                                   c 
                                   9 
                                 
                               
                               
                                 
                                   c 
                                   10 
                                 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 
                                   c 
                                   11 
                                 
                               
                               
                                 
                                   c 
                                   12 
                                 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 
                                   c 
                                   13 
                                 
                               
                               
                                 
                                   c 
                                   14 
                                 
                               
                             
                             
                               
                                 
                                   c 
                                   15 
                                 
                               
                               
                                 
                                   c 
                                   16 
                                 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 
                                   c 
                                   17 
                                 
                               
                               
                                 
                                   c 
                                   18 
                                 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 
                                   c 
                                   19 
                                 
                               
                               
                                 
                                   c 
                                   20 
                                 
                               
                             
                             
                               
                                 
                                   c 
                                   21 
                                 
                               
                               
                                 
                                   c 
                                   22 
                                 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 
                                   c 
                                   23 
                                 
                               
                               
                                 
                                   c 
                                   24 
                                 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 
                                   c 
                                   25 
                                 
                               
                               
                                 
                                   c 
                                   26 
                                 
                               
                             
                             
                               
                                 
                                   c 
                                   27 
                                 
                               
                               
                                 
                                   c 
                                   28 
                                 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 
                                   c 
                                   29 
                                 
                               
                               
                                 
                                   c 
                                   30 
                                 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                               
                                 
                                   c 
                                   31 
                                 
                               
                               
                                 
                                   c 
                                   32 
                                 
                               
                               
                                 0 
                               
                               
                                 0 
                               
                             
                           
                           ⁢ 
                           
                               
                           
                           ) 
                         
                         ⁢ 
                         
                             
                         
                         · 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                               
                           
                           ⁢ 
                           
                             
                               
                                 
                                   s 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   s 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   s 
                                   3 
                                 
                               
                             
                             
                               
                                 
                                   s 
                                   4 
                                 
                               
                             
                             
                               
                                 
                                   s 
                                   5 
                                 
                               
                             
                             
                               
                                 
                                   s 
                                   6 
                                 
                               
                             
                             
                               
                                 
                                   s 
                                   7 
                                 
                               
                             
                             
                               
                                 
                                   s 
                                   8 
                                 
                               
                             
                           
                           ⁢ 
                           
                               
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     12 
                   
                   ] 
                 
               
             
           
         
       
     
     A code matrix of [Math Figure 12] may be variously formatted depending on a combination of data symbols for the corresponding antenna, and a space-time code may be represented as a codeword matrix C defined by [Math Figure 13].  FIG. 6  shows a MIMO system that uses such a codeword matrix. 
     
       
         
           
             
               
                 
                   
                     
                       
                         C 
                         = 
                         
                           ( 
                           
                             
                               
                                 
                                   y 
                                   1 
                                 
                               
                               
                                 
                                   y 
                                   5 
                                 
                               
                               
                                 
                                   y 
                                   9 
                                 
                               
                               
                                 
                                   y 
                                   13 
                                 
                               
                             
                             
                               
                                 
                                   y 
                                   2 
                                 
                               
                               
                                 
                                   y 
                                   6 
                                 
                               
                               
                                 
                                   y 
                                   10 
                                 
                               
                               
                                 
                                   y 
                                   14 
                                 
                               
                             
                             
                               
                                 
                                   y 
                                   3 
                                 
                               
                               
                                 
                                   y 
                                   7 
                                 
                               
                               
                                 
                                   y 
                                   11 
                                 
                               
                               
                                 
                                   y 
                                   15 
                                 
                               
                             
                             
                               
                                 
                                   y 
                                   4 
                                 
                               
                               
                                 
                                   y 
                                   8 
                                 
                               
                               
                                 
                                   y 
                                   12 
                                 
                               
                               
                                 
                                   y 
                                   16 
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           ( 
                           
                             
                               
                                 
                                   
                                     
                                       c 
                                       1 
                                     
                                     ⁢ 
                                     
                                       s 
                                       1 
                                     
                                   
                                   + 
                                   
                                     
                                       c 
                                       2 
                                     
                                     ⁢ 
                                     
                                       s 
                                       2 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       c 
                                       9 
                                     
                                     ⁢ 
                                     
                                       s 
                                       3 
                                     
                                   
                                   + 
                                   
                                     
                                       c 
                                       10 
                                     
                                     ⁢ 
                                     
                                       s 
                                       4 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       c 
                                       17 
                                     
                                     ⁢ 
                                     
                                       s 
                                       5 
                                     
                                   
                                   + 
                                   
                                     
                                       c 
                                       18 
                                     
                                     ⁢ 
                                     
                                       s 
                                       6 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       c 
                                       25 
                                     
                                     ⁢ 
                                     
                                       s 
                                       7 
                                     
                                   
                                   + 
                                   
                                     
                                       c 
                                       26 
                                     
                                     ⁢ 
                                     
                                       s 
                                       8 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     
                                       c 
                                       3 
                                     
                                     ⁢ 
                                     
                                       s 
                                       3 
                                     
                                   
                                   + 
                                   
                                     
                                       c 
                                       4 
                                     
                                     ⁢ 
                                     
                                       s 
                                       4 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       c 
                                       11 
                                     
                                     ⁢ 
                                     
                                       s 
                                       5 
                                     
                                   
                                   + 
                                   
                                     
                                       c 
                                       12 
                                     
                                     ⁢ 
                                     
                                       s 
                                       6 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       c 
                                       19 
                                     
