Patent Publication Number: US-9900785-B2

Title: Wireless device

Description:
TECHNICAL FIELD 
     The present invention relates to a wireless communication technology using a plurality of antennas for transmission. 
     BACKGROUND 
     In an art of a transmit diversity, it is possible to improve robustness of communication by using an MIMO channel. At this time, a transmission signal is carefully designed as for both space and time, and a rank of an MIMO channel matrix is effectively used. For example, the transmission signal is made to be a quadrature signal, and thereby, it is possible to avoid an array interference generated by using a plurality of antennas. In this art, it is possible to generate an estimation of quadrature information in which the MIMO channel matrix becomes a full rank from a mixed signal of signals transmitted from a plurality of transmission antennas at a reception side. However, in a cellular network or the like covering a wide area, robustness for a deep fading is required at a cell boundary, and an application of only full diversity is not sufficient. 
     The present invention is one to further provide a gain due to the array interference of a system in addition to maintain a maximum diversity (to provide the MIMO matrix of full rank). This special gain is one which is obtained by carefully designing a transmission symbol transmitted from each of transmission antennas, and the array interference is positively used at the reception side. 
     In the art of the transmit diversity, the robustness of the communication in the MIMO channel is improved by using space-time block codes or the like. However, in such an art, it is limited to a coefficient of the diversity, and therefore, there is a problem in which a reception quality in a vicinity of a cell boundary and system performance are insufficient. 
     PRIOR ART DOCUMENT 
     Non-Patent Document 
     
         
         Non-Patent Document 1: S. M. Alamouti, “A Simple Transmit Diversity Technique for Wireless Communications”. IEEE Journal on Selected Areas in Communications 16 (8): 1451-1458. 
         Non-Patent Document 2: V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-Time Block Codes from Orthogonal Designs”, IEEE Transactions on Information Theory 45(5): 744-765. 
       
    
     SUMMARY OF THE INVENTION 
     Problems to be Solved by the Invention 
     As stated above, according to the conventional art, there is a problem in which a maximum diversity gain obtained from the rank of the MIMO channel matrix is limited. The present invention is made to solve the problem as stated above, and an object thereof is to provide a wireless device capable of enabling improvement in reliability of communication, enlargement of cell regions, improvement in PER, and improvement in system performance. 
     Means for Solving the Problems 
     To solve the above-stated problem, a wireless device according to an embodiment is a wireless device which transmits information for a counterpart wireless device, includes: a signal processing unit which generates a symbol sequence; a transmission vector calculating unit which converts the symbol sequence into a plurality of transmission symbol sequences, and controls phases by the transmission symbol sequences to be a same phase or an opposite phase based on a channel estimation to the counterpart wireless device; and a plurality of antennas which respectively transmit the plurality of transmission symbol sequences. 
     Effect of the Invention 
     According to the present invention, it is possible to provide a wireless device capable of enabling improvement in reliability of communication, enlargement of cell regions, improvement in PER, and improvement in system performance. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  A block diagram illustrating a configuration of a wireless device according to a first embodiment. 
         FIG. 2  A flowchart illustrating operations of the wireless device according to the first embodiment. 
         FIG. 3  A block diagram illustrating a configuration of a wireless device according to a second embodiment. 
         FIG. 4  A flowchart illustrating operations of the wireless device according to the second embodiment. 
         FIG. 5  A block diagram illustrating a configuration of a wireless device according to a third embodiment. 
         FIG. 6  A block diagram illustrating a configuration of a wireless device according to a fourth embodiment. 
         FIG. 7  A conceptual view illustrating an application example of the present invention. 
         FIG. 8  A conceptual view illustrating an application example of the present invention. 
     
    
    
     MODES FOR CARRYING OUT THE INVENTION 
     A special gain is required to provide a high reception quality for a reception side positioning in a vicinity of a cell boundary and to improve system performance. In a wireless system of the embodiment, the special gain can be obtained by designing a symbol transmitted from a transmission antenna. A total gain of the wireless system is improved by using interference energy obtained by an array interference in addition to a diversity gain obtained from a rank of an MIMO channel matrix. It is thereby possible to improve link reliability compared to a conventional transmit diversity, namely the art using the space-time block codes (STBC). 
     Specifically, a total gain (diversity gain+array gain) contributes to reduce a bit-error probability (BEP) compared to a case of only the diversity gain generated by the conventional STBC. 
     First Embodiment 
     A wireless system according to a first embodiment is described in detail with reference to  FIG. 1 . As illustrated in  FIG. 1 , a wireless system  1  according to the first embodiment includes a first wireless device  11  transmitting data sequences, and a second wireless device  21  receiving the data sequences transmitted from the first wireless device  11 . 
     The first wireless device  11  includes a transmission signal processing unit  100  generating a transmission signal including the data sequences, a transmission vector selecting unit  105  outputting a plurality of transmission signals by performing a vector calculation of the data sequences of the transmission signals, and a plurality of transmission antennas respectively transmitting the plurality of transmission signals output from the transmission vector selecting unit  105 . In an example illustrated in  FIG. 1 , two transmission antennas  110   a ,  110   b  (n t =2) are array configured as the plurality of transmission antennas. 
     The transmission signal processing unit  100  generates data sequences transmitted by the first wireless device  11 , and generates a high-frequency signal by performing a modulation/frequency conversion. In the embodiment illustrated in  FIG. 1 , the transmission signal processing unit  100  generates the transmission signal including a data sequence S (symbol sequence) and transmits it to the transmission vector selecting unit  105 . 
     The transmission vector selecting unit  105  distributes the transmission signal into plural, and performs a predetermined vector calculation. The transmission vector selecting unit  105  distributes the received transmission signal, and supplies the data sequence S to each of the transmission antenna  110   a  and the transmission antenna  110   b . In addition, the transmission vector selecting unit  105  controls phases of symbols between the data sequence S supplied to the transmission antenna  110   a  and the data sequence S supplied to the reception antenna  110   b  by the vector calculation. 
     In the embodiment illustrated in  FIG. 1 , there are two transmission antennas of the first wireless device  11 , and therefore, the transmission vector selecting unit  105  performs either a calculation in which transmission symbols of the transmission antennas  110   a  and  110   b  are both in a same phase [s s] or a calculation in which the respective transmission symbols are in an opposite phase [s −s]. In the following description, the former calculation is called as a calculation of a transmission vector G 0 [s s], and the latter calculation is called as a calculation of a transmission vector G 1 [s −s]. When the calculation of the transmission vector G 0  is performed, the transmission antennas  110   a  and  110   b  each transmit the same symbol sequence “s”, and when the calculation of the transmission vector G 1  is performed, the transmission antennas  110   a  and  110   b  respectively transmit symbol sequences “s”, “−s” in the opposite phase. Namely, the transmission antennas  110   a  and  110   b  transmit the symbol sequences in the same phase with each other or the symbol sequences in the opposite phase from one another. 
     Further, the first wireless device  11  includes a reception antenna  145  and a feedback (F/B) receiving unit  150  which receive a feedback signal from the second wireless device  21 . In the wireless system  1  of this embodiment, a frequency f 1  transmitted by the first wireless device  11  to the second wireless device  21  and a frequency f 2  received by the first wireless device  11  from the second wireless device  21  are different frequencies. Namely, the wireless system  1  of this embodiment constitutes an FDD system. Note that the feedback signal may be transmitted not by wireless but by wired. 
     The feedback receiving unit  150  receives an index m from the second wireless device  21 . The index m indicates the transmission vector which is to be selected by the transmission vector selecting unit  105 , and when the “m” is “0” (zero), the transmission vector selecting unit  105  performs the calculation of the G 0 , and when the “m” is “1”, the transmission vector selecting unit  105  performs the calculation of the G 1 . Namely, the transmission vector selecting unit  105  selects a calculation of a transmission vector G m  based on the index m transmitted from the second wireless device  21 . 
     The second wireless device  21  includes a (reception) antenna  115  receiving a reception signal, a channel estimating unit  125  estimating a channel estimation H by using the reception signal, and an array gain controlling unit  130  calculating an array interference by using the estimated channel estimation H. The channel estimation H is a channel estimation (propagation estimation) of each of a channel h 1  (propagation path h 1 ) from the transmission antenna  110   a  to the reception antenna  115  and a channel h 2  (propagation path h 2 ) from the transmission antenna  110   b  to the reception antenna  115 . The array gain controlling unit  130  determines the index m indicating the transmission vector which is to be selected by the first wireless device  11  by using the calculated array interference. 
     The second wireless device  21  further includes a feedback (F/B) transmitting unit  135  and a transmission antenna  140  which feed back the index m determined by the array gain controlling unit  130  to the first wireless device  11 , a combining unit  155  which calculates a symbol estimation S by using the channel estimation H and the index m, a maximum likelihood decision unit  160  which generates a reception data sequence by using the channel estimation H and the symbol estimation S, and a reception signal processing unit  165  which processes the reception data sequence. The index m is just to indicate the transmission vector which is to be selected by the first wireless device  11 , and therefore, a circuit of the frequency f 2  which is transmitted by the feedback transmitting unit  135  is not necessarily be a wide band. 
     Operations of First Embodiment 
     Operations of the wireless system  1  of the first embodiment are described with reference to  FIGS. 1 and 2 . In the wireless system of this embodiment, the index m which is used by the first wireless device  11  being a transmission side to determine the transmission vector G m  is generated by the second wireless device  21  being a reception side. Namely, the second wireless device  21  performs a channel estimation of a propagation path from the first wireless device  11  to the second wireless device  21 . Therefore, the first wireless device  11  transmits a radio wave for the channel estimation as a first stage. The transmission signal processing unit  100  generates the transmission signal S at the frequency f 1  (step  200 . Hereinafter, referred to as “S 200 ”), and the transmission vector selecting unit  105  temporality performs the calculation of the transmission vector G 0 . The transmission antennas  110   a ,  110   b  each transmit the transmission signal S in the same phase (S 205 ). 
     The reception antenna  115  of the second wireless device  21  receives the transmission signals S via transmission paths h 1  and h 2  (S 210 ). At this time, noises n are mixed into the reception signal at the second wireless device  21  ( 120  in  FIG. 1 ). 
     The channel estimating unit  125  performs the channel estimation based on the reception signal (S 215 ). In a system in which there are two transmission side antennas and one reception side antenna as illustrated in  FIG. 1 , namely, in an MISO (the Multiple-Input-Single-Output) configuration system, a channel vector H is represented by a mathematical expression 1.
 
