# Patent

## Title
Data transmission device, data reception device, and wireless communications system

## Abstract

When an error correction decoding unit 26 of a data reception device 2 fails in error correction decoding of a codeword, an MIMO processing unit 15 of a data transmission device 1 deforms transmitted codewords according to a predetermined rule, and transmits the codewords, and the error correction decoding unit 26 of the data reception device 2 reproduces data by using the deformed codewords. As a result, not only the noise but the interference wave components can be reduced, and the success rates of the demodulation and error correction decoding can be improved greatly.

## Background
FIELD OF THE INVENTION
The present invention relates to a data transmission device that transmits a plurality of codewords simultaneously by using a plurality of antennas, a data reception device that receives a plurality of codewords simultaneously by using a plurality of antennas, and a wireless communications system consisting of the data transmission device and the data reception device.
BACKGROUND OF THE INVENTION
For example, a related art wireless communications system currently disclosed by following nonpatent reference 1 is comprised of the following components.
(1) A Data Transmission Device


    
    
        an error correction encoding unit for carrying out error correction encoding of data which is a transmission object to create a codeword
        a modulating unit for modulating the codeword created by the error correction encoding unit by using QPSK or the like.
        an S/P conversion unit for carrying out serial parallel conversion of the codeword modulated by the modulating unit, and for dividing the codeword into codewords.
        an inverse discrete Fourier transform unit for carrying out IDFT (inverse discrete Fourier transform) of the codewords obtained by the S/P conversion unit in the case of OFDM modulation.
        an MIMO processing unit for simultaneously transmitting the codewords on which the IDFT is performed by the inverse discrete Fourier transform unit by using a plurality of transmitting antennas (the MIMO processing unit includes up conversion from a baseband to a high frequency band).

(2) A Data Reception Device

        an MIMO processing unit for receiving the plurality of codewords simultaneously transmitted from the data transmission device by using a plurality of receiving antennas (the MIMO processing unit includes down conversion from a high frequency band to a baseband).
        a discrete Fourier transform unit for carrying out DFT (discrete Fourier transform) of the codewords received by the MIMO processing unit in the case of OFDM modulation.
        a P/S conversion unit for carrying out parallel serial conversion of the codewords on which the DFT is performed by the discrete Fourier transform unit, and for unifying the plurality of codewords into a codeword.
        a demodulating unit for demodulating the codeword into which the plurality of codewords are unified by the P/S conversion unit.
        an error correction decoding unit for carrying out error correction decoding of the codeword demodulated by the demodulating unit to reproduce the data.
    
    


In the case in which the MIMO processing unit of the data transmission device transmits a plurality of codewords simultaneously by using the plurality of antennas, an improvement in the transfer rate of the data, etc. can be provided. However, there is a case in which interference occurs among the plurality of communication channels.
Hereafter, a case in which a plurality of codewords are transmitted by way of three communication channels and interference occurs among the three communication channels will be explained.
First, a communication channel response matrix H is assumed as follows.




  
    
      
        H
        =
        
          [
          
            
              
                
                  h
                  
                    1
                    ,
                    1
                  
                
              
              
                
                  h
                  
                    1
                    ,
                    2
                  
                
              
              
                
                  h
                  
                    1
                    ,
                    3
                  
                
              
            
            
              
                
                  h
                  
                    2
                    ,
                    1
                  
                
              
              
                
                  h
                  
                    2
                    ,
                    2
                  
                
              
              
                
                  h
                  
                    2
                    ,
                    3
                  
                
              
            
            
              
                
                  h
                  
                    3
                    ,
                    1
                  
                
              
              
                
                  h
                  
                    3
                    ,
                    2
                  
                
              
              
                
                  h
                  
                    3
                    ,
                    3
                  
                
              
            
          
          ]
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          1
        
        ]
      
    
  




where hi,j is a communication channel response from j-th transmitting antenna to i-th receiving antenna.

Furthermore, the symbols of the codewords transmitted from the MIMO processing unit of the data transmission device (symbols which are obtained by modulating an error correcting code expressed by two elements) are expressed as S. For the sake of simplicity, it is assumed that no OFDM modulation is carried out in this example.




  
    
      
        S
        =
        
          [
          
            
              
                
                  S
                  1
                
              
            
            
              
                
                  S
                  2
                
              
            
            
              
                
                  S
                  3
                
              
            
          
          ]
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          2
        
        ]
      
    
  




When the MIMO processing unit of the data transmission device transmits the symbol S of the codewords by using the three transmitting antennas, the MIMO processing unit of the data reception device receives a symbol of codewords by using the three receiving antennas. When the received signal is expressed as r, the received signal r is shown as follows.




  
    
      
        
          r
          =
          
            
              HS
              +
              n
            
            =
            
              
                [
                
                  
                    
                      
                        
                          
                            h
                            
                              1
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            
                              1
                              ,
                              2
                            
                          
                          ⁢
                          
                            S
                            2
                          
                        
                        +
                        
                          
                            h
                            
                              1
                              ,
                              3
                            
                          
                          ⁢
                          
                            S
                            3
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            h
                            
                              2
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            
                              2
                              ,
                              2
                            
                          
                          ⁢
                          
                            S
                            2
                          
                        
                        +
                        
                          
                            h
                            
                              2
                              ,
                              3
                            
                          
                          ⁢
                          
                            S
                            3
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            h
                            
                              3
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            
                              3
                              ,
                              2
                            
                          
                          ⁢
                          
                            S
                            2
                          
                        
                        +
                        
                          
                            h
                            
                              3
                              ,
                              3
                            
                          
                          ⁢
                          
                            S
                            3
                          
                        
                      
                    
                  
                
                ]
              
              +
              
                [
                
                  
                    
                      
                        n
                        1
                      
                    
                  
                  
                    
                      
                        n
                        2
                      
                    
                  
                  
                    
                      
                        n
                        3
                      
                    
                  
                
                ]
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            where
            ⁢
            
              
            
            ⁢
            n
          
          =
          
            [
            
              
                
                  
                    n
                    1
                  
                
              
              
                
                  
                    n
                    2
                  
                
              
              
                
                  
                    n
                    3
                  
                
              
            
            ]
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          3
        
        ]
      
    
  




is a sequence consisting of noise components of receiving antennas.

In this case, when demodulating S1, S2, and S3 which construct the symbol S of the codewords from the received signal received by the receiving antennas 1, 2, and 3, the receiving point of the receiving antenna 1 expressed on the complex plane is shown in FIG. 3(i) at the time of the first-time transmission of the symbol S (according to a simple decoding method, both interference and noise are assumed to be degradation components).
At this time, the received signal is shown as follows.

(h1,1S1+h1,2S2+h1,3S3+n1)h1,1*=S1+h1,2h1,1*S2+h1,3h1,1*S3+h1,1*n1   [Equation 4]

where h1,1h1,1*=1, and h1,2h1,1*S2+h1,3h1,1*S3+h1,1*n1 is all noise components at time of demodulation.