                                     ⁢ 
                                     
                                       s 
                                       7 
                                     
                                   
                                   + 
                                   
                                     
                                       c 
                                       20 
                                     
                                     ⁢ 
                                     
                                       s 
                                       8 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       c 
                                       27 
                                     
                                     ⁢ 
                                     
                                       s 
                                       1 
                                     
                                   
                                   + 
                                   
                                     
                                       c 
                                       28 
                                     
                                     ⁢ 
                                     
                                       s 
                                       2 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     
                                       c 
                                       5 
                                     
                                     ⁢ 
                                     
                                       s 
                                       5 
                                     
                                   
                                   + 
                                   
                                     
                                       c 
                                       6 
                                     
                                     ⁢ 
                                     
                                       s 
                                       6 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       c 
                                       13 
                                     
                                     ⁢ 
                                     
                                       s 
                                       7 
                                     
                                   
                                   + 
                                   
                                     
                                       c 
                                       14 
                                     
                                     ⁢ 
                                     
                                       s 
                                       8 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       c 
                                       21 
                                     
                                     ⁢ 
                                     
                                       s 
                                       1 
                                     
                                   
                                   + 
                                   
                                     
                                       c 
                                       22 
                                     
                                     ⁢ 
                                     
                                       s 
                                       2 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       c 
                                       29 
                                     
                                     ⁢ 
                                     
                                       s 
                                       3 
                                     
                                   
                                   + 
                                   
                                     
                                       c 
                                       30 
                                     
                                     ⁢ 
                                     
                                       s 
                                       4 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     
                                       c 
                                       7 
                                     
                                     ⁢ 
                                     
                                       s 
                                       7 
                                     
                                   
                                   + 
                                   
                                     
                                       c 
                                       8 
                                     
                                     ⁢ 
                                     
                                       s 
                                       8 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       c 
                                       15 
                                     
                                     ⁢ 
                                     
                                       s 
                                       1 
                                     
                                   
                                   + 
                                   
                                     
                                       c 
                                       16 
                                     
                                     ⁢ 
                                     
                                       s 
                                       2 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       c 
                                       23 
                                     
                                     ⁢ 
                                     
                                       s 
                                       3 
                                     
                                   
                                   + 
                                   
                                     
                                       c 
                                       24 
                                     
                                     ⁢ 
                                     
                                       s 
                                       4 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       c 
                                       31 
                                     
                                     ⁢ 
                                     
                                       s 
                                       5 
                                     
                                   
                                   + 
                                   
                                     
                                       c 
                                       32 
                                     
                                     ⁢ 
                                     
                                       s 
                                       6 
                                     
                                   
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     13 
                   
                   ] 
                 
               
             
           
         
       
     
     One of design criteria for determining a combining coefficient c i,j  to generate a space-time code is to maintain an average transmit power of a signal transmitted from each transmit antenna at every time slot to be equal, according to an embodiment of the present invention. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                            
                           
                             c 
                             
                               1 
                               , 
                               1 
                             
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             
                               1 
                               , 
                               2 
                             
                           
                            
                         
                         2 
                       
                       + 
                       … 
                       + 
                       
                         
                            
                           
                             c 
                             
                               1 
                               , 
                               
                                 
                                   N 
                                   t 
                                 
                                 · 
                                 r 
                               
                             
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       
                         P 
                         1 
                       
                       / 
                       
                         N 
                         t 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             
                               2 
                               , 
                               1 
                             
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             
                               2 
                               , 
                               2 
                             
                           
                            
                         
                         2 
                       
                       + 
                       … 
                       + 
                       
                         
                            
                           
                             c 
                             
                               2 
                               , 
                               
                                 
                                   N 
                                   t 
                                 
                                 · 
                                 r 
                               
                             
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       
                         P 
                         1 
                       
                       / 
                       
                         N 
                         t 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   ⋮ 
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             
                               
                                 N 
                                 t 
                               
                               , 
                               1 
                             
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             
                               
                                 N 
                                 t 
                               
                               , 
                               2 
                             
                           
                            
                         
                         2 
                       
                       + 
                       … 
                       + 
                       
                         
                            
                           
                             c 
                             
                               
                                 N 
                                 t 
                               
                               , 
                               
                                 
                                   N 
                                   t 
                                 
                                 · 
                                 r 
                               
                             
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       
                         P 
                         1 
                       
                       / 
                       
                         N 
                         t 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             
                               
                                 
                                   N 
                                   t 
                                 
                                 + 
                                 1 
                               
                               , 
                               1 
                             
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             
                               
                                 
                                   N 
                                   t 
                                 
                                 + 
                                 1 
                               
                               , 
                               2 
                             
                           
                            
                         
                         2 
                       
                       + 
                       … 
                       + 
                       
                         
                            
                           
                             c 
                             
                               
                                 
                                   N 
                                   t 
                                 
                                 + 
                                 1 
                               
                               , 
                               
                                 
                                   N 
                                   t 
                                 
                                 · 
                                 r 
                               
                             
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       
                         P 
                         2 
                       
                       / 
                       
                         N 
                         t 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   ⋮ 
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             
                               
                                 
                                   N 
                                   t 
                                 
                                 · 
                                 
                                   N 
                                   t 
                                 
                               
                               , 
                               1 
                             
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             
                               
                                 
                                   N 
                                   t 
                                 
                                 · 
                                 
                                   N 
                                   t 
                                 
                               
                               , 
                               2 
                             
                           
                            
                         
                         2 
                       
                       + 
                       … 
                       + 
                       
                         
                            
                           
                             c 
                             
                               
                                 
                                   N 
                                   t 
                                 
                                 · 
                                 
                                   N 
                                   t 
                                 
                               
                               , 
                               
                                 
                                   N 
                                   t 
                                 
                                 · 
                                 r 
                               
                             
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       
                         P 
                         
                           N 
                           t 
                         
                       
                       / 
                       
                         N 
                         t 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     14 
                   
                   ] 
                 
               
             
           
         
       
     
     In [Math Figure 14], P t  (t=1, 2, . . . , T(=N t )) denotes a transmit power allocated to a t-th time slot within a code block period. T is the number of time slots in a code block period. 
     Second one of design criteria is to maintain an average transmit power of all transmit signals at every time slot to be equal, as given in [Math Figure 15].
 