[Expression 1]
 
 H=[h   1   h   2 ]ε   1×nt   (I)
 
     At a frequency band of the VHF/UHF band such as the TV white space (TVWS), Doppler diffusion is small, and therefore, the channel vector H has a quasi-static and extremely low time selectivity. Namely, the channel vector H of this embodiment has a relatively small temporal variation. The channel estimating unit  125  transmits the obtained channel estimation to the array gain controlling unit  130 . 
     The array gain controlling unit  130  calculates an array interference I Am  by using the obtained channel estimation (S 220 ). In the system of the MISO configuration, there are two peculiar transmission vectors G m  (m=0, 1), and the respective G m  (G 0 , G 1 ) generate the array interferences I Am  (I A1 , I A2 ) respectively corresponding thereto. The array interference I Am  is a function of a fading channel H, and therefore, it is possible to calculate in advance. Accordingly, the array interference I Am  can be stored at a memory in the channel estimating unit  125  of the second wireless device  21 , and it is possible to calculate a total gain by using the channel estimation. The array gain controlling unit  130  compares the two I Am  and selects one which takes a maximum value (mathematical expression 2). 
     
       
         
           
             
               
                 
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     When it is assumed that the Doppler frequency is low such as the VHF/UHF band and a transmission path H does not largely change, the G m  becomes a factor controlling a total gain of the system. The array gain controlling unit  130  searches the I Am  in which the total gain of the system becomes the maximum via the channel estimation. 
     When the I Am  in which the total gain of the system becomes the maximum is selected, the array gain controlling unit  130  determines the index m which corresponds to the I A , and transmits to the feedback transmitting unit  135  and the combining unit  155  (S 225 ). The feedback transmitting unit  135  transmits the index m determined by the array gain controlling unit  130  to the first wireless device  11  as the feedback signal at the frequency f 2  (S 230 ). 
     The feedback receiving unit  150  of the first wireless device  11  receives the feedback signal via the reception antenna  145 , and transmits the index m to the transmission vector selecting unit  105  (S 235 ). 
     The transmission vector selecting unit  105  selects the transmission vector G m  from the G 0 /G 1  based on the received index m, and performs the calculation of the transmission vector G m  for the transmission signal S (S 240 ). The transmission vector selecting unit  105  transmits the signals of [s s] or [s −s] from the transmission antennas  110   a  and  110   b  in accordance with the transmission vector G m  (S 245 ). For example, when the index m fed back from the second wireless device  21  is “1”, the first wireless device  11  performs the calculation of the G 1 , and transmits “s” from the transmission antenna  110   a  and “−s” from the transmission antenna  110   b.    
     The second wireless device  21  receives the transmission signals S each of which is performed the calculation of the transmission vector G m  via the reception antenna  115  (S 250 ). The combining unit  155  performs a combining process by using the channel estimation estimated at the step  215  and the index m generated by the array gain controlling unit  130 , and generates a symbol estimation (S 255 ). For example, when the index m determined by the array gain controlling unit  130  is “1”, the combining unit  155  generates the symbol estimation by using a weight vector W 1 . It is because the transmission signal which is transmitted via the calculation of the transmission vector G 1  generates the largest array interference by using the weight vector W 1  by the combining unit  155 . 
     When the communication is started by using the determined transmission vector G m , the combining unit  155  performs a proper signal operation by using the channel estimation received from the channel estimating unit  125 , and provides the symbol estimation to the maximum likelihood detecting unit  160 . The maximum likelihood detecting unit  160  transmits the finally obtained reception signal to the reception signal processing unit  165 . The array gain controlling unit  130  continues to search the array interference I Am  which maximizes the total gain of the system based on the channel estimation transmitted from the channel estimating unit  125 . Note that the channel estimation H can be estimated by the conventional art. 
     Principle of Operation of First Embodiment 
     Next, a principle of operation of the first embodiment is described. 
     &lt;Array Gain Controlling Unit  130 &gt; 
     The array gain controlling unit  130  stores the array interference I A , as the function of the channel vector H. The array interference I Am  (m=0, 1) is represented by a mathematical expression 3.
 