The data transmission device has a mechanism of implementing HARQ-CC (Hybrid Auto-Repeat reQuest-Chase Combining) as a mechanism of, when the data reception device fails to receive the symbol S, automatically transmitting the same symbol S again.
When the same symbol S is retransmitted thereto, the data reception device adds the symbol S to that received at the time of the first-time transmission to calculate the average, thereby reducing the energy of the noise on average by 3 dB to raise the success rates of the demodulation and error correction decoding.
However, as shown in FIG. 3(ii), because interference wave components including h1,2h1,1*S2+h1,3h1,1*S3 remain without being reduced, there are few improvements in the performance (according to the conventional method, only the noise becomes small because of HARQ-CC).
[Nonpatent reference 1] IEEE C802.16m-07/189
DESCRIPTION OF THE INVENTION
Because the conventional wireless communications system is constructed as mentioned above, and the data transmission device is provided with the mechanism of, when the data reception device fails in the reception of the symbol S, retransmitting the same symbol S automatically, the energy of the noise can be reduced on average by 3 dB. However, because the interference wave components cannot be removed, there is a problem that the success rates of the demodulation and error correction decoding cannot be improved greatly.
The present invention is made in order to solve the above-mentioned problem, and it is therefore an object of the present invention to provide a data transmission device, a data reception device, and a wireless communications system which can reduce not only noise but interference wave components, and which can improve the success rates of demodulation and error correction decoding greatly.
In a wireless communications system in accordance with the present invention, when an error correction decoding means of a data reception device fails in error correction decoding of a codeword, a codeword transmitting means of a data transmission device deforms transmitted codewords according to a predetermined rule, and transmits the codewords, and the error correction decoding means of the data reception device reproduces data by using the deformed codewords.
According to the present invention, the codeword transmitting means of the data transmission device is configured in such a way as to, when the error correction decoding means of the data reception device fails in the error correction decoding of a codeword, deform transmitted codewords according to the predetermined rule, and transmit the codewords, and the error correction decoding means of the data reception device is configured in such a way as to reproduce data by using the deformed codewords. As a result, there is provided an advantage of being able to reduce not only the noise but the interference wave components, and to improve the success rates of the demodulation and error correction decoding greatly.



BRIEF DESCRIPTION OF THE FIGURES
FIG. 1 is a block diagram showing a wireless communications system in accordance with Embodiment 1 of the present invention;
FIG. 2 is an explanatory drawing showing a principle on which reduction of noise and interference wave components is based; and
FIG. 3 is an explanatory drawing showing a principle on which reduction of only noise is based.



PREFERRED EMBODIMENTS OF THE INVENTION
Hereafter, in order to explain this invention in greater detail, the preferred embodiments of the present invention will be described with reference to the accompanying drawings.
Embodiment 1
FIG. 1 is a block diagram showing a wireless communications system in accordance with Embodiment 1 of the present invention. In the figure, a data transmission device 1 is a transmitter that transmits a plurality of codewords simultaneously by using a plurality of antennas.
A data reception device 2 is a receiver that receives the plurality of codewords simultaneously by using a plurality of antennas.
An error correction encoding unit 11 of the data transmission device 1 carries out a process of performing error correction encoding of data which is a transmission object to create a codeword. The error correction encoding unit 11 constructs an error correction encoding means.
A modulating unit 12 of the data transmission device 1 carries out a process of modulating the codeword created by the error correction encoding unit 11 by using QPSK or the like. The modulating unit 12 constructs a modulating means.
An S/P conversion unit 13 of the data transmission device 1 carries out a process of performing serial parallel conversion of the codeword modulated by the modulating unit 12, and dividing the codeword into codewords.
Inverse discrete Fourier transform units 14a, 14b, 14c, and 14d of the data transmission device 1 perform IDFT (inverse discrete Fourier transform) on the codewords divided by the S/P conversion unit 13 in the case of OFDM modulation.
An MIMO processing unit 15 of the data transmission device 1 carries out a process of simultaneously transmitting the codewords on which the IDFT is performed by the inverse discrete Fourier transform units 14a, 14b, 14c, and 14d by using transmitting antennas 16a, 16b, 16c, and 16d. The MIMO processing unit 15 also carries out up conversion from a baseband to a high frequency band.
The MIMO processing unit 15 is further provided with a mechanism of implementing HARQ-CC (Hybrid Auto-Repeat reQuest-Chase Combining), and carries out a process of, when an error correction decoding unit 26 of the data reception device 2 fails in error correction decoding of the codewords, deforming the codewords transmitted to the data reception device according to a predetermined rule and transmitting the deformed codewords.
A codeword transmitting means is comprised of the S/P conversion unit 13, the inverse discrete Fourier transform units 14a, 14b, 14c and 14d, and the MIMO processing unit 15.
An MIMO processing unit 22 of the data reception device 2 carries out a process of receiving the plurality of codewords simultaneously transmitted from the data transmission device 1 by using receiving antennas 21a, 21b, 21c, and 21d. The MIMO processing unit 22 also carries out down conversion from a high frequency band to a baseband.
The MIMO processing unit 22 constructs a codeword receiving means.
Discrete Fourier transform units 23a, 23b, 23c, and 23d of the data reception device 2 perform DFT (discrete Fourier transform) on the codewords received by the MIMO processing unit 22 in the case of OFDM modulation.
A P/S conversion unit 24 of the data reception device 2 carries out a process of performing parallel serial conversion on the codewords on which the DFT is performed by the discrete Fourier transform units 23a, 23b, 23c and 23d, and unifying the plurality of codewords into a codeword.
A demodulating unit 25 of the data reception device 2 carries out a process of demodulating the codeword into which the plurality of codewords are unified by the P/S conversion unit 24.
A demodulating means is comprised of the discrete Fourier transform units 23a, 23b, 23c and 23d, the P/S conversion unit 24, and the demodulating unit 25.
The error correction decoding unit 26 of the data reception device 2 carries out a process of performing error correction decoding on the codeword demodulated by the demodulating unit 25 to reproduce the data.
The error correction decoding unit 26 also carries out a process of, when the codewords deformed using HARQ-CC is transmitted from the data transmission device 1, reproducing the data by using the deformed codewords.
The error correction decoding unit 26 constructs an error correction decoding means.
Next, the operation of the system will be explained.
When receiving data which is a transmission object, the error correction encoding unit 11 of the data transmission device 1 carries out error correction encoding of the data to create a codeword.
After the error correction encoding unit 11 creates the codeword, the modulating unit 12 of the data transmission device 1 modulates the codeword by using QPSK or the like.
After the modulating unit 12 modulates the codeword, the S/P conversion unit 13 of the data transmission device 1 carries out serial parallel conversion of the codeword and divides the codeword into codewords.
In the example of FIG. 1, the S/P conversion unit divides the codeword into four codewords, and outputs the four divided codewords to the inverse discrete Fourier transform units 14a, 14b, 14c, and 14d respectively.
In the case of OFDM modulation, the inverse discrete Fourier transform units 14a, 14b, 14c, and 14d of the data transmission device 1 perform IDFT on the codewords into which the codeword is divided by the S/P conversion unit 13 respectively.
The MIMO processing unit 15 of the data transmission device 1 simultaneously transmits the codewords on which the IDFT is performed by the inverse discrete Fourier transform units 14a, 14b, 14c, and 14d by using the transmitting antennas 16a, 16b, 16c, and 16d respectively.
When the data transmission device 1 transmits the plurality of codewords simultaneously, the MIMO processing unit 22 of the data reception device 2 receives the plurality of codewords transmitted from the data transmission device 1 by using the receiving antennas 21a, 21b, 21c, and 21d. 
In the case of OFDM modulation, the discrete Fourier transform units 23a, 23b, 23c, and 23d of the data reception device 2 perform DFT on the codewords received by the MIMO processing unit 22 respectively.
The P/S conversion unit 24 of the data reception device 2 carries out parallel serial conversion of the codewords on which the DFT is performed by the discrete Fourier transform units 23a, 23b, 23c, and 23d, and unifies the plurality of codewords into a codeword.
After the P/S conversion unit 24 unifies the codewords into a codeword, the demodulating unit 25 of the data reception device 2 demodulates the codeword into which the plurality of codewords are unified.
After the demodulating unit 25 demodulates the codeword, the error correction decoding unit 26 of the data reception device 2 carries out error correction decoding of the codeword to reproduce the data.
When the error correction decoding unit 26 of the data reception device 2 has succeeded in the error correction decoding of the codeword, the data outputted from the error correction decoding unit 26 are correct, though in the case in which the plurality of codewords are transmitted via the four communication channels, interference may occur among the four communication channels, and, in this case, the error correction decoding unit 26 may fail in the error correction decoding of the codeword.
When the error correction decoding unit 26 of the data reception device 2 fails in the error correction decoding of the codeword, the MIMO processing unit 15 of the data transmission device 1 deforms the codewords transmitted to the data reception device according to the predetermined rule, and then transmits the deformed codewords.
When the codewords deformed using HARQ-CC from the data transmission device 1 are transmitted to the data reception device 2, the error correction decoding unit 26 of the data reception device 2 reproduces the data by using the deformed codewords.
Hereafter, a case in which the codewords deformed using HARQ-CC are transmitted from the data transmission device 1 will be explained in detail.
For convenience in description, it is assumed that the codewords are transmitted via the three communication channels and interference occurs among the three communication channels.
First, the communication channel response matrix H is assumed as follows.