P 1 =P 2 = . . . =P T.   [Math Figure 15]
 
     where P denotes a total signal power transmitted through all transmit antennas at one slot time. 
     Third one is to maintain total average transmit powers allocated to the respective data symbols during a code block period to be equal since one data symbol is transmitted over several time slots in the code block period. This may be defined by [Math Figure 16]. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                            
                           
                             c 
                             
                               1 
                               , 
                               1 
                             
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             
                               2 
                               , 
                               1 
                             
                           
                            
                         
                         2 
                       
                       + 
                       … 
                       + 
                       
                         
                            
                           
                             c 
                             
                               
                                 
                                   N 
                                   t 
                                 
                                 · 
                                 
                                   N 
                                   t 
                                 
                               
                               , 
                               1 
                             
                           
                            
                         
                         2 
                       
                     
                     = 
                     P 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             
                               1 
                               , 
                               2 
                             
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             
                               2 
                               , 
                               2 
                             
                           
                            
                         
                         2 
                       
                       + 
                       … 
                       + 
                       
                         
                            
                           
                             c 
                             
                               
                                 
                                   N 
                                   t 
                                 
                                 · 
                                 
                                   N 
                                   t 
                                 
                               
                               , 
                               2 
                             
                           
                            
                         
                         2 
                       
                     
                     = 
                     P 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   ⋮ 
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             
                               1 
                               , 
                               
                                 
                                   N 
                                   t 
                                 
                                 · 
                                 R 
                               
                             
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             
                               2 
                               , 
                               
                                 
                                   N 
                                   t 
                                 
                                 · 
                                 R 
                               
                             
                           
                            
                         
                         2 
                       
                       + 
                       … 
                       + 
                       
                         
                            
                           
                             c 
                             
                               
                                 
                                   N 
                                   t 
                                 
                                 · 
                                 
                                   N 
                                   t 
                                 
                               
                               , 
                               
                                 
                                   N 
                                   t 
                                 
                                 · 
                                 r 
                               
                             
                           
                            
                         
                         2 
                       
                     
                     = 
                     P 
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     16 
                   
                   ] 
                 
               
             
           
         
       
     
     In [Math Figure 16], P is a value obtained by dividing a total average transmit power (P total−block ) transmitted over T time slots during one code block period by T. In other words, P=P total−block /T. 
     In the following examples, the average transmit power design criteria as shown in [Math Figure 14] to [Math Figure 16] are applied to the above-mentioned five codeword examples corresponding to the number of transmit antennas and the spatial multiplexing rate, where the combining coefficients can be determined optimally. 
     In a like manner of the first codeword example, if N t =2 and r=2, a combining coefficient C k  (K=1, . . . , 8) may be determined by [Math Figure 17] and [Math Figure 18] when [Math Figure 14] is applied to maintain the average transmit power of each signal transmitted through the corresponding transmit antenna to be equal at every time slot, and [Math Figure 16] is applied to maintain a total average transmit powers allocated to the respective data symbols to be equal during one code block period. 
                                c   1          2     +            c   2          2       =     P   2       ⁢     
     ⁢                c   3          2     +            c   4          2       =     P   2       ⁢     
     ⁢                c   5          2     +            c   6          2       =     P   2       ⁢     
     ⁢                c   7          2     +            c   8          2       =     P   2               [     Math   ⁢           ⁢   Figure   ⁢           ⁢   17     ]               | c   1 | 2   +|c   2 | 2   +|c   7 | 2   +|c   8 | 2   =P    | c   3 | 2   +|c   4 | 2   +|c   5 | 2   +|c   6 | 2   =P   [Math Figure 18]
 
     If N t =3 and r=1 in a like manner of the second codeword example, a combining coefficient C k  (k=1, . . . , 9) may be determined by [Math Figure 19] and [Math Figure 20] when [Math Figure 15] is applied to maintain the total average transmit power to be equal at every time slot, and [Math Figure 16] is applied to maintain the total average transmit powers allocated to the respective data symbols to be equal during one code block period.
 
| c   1 | 2   +|c   2 | 2   +|c   3 | 2   =P  
 
| c   4 | 2   +|c   5 | 2   +|c   6 | 2   =P  
 
| c   7 | 2   +|c   8 | 2   +|c   9 | 2   =P   [Math Figure 19]
 
| c   1 | 2   +|c   6 | 2   +|c   8 | 2   =P  
 
| c   2 | 2   +|c   4 | 2   +|c   9 | 2   =P  
 
| c   3 | 2   +|c   5 | 2   +|c   7 | 2   =P   [Math Figure 20]
 
     Similar to the third example, if N t =3 and r=2, a combining coefficient C k  (K=1, . . . , 18) may by determined by [Math Figure 21] and [Math Figure 22] when [Math Figure 14] is applied to maintain the average transmit power of a signal transmitted through the corresponding transmit antenna at every time slot, and [Math Figure 16] is applied to maintain the total average transmit powers allocated to the respective data symbols to be equal during one code block period. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                              
                             