[Expression 3]
 
 I   A0   =h   1   *h   2   +h   1   h   2 *
 
 I   A1   =h   1   *h   2   −h   1   h   2 *  (3)
 
     The array gain controlling unit  130  performs a calculation of a mathematical expression 4 to select the I Am  which maximizes the system gain. 
     
       
         
           
             
               
                 
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     Namely, the largest I Am  between the I A0  and the I A1  is selected. The array gain controlling unit  130  transmits the index m which corresponds to the selected I Am  to the feedback transmitting unit  135  and the combining unit  155 . The feedback transmitting unit  135  transmits the index m to the first wireless device  11 . 
     &lt;Transmission Vector Selecting Unit  105 &gt; 
     In the following description, the index m is represented by a value of three bits. When the transmission vector selecting unit  105  receives an index [000], it performs the calculation by the transmission vector G 0  and transmits, and when the transmission vector selecting unit  105  receives an index [001], it performs the calculation by the transmission vector G 1  and transmits (mathematical expression 5).
 
[Expression 5]
 
 G   0   =[s s] 
 
 G   1   =[s −s]   (5)
 
     Namely, when the index m is [000], the transmission antennas  110   a  and  110   b  transmit the symbol sequences “s” and “s”, and when the index m is [001], they transmit the symbol sequences “s” and “−s”. 
     &lt;Combining Unit  155 &gt; 
     When the channel vector H is set to be [h 1 , h 2 ], “T” is the transposed matrix operation, and “n” is set to be a zero-mean additive white Gaussian noise (AWGN), a received signal “y” is represented by a mathematical expression 6 when the combining unit  155  receives [000] as the index m.
 
[Expression 6]
 
 y=G   0   ·H   T   +n   (6)
 
     Subsequently, the combining unit  155  performs the combining process by using a weight vector W 0  (mathematical expression 7).
 
[Expression 7]
 
 w   0 =[1 1]  (7)
 
     Note that when the index m is [000], a multiplication of the weight vector W 0  is not necessary. The combining unit  155  performs a calculation represented by a mathematical expression 8 as the combining process. 
     
       
         
           
             
               
                 
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     The symbol estimation which is obtained by the combining unit  155  with the mathematical expression 8 is transmitted to the maximum likelihood decision unit  160  to perform decoding of the symbol. Note that as it is illustrated in the mathematical expression 8 (especially in a third expression), it is a first term which is affected by the gain resulting from a full diversity, and it is a second term (refer to the mathematical expression 3) which is affected by an array gain. 
     When the combining unit  155  receives [001] as the index m, the received signal is represented by a mathematical expression 9.
 
[Expression 9]
 
 y=G   1   ·H   T   +n   (9)
 
     Subsequently, the combining unit  155  performs the combining process by using a weight vector W 1  (mathematical expression 10).
 
[Expression 10]
 
 w   1 =[1 −1]  (10)
 
     The combining unit  155  performs a calculation represented by a mathematical expression 11 as the combining process. 
     
       
         
           
             
               
                 
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     A symbol estimation which is obtained by the combining unit  155  with the mathematical expression 11 is transmitted to the maximum likelihood decision unit  160  to perform the decoding of the symbol. Note that as illustrated in the mathematical expression 11 (especially in a third expression), it is a first term which is affected by the gain resulting from the full diversity, and it is a second term (refer to the mathematical expression 3) which is affected by the array gain. 
     As stated above, in the wireless system of this embodiment, the first wireless device being the transmission side selects the transmission vector based on the channel estimation estimated by the second wireless device being the reception side, and therefore, it is possible to improve the total gain of the system. Besides, in the wireless system of this embodiment, only the index indicating the transmission vector which is to be selected by the first wireless device is to be fed back from the second wireless device, and therefore, a broadband line is not necessary for the feedback. 
     Second Embodiment 
     Next, a wireless system according to a second embodiment is described in detail with reference to  FIG. 3 . As illustrated in  FIG. 3 , a wireless system  2  of this embodiment includes a first wireless device  12  and a second wireless device  22 . The first wireless device  12  in the second embodiment includes an uplink (U/L) receiving unit  250 , a channel estimating unit  255 , and an array gain controlling unit  260  instead of the feedback receiving unit. Besides, the second wireless device  22  in the second embodiment includes a communication controlling unit  230  and an uplink (U/L) transmitting unit  235  instead of the feedback transmitting unit. In the following description, common reference numerals and symbols are used to designate common elements to the first embodiment illustrated in  FIG. 1 , and redundant description is not given. 
     The communication controlling unit  230  is a signal processing block controlling a data transmission (uplink) from the second wireless device  22  to the first wireless device  12 . The uplink transmitting unit  235  transmits an uplink signal transmitted from the communication controlling unit  230  to the first wireless device  12  via the (reception) antenna  115  at the frequency f 1 . The uplink receiving unit  250  receives a signal from the uplink transmitting unit  235  via the (transmission) antennas  110   a / 110   b . The channel estimating unit  255  has a function common to the channel estimating unit  125  of the second wireless device  22 , and performs the channel estimation relating to propagation paths h up  (h up1 , h up2 ) from the (reception) antenna  115  to the (transmission) antennas  110   a / 110   b . The array gain controlling unit  260  corresponds to the array gain controlling unit  130  of the second wireless device  22 , and determines the index m by using the channel estimation found by the channel estimating unit  255 . 
     Namely, the wireless system  2  of this embodiment constitutes a TDD system in which a downlink frequency from the first wireless device  12  to the second wireless device  22  and an uplink frequency from the second wireless device  22  to the first wireless device  12  are common (f 1  in  FIG. 3 ). In case of the TDD system, both the first wireless device  12  being the data transmission side and the second wireless device  22  being the data reception side alternately emit radio waves in the same frequency channel at different time slots. Besides, as a communication system, the transmission side and the reception side alternately play the part. For example, when the first wireless device  12  transmits at a time T n , the second wireless device  22  transmits at a successive time T n+1 . As a result, the first wireless device  12  and the second wireless device  22  are able to perform the estimation of a wireless channel H while they each operate as a receiver. 
     In an example illustrated in  FIG. 3 , the second wireless device  22  performs the estimations of the propagation paths h 1 , h 2 , and the first wireless device  12  performs the estimation of the propagation path h up . Strictly speaking, the propagation paths h 1 , h 2 , h up  are different propagation paths, but when the channel estimation relating to the propagation path h up  is performed, it can be regarded to be the channel estimations relating to the propagation paths h 1 , h 2  in consideration that they are in the same frequency channel and the Doppler diffusion thereof is small as stated above. As a result, the wireless system  2  of the second embodiment does not need the feedback channel in the wireless system  1  of the first embodiment. On the other hand, in the first wireless device  12  in the second embodiment, the array gain controlling unit  260  is included, and thereby, it is possible to enable the calculation maximizing the total gain of the system for itself. 
     Operations of Second Embodiment 
     Subsequently, operations of the wireless system  2  of this embodiment are described with reference to  FIGS. 3 and 4 . In the wireless system of this embodiment, the index m which is used by the first wireless device  12  being the transmission side to determine the transmission vector G m  is determined by the first wireless device  12  being the transmission side for oneself Namely, the first wireless device  12  performs the channel estimation for itself. The wireless system  2  of the second embodiment is the TDD system, and therefore, the first wireless device  12  and the second wireless device  22  each communicate by using the same frequency f 1  at different timings. 
     The uplink transmitting unit  235  of the second wireless device  22  transmits the uplink signal at the frequency f 1  by the control of the communication controlling unit  230  (S 300 ). The uplink receiving unit  250  of the first wireless device  12  receives the uplink signal from the second wireless device  22  (S 305 ). 
     The channel estimating unit  255  performs the channel estimation of the propagation path h up  based on the uplink signal received by the uplink receiving unit  250  (S 310 ). As stated above, at the frequency band of the VHF/UHF band such as the TV white space (TVWS), the Doppler diffusion is small, and therefore, the channel vector H has a quasi-static and extremely low time selectivity, and the temporal variation is relatively small. Accordingly, the channel estimating unit  255  obtains the channel estimations at the h 1 , h 2  by using the channel estimation at the propagation path h up . The channel estimating unit  255  transmits the obtained channel estimation to the array gain controlling unit  260 . 
     The array gain controlling unit  260  calculates the array interference I Am  by using the obtained channel estimation (S 315 ). Similar to the first embodiment, there are two peculiar transmission vectors G m  (m=0, 1), and the array interferences I Am  (I A0 , I A1 ) respectively corresponding to the G m  (G 0 , G 1 ) are generated. Besides, the array interferences I Am  are each a function of the fading channel H, and therefore, it is possible to calculate in advance. Accordingly, it is possible to store the array interference I Am  at a memory in the channel estimating unit  255  of the first wireless device  12 , and to calculate the total gain by using the channel estimation. The array gain controlling unit  260  selects one which takes the maximum value by comparing the two I Am  (mathematical expression 12). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     12 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       argmax 
                       m 
                     