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          5
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        H
        =
        
          [
          
            
              
                
                  h
                  
                    1
                    ,
                    1
                  
                
              
              
                
                  h
                  
                    1
                    ,
                    2
                  
                
              
              
                
                  h
                  
                    1
                    ,
                    3
                  
                
              
            
            
              
                
                  h
                  
                    2
                    ,
                    1
                  
                
              
              
                
                  h
                  
                    2
                    ,
                    2
                  
                
              
              
                
                  h
                  
                    2
                    ,
                    3
                  
                
              
            
            
              
                
                  h
                  
                    3
                    ,
                    1
                  
                
              
              
                
                  h
                  
                    3
                    ,
                    2
                  
                
              
              
                
                  h
                  
                    3
                    ,
                    3
                  
                
              
            
          
          ]
        
      
    
    
      
        (
        21
        )
      
    
  




where hi,j is a communication channel response from j-th transmitting antenna to i-th receiving antenna.

Furthermore, the symbols of the codewords transmitted from the MIMO processing unit 15 of the data transmission device 1 (symbols which are obtained by modulating an error correcting code expressed by two elements) are expressed as S. For the sake of simplicity, it is assumed that no OFDM modulation is carried out in this example.




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          6
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        S
        =
        
          [
          
            
              
                
                  S
                  1
                
              
            
            
              
                
                  S
                  2
                
              
            
            
              
                
                  S
                  3
                
              
            
          
          ]
        
      
    
    
      
        (
        22
        )
      
    
  




When the MIMO processing unit 15 of the data transmission device 1 transmits the symbols S of the codewords by using the three transmitting antennas 16a, 16b, and 16c, the MIMO processing unit 22 of the data reception device 2 receives the symbols of codewords by using the three receiving antennas 21a, 21b, and 21c. When the received signal is expressed as r, the received signal r is shown as follows.




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          7
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        
          r
          =
          
            
              HS
              +
              n
            
            =
            
              
                [
                
                  
                    
                      
                        
                          
                            h
                            
                              1
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            
                              1
                              ,
                              2
                            
                          
                          ⁢
                          
                            S
                            2
                          
                        
                        +
                        
                          
                            h
                            
                              1
                              ,
                              3
                            
                          
                          ⁢
                          
                            S
                            3
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            h
                            
                              2
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            
                              2
                              ,
                              2
                            
                          
                          ⁢
                          
                            S
                            2
                          
                        
                        +
                        
                          
                            h
                            
                              2
                              ,
                              3
                            
                          
                          ⁢
                          
                            S
                            3
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            h
                            
                              3
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            
                              3
                              ,
                              2
                            
                          
                          ⁢
                          
                            S
                            2
                          
                        
                        +
                        
                          
                            h
                            
                              3
                              ,
                              3
                            
                          
                          ⁢
                          
                            S
                            3
                          
                        
                      
                    
                  
                
                ]
              
              +
              
                [
                
                  
                    
                      
                        n
                        1
                      
                    
                  
                  
                    
                      
                        n
                        2
                      
                    
                  
                  
                    
                      
                        n
                        3
                      
                    
                  
                
                ]
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            where
            ⁢
            
              
            
            ⁢
            n
          
          =
          
            [
            
              
                
                  
                    n
                    1
                  
                
              
              
                
                  
                    n
                    2
                  
                
              
              
                
                  
                    n
                    3
                  
                
              
            
            ]
          
        
      
    
    
      
        (
        23
        )
      
    
  




is a sequence consisting of noise components of receiving antennas.

When the symbols S(1) of the codewords which are transmitted for the first time (at the time of the first-time transmission) are not decoded normally by the error correction decoding unit 26 of the data reception device 2, the MIMO processing unit 15 of the data transmission device 1 multiplies the symbols S(1) by a part of an orthogonal code to deform the symbols S(1) into symbols S(2). The MIMO processing unit also multiplies the symbols S(1) by a part of the orthogonal code to deform the symbols S(1) into symbols S(3).
After creating the symbols S(2) and S(3) in the above-mentioned way, the MIMO processing unit 15 of the data transmission device 1 transmits the symbols S(2) and S(3) by using the three transmitting antennas 16a, 16b, and 16c after transmitting the symbols S(1).




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          8
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        
          
            S
            
              (
              1
              )
            
          
          =
          
            [
            
              
                
                  
                    S
                    1
                  
                
              
              
                
                  
                    S
                    2
                  
                
              
              
                
                  
                    S
                    3
                  
                
              
            
            ]
          
        
        ,
        
          
            S
            
              (
              2
              )
            
          
          =
          
            [
            
              
                
                  
                    S
                    1
                  
                
              
              
                
                  
                    
                      e
                      
                        
                          -
                          j2π
                        
                        ⁢
                        
                          1
                          3
                        
                      
                    
                    ·
                    
                      S
                      2
                    
                  
                
              
              
                
                  
                    
                      e
                      
                        
                          -
                          j2π
                        
                        ⁢
                        
                          2
                          3
                        
                      
                    
                    ·
                    
                      S
                      3
                    
                  
                
              
            
            ]
          
        
        ,
        
          
            S
            
              (
              3
              )
            
          
          =
          
            [
            
              
                
                  
                    S
                    1
                  
                
              
              
                
                  
                    
                      e
                      
                        
                          -
                          j2π
                        
                        ⁢
                        
                          2
                          3
                        
                      
                    
                    ·
                    
                      S
                      2
                    
                  
                
              
              
                
                  
                    
                      e
                      
                        
                          -
                          j2π
                        
                        ⁢
                        
                          1
                          3
                        
                      
                    
                    ·
                    
                      S
                      3
                    
                  
                
              
            
            ]
          
        
      
    
    
      
        (
        24
        )
      
    
  




After the MIMO processing unit 15 of the data transmission device 1 transmits the sequence S(1, 2, 3) of the symbols S(1), S(2), and S(3), the MIMO processing unit 22 of the data reception device 2 receives a sequence r(1, 2, 3) of symbols by using the three receiving antennas 21a, 21b, and 21c. This sequence r(1, 2, 3) is shown as follows.