                               c 
                               1 
                             
                              
                           
                           2 
                         
                         + 
                         
                           
                              
                             
                               c 
                               2 
                             
                              
                           
                           2 
                         
                       
                       = 
                       
                         P 
                         3 
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         
                           
                              
                             
                               c 
                               3 
                             
                              
                           
                           2 
                         
                         + 
                         
                           
                              
                             
                               c 
                               4 
                             
                              
                           
                           2 
                         
                       
                       = 
                       
                         P 
                         3 
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         
                           
                              
                             
                               c 
                               5 
                             
                              
                           
                           2 
                         
                         + 
                         
                           
                              
                             
                               c 
                               6 
                             
                              
                           
                           2 
                         
                       
                       = 
                       
                         P 
                         3 
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         
                           
                              
                             
                               c 
                               7 
                             
                              
                           
                           2 
                         
                         + 
                         
                           
                              
                             
                               c 
                               8 
                             
                              
                           
                           2 
                         
                       
                       = 
                       
                         P 
                         3 
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         
                           
                              
                             
                               c 
                               9 
                             
                              
                           
                           2 
                         
                         + 
                         
                           
                              
                             
                               c 
                               10 
                             
                              
                           
                           2 
                         
                       
                       = 
                       
                         P 
                         3 
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         
                           
                              
                             
                               c 
                               11 
                             
                              
                           
                           2 
                         
                         + 
                         
                           
                              
                             
                               c 
                               12 
                             
                              
                           
                           2 
                         
                       
                       = 
                       
                         P 
                         3 
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         
                           
                              
                             
                               c 
                               13 
                             
                              
                           
                           2 
                         
                         + 
                         
                           
                              
                             
                               c 
                               14 
                             
                              
                           
                           2 
                         
                       
                       = 
                       
                         P 
                         3 
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         
                           
                              
                             
                               c 
                               15 
                             
                              
                           
                           2 
                         
                         + 
                         
                           
                              
                             
                               c 
                               16 
                             
                              
                           
                           2 
                         
                       
                       = 
                       
                         P 
                         3 
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         
                            
                           
                             c 
                             17 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             18 
                           
                            
                         
                         2 
                       
                     
                   
                   = 
                   
                     P 
                     3 
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     21 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     
                       
                         
                            
                           
                             c 
                             1 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             11 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             15 
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       P 
                       2 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             2 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             12 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             16 
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       P 
                       2 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             3 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             7 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             17 
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       P 
                       2 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             4 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             8 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             18 
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       P 
                       2 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             5 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             9 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             13 
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       P 
                       2 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             6 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             10 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             14 
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       P 
                       2 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     22 
                   
                   ] 
                 
               
             
           
         
       
     
     Similar to the fourth example, if N t =4 and r=1, a combining coefficient C k  (K=1, . . . , 16) may by determined by [Math Figure 23] and [Math Figure 24] when [Math Figure 15] is applied to maintain an total average transmit power at every time slot to be equal, and [Math Figure 16] is applied to maintain the total average transmit powers allocated to the respective data symbols to be equal during one code block period.
 
| c   1 | 2   +|c   2 | 2   +|c   3 | 2   +|c   4 | 2   =P  
 
| c   5 | 2   +|c   6 | 2   +|c   7 | 2   +|c   8 | 2   =P  
 
| c   9 | 2   +|c   10 | 2   +|c   11 | 2   +|c   12 | 2   =P  
 
| c   13 | 2   +|c   14 | 2   +|c   15 | 2   +|c   16 | 2   =P   [Math Figure 23]
 
| c   1 | 2   +|c   8 | 2   +|c   11 | 2   +|c   14 | 2   =P  
 
| c   2 | 2   +|c   5 | 2   +|c   12 | 2   +|c   15 | 2   =P  
 
| c   3 | 2   +|c   6 | 2   +|c   9 | 2   +|c   16 | 2   =P  
 
| c   4 | 2   +|c   7 | 2   +|c   10 | 2   +|c   13 | 2   =P   [Math Figure 24]
 
     Similar to the fifth example, if N t =4 and r=2, a combining coefficient C k  (K=1, . . . , 32) may by determined by [Math Figure 25], [Math Figure 26], and [Math Figure 27] when [Math Figure 14] is applied to maintain the average transmit power of a signal transmitted through the corresponding transmit antenna at every time slot to be equal, [Math Figure 15] is applied to maintain the total average transmit power at every time slot to be equal, and [Math Figure 16] is applied to maintain the total average transmit powers allocated to the respective data symbols to be equal during one code block period. 
                                c   1          2     +            c   2          2       =     P   4       ⁢     
     ⁢                c   3          2     +            c   4          2       =     P   4       ⁢     
     ⁢                c   5          2     +            c   6          2       =     P   4       ⁢     
     ⁢                c   7          2     +            c   8          2       =     P   4       ⁢     
     ⁢                c   9          2     +            c   10          2       =     P   4       ⁢     
     ⁢                c   11          2     +            c   12          2       =     P   4       ⁢     
     ⁢                c   13          2     +            c   14          2       =     P   4       ⁢     
     ⁢                c   15          2     +            c   16          2       =     P   4       ⁢     
     ⁢                c   17          2     +            c   18          2       =     P   4       ⁢     
     ⁢                c   19          2     +            c   20          2       =     P   4       ⁢     
     ⁢                c   21          2     +            c   22          2       =     P   4       ⁢     
     ⁢                c   23          2     +            c   24          2       =     P   4       ⁢     
     ⁢                c   25          2     +            c   26          2       =     P   4       ⁢     
     ⁢                c   27          2     +            c   28          2       =     P   4       ⁢     
     ⁢                c   29          2     +            c   30          2       =     P   4       ⁢     
     ⁢                c   31          2     +            c   32          2       =     P   4               [     Math   ⁢           ⁢   Figure   ⁢           ⁢   25     ]               | c   1 | 2   +|c   2 | 2   +|c   3 | 2   +|c   4 | 2   +|c   5 | 2   +|c   6 | 2   +|c   7 | 2   +|c   8 | 2   =P    | c   9 | 2   +|c   10 | 2   +|c   11 | 2   +|c   12 | 2   +|c   13 | 2   +|c   14 | 2   +|c   15 | 2   +|c   16 | 2   =P    | c   17 | 2   +|c   18 | 2   +|c   19 | 2   +|c   20 | 2   +|c   21 | 2   +|c   22 | 2   +|c   23 | 2   +|c   24 | 2   =P    | c   25 | 2   +|c   26 | 2   +|c   27 | 2   +|c   27 | 2   +|c   28 | 2   +|c   29 | 2   +|c   30 | 2   +|c   31 | 2   +|c   32 | 2   =P   [Math Figure 26]
 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                            
                           