                     ⁡ 
                     
                       ( 
                       
                         I 
                         Am 
                       
                       ) 
                     
                   
                   , 
                   
                     ∀ 
                     
                       m 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     The array gain controlling unit  260  determines the index m in which the array interference becomes the maximum, and transmits to the transmission vector selecting unit  105  (S 320 ). 
     The transmission signal processing unit  100  generates the transmission signal S at the frequency f 1  (S 325 ), the transmission vector selecting unit  105  selects the transmission vector G m  from the G 0 /G 1  based on the index m, and performs the calculation of the transmission vector G m  for the transmission signal S (S 330 ). 
     The transmission vector selecting unit  105  transmits the signals of [s s] or [s −s] from the transmission antennas  110   a  and  110   b  (S 335 ). For example, when the index m determined by the array gain controlling unit  260  is “1”, the first wireless device  11  performs the calculation of the G 1 , and transmits [s, −s]. Namely, the symbol sequence “s” is transmitted from the transmission antenna  110   a , and the symbol sequence “−s” is transmitted from the transmission antenna  110   b.    
     The reception antenna  115  of the second wireless device  22  receives the transmission signals S via the transmission paths h 1  and h 2  (S 340 ). At this time, noises n are mixed into a reception signal at the second wireless device  22 . 
     The channel estimating unit  125  performs the channel estimation based on the reception signal (S 345 ). The channel estimating unit  125  transmits the obtained channel estimation to the array gain controlling unit  130 . 
     The array gain controlling unit  130  calculates the array interference I Am  by using the obtained channel estimation (S 350 ). In the system of the MISO configuration, there are two peculiar transmission vectors G m  (m=0, 1), and the array interferences I Am  (I A0 , I A1 ) respectively corresponding to the G m  (G 0 , G 1 ) are generated. The array interferences I Am  are each the function of the fading channel H, and therefore, it is possible to calculate in advance. Accordingly, it is possible to store the array interferences I Am  at a memory in the channel estimating unit  125  of the second wireless device  22 , and to calculate the total gain by using the channel estimation. The array gain controlling unit  130  selects one which takes the maximum value by comparing the two I Am . 
     When the I Am  taking the maximum value is selected, the array gain controlling unit  130  determines the corresponding index m and transmits to the combining unit  155  (S 355 ). 
     The combining unit  155  performs the combining process by using the channel estimation estimated at the step  345  and the index m generated by the array gain controlling unit  130 , and generates the symbol estimation (S 360 ). For example, when the determined index m is “1”, the combining unit  155  generates the symbol estimation by using the weight vector W 1 . 
     When the communication is started by using the determined transmission vector G m , the combining unit  155  performs a proper signal operation by using the channel estimation received from the channel estimating unit  125 , and provides the symbol estimation to the maximum likelihood detecting unit  160 . The maximum likelihood detecting unit  160  transmits the finally obtained reception signal to the reception signal processing unit  165 . The array gain controlling unit  130  continues to search the maximum array interference I Am  based on the channel estimation constantly transmitted from the channel estimating unit  125 . Note that the channel estimation H can be estimated by the conventional art. 
     As stated above, in the wireless system of this embodiment, the first wireless device being the transmission side selects the transmission vector based on the channel estimation estimated by the first wireless device being the transmission side, and therefore, it is possible to improve the total gain of the system even if there is not the feedback line from the second wireless device. In particular, it is effective in the TDD system where the frequency of the transmission/reception circuits are common. 
     Third Embodiment 
     Next, a wireless system according to a third embodiment is described in detail with reference to  FIG. 5 . As illustrated in  FIG. 5 , a wireless system  3  of this embodiment includes a first wireless device  13  and a second wireless device  23 . The wireless system  3  of this embodiment is one in which four transmission antennas are provided as transmission antennas  110   a  to  110   d  instead of the transmission antennas  110   a  and  110   b  of the first wireless device  11  according to the first embodiment illustrated in  FIGS. 1 and 2 . In the following description, common reference numerals and symbols are used to designate common elements to the first embodiment illustrated in  FIG. 1 , and redundant description is not given. 
     Principle of Operation of Third Embodiment 
     Hereinafter, a principle of operation of the third embodiment is described. 
     &lt;Array Gain Controlling Unit&gt; 
     In the wireless system  3  of this embodiment, transfer paths of the channel estimation estimated by the channel estimating unit  125  are four kinds of h 1  to h 4 , and combinations of the array interferences searched by the array gain controlling unit  130  become 8 kinds. Namely, the transmission vectors G m  and the weight vectors W m  are respectively selected from 8 kinds of G 0  to G 7 , W 0  to W 7 . Accordingly, the combinations of the array interferences I Am  become 8 kinds represented by a mathematical expression 13.
 
[Expression 13]
 
 I   A0   =h   1   *h   2   +h   1   h   2   *+h   1   *h   3   +h   1   h   3   *+h   1   *h   4   +h   1   h   4   *+h   2   *h   3   +h   2   h   3   *+h   2   *h   4   +h   2   h   4   *+h   3   *h   4   +h   3   h   4 *
 
 I   A1   =−h   1   *h   2   −h   1   h   2   *−h   1   *h   4   −h   1   h   4   *+h   2   *h   3   −h   2   h   3   *−h   3   *h   4   −h   3   h   4   *+h   1   *h   3   +h   1   h   3   *+h   2   *h   4   +h   3   h   4 *
 
 I   A2   =−h   1   *h   3   −h   1   h   3   *−h   1   *h   4   −h   1   h   4   *−h   2   *h   3   −h   2   h   3   *−h   2   *h   4   −h   2   h   4   *+h   1   *h   2   +h   1   h   2   *+h   3   *h   4   +h   3   h   4 *
 
 I   A3   =−h   1   *h   2   −h   1   h   2   *−h   1   *h   3   −h   1   h   3   *−h   2   *h   4   +h   2   h   4   *−h   3   *h   4   +h   3   h   4   *+h   1   *h   4   +h   1   h   4   *+h   2   *h   3   +h   2   h   3 *
 