  
    
      
        
          
        
        ⁢
        
          [
          
            Equation
            ⁢
            
              
            
            ⁢
            9
          
          ]
        
      
    
    
      
        
      
    
  
  
    
      
        
          r
          
            (
            
              1
              ,
              2
              ,
              3
            
            )
          
        
        =
        
          
            
              H
              ⁡
              
                [
                
                  
                    
                      
                        S
                        
                          (
                          1
                          )
                        
                      
                    
                    
                      
                        S
                        
                          (
                          2
                          )
                        
                      
                    
                    
                      
                        S
                        
                          (
                          3
                          )
                        
                      
                    
                  
                
                ]
              
            
            +
            
              n
              
                (
                
                  1
                  ,
                  2
                  ,
                  3
                
                )
              
            
          
          =
          
            
              
                
                  [
                  
                    
                      
                        
                          h
                          
                            1
                            ,
                            1
                          
                        
                      
                      
                        
                          h
                          
                            1
                            ,
                            2
                          
                        
                      
                      
                        
                          h
                          
                            1
                            ,
                            3
                          
                        
                      
                    
                    
                      
                        
                          h
                          
                            2
                            ,
                            1
                          
                        
                      
                      
                        
                          h
                          
                            2
                            ,
                            2
                          
                        
                      
                      
                        
                          h
                          
                            2
                            ,
                            3
                          
                        
                      
                    
                    
                      
                        
                          h
                          
                            3
                            ,
                            1
                          
                        
                      
                      
                        
                          h
                          
                            3
                            ,
                            2
                          
                        
                      
                      
                        
                          h
                          
                            3
                            ,
                            3
                          
                        
                      
                    
                  
                  ]
                
                ⁡
                
                  [
                  
                    
                      
                        
                          S
                          1
                        
                      
                      
                        
                          S
                          1
                        
                      
                      
                        
                          S
                          1
                        
                      
                    
                    
                      
                        
                          S
                          2
                        
                      
                      
                        
                          
                            e
                            
                              
                                -
                                j2π
                              
                              ⁢
                              
                                1
                                3
                              
                            
                          
                          ·
                          
                            S
                            2
                          
                        
                      
                      
                        
                          
                            e
                            
                              
                                -
                                j2π
                              
                              ⁢
                              
                                2
                                3
                              
                            
                          
                          ·
                          
                            S
                            2
                          
                        
                      
                    
                    
                      
                        
                          S
                          3
                        
                      
                      
                        
                          
                            e
                            
                              
                                -
                                j2π
                              
                              ⁢
                              
                                2
                                3
                              
                            
                          
                          ·
                          
                            S
                            3
                          
                        
                      
                      
                        
                          
                            e
                            
                              
                                -
                                j2π
                              
                              ⁢
                              
                                1
                                3
                              
                            
                          
                          ·
                          
                            S
                            3
                          
                        
                      
                    
                  
                  ]
                
              
              +
              
                [
                
                  
                    
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                    
                    
                      
                        n
                        1
                        
                          (
                          2
                          )
                        
                      
                    
                    
                      
                        n
                        1
                        
                          (
                          3
                          )
                        
                      
                    
                  
                  
                    
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                    
                    
                      
                        n
                        2
                        
                          (
                          2
                          )
                        
                      
                    
                    
                      
                        n
                        2
                        
                          (
                          3
                          )
                        
                      
                    
                  
                  
                    
                      
                        n
                        3
                        
                          (
                          1
                          )
                        
                      
                    
                    
                      
                        n
                        3
                        
                          (
                          2
                          )
                        
                      
                    
                    
                      
                        n
                        3
                        
                          (
                          3
                          )
                        
                      
                    
                  
                
                ]
              
            
            =
            
              

            
            ⁢
            
              
                [
                
                  
                
                ⁢
                
                  
                    
                      
                        
                          
                            h
                            
                              1
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            
                              1
                              ,
                              2
                            
                          
                          ⁢
                          
                            S
                            2
                          
                        
                        +
                        
                          
                            h
                            
                              1
                              ,
                              3
                            
                          
                          ⁢
                          
                            S
                            3
                          
                        
                      
                    
                    
                      
                        
                          
                            h
                            
                              1
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            
                              1
                              ,
                              2
                            
                          
                          ⁢
                          
                            
                              e
                              
                                
                                  -
                                  j2π
                                
                                ⁢
                                
                                  1
                                  3
                                
                              
                            
                            ·
                            
                              S
                              2
                            
                          
                        
                        +
                        
                          
                            h
                            
                              1
                              ,
                              3
                            
                          
                          ⁢
                          
                            
                              e
                              
                                
                                  -
                                  j2π
                                
                                ⁢
                                
                                  2
                                  3
                                
                              
                            
                            ·
                            
                              S
                              3
                            
                          
                        
                      
                    
                    
                      
                        
                          
                            h
                            
                              1
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            
                              1
                              ,
                              2
                            
                          
                          ⁢
                          
                            
                              e
                              
                                
                                  -
                                  j2π
                                
                                ⁢
                                
                                  2
                                  3
                                
                              
                            
                            ·
                            
                              S
                              2
                            
                          
                        
                        +
                        
                          
                            h
                            
                              1
                              ,
                              3
                            
                          
                          ⁢
                          
                            
                              e
                              
                                
                                  -
                                  j2π
                                
                                ⁢
                                
                                  1
                                  3
                                
                              
                            
                            ·
                            
                              S
                              3
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            h
                            
                              2
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            
                              2
                              ,
                              2
                            
                          
                          ⁢
                          
                            S
                            2
                          
                        
                        +
                        
                          
                            h
                            
                              2
                              ,
                              3
                            
                          
                          ⁢
                          
                            S
                            3
                          
                        
                      
                    
                    
                      
                        
                          
                            h
                            
                              2
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            
                              2
                              ,
                              2
                            
                          
                          ⁢
                          
                            
                              e
                              
                                
                                  -
                                  j2π
                                
                                ⁢
                                
                                  1
                                  3
                                
                              
                            
                            ·
                            
                              S
                              2
                            
                          
                        
                        +
                        
                          
                            h
                            
                              2
                              ,
                              3
                            
                          
                          ⁢
                          
                            
                              e
                              
                                
                                  -
                                  j2π
                                
                                ⁢
                                
                                  2
                                  3
                                
                              
                            
                            ·
                            
                              S
                              3
                            
                          
                        
                      
                    
                    
                      
                        
                          
                            h
                            
                              2
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            
                              2
                              ,
                              2
                            
                          
                          ⁢
                          
                            
                              e
                              
                                
                                  -
                                  j2π
                                
                                ⁢
                                
                                  2
                                  3
                                
                              
                            
                            ·
                            
                              S
                              2
                            
                          
                        
                        +
                        
                          
                            h
                            
                              2
                              ,
                              3
                            
                          
                          ⁢
                          
                            
                              e
                              
                                
                                  -
                                  j2π
                                
                                ⁢
                                
                                  1
                                  3
                                
                              
                            
                            ·
                            
                              S
                              3
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            h
                            
                              3
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            
                              3
                              ,
                              2
                            
                          
                          ⁢
                          
                            S
                            2
                          
                        
                        +
                        
                          
                            h
                            
                              3
                              ,
                              3
                            
                          
                          ⁢
                          
                            S
                            3
                          
                        
                      
                    
                    
                      
                        
                          
                            h
                            
                              3
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            
                              3
                              ,
                              2
                            
                          
                          ⁢
                          
                            
                              e
                              
                                
                                  -
                                  j2π
                                
                                ⁢
                                
                                  1
                                  3
                                
                              
                            
                            ·
                            
                              S
                              2
                            
                          
                        
                        +
                        
                          
                            h
                            
                              3
                              ,
                              3
                            
                          
                          ⁢
                          
                            
                              e
                              
                                
                                  -
                                  j2π
                                
                                ⁢
                                
                                  2
                                  3
                                
                              
                            