                             c 
                             1 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             15 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             21 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             27 
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       P 
                       2 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             2 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             16 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             22 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             28 
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       P 
                       2 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             3 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             9 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             23 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             29 
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       P 
                       2 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             4 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             10 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             24 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             30 
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       P 
                       2 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             5 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             11 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             17 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             31 
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       P 
                       2 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             6 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             12 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             18 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             32 
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       P 
                       2 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             7 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             13 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             19 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             25 
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       P 
                       2 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                            
                           
                             c 
                             8 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             14 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             20 
                           
                            
                         
                         2 
                       
                       + 
                       
                         
                            
                           
                             c 
                             26 
                           
                            
                         
                         2 
                       
                     
                     = 
                     
                       P 
                       2 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     27 
                   
                   ] 
                 
               
             
           
         
       
     
     where P represents a transmit power allocated at every time slot in the above five codeword examples. 
     The combining coefficients corresponding to the foregoing five codeword examples according to the number of transmit antennas and the spatial multiplexing rate are first determined, and such the combining coefficients are represented by using complex numbers. The representation of the combining coefficients will now be described in conjunction with the above five codeword examples. 
     Similar to the first example, if N t =2 and r=2, combining coefficients {C i } (i=1, . . . , 8) are represented by using r 1 , r 2 , θ 1 , θ 2 , θ 3 , θ 4 , θ 5 , θ 6 , θ 7 , and θ 8  as shown in [Math Figure 28] (r 1  and r 2  are real numbers greater than zero, and θ 1 , θ 2 , θ 3 , θ 4 , θ 5 , θ 6 , θ 7 , and θ 8  are respectively defined between 0 and 2π). 
     
       
         
           
             
               
                 
                   
                     
                       c 
                       1 
                     
                     = 
                     
                       
                         1 
                         
                           
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   r 
                                   1 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             1 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       2 
                     
                     = 
                     
                       
                         
                           r 
                           1 
                         
                         
                           
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   r 
                                   1 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             2 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       3 
                     
                     = 
                     
                       
                         1 
                         
                           
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   r 
                                   2 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             3 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       4 
                     
                     = 
                     
                       
                         
                           r 
                           2 
                         
                         
                           
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   r 
                                   2 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             4 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       5 
                     
                     = 
                     
                       
                         
                           r 
                           2 
                         
                         
                           
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   r 
                                   2 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             5 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       6 
                     
                     = 
                     
                       
                         1 
                         
                           
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   r 
                                   2 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             6 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       7 
                     
                     = 
                     
                       
                         
                           r 
                           1 
                         
                         
                           
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   r 
                                   1 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             7 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       8 
                     
                     = 
                     
                       
                         1 
                         
                           
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   r 
                                   1 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             8 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     28 
                   
                   ] 
                 
               
             
           
         
       
     
     Similar to the second example, if N t =3 and r=1, combining coefficients {C j } (j=1, . . . , 9) are represented by using θ 1 , θ 2 , θ 3 , θ 4 , θ 5 , θ 6 , θ 7 , θ 8 , and θ 9  as shown in [Math Figure 29] (θ 9  is defined to be between 0 and 2π). 
     
       
         
           
             
               
                 
                   
                     
                       c 
                       1 
                     
                     = 
                     
                       
                         1 
                         
                           3 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           1 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       2 
                     
                     = 
                     
                       
                         1 
                         
                           3 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           2 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       3 
                     
                     = 
                     
                       
                         1 
                         
                           3 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           3 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       4 
                     
                     = 
                     
                       
                         1 
                         
                           3 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           4 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       5 
                     
                     = 
                     
                       
                         1 
                         
                           3 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           5 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       6 
                     
                     = 
                     
                       
                         1 
                         
                           3 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             6 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       7 
                     
                     = 
                     
                       
                         1 
                         
                           3 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           7 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       8 
                     
                     = 
                     
                       
                         1 
                         
                           3 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           8 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       9 
                     
                     = 
                     
                       
                         1 
                         
                           3 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           9 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     29 
                   
                   ] 
                 
               
             
           
         
       
     
     Similar to the fourth example, if N t =4 and r=1, combining coefficients {C k } (k=1, . . . , 16) is represented by using θ 1 , θ 2 , θ 3 , . . . , and θ 16  as shown in [Math Figure 30] (θ 10  to θ 16  are defined to be between 0 and 2π). 
     