 I   A4   =−h   1   *h   4   −h   1   h   4   *−h   2   *h   4   −h   2   h   4   *−h   3   *h   4   −h   3   h   4   *+h   1   *h   2   +h   1   h   2   *+h   1   *h   3   +h   1   h   3   *+h   2   *h   3   +h   2   h   3 *
 
 I   A5   =−h   1   *h   3   −h   1   h   3   *−h   2   *h   3   −h   2   h   3   *−h   3   *h   4   −h   3   h   4   *+h   1   *h   2   +h   1   h   2   *+h   1   *h   4   +h   1   h   4   *+h   2   *h   4   +h   2   h   4 *
 
 I   A6   =−h   1   *h   2   −h   1   h   2   *−h   2   *h   3   −h   2   h   3   *−h   2   *h   4   −h   2   h   4   *+h   1   *h   3   +h   1   h   3   *+h   1   *h   4   +h   1   h   4   *+h   3   *h   4   +h   3   h   4 *
 
 I   A7   =−h   1   *h   2   −h   1   h   2   *−h   1   *h   3   −h   1   h   3   *−h   1   *h   4   −h   1   h   4   *+h   2   *h   3   +h   2   h   3   *+h   2   *h   4   +h   2   h   4   *+h   3   *h   4   +h   3   h   4 *  (13)
 
     The array gain controlling unit  130  searches the array interference I Am  to be the maximum (mathematical expression 14). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     14 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       argmax 
                       m 
                     
                     ⁡ 
                     
                       ( 
                       
                         I 
                         Am 
                       
                       ) 
                     
                   
                   , 
                   
                     ∀ 
                     
                       m 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           2 
                           , 
                           3 
                           , 
                           4 
                           , 
                           5 
                           , 
                           6 
                           , 
                           7 
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     Namely, the I Am  which is the maximum is selected from among I A0  to I A7 . The array gain controlling unit  130  transmits the index m corresponding to the selected I Am  to the feedback transmitting unit  135  and the combining unit  155 . The feedback transmitting unit  135  transmits the index m to the first wireless device  13 . 
     &lt;Transmission Vector Selecting Unit  105 &gt; 
     In the following description, the index m is represented by a value of three bits. The transmission vector selecting unit  105  receives the indexes [000] [001] [010] [011] [110] [111], performs the calculations by the transmission vectors G 0  to G 7  respectively, and transmits them (mathematical expression 15).
 
[Expression 15]
 
 G   0   =[s s s s] 
 
 G   1   =[s −s s −s] 
 
 G   2   =[s s −s −s] 
 
 G   3   =[s −s −s s] 
 
 G   4   =[s s s −s] 
 
 G   5   =[S s −s s] 
 
 G   6   =[s −s s s] 
 
 G   7   =[−s s s s]   (15)
 
     &lt;Combining unit  155 &gt; 
     The channel vectors H are set to be [h 1  h 2  h 3  h 4 ], and it is assumed that the channel estimation is perfectly performed to simplify the description (mathematical expression 16).
 
[Expression 16]
 
 {tilde over (H)}=H   (16)
 
     When the combining unit  155  receives [000] from the array gain controlling unit  130  as the index m, the combining unit  155  performs the combining process represented by a mathematical expression 18 by using a weight vector represented by a mathematical expression 17. 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       17 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       w 
                       0 
                     
                     = 
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
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                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       18 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         S 
                         ~ 
                       
                       = 
                       
                         
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                           * 
                         
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                     ⁢ 
                     
                         
                     
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                                 h 
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                                 * 
                               
                             
                             ] 
                           
                         
                         · 
                         
                           ( 
                           
                             
                               
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                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
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                         ~ 
                       
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                           ⁡ 
                           
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                             ( 
                             
                               
                                 
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                                   1 
                                   * 
                                 
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                                   2 
                                 
                               
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                                   1 
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                                   h 
                                   3 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   2 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   2 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   3 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   3 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           nh 
                           1 
                           * 
                         
                         + 
                         
                           nh 
                           2 
                           * 
                         
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                           nh 
                           3 
                           * 
                         
                         + 
                         
                           nh 
                           4 
                           * 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     A symbol estimation obtained by the combining unit  155  by the mathematical expression 18 is transmitted to the maximum likelihood decision unit  160  to perform the decoding of a symbol. 
     When the combining unit  155  receives [001] from the array gain controlling unit  130  as the index m, the combining unit  155  performs the combining process represented by a mathematical expression 20 by using a weight vector represented by a mathematical expression 19. 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       19 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       w 
                       1 
                     
                     = 
                     
                       [ 
                       
                         
                           
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                               1 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       20 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         S 
                         ~ 
                       
                       = 
                       
                         
                           yH 
                           * 
                         
                         · 
                         
                           w 
                           1 
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                     ⁢ 
                     
                       
 
                     
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                         ~ 
                       
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                                   4 
                                   * 
                                 
                               
                               + 
                               
                                 
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                                   1 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   1 
                                 
                                 ⁢ 
                                 
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                                   3 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   2 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
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                                   h 
                                   2 
                                 
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                                   4 
                                   * 
                                 
                               
                             
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                         + 
                         
                           nh 
                           1 
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                         - 
                         
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                           4 
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                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     A symbol estimation obtained by the combining unit  155  by the mathematical expression 20 is transmitted to the maximum likelihood decision unit  160  to perform the decoding of the symbol. 
     When the combining unit  155  receives [010] from the array gain controlling unit  130  as the index m, the combining unit  155  performs the combining process represented by a mathematical expression 22 by using a weight vector represented by a mathematical expression 21. 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       21 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       w 
                       2 
                     
                     = 
                     
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                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       22 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
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                           * 
                         
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                     ⁢ 
                     
                       
 
                     
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                                 2 
                               
                               + 
                               
                                 
                                    
                                   
                                     h 
                                     3 
                                   
                                    
                                 
                                 2 
                               
                               + 
                               
                                 
                                    
                                   
                                     h 
                                     4 
                                   
                                    
                                 
                                 2 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           S 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   - 
                                   
                                     h 
                                     1 
                                     * 
                                   
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   1 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                   * 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   1 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   1 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   2 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   2 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                   * 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   2 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   2 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   1 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   2 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   1 
                                 
                                 ⁢ 
                                 
                                   h 
                                   2 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   3 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   3 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           nh 
                           1 
                           * 
                         
                         + 
                         
                           nh 
                           2 
                           * 
                         
                         - 
                         
                           nh 
                           3 
                           * 
                         
                         - 
                         
                           nh 
                           4 
                           * 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     A symbol estimation obtained by the combining unit  155  by the mathematical expression 22 is transmitted to the maximum likelihood decision unit  160  to perform the decoding of the symbol. 
     When the combining unit  155  receives [011] from the array gain controlling unit  130  as the index m, the combining unit  155  performs the combining process represented by a mathematical expression 24 by using a weight vector represented by a mathematical expression 23. 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       23 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       w 
                       3 
                     
                     = 
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             1 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       24 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         S 
                         ~ 
                       
                       = 
                       
                         
                           yH 
                           * 
                         
                         · 
                         
                           w 
                           3 
                           T 
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         S 
                         ~ 
                       