                            ·
                            
                              S
                              3
                            
                          
                        
                      
                    
                    
                      
                        
                          
                            h
                            
                              3
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            
                              3
                              ,
                              2
                            
                          
                          ⁢
                          
                            
                              e
                              
                                
                                  -
                                  j2π
                                
                                ⁢
                                
                                  2
                                  3
                                
                              
                            
                            ·
                            
                              S
                              2
                            
                          
                        
                        +
                        
                          
                            h
                            
                              3
                              ,
                              3
                            
                          
                          ⁢
                          
                            
                              e
                              
                                
                                  -
                                  j2π
                                
                                ⁢
                                
                                  1
                                  3
                                
                              
                            
                            ·
                            
                              S
                              3
                            
                          
                        
                      
                    
                  
                
                ]
              
              +
              
                

              
              ⁢
              
                
              
              ⁢
              
                [
                
                  
                    
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                    
                    
                      
                        n
                        1
                        
                          (
                          2
                          )
                        
                      
                    
                    
                      
                        n
                        1
                        
                          (
                          3
                          )
                        
                      
                    
                  
                  
                    
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                    
                    
                      
                        n
                        2
                        
                          (
                          2
                          )
                        
                      
                    
                    
                      
                        n
                        2
                        
                          (
                          3
                          )
                        
                      
                    
                  
                  
                    
                      
                        n
                        3
                        
                          (
                          1
                          )
                        
                      
                    
                    
                      
                        n
                        3
                        
                          (
                          2
                          )
                        
                      
                    
                    
                      
                        n
                        3
                        
                          (
                          3
                          )
                        
                      
                    
                  
                
                ]
              
            
          
        
      
    
    
      
        (
        25
        )
      
    
  




After the MIMO processing unit 22 receives the sequence r(1, 2, 3) by using the three receiving antennas 21a, 21b, and 21c, the error correction decoding unit 26 of the data reception device 2 multiplies the received sequence r(1, 2, 3) by an orthogonal code to deform equation (25), as will be shown below.




  
    
      
        
          
        
        ⁢
        
          [
          
            Equation
            ⁢
            
              
            
            ⁢
            10
          
          ]
        
      
    
    
      
        
      
    
  
  
    
      
        
          
            r
            
              (
              
                1
                ,
                2
                ,
                3
              
              )
            
          
          ⁡
          
            [
            
              
                
                  1
                
                
                  1
                
                
                  1
                
              
              
                
                  1
                
                
                  
                    e
                    
                      
                        -
                        j2π
                      
                      ⁢
                      
                        2
                        3
                      
                    
                  
                
                
                  
                    e
                    
                      
                        -
                        j2π
                      
                      ⁢
                      
                        1
                        3
                      
                    
                  
                
              
              
                
                  1
                
                
                  
                    e
                    
                      
                        -
                        j2π
                      
                      ⁢
                      
                        1
                        3
                      
                    
                  
                
                
                  
                    e
                    
                      
                        -
                        j2π
                      
                      ⁢
                      
                        2
                        3
                      
                    
                  
                
              
            
            ]
          
        
        =
        
          
            3
            ⁡
            
              [
              
                
                  
                    
                      
                        h
                        
                          1
                          ,
                          1
                        
                      
                      ⁢
                      
                        S
                        1
                      
                    
                  
                  
                    
                      
                        h
                        
                          1
                          ,
                          2
                        
                      
                      ⁢
                      
                        S
                        2
                      
                    
                  
                  
                    
                      
                        h
                        
                          1
                          ,
                          3
                        
                      
                      ⁢
                      
                        S
                        3
                      
                    
                  
                
                
                  
                    
                      
                        h
                        
                          2
                          ,
                          1
                        
                      
                      ⁢
                      
                        S
                        1
                      
                    
                  
                  
                    
                      
                        h
                        
                          2
                          ,
                          2
                        
                      
                      ⁢
                      
                        S
                        2
                      
                    
                  
                  
                    
                      
                        h
                        
                          2
                          ,
                          3
                        
                      
                      ⁢
                      
                        S
                        3
                      
                    
                  
                
                
                  
                    
                      
                        h
                        
                          3
                          ,
                          1
                        
                      
                      ⁢
                      
                        S
                        1
                      
                    
                  
                  
                    
                      
                        h
                        
                          3
                          ,
                          2
                        
                      
                      ⁢
                      
                        S
                        2
                      
                    
                  
                  
                    
                      
                        h
                        
                          3
                          ,
                          3
                        
                      
                      ⁢
                      
                        S
                        3
                      
                    
                  
                
              
              ]
            
          
          +
          
             
            
              [
              
                
                  
                    
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                      +
                      
                        n
                        1
                        
                          (
                          2
                          )
                        
                      
                      +
                      
                        n
                        1
                        
                          (
                          3
                          )
                        
                      
                    
                  
                  
                    
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                      +
                      
                        
                          e
                          
                            
                              -
                              j2π
                            
                            ⁢
                            
                              2
                              3
                            
                          
                        
                        ⁢
                        
                          n
                          1
                          
                            (
                            2
                            )
                          
                        
                      
                      +
                      
                        
                          e
                          
                            
                              -
                              j2π
                            
                            ⁢
                            
                              1
                              3
                            
                          
                        
                        ⁢
                        
                          n
                          1
                          
                            (
                            3
                            )
                          
                        
                      
                    
                  
                  
                    
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                      +
                      
                        
                          e
                          
                            
                              -
                              j2π
                            
                            ⁢
                            
                              1
                              3
                            
                          
                        
                        ⁢
                        
                          n
                          1
                          
                            (
                            2
                            )
                          
                        
                      
                      +
                      
                        
                          e
                          
                            
                              -
                              j2π
                            
                            ⁢
                            
                              2
                              3
                            
                          
                        
                        ⁢
                        
                          n
                          1
                          
                            (
                            3
                            )
                          
                        
                      
                    
                  
                
                
                  
                    
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                      +
                      
                        n
                        2
                        
                          (
                          2
                          )
                        
                      
                      +
                      
                        n
                        2
                        
                          (
                          3
                          )
                        
                      
                    
                  
                  
                    
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                      +
                      
                        
                          e
                          
                            
                              -
                              j2π
                            
                            ⁢
                            
                              2
                              3
                            
                          
                        
                        ⁢
                        
                          n
                          2
                          
                            (
                            2
                            )
                          
                        
                      
                      +
                      
                        
                          e
                          
                            
                              -
                              j2π
                            
                            ⁢
                            
                              1
                              3
                            
                          
                        
                        ⁢
                        
                          n
                          2
                          
                            (
                            3
                            )
                          
                        
                      
                    
                  
                  
                    
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                      +
                      
                        
                          e
                          
                            
                              -
                              j2π
                            
                            ⁢
                            
                              1
                              3
                            
                          
                        
                        ⁢
                        
                          n
                          2
                          
                            (
                            2
                            )
                          
                        
                      
                      +
                      
                        
                          e
                          
                            
                              -
                              j2π
                            
                            ⁢
                            
                              2
                              3
                            
                          
                        
                        ⁢
                        
                          n
                          2
                          
                            (
                            3
                            )
                          
                        
                      
                    
                  
                
                
                  
                    
                      
                        n
                        3
                        
                          (
                          1
                          )
                        
                      
                      +
                      
                        n
                        3
                        
                          (
                          2
                          )
                        
                      
                      +
                      
                        n
                        3
                        
                          (
                          3
                          )
                        
                      
                    