       
         
           
             
               
                 
                   
                     
                       c 
                       1 
                     
                     = 
                     
                       
                         1 
                         
                           4 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           1 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       2 
                     
                     = 
                     
                       
                         1 
                         
                           4 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           2 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       3 
                     
                     = 
                     
                       
                         1 
                         
                           4 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           3 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       4 
                     
                     = 
                     
                       
                         1 
                         
                           4 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           4 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       5 
                     
                     = 
                     
                       
                         1 
                         
                           4 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           5 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       6 
                     
                     = 
                     
                       
                         1 
                         
                           4 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             6 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       7 
                     
                     = 
                     
                       
                         1 
                         
                           4 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           7 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       8 
                     
                     = 
                     
                       
                         1 
                         
                           4 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           8 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       9 
                     
                     = 
                     
                       
                         1 
                         
                           4 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           9 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       10 
                     
                     = 
                     
                       
                         1 
                         
                           4 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           10 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       11 
                     
                     = 
                     
                       
                         1 
                         
                           4 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           11 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       12 
                     
                     = 
                     
                       
                         1 
                         
                           4 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           12 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       13 
                     
                     = 
                     
                       
                         1 
                         
                           4 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           13 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       14 
                     
                     = 
                     
                       
                         1 
                         
                           4 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           14 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       15 
                     
                     = 
                     
                       
                         1 
                         
                           4 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             15 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       16 
                     
                     = 
                     
                       
                         1 
                         
                           4 
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           jθ 
                           16 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     30 
                   
                   ] 
                 
               
             
           
         
       
     
     Similar to the fifth example, if N t =4 and r=2, combining coefficients {C k } (k=1, . . . , 32) is represented by using r 1 , r 2 , r 3 ,
     θ b , θ d , θ f ,   θ b , θ d , θ f , θ h , θ i , θ j , θ k , θ l , θ m , θ n , θ o , θ p , θ q , θ r , θ s , θ t , θ u , θ v , θ w , θ x , θ y , θ α , θ γ , and   θ ε  (here, r 3  is a real number greater than zero, and   θ b , θ d , θ f ,   θ b , θ d , θ f , θ h , θ i , θ j , θ k , θ l , θ m , θ n , θ o , θ p , θ q , θ r , θ s , θ t , θ u , θ v , θ w , θ x , θ y , θ α , θ γ , and   θ ε  are defined to be between 0 and 2π).   

     
       
         
           
             
               
                 
                   
                     
                       
                         c 
                         1 
                       
                       = 
                       
                         ± 
                         
                           1 
                           
                             
                               4 
                               ⁢ 
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   
                                     r 
                                     3 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         c 
                         15 
                       
                       = 
                       
                         
                           r 
                           1 
                         
                         ⁢ 
                         
                           
                             c 
                             1 
                           
                           · 
                           
                             ⅇ 
                             
                               jθ 
                               o 
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         c 
                         21 
                       
                       = 
                       
                         
                           r 
                           2 
                         
                         ⁢ 
                         
                           
                             c 
                             1 
                           
                           · 
                           
                             ⅇ 
                             
                               j 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 θ 
                                 u 
                               
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         c 
                         27 
                       
                       = 
                       
                         
                           r 
                           3 
                         
                         ⁢ 
                         
                           
                             c 
                             1 
                           
                           · 
                           
                             ⅇ 
                             
                               j 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 θ 
                                 u 
                               
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         c 
                         2 
                       
                       = 
                       
                         
                           r 
                           3 
                         
                         ⁢ 
                         
                           
                             c 
                             1 
                           
                           · 
                           
                             ⅇ 
                             
                               jθ 
                               b 
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         c 
                         16 
                       
                       = 
                       
                         
                           r 
                           2 
                         
                         ⁢ 
                         
                           
                             c 
                             1 
                           
                           · 
                           
                             ⅇ 
                             
                               jθ 
                               p 
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         c 
                         22 
                       
                       = 
                       
                         
                           r 
                           1 
                         
                         ⁢ 
                         
                           
                             c 
                             1 
                           
                           · 
                           
                             ⅇ 
                             
                               jθ 
                               v 
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         c 
                         28 
                       
                       = 
                       
                         ± 
                         
                           1 
                           
                             
                               4 
                               ⁢ 
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   
                                     r 
                                     3 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         c 
                         3 
                       
                       = 
                       
                         ± 
                         
                           1 
                           
                             
                               4 
                               ⁢ 
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   
                                     r 
                                     3 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         c 
                         9 
                       
                       = 
                       
                         
                           r 
                           1 
                         
                         ⁢ 
                         
                           
                             c 
                             3 
                           
                           · 
                           
                             ⅇ 
                             
                               jθ 
                               i 
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         c 
                         23 
                       
                       = 
                       
                         
                           r 
                           2 
                         
                         ⁢ 
                         
                           
                             c 
                             3 
                           
                           · 
                           
                             ⅇ 
                             
                               jθ 
                               w 
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         c 
                         29 
                       
                       = 
                       
                         
                           r 
                           3 
                         
                         ⁢ 
                         
                           
                             c 
                             3 
                           
                           · 
                           
                             ⅇ 
                             
                               jθ 
                               r 
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         c 
                         4 
                       
                       = 
                       
                         
                           r 
                           3 
                         
                         ⁢ 
                         
                           
                             c 
                             3 
                           
                           · 
                           
                             ⅇ 
                             
                               jθ 
                               d 
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         c 
                         10 
                       