                       = 
                       
                         
                           y 
                           ⁡ 
                           
                             [ 
                             
                               
                                 h 
                                 1 
                                 * 
                               
                               ⁢ 
                               
                                 h 
                                 2 
                                 * 
                               
                               ⁢ 
                               
                                 h 
                                 3 
                                 * 
                               
                               ⁢ 
                               
                                 h 
                                 4 
                                 * 
                               
                             
                             ] 
                           
                         
                         · 
                         
                           ( 
                           
                             
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                             
                               
                                 1 
                               
                             
                           
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         S 
                         ~ 
                       
                       = 
                       
                         
                           S 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                    
                                   
                                     h 
                                     1 
                                   
                                    
                                 
                                 2 
                               
                               + 
                               
                                 
                                    
                                   
                                     h 
                                     2 
                                   
                                    
                                 
                                 2 
                               
                               + 
                               
                                 
                                    
                                   
                                     h 
                                     3 
                                   
                                    
                                 
                                 2 
                               
                               + 
                               
                                 
                                    
                                   
                                     h 
                                     4 
                                   
                                    
                                 
                                 2 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           S 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   - 
                                   
                                     h 
                                     1 
                                     * 
                                   
                                 
                                 ⁢ 
                                 
                                   h 
                                   2 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   1 
                                 
                                 ⁢ 
                                 
                                   h 
                                   2 
                                   * 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   1 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   1 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                   * 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   2 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   2 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   3 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   3 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   1 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   1 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   2 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   2 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                   * 
                                 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           nh 
                           1 
                           * 
                         
                         - 
                         
                           nh 
                           2 
                           * 
                         
                         - 
                         
                           nh 
                           3 
                           * 
                         
                         + 
                         
                           nh 
                           4 
                           * 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
     A symbol estimation obtained by the combining unit  155  by the mathematical expression 24 is transmitted to the maximum likelihood decision unit  160  to perform the decoding of the symbol. 
     When the combining unit  155  receives [100] from the array gain controlling unit  130  as the index m, the combining unit  155  performs the combining process represented by a mathematical expression 26 by using a weight vector represented by a mathematical expression 25. 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       25 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       w 
                       4 
                     
                     = 
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             1 
                           
                           
                             1 
                           
                           
                             
                               - 
                               1 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       26 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         S 
                         ~ 
                       
                       = 
                       
                         
                           yH 
                           * 
                         
                         · 
                         
                           w 
                           4 
                           T 
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         S 
                         ~ 
                       
                       = 
                       
                         
                           y 
                           ⁡ 
                           
                             [ 
                             
                               
                                 h 
                                 1 
                                 * 
                               
                               ⁢ 
                               
                                 h 
                                 2 
                                 * 
                               
                               ⁢ 
                               
                                 h 
                                 3 
                                 * 
                               
                               ⁢ 
                               
                                 h 
                                 4 
                                 * 
                               
                             
                             ] 
                           
                         
                         · 
                         
                           ( 
                           
                             
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         S 
                         ~ 
                       
                       = 
                       
                         
                           S 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                    
                                   
                                     h 
                                     1 
                                   
                                    
                                 
                                 2 
                               
                               + 
                               
                                 
                                    
                                   
                                     h 
                                     2 
                                   
                                    
                                 
                                 2 
                               
                               + 
                               
                                 
                                    
                                   
                                     h 
                                     3 
                                   
                                    
                                 
                                 2 
                               
                               + 
                               
                                 
                                    
                                   
                                     h 
                                     4 
                                   
                                    
                                 
                                 2 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           S 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   - 
                                   
                                     h 
                                     1 
                                     * 
                                   
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   1 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   2 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   2 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   3 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   3 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   1 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   2 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   1 
                                 
                                 ⁢ 
                                 
                                   h 
                                   2 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   1 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   1 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   2 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   2 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                   * 
                                 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           nh 
                           1 
                           * 
                         
                         + 
                         
                           nh 
                           2 
                           * 
                         
                         + 
                         
                           nh 
                           3 
                           * 
                         
                         - 
                         
                           nh 
                           4 
                           * 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
     A symbol estimation obtained by the combining unit  155  by the mathematical expression 26 is transmitted to the maximum likelihood decision unit  160  to perform the decoding of the symbol. 
     When the combining unit  155  receives [101] from the array gain controlling unit  130  as the index m, the combining unit  155  performs the combining process represented by a mathematical expression 28 by using a weight vector represented by a mathematical expression 27. 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       27 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       w 
                       3 
                     
                     = 
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             1 
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             1 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       28 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         S 
                         ~ 
                       
                       = 
                       
                         
                           yH 
                           * 
                         
                         · 
                         
                           w 
                           5 
                           T 
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         S 
                         ~ 
                       
                       = 
                       
                         
                           y 
                           ⁡ 
                           
                             [ 
                             
                               
                                 h 
                                 1 
                                 * 
                               
                               ⁢ 
                               
                                 h 
                                 2 
                                 * 
                               
                               ⁢ 
                               
                                 h 
                                 3 
                                 * 
                               
                               ⁢ 
                               
                                 h 
                                 4 
                                 * 
                               
                             
                             ] 
                           
                         
                         · 
                         
                           ( 
                           
                             
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                             
                               
                                 1 
                               
                             
                           
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         S 
                         ~ 
                       
                       = 
                       
                         
                           S 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                    
                                   
                                     h 
                                     1 
                                   
                                    
                                 
                                 2 
                               
                               + 
                               
                                 
                                    
                                   
                                     h 
                                     2 
                                   
                                    
                                 
                                 2 
                               
                               + 
                               
                                 
                                    
                                   
                                     h 
                                     3 
                                   
                                    
                                 
                                 2 
                               
                               + 
                               
                                 
                                    
                                   
                                     h 
                                     4 
                                   
                                    
                                 
                                 2 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           S 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   - 
                                   
                                     h 
                                     1 
                                     * 
                                   
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   1 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                   * 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   2 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   2 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                   * 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   3 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   3 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   1 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   2 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   1 
                                 
                                 ⁢ 
                                 
                                   h 
                                   2 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   1 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   1 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   2 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   2 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           nh 
                           1 
                           * 
                         
                         + 
                         
                           nh 
                           2 
                           * 
                         
                         - 
                         
                           nh 
                           3 
                           * 
                         
                         + 
                         
                           nh 
                           4 
                           * 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
           
         
       
     
     A symbol estimation obtained by the combining unit  155  by the mathematical expression 28 is transmitted to the maximum likelihood decision unit  160  to perform the decoding of the symbol. 
     When the combining unit  155  receives [110] from the array gain controlling unit  130  as the index m, the combining unit  155  performs the combining process represented by a mathematical expression 30 by using a weight vector represented by a mathematical expression 29. 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       29 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       w 
                       6 
                     
                     = 
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             
                               - 
                               1 
                             
                           
                           
                             1 
                           
                           
                             1 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       30 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         S 
                         ~ 
                       
                       = 
                       
                         
                           yH 
                           * 
                         
                         · 
                         
                           w 
                           6 
                           T 
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         S 
                         ~ 
                       
                       = 
                       
                         
                           y 
                           ⁡ 
                           
                             [ 
                             
                               
                                 h 
                                 1 
                                 * 
                               
                               ⁢ 
                               
                                 h 
                                 2 
                                 * 
                               
                               ⁢ 
                               
                                 h 
                                 3 
                                 * 
                               
                               ⁢ 
                               
                                 h 
                                 4 
                                 * 
                               
                             
                             ] 
                           