                  
                  
                    
                      
                        n
                        3
                        
                          (
                          1
                          )
                        
                      
                      +
                      
                        
                          e
                          
                            
                              -
                              j2π
                            
                            ⁢
                            
                              2
                              3
                            
                          
                        
                        ⁢
                        
                          n
                          3
                          
                            (
                            2
                            )
                          
                        
                      
                      +
                      
                        
                          e
                          
                            
                              -
                              j2π
                            
                            ⁢
                            
                              1
                              3
                            
                          
                        
                        ⁢
                        
                          n
                          3
                          
                            (
                            3
                            )
                          
                        
                      
                    
                  
                  
                    
                      
                        n
                        3
                        
                          (
                          1
                          )
                        
                      
                      +
                      
                        
                          e
                          
                            
                              -
                              j2π
                            
                            ⁢
                            
                              1
                              3
                            
                          
                        
                        ⁢
                        
                          n
                          3
                          
                            (
                            2
                            )
                          
                        
                      
                      +
                      
                        
                          e
                          
                            
                              -
                              j2π
                            
                            ⁢
                            
                              2
                              3
                            
                          
                        
                        ⁢
                        
                          n
                          3
                          
                            (
                            3
                            )
                          
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    
      
        (
        26
        )
      
    
  




The error correction decoding unit 26 of the data reception device 2 also extracts S1, S2, and S3 which construct the symbols S of the codewords by arranging equation (26) to form equation (27) and then calculating equation (27).
[Equation 11]

3h1,1S1h*1,1+3h2,1S1h*2,1+3h3,1S1h*3,1+n′1=3(|h1,1|2+|h2,1|2+|h3,1|2)·S1+n′1 

3h1,2S2h*1,2+3h2,2S2h*2,2+3h3,2S2h*3,2+n′2=3(|h1,2|2+|h2,2|2+|h3,2|2)·S2+n′2 

3h1,3S3h*1,3+3h2,3S3h*2,3+3h3,3S3h*3,3+n′3=3(|h1,3|2+|h2,3|2+|h3,3|2)·S3+n′3   (27)

where when n′1, n′2, n′3 are defined as follows:





  
    [
    
      
        
          
            n
            
              1
              ,
              1
            
            ′
          
        
        
          
            n
            
              1
              ,
              2
            
            ′
          
        
        
          
            n
            
              1
              ,
              3
            
            ′
          
        
      
      
        
          
            n
            
              2
              ,
              1
            
            ′
          
        
        
          
            n
            
              2
              ,
              2
            
            ′
          
        
        
          
            n
            
              2
              ,
              3
            
            ′
          
        
      
      
        
          
            n
            
              3
              ,
              1
            
            ′
          
        
        
          
            n
            
              3
              ,
              2
            
            ′
          
        
        
          
            n
            
              3
              ,
              3
            
            ′
          
        
      
    
    ]
  
  =
  
     
    
      [
      
        
          
            
              
                n
                1
                
                  (
                  1
                  )
                
              
              +
              
                n
                1
                
                  (
                  2
                  )
                
              
              +
              
                n
                1
                
                  (
                  3
                  )
                
              
            
          
          
            
              
                n
                1
                
                  (
                  1
                  )
                
              
              +
              
                
                  e
                  
                    
                      -
                      j2π
                    
                    ⁢
                    
                      2
                      3
                    
                  
                
                ⁢
                
                  n
                  1
                  
                    (
                    2
                    )
                  
                
              
              +
              
                
                  e
                  
                    
                      -
                      j2π
                    
                    ⁢
                    
                      1
                      3
                    
                  
                
                ⁢
                
                  n
                  1
                  
                    (
                    3
                    )
                  
                
              
            
          
          
            
              
                n
                1
                
                  (
                  1
                  )
                
              
              +
              
                
                  e
                  
                    
                      -
                      j2π
                    
                    ⁢
                    
                      1
                      3
                    
                  
                
                ⁢
                
                  n
                  1
                  
                    (
                    2
                    )
                  
                
              
              +
              
                
                  e
                  
                    
                      -
                      j2π
                    
                    ⁢
                    
                      2
                      3
                    
                  
                
                ⁢
                
                  n
                  1
                  
                    (
                    3
                    )
                  
                
              
            
          
        
        
          
            
              
                n
                2
                
                  (
                  1
                  )
                
              
              +
              
                n
                2
                
                  (
                  2
                  )
                
              
              +
              
                n
                2
                
                  (
                  3
                  )
                
              
            
          
          
            
              
                n
                2
                
                  (
                  1
                  )
                
              
              +
              
                
                  e
                  
                    
                      -
                      j2π
                    
                    ⁢
                    
                      2
                      3
                    
                  
                
                ⁢
                
                  n
                  2
                  
                    (
                    2
                    )
                  
                
              
              +
              
                
                  e
                  
                    
                      -
                      j2π
                    
                    ⁢
                    
                      1
                      3
                    
                  
                
                ⁢
                
                  n
                  2
                  
                    (
                    3
                    )
                  
                
              
            
          
          
            
              
                n
                2
                
                  (
                  1
                  )
                
              
              +
              
                
                  e
                  
                    
                      -
                      j2π
                    
                    ⁢
                    
                      1
                      3
                    
                  
                
                ⁢
                
                  n
                  2
                  
                    (
                    2
                    )
                  
                
              
              +
              
                
                  e
                  
                    
                      -
                      j2π
                    
                    ⁢
                    
                      2
                      3
                    
                  
                
                ⁢
                
                  n
                  2
                  
                    (
                    3
                    )
                  
                
              
            
          
        
        
          
            
              
                n
                3
                
                  (
                  1
                  )
                
              
              +
              
                n
                3
                
                  (
                  2
                  )
                
              
              +
              
                n
                3
                
                  (
                  3
                  )
                
              
            
          
          
            
              
                n
                3
                
                  (
                  1
                  )
                
              
              +
              
                
                  e
                  
                    
                      -
                      j2π
                    
                    ⁢
                    
                      2
                      3
                    
                  
                
                ⁢
                
                  n
                  3
                  
                    (
                    2
                    )
                  
                
              
              +
              
                
                  e
                  
                    
                      -
                      j2π
                    
                    ⁢
                    
                      1
                      3
                    
                  
                
                ⁢
                
                  n
                  3
                  
                    (
                    3
                    )
                  
                
              
            
          
          
            
              
                n
                3
                
                  (
                  1
                  )
                
              
              +
              
                
                  e
                  
                    
                      -
                      j2π
                    
                    ⁢
                    
                      1
                      3
                    
                  
                
                ⁢
                
                  n
                  3
                  
                    (
                    2
                    )
                  
                
              
              +
              
                
                  e
                  
                    
                      -
                      j2π
                    
                    ⁢
                    
                      2
                      3
                    
                  
                
                ⁢
                
                  n
                  3
                  
                    (
                    3
                    )
                  
                
              
            
          
        
      
      ]
    
  




they are expressed as follows:

n′1=h*1.1n′1.1+h*2.1n′2.1+h*3.1n′3.1,

n′2=h*1.2n′1.2+h*2.2n′2.2+h*3.2n′3.2,

n′2=h*1.3n′1.3+h*2.3n′2.3+h*3.3n′3.3.   (28)