                       = 
                       
                         
                           r 
                           2 
                         
                         ⁢ 
                         
                           
                             c 
                             3 
                           
                           · 
                           
                             ⅇ 
                             
                               jθ 
                               j 
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         c 
                         24 
                       
                       = 
                       
                         
                           r 
                           1 
                         
                         ⁢ 
                         
                           
                             c 
                             3 
                           
                           · 
                           
                             ⅇ 
                             
                               j 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               x 
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         c 
                         30 
                       
                       = 
                       
                         ± 
                         
                           1 
                           
                             
                               4 
                               ⁢ 
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   
                                     r 
                                     3 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       5 
                     
                     = 
                     
                       ± 
                       
                         1 
                         
                           
                             4 
                             ⁢ 
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   r 
                                   3 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       11 
                     
                     = 
                     
                       
                         r 
                         1 
                       
                       ⁢ 
                       
                         
                           c 
                           5 
                         
                         · 
                         
                           ⅇ 
                           
                             jθ 
                             k 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       17 
                     
                     = 
                     
                       
                         r 
                         2 
                       
                       ⁢ 
                       
                         
                           c 
                           5 
                         
                         · 
                         
                           ⅇ 
                           
                             jθ 
                             a 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       31 
                     
                     = 
                     
                       
                         r 
                         3 
                       
                       ⁢ 
                       
                         
                           c 
                           5 
                         
                         · 
                         
                           ⅇ 
                           
                             jθ 
                             c 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       6 
                     
                     = 
                     
                       
                         r 
                         3 
                       
                       ⁢ 
                       
                         
                           c 
                           5 
                         
                         · 
                         
                           ⅇ 
                           
                             jθ 
                             f 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       12 
                     
                     = 
                     
                       
                         r 
                         2 
                       
                       ⁢ 
                       
                         
                           c 
                           5 
                         
                         · 
                         
                           ⅇ 
                           
                             jθ 
                             l 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       18 
                     
                     = 
                     
                       
                         r 
                         1 
                       
                       ⁢ 
                       
                         
                           c 
                           5 
                         
                         · 
                         
                           ⅇ 
                           
                             j 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             r 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       32 
                     
                     = 
                     
                       ± 
                       
                         1 
                         
                           4 
                           ⁢ 
                           
                             ( 
                             
                               1 
                               + 
                               
                                 r 
                                 3 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       7 
                     
                     = 
                     
                       ± 
                       
                         1 
                         
                           4 
                           ⁢ 
                           
                             ( 
                             
                               1 
                               + 
                               
                                 r 
                                 3 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       13 
                     
                     = 
                     
                       
                         r 
                         1 
                       
                       ⁢ 
                       
                         
                           c 
                           7 
                         
                         · 
                         
                           ⅇ 
                           
                             jθ 
                             m 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       19 
                     
                     = 
                     
                       
                         r 
                         2 
                       
                       ⁢ 
                       
                         
                           c 
                           7 
                         
                         · 
                         
                           ⅇ 
                           
                             jθ 
                             s 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       25 
                     
                     = 
                     
                       
                         r 
                         3 
                       
                       ⁢ 
                       
                         
                           c 
                           7 
                         
                         · 
                         
                           ⅇ 
                           
                             j 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               θ 
                               y 
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       8 
                     
                     = 
                     
                       
                         r 
                         3 
                       
                       ⁢ 
                       
                         
                           c 
                           7 
                         
                         · 
                         
                           ⅇ 
                           
                             j 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               θ 
                               h 
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       14 
                     
                     = 
                     
                       
                         r 
                         2 
                       
                       ⁢ 
                       
                         
                           c 
                           7 
                         
                         · 
                         
                           ⅇ 
                           
                             j 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               θ 
                               r 
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       20 
                     
                     = 
                     
                       
                         r 
                         1 
                       
                       ⁢ 
                       
                         
                           c 
                           7 
                         
                         · 
                         
                           ⅇ 
                           
                             j 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             t 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       c 
                       26 
                     
                     = 
                     
                       ± 
                       
                         1 
                         
                           
                             4 
                             ⁢ 
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   r 
                                   3 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     31 
                   
                   ] 
                 
               
             
           
         
       
     
     A complex weight C i,j  that is a combining coefficient for the full diversity gain and the full spatial multiplexing gain according to an embodiment of the present invention is obtained by determining a weight Ci,j that maximizes a minimum determinant of a space-time codeword matrix difference of [Math Figure 1] or [Math Figure 13] while satisfying criteria of [Math Figure 14], [Math Figure 15], and [Math Figure 16], or maximizes an average determinant of difference matrix of the space-time codeword matrix. The following [Math Figure 32] is designed to maximize a minimum determinant, and [Math Figure 33] is designed to maximize an average determinant. 
     
       
         
           
             
               
                 
                   max 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       min 
                       
                         
                           C 
                           1 
                         
                         ≠ 
                         
                           C 
                           2 
                         
                       
                     
                     ⁢ 
                     
                       
                          
                         
                           det 
                           ⁡ 
                           
                             ( 
                             
                               
                                 C 
                                 1 
                               
                               - 
                               
                                 C 
                                 2 
                               
                             
                             ) 
                           
                         
                          
                       
                       2 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     32 
                   
                   ] 
                 
               
             
             
               
                 
                   max 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     avg 
                     
                       
                         C 
                         1 
                       
                       ≠ 
                       
                         C 
                         2 
                       
                     
                   
                   ⁢ 
                   
                     
                        
                       
                         det 
                         ⁡ 
                         
                           ( 
                           
                             
                               C 
                               1 
                             
                             - 
                             
                               C 
                               2 
                             
                           
                           ) 
                         
                       
                        
                     
                     2 
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     33 
                   
                   ] 
                 
               
             
           
         
       
     
     If [Math Figure 32] is applied to the example of determining the combining coefficients by using r 1  and r 2  when N t =2 and r=2 as shown in [Math Figure 28], r 1  and r 2  may be defined by [Math Figure 34]. 
     