                         
                         · 
                         
                           ( 
                           
                             
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                             
                               
                                 1 
                               
                             
                             
                               
                                 1 
                               
                             
                           
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         S 
                         ~ 
                       
                       = 
                       
                         
                           S 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                    
                                   
                                     h 
                                     1 
                                   
                                    
                                 
                                 2 
                               
                               + 
                               
                                 
                                    
                                   
                                     h 
                                     2 
                                   
                                    
                                 
                                 2 
                               
                               + 
                               
                                 
                                    
                                   
                                     h 
                                     3 
                                   
                                    
                                 
                                 2 
                               
                               + 
                               
                                 
                                    
                                   
                                     h 
                                     4 
                                   
                                    
                                 
                                 2 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           S 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   - 
                                   
                                     h 
                                     1 
                                     * 
                                   
                                 
                                 ⁢ 
                                 
                                   h 
                                   2 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   1 
                                 
                                 ⁢ 
                                 
                                   h 
                                   2 
                                   * 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   2 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   2 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                   * 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   2 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               - 
                               
                                 
                                   h 
                                   2 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   1 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   1 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   1 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   1 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   3 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   3 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           nh 
                           1 
                           * 
                         
                         - 
                         
                           nh 
                           2 
                           * 
                         
                         + 
                         
                           nh 
                           3 
                           * 
                         
                         + 
                         
                           nh 
                           4 
                           * 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   30 
                   ) 
                 
               
             
           
         
       
     
     A symbol estimation obtained by the combining unit  155  by the mathematical expression 30 is transmitted to the maximum likelihood decision unit  160  to perform the decoding of the symbol. 
     When the combining unit  155  receives [111] from the array gain controlling unit  130  as the index m, the combining unit  155  performs the combining process represented by a mathematical expression 32 by using a weight vector represented by a mathematical expression 31. 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       31 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       w 
                       7 
                     
                     = 
                     
                       [ 
                       
                         - 
                         
                           
                             
                               1 
                             
                             
                               1 
                             
                             
                               1 
                             
                             
                               1 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   31 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       32 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         S 
                         ~ 
                       
                       = 
                       
                         
                           yH 
                           * 
                         
                         · 
                         
                           w 
                           7 
                           T 
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         S 
                         ~ 
                       
                       = 
                       
                         
                           y 
                           ⁡ 
                           
                             [ 
                             
                               
                                 h 
                                 1 
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                                 2 
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                               ⁢ 
                               
                                 h 
                                 3 
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                               ⁢ 
                               
                                 h 
                                 4 
                                 * 
                               
                             
                             ] 
                           
                         
                         · 
                         
                           ( 
                           
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                             
                             
                               
                                 1 
                               
                             
                             
                               
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                           ) 
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         S 
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                           ⁡ 
                           
                             ( 
                             
                               
                                 
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                                 2 
                               
                             
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                           S 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
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                               - 
                               
                                 
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                                   1 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                   * 
                                 
                               
                               - 
                               
                                 
                                   h 
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                                   * 
                                 
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                               - 
                               
                                 
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                                   * 
                                 
                               
                               + 
                               
                                 
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                                   h 
                                   3 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   2 
                                 
                                 ⁢ 
                                 
                                   h 
                                   3 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   2 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   2 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   3 
                                   * 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   3 
                                 
                                 ⁢ 
                                 
                                   h 
                                   4 
                                   * 
                                 
                               
                             
                             ) 
                           
                         
                         - 
                         
                           nh 
                           1 
                           * 
                         
                         + 
                         
                           nh 
                           2 
                           * 
                         
                         + 
                         
                           nh 
                           3 
                           * 
                         
                         + 
                         
                           nh 
                           4 
                           * 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   32 
                   ) 
                 
               
             
           
         
       
     
     A symbol estimation obtained by the combining unit  155  by the mathematical expression 32 is transmitted to the maximum likelihood decision unit  160  to perform the decoding of the symbol. 
     As illustrated in each of the mathematical expressions 18, 20, 22, 24, 26, 28, 30, and 32 (especially in the third expression each thereof), it is a first term which is affected by the gain resulting from the full diversity, and it is a second term (refer to the mathematical expression 13) which is affected by the array gain. 
     Note that the third embodiment is one in which the number of transmission antennas in the first embodiment is increased, but it is not limited thereto. The similar effect can be obtained also in a case when the number of transmission antennas in the second embodiment is increased. Namely, it can be applied to both the FDD system and the TDD system. 
     As stated above, in the wireless system of this embodiment, the number of transmission antennas of the first wireless device is increased, and therefore, it is possible to increase the number of selective combinations of the array interferences. Namely, it is possible to carefully improve the gain by the array interference. 
     Fourth Embodiment 
     Subsequently, a wireless system according to a fourth embodiment is described in detail with reference to  FIG. 6 . The wireless system of this embodiment is one in which the reception antenna of the second wireless device  21  in the wireless system  1  according to the first embodiment illustrated in  FIG. 1  is pluralized. In the following description, common reference numerals and symbols are used to designate common elements to the first embodiment illustrated in  FIG. 1 , and redundant description is not given. As illustrated in  FIG. 6 , a second wireless device  24  of this embodiment includes a maximum ratio combining unit  116 . The maximum ratio combining unit  116  combines reception signals received by reception antennas  115   a  and  115   b  by a maximum ratio combining (MRC) method. 
     Principle of Operation of Fourth Embodiment 
     Hereinafter, a principle of operation of the fourth embodiment is described. The maximum ratio combining unit  116  combines the reception signals received by the reception antennas  115   a  and  115   b , and transmits to the channel estimating unit  125  and the combining unit  155 . 
     &lt;Array Gain Controlling Unit  130 &gt; 
     The array gain controlling unit  130  performs a calculation represented by a mathematical expression 33. In the following description, a case in which the number of reception antennas of the second wireless device is two and the number of transmission antennas of a first transmission device is four is described. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     33 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       argmax 
                       m 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           I 
                           Am 
                         
                         + 
                         
                           I 
                           Am 
                           ′ 
                         
                       
                       ) 
                     
                   
                   , 
                   
                     ∀ 
                     
                       m 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
                   33 
                   ) 
                 
               
             
           
         
       
     
     Similarly, when the number of transmission antennas of the first wireless device  14  is four, the array gain controlling unit  130  performs a calculation represented by a mathematical expression 34. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     34 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       argmax 
                       m 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           I 
                           Am 
                         
                         + 
                         
                           I 
                           Am 
                           ′ 
                         
                       
                       ) 
                     
                   
                   , 
                   
                     ∀ 
                     
                       m 
                       ∈ 
                       
                         { 
                         
                           0 
                           , 
                           1 
                           , 
                           2 
                           , 
                           3 
                           , 
                           4 
                           , 
                           5 
                           , 
                           6 
                           , 
                           7 
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
                   34 
                   ) 
                 
               
             
           
         
       
     
     Here, the I Am  represents the array interference received by the first reception antenna  115   a  of the second wireless device, and this is the same as the first embodiment. The I′A m  represents an array interference received by the second reception antenna  115   b  of the second wireless device. The channel vectors H to the second reception antenna  115   b  of the second wireless device are represented by [h3 h4] when the number of transmission antennas is two, and by [h5 h6 h7 h8] when the number of transmission antennas is four. The array interferences I′ Am  for the second reception antenna are represented by a mathematical expression 35 when the number of transmission antennas is two, and by a mathematical expression 36 when the number of transmission antennas is four.
 