More specifically, the error correction decoding unit 26 of the data reception device 2 sets h1,2h1,1*S2+h1,3h1,1*S3 which is an interference wave to be zero (h1,2h1,1*S2=0, h1,3h1,1*S3=0), and detects S1 from both the addition of signals h2,1*h2,1S1 and h3,1*h3,1S1 which are desired waves, and the average of noise components.
In this case, the degradation components include only the noise and the detection probability is improved (refer to FIG. 2).
According to a simple decoding method, it is assumed that both the interference and noise are degradation components as shown in FIG. 2(a). In contrast, according to a conventional method, only the noise becomes small according to HARQ-CC as shown in FIG. 2(b).
In contrast with this, in accordance with this Embodiment 1, because S1 is detected from both the addition of signals h2,1*h2,1S1 and h3,1*h3,1S1 which are desired waves, and the average of the noise components, as mentioned above, the degradation components include only the noise as shown in FIG. 2(c).
In this Embodiment 1, as shown in FIG. 2(d), because the electric power of the noise components is reduced even at the time of the retransmission time with 3×3 MIMO, the improvement can be effected.
As can be seen from the above description, in accordance with this Embodiment 1, when the error correction decoding unit 26 of the data reception device 2 fails in the error correction decoding of the codeword, the MIMO processing unit 15 of the data transmission device 1 deforms the transmitted codewords according to the predetermined rule and then transmits the deformed codewords and the error correction decoding unit 26 of the data reception device 2 reproduces the data by using the deformed codewords. As a result, there is provided an advantage of being able to reduce not only the noise but the interference wave components, and to improve the success rates of the demodulation and error correction decoding greatly.
In this Embodiment 1, the case in which the error correction decoding unit 26 of the data reception device 2 extracts S1, S2, and S3 which construct the symbols S of the codewords by arranging equation (26) to form equation (27), and calculating equation (27) is shown. As an alternative, the error correction decoding unit can extract S1, S2 and S3 which construct the symbols S of the codewords by simplifying equation (27) into equation (29) and then calculating equation (29).

[Equation 12]

3h1.1S1h*1.1+h*1.1n′1.1=3(|h1.1|2)·S1+h*1.1n′1.1 

3h2.2S2h*2.2+h*2.2n′2.2=3(|h2.2|2)·S2+h*2.2n′2.2 

3h3.3S3h*3.3+h*3.3n′3.3=3(|h3.3|2)·S3+h*3.3n′3.3   (29)

Embodiment 2
In above-mentioned Embodiment 1, the example in which codewords are transmitted via three communication channels and interference occurs among the three communication channels is shown. In contrast, in accordance with this Embodiment 2, the example is generalized to a case in which codewords are transmitted via N communication channels and interference occurs among the N communication channels, as will be explained below.
First, a communication channel response matrix H is assumed as follows.




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          13
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        H
        =
        
          [
          
            
              
                
                  h
                  
                    1
                    ,
                    1
                  
                
              
              
                
                  h
                  
                    1
                    ,
                    2
                  
                
              
              
                ⋯
              
              
                ⋯
              
              
                
                  h
                  
                    1
                    ,
                    N
                  
                
              
            
            
              
                
                  h
                  
                    2
                    ,
                    1
                  
                
              
              
                ⋱
              
              
                ⋱
              
              
                ⋱
              
              
                ⋮
              
            
            
              
                ⋮
              
              
                ⋱
              
              
                
                  h
                  
                    i
                    ,
                    j
                  
                
              
              
                ⋱
              
              
                ⋮
              
            
            
              
                ⋮
              
              
                ⋱
              
              
                ⋱
              
              
                ⋱
              
              
                ⋮
              
            
            
              
                
                  h
                  
                    N
                    ,
                    1
                  
                
              
              
                ⋯
              
              
                ⋯
              
              
                ⋯
              
              
                
                  h
                  
                    N
                    ,
                    N
                  
                
              
            
          
          ]
        
      
    
    
      
        (
        30
        )
      
    
  




where hi,j is a communication channel response from j-th transmitting antenna to i-th receiving antenna.

Furthermore, the symbols of codewords transmitted from an MIMO processing unit 15 of a data transmission device 1 (symbols which are obtained by modulating an error correcting code expressed by two elements) are expressed as S. For the sake of simplicity, it is assumed that no OFDM modulation is carried out in this example.




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          14
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        S
        =
        
          [
          
            
              
                
                  S
                  1
                
              
            
            
              
                
                  S
                  2
                
              
            
            
              
                ⋮
              
            
            
              
                
                  S
                  N
                
              
            
          
          ]
        
      
    
    
      
        (
        31
        )
      
    
  




When the MIMO processing unit 15 of the data transmission device 1 transmits the symbols S of the codewords by using N transmitting antennas, an MIMO processing unit 22 of a data reception device 2 receives the symbols of the codewords by using N receiving antennas. When the received signal is expressed as r, the received signal r is shown as follows.




  
    
      
        
          
        
        ⁢
        
          [
          
            Equation
            ⁢
            
              
            
            ⁢
            15
          
          ]
        
      
    
    
      
        
      
    
  
  
    
      
        
          
        
        ⁢
        
          r
          =
          
            
              HS
              +
              n
            
            =
            
              
                
                  
                    [
                    
                      
                        
                          
                            h
                            
                              1
                              ,
                              1
                            
                          
                        
                        
                          
                            h
                            
                              1
                              ,
                              2
                            
                          
                        
                        
                          ⋯
                        
                        
                          ⋯
                        
                        
                          
                            h
                            
                              1
                              ,
                              N
                            
                          
                        
                      
                      
                        
                          
                            h
                            
                              2
                              ,
                              1
                            
                          
                        
                        
                          ⋱
                        
                        
                          ⋱
                        
                        
                          ⋱
                        
                        
                          ⋮
                        
                      
                      
                        
                          ⋮
                        
                        
                          ⋱
                        
                        
                          
                            h
                            
                              i
                              ,
                              j
                            
                          
                        
                        
                          ⋱
                        
                        
                          ⋮
                        
                      
                      
                        
                          ⋮
                        
                        
                          ⋱
                        
                        
                          ⋱
                        
                        
                          ⋱
                        
                        
                          ⋮
                        
                      
                      
                        
                          
                            h
                            
                              N
                              ,
                              1
                            
                          
                        
                        
                          ⋯
                        
                        
                          ⋯
                        
                        
                          ⋯
                        
                        
                          
                            h
                            
                              N
                              ,
                              N
                            
                          
                        
                      
                    
                    ]
                  
                  ⁢
                  
                    

                  
                  [
                  
                    
                      
                        
                          S
                          1
                        
                      
                    
                    
                      
                        
                          S
                          2
                        
                      
                    
                    
                      
                        ⋮
                      
                    
                    
                      
                        
                          S
                          N
                        
                      
                    
                  
                  ]
                
                +
                
                  [
                  
                    
                      
                        
                          n
                          1
                        
                      
                    
                    
                      
                        
                          n
                          2
                        
                      
                    
                    
                      
                        ⋮
                      
                    
                    
                      
                        
                          n
                          N
                        
                      
                    
                  
                  ]
                
              
              =
              
                
                  [
                  
                    
                      
                        
                          
                            
                              h
                              
                                1
                                ,
                                1
                              
                            
                            ⁢
                            
                              S
                              1
                            
                          
                          +
                          
                            
                              h
                              
                                1
                                ,
                                2
                              
                            
                            ⁢
                            
                              S
                              2
                            
                          
                          +
                          ...
                          +
                          
                            
                              h
                              
                                1
                                ,
                                N
                              
                            
                            ⁢
                            
                              S
                              N
                            
                          
                        
                      
                    
                    
                      
                        
                          
                            
                              h
                              
                                2
                                ,
                                1
                              
                            
                            ⁢
                            
                              S
                              1
                            
                          
                          +
                          
                            
                              h
                              
                                2
                                ,
                                2
                              
                            
                            ⁢
                            
                              S
                              2
                            
                          
                          +
                          ...
                          +
                          
                            
                              h
                              
                                2
                                ,
                                N
                              
                            
                            ⁢
                            
                              S
                              N
                            
                          
                        
                      
                    
                    
                      
                        ⋮
                      
                    
                    
                      
                        
                          
                            
                              h
                              
                                N
                                ,
                                1
                              
                            
                            ⁢
                            
                              S
                              1
                            
                          
                          +
                          
                            
                              h
                              
                                N
                                ,
                                2
                              
                            
                            ⁢
                            
                              S
                              2
                            
                          
                          +
                          ...
                          +
                          
                            
                              h
                              
                                N
                                ,
                                N
                              
                            
                            ⁢
                            
                              S
                              N
                            
                          
                        
                      
                    
                  
                  ]
                
                +
                
                  [
                  
                    
                      
                        
                          n
                          1
                        
                      
                    
                    
                      
                        
                          n
                          2
                        
                      
                    
                    
                      
                        ⋮
                      
                    
                    
                      
                        
                          n
                          N
                        
                      
                    
                  
                  ]
                
              
            
          
        
      
    
    
      
        (
        32
        )
      
    
  




When the symbols S(1) of the codewords which are transmitted for the first time (at the time of the first-time transmission) are not decoded normally by an error correction decoding unit 26 of the data reception device 2, the MIMO processing unit 15 of the data transmission device 1 multiplies the symbols S(1) by a part of an orthogonal code to deform the symbols S(1) into symbols S(2). The MIMO processing unit similarly multiplies the symbols S(1) by a part of the orthogonal code to deform the symbols S(1) into symbols S(N).
After creating the symbols S(2), . . . , and S(N) in the above-mentioned way, the MIMO processing unit 15 of the data transmission device 1 sequentially transmits the symbols S(2), . . . , and S(N) by using the N transmitting antennas every time when a transmission request is sent to the data transmission device from the receiver after transmitting the symbols S(1).




  
    
      
        
          
        
        ⁢
        
          [
          
            Equation
            ⁢
            
              
            
            ⁢
            16
          
          ]
        
      
    
    
      
        
      
    
  
  
    
      
        
          S
          
            (
            
              1
              :
              N
            
            )
          
        
        =
        
          
            [
            
              
                
                  
                    S
                    
                      (
                      1
                      )
                    
                  
                
                
                  
                    S
                    
                      (
                      2
                      )
                    
                  
                
                
                  ⋯
                
                
                  
                    S
                    
                      (
                      N
                      )
                    
                  
                
              
            
            ]
          
          =
          
            

          
          ⁢
          
            [
            
              
                
                  
                    
                      α
                      0
                    
                    ⁢
                    
                      S
                      1
                    
                  
                
                
                  
                    
                      α
                      0
                    
                    ⁢
                    
                      S
                      1
                    
                  
                
                
                  
                    
                      α
                      0
                    
                    ⁢
                    
                      S
                      1
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      α
                      0
                    
                    ⁢
                    
                      S
                      1
                    
                  
                
                
                  
                    
                      α
                      0
                    
                    ⁢
                    
                      S
                      1
                    
                  
                
              
              
                
                  
                    
                      α
                      0
                    
                    ⁢
                    
                      S
                      2
                    
                  
                
                
                  
                    
                      α
                      1
                    
                    ⁢
                    
                      S
                      2
                    
                  
                
                
                  
                    
                      α
                      2
                    
                    ⁢
                    
                      S
                      2
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      α
                      
                        N
                        -
                        2
                      
                    
                    ⁢
                    
                      S
                      2
                    
                  
                
                
                  
                    
                      α
                      
                        N
                        -
                        1
                      
                    
                    ⁢
                    
                      S
                      2
                    
                  
                
              
              
                
                  
                    
                      α
                      0
                    
                    ⁢
                    
                      S
                      3
                    
                  
                
                
                  
                    
                      α
                      2
                    
                    ⁢
                    
                      S
                      3
                    
                  
                
                
                  
                    
                      α
                      3
                    
                    ⁢
                    
                      S
                      3
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      α
                      
                        N
                        -
                        1
                      
                    
                    ⁢
                    
                      S
                      3
                    
                  
                
                
                  
                    
                      α
                      1
                    
                    ⁢
                    
                      S
                      3
                    
                  
                
              
              
                
                  ⋮
                
                
                  ⋮
                
                
                  ⋮
                
                
                  ⋱
                
                
                  ⋮
                
                
                  ⋮
                
              
              
                
                  
                    
                      α
                      0
                    
                    ⁢
                    
                      S
                      
                        N
                        -
                        1
                      
                    
                  
                
                
                  
                    
                      α
                      
                        N
                        -
                        2
                      
                    
                    ⁢
                    
                      S
                      
                        N
                        -
                        1
                      
                    
                  
                
                
                  
                    
                      α
                      
                        N
                        -
                        1
                      
                    
                    ⁢
                    
                      S
                      
                        N
                        -
                        1
                      
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      α
                      
                        N
                        -
                        4
                      
                    
                    ⁢
                    
                      S
                      
                        N
                        -
                        1
                      
                    
                  
                
                
                  
                    
                      α
                      
                        N
                        -
                        3
                      
                    
                    ⁢
                    
                      S
                      
                        N
                        -
                        1
                      
                    
                  
                
              
              
                
                  
                    
                      α
                      0
                    
                    ⁢
                    
                      S
                      N
                    
                  
                
                
                  
                    
                      α
                      
                        N
                        -
                        1
                      
                    
                    ⁢
                    
                      S
                      N
                    
                  
                
                
                  
                    
                      α
                      1
                    
                    ⁢
                    
                      S
                      N
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      α
                      
                        N
                        -
                        3
                      
                    
                    ⁢
                    
                      S
                      N
                    
                  
                
                
                  
                    
                      α
                      
                        N
                        -
                        2
                      
                    
                    ⁢
                    
                      S
                      N
                    
                  
                
              
            
            ]
          
        
      
    
    
      
        (
        33
        )
      
    
  




where αi=exp(−j2π·i/N)

After the MIMO processing unit 15 of the data transmission device 1 transmits the sequence S(1:N) of the symbols S(2), . . . , and S(N), the MIMO processing unit 22 of the data reception device 2 receives a sequence r(1:N) of symbols by using the N receiving antennas. This sequence r(1:N) is shown as follows.




  
    
      
        
          
        
        ⁢
        
          [
          
            Equation
            ⁢
            
              
            
            ⁢
            17
          
          ]
        
      
    
    
      
        
      
    
  
  
    
      
        
          
        
        ⁢
        
          
            r
            
              (
              
                1
                :
                N
              
              )
            
          
          =
          
            
              
                HS
                
                  (
                  
                    1
                    :
                    N
                  
                  )
                
              
              +
              
                n
                
                  (
                  
                    1
                    :
                    N
                  
                  )
                
              
            
            =
            
              

            
            ⁢
            
              
            
            ⁢
            
              
                [
                
                  
                    
                      
                        
                          
                            
                              
                                
                                  
                                    h
                                    
                                      1
                                      ,
                                      1
                                    
                                  
                                  ⁢
                                  
                                    α
                                    0
                                  
                                  ⁢
                                  
                                    S
                                    1
                                  
                                
                                +
                              
                            
                          
                          
                            
                              
                                
                                  
                                    
                                      h
                                      
                                        1
                                        ,
                                        2
                                      
                                    
                                    ⁢
                                    
                                      α
                                      0
                                    
                                    ⁢