       
         
           
             
               
                 
                   
                     
                       r 
                       1 
                     
                     = 
                     
                       
                         
                           1 
                           + 
                           
                             5 
                           
                         
                         2 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       or 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           
                             - 
                             1 
                           
                           + 
                           
                             5 
                           
                         
                         2 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       r 
                       2 
                     
                     = 
                     
                       
                         
                           1 
                           + 
                           
                             5 
                           
                         
                         2 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       or 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           
                             - 
                             1 
                           
                           + 
                           
                             5 
                           
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     34 
                   
                   ] 
                 
               
             
           
         
       
     
     In addition, if [Math Figure 32] is applied to the example of determining the combining coefficients by using θ 1 , θ 2 , θ 3 , θ 4 , θ 5 , θ 5 , θ 6 , θ 7 , and θ 8 , values of θ 1 , θ 2 , θ 3 , θ 4 , θ 5 , θ 6 , θ 7 , and θ 8  may be defined by [Math Figure 35]. 
     
       
         
           
             
               
                 
                   
                     
                       
                         θ 
                         1 
                       
                       + 
                       
                         θ 
                         8 
                       
                     
                     = 
                     
                       
                         θ 
                         2 
                       
                       + 
                       
                         θ 
                         7 
                       
                       + 
                       π 
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         θ 
                         3 
                       
                       + 
                       
                         θ 
                         6 
                       
                     
                     = 
                     
                       
                         θ 
                         4 
                       
                       + 
                       
                         θ 
                         5 
                       
                       + 
                       π 
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         θ 
                         4 
                       
                       + 
                       
                         θ 
                         5 
                       
                     
                     = 
                     
                       
                         
                           θ 
                           2 
                         
                         + 
                         
                           θ 
                           7 
                         
                         + 
                         
                           
                             π 
                             2 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           or 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             4 
                           
                         
                         + 
                         
                           θ 
                           5 
                         
                       
                       = 
                       
                         
                           θ 
                           2 
                         
                         + 
                         
                           θ 
                           7 
                         
                         - 
                         
                           π 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     35 
                   
                   ] 
                 
               
             
           
         
       
     
     If [Math Figure 32] is applied to the example of determining the combining coefficients by using θ 1 , θ 2 , θ 3 , θ 4 , θ 5 , θ 6 , θ 7 , θ 8  and θ 9  when N t =3 and r=1 as shown in [Math Figure 29], values of θ 1 , θ 2 , θ 3 , θ 4 , θ 5 , θ 6 , θ 7 , θ 8 , and θ 9  may be defined by [Math Figure 36]. 
     
       
         
           
             
               
                 
                   
                     
                       
                         θ 
                         1 
                       
                       + 
                       
                         θ 
                         5 
                       
                       + 
                       
                         θ 
                         9 
                       
                     
                     = 
                     
                       
                         
                           θ 
                           3 
                         
                         + 
                         
                           θ 
                           4 
                         
                         + 
                         
                           θ 
                           8 
                         
                         + 
                         
                           π 
                           2 
                         
                       
                       = 
                       
                         
                           θ 
                           2 
                         
                         + 
                         
                           θ 
                           6 
                         
                         + 
                         
                           θ 
                           7 
                         
                         + 
                         π 
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         θ 
                         1 
                       
                       + 
                       
                         θ 
                         6 
                       
                       + 
                       
                         θ 
                         8 
                       
                     
                     = 
                     0 
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         θ 
                         2 
                       
                       + 
                       
                         θ 
                         4 
                       
                       + 
                       
                         θ 
                         9 
                       
                     
                     = 
                     
                       π 
                       8 
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         θ 
                         3 
                       
                       + 
                       
                         θ 
                         5 
                       
                       + 
                       
                         θ 
                         7 
                       
                     
                     = 
                     
                       π 
                       4 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Figure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     36 
                   
                   ] 
                 
               
             
           
         
       
     
     The space-time code according to the foregoing embodiment may be applied to various modulation systems such as Quadrature Phase Shift Keying (QPSK), 16 Quadrature Amplitude Modulation (QAM), and 64 QAM. In addition, a bit error rate (BER) of a space-time code in an uncoded state is comparatively lower than a conventional matrix B system and the FDFR system as shown in  FIG. 7 , and BER performance in a coded state is enhanced compared to the conventional matrix B system. 
     According to the present invention, the MIMO system that uses multiple transmit antennas effectively responds to channel variation since the MIMO system uses a space-time code designed to simultaneously obtain a full diversity gain and a full spatial multiplexing gain with a minimum delay. In addition, a signal is generated from combinations of data symbols of each antenna at every time slot, and therefore the Euclidean distance of the data symbols increases, resulting in a high encoding gain. 
     In addition, the space-time code may be applied to various MIMO systems since the number of transmit/receive antennas and the spatial multiplexing rate are regularly defined, and thus a structure of the space-time code may be easily modified depending on a channel condition. Further, the space-time code may be designed to obtain the full diversity and the coding gains when the spatial multiplexing rate is determined, and thus capacity of the MIMO system may be used fully. 
     While this invention has been described in connection with what is presently considered to be practical exemplary embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.