[Expression 35]
 
 I′   A0   =h   3   *h   4   +h   3   h   4 *
 
 I′   A1   =h   3   *h   4   −h   3   h   4 *  (35)
 
[Expression 36]
 
 I′   A0   =h   5   *h   6   +h   5   h   6   *+h   5   *h   7   +h   5   h   7   *+h   5   *h   8   +h   5   h   8   *+h   6   *h   7   +h   6   h   7   *+h   6   *h   8   +h   6   h   8   *+h   7   *h   8   +h   7   h   8 *
 
 I′   A1   =−h   5   *h   6   −h   5   h   6   *−h   5   *h   8   −h   5   h   8   *−h   6   *h   7   −h   6   h   7   *−h   7   *h   8   −h   7   h   8   *+h   5   *h   7   +h   5   h   7   *+h   6   *h   8   +h   6   h   8 *
 
 I′   A2   =−h   5   *h   7   −h   5   h   7   *−h   5   *h   8   −h   5   h   8   *−h   6   *h   7   −h   6   h   7   *−h   6   *h   8   −h   6   h   8   *+h   5   *h   6   +h   5   h   6   *+h   7   *h   8   +h   7   h   8 *
 
 I′   A3   =−h   5   *h   6   −h   5   h   6   *−h   5   *h   7   −h   5   h   7   *−h   6   *h   8   −h   6   h   8   *−h   7   *h   8   −h   7   h   8   *+h   5   *h   8   +h   5   h   8   *+h   6   *h   7   +h   6   h   7 *
 
 I′   A4   =−h   5   *h   8   −h   5   h   8   *−h   6   *h   8   −h   6   h   8   *−h   7   *h   8   −h   7   h   8   *+h   5   *h   6   +h   5   h   6   *+h   5   *h   7   +h   5   h   7   *+h   6   *h   7   +h   6   h   7 *
 
 I′   A5   =−h   5   *h   7   −h   5   h   7   *−h   6   *h   7   −h   6   h   7   *−h   7   *h   8   −h   7   h   8   *+h   5   *h   6   +h   5   h   6   *+h   5   *h   8   +h   5   h   8   *+h   6   *h   8   +h   6   h   8 *
 
 I′   A6   =−h   5   *h   6   −h   5   h   6   *−h   6   *h   7   −h   6   h   7   *−h   6   *h   8   −h   6   h   8   *+h   5   *h   7   +h   5   h   7   *+h   5   *h   8   +h   5   h   8   *+h   7   *h   8   +h   7   h   8 *
 
 I′   A7   =−h   5   *h   6   −h   5   h   6   *−h   5   *h   7   −h   5   h   7   *−h   5   *h   8   −h   5   h   8   *+h   6   *h   7   +h   6   h   7   *+h   6   *h   8   +h   6   h   8   *+h   7   *h   8   +h   7   h   8 *  (36)
 
     The array gain controlling unit  130  determines the index m which maximizes a sum of (I Am +I′ Am ), and transmits to the first wireless device via the feedback transmitting unit  135  and the feedback receiving unit  150 , and transmits to the combining unit  155 . The combining unit  155  transmits a combined signal represented by a mathematical expression 37 to the maximum likelihood decision unit  160 .
 
[Expression 37]
 
 {tilde over (S)}+{tilde over (S)}′   (37)
 
     Here, parameters illustrated in a mathematical expression 38 are similar to the first embodiment.
 
[Expression 38]
 
 Ś   (38)
 
     Besides, parameters illustrated in a mathematical expression 39 are given by a mathematical expression 40.
 
[Expression 39]
 
 {tilde over (S)}′   (39)
 
[Expression 40]
 
 {tilde over (S)}′=y′H*·w   m   T   (40)
 
     Here, the “y′” is a signal received by the second reception antenna, the “H*” is the channel vector [h 3  h 4 ] (when the number of transmission antennas is two) or [h 5  h 6  h 8 ] (when the number of transmission antennas is four). 
     Note that the fourth embodiment is one in which the number of reception antennas in the first embodiment is increased, but it is not limited thereto. The similar effect can be obtained also in a case when the number of reception antennas in the second embodiment is increased. Namely, it can be applied to both the FDD system and the TDD system. Besides, the third embodiment and the fourth embodiment may be combined and the number of transmission antennas of the first wireless device and the number of reception antennas of the second wireless device may each be increased. 
     As stated above, in the wireless system of this embodiment, the number of reception antennas of the second wireless device is increased, and therefore, it is possible to increase selective combinations of the array interferences. Namely, it is possible to carefully improve the gain by the array interference. 
     As it is described hereinabove, according to the present embodiments, it is possible to enable improvement in reliability of communication, enlargement of cell regions, improvement in PER, and improvement in system performance by adding the array gain in addition to the diversity of full rank. 
     (Application Examples of Embodiments) 
     Here, concrete application examples of the present invention are described with reference to  FIGS. 7 and 8 . For example, a multi-hop relay has been studied in 802.22b standardization initiative. This is to provide a monitoring network covering a relatively long distance d from a base station to a relay node with a low transmission power. 
     The present invention is advantageous in a quasi-static fading channel peculiar to 802.22b, and it is possible to use the array interference because the electric powers at the base station and the relay node are reduced while keeping a target packet error rate (PER). An upper side in  FIG. 7  is a case when the base station transmits with a power P tx =x [W] and the relay node transmits with a power P tx =y [W], and it is an example when the PER becomes “z” according to the conventional art. In case of a lower side where the present invention is applied, it becomes possible to reduce the powers P tx  required for the base station and the relay node under a state in which the PER at the distance d is kept. 
     In other words, when the present invention is applied, it becomes possible to enlarge a distance between the relay nodes covering the same area with the same transmission power. In this case, the transmission powers of the base station and the relay node are kept, but the number of relay nodes required to cover the same distance d becomes small. An upper side in  FIG. 8  is a case when the base station transmits with the power P tx =x [W] and the relay node transmits with the power P tx =y [W], and it is an example when the PER becomes “z” according to the conventional art. In case of a lower side where the present invention is applied, it becomes possible to reduce the number of relay nodes required to cover the same distance d at the same PER when the transmission powers P tx  of the base station and the relay node are kept. 
     It should be noted that the present invention is not limited to the above-described embodiments as they are, and in an implementation stage, it can be embodied by modifying components thereof within a range not departing from the spirit of the invention. Also, the plural components disclosed in the above-described embodiments can be appropriately combined to form various inventions. For example, some of all the components shown in the embodiments may be eliminated. Moreover, components from different embodiments may be combined appropriately. 
     EXPLANATION OF REFERENCE SIGNS 
       1  . . . wireless system,  11  . . . first wireless device,  100  . . . transmission signal processing unit,  105  . . . transmission vector selecting unit  105 ,  110   a ,  110   b  . . . transmission antenna,  115  . . . (reception) antenna,  120  . . . noise mixture source,  125  . . . channel estimating unit,  130  . . . array gain controlling unit,  135  . . . feedback transmitting unit,  140  . . . transmission antenna,  145  . . . reception antenna,  150  . . . feedback receiving unit,  155  . . . combining unit,  160  . . . maximum likelihood detecting unit,  165  . . . reception signal processing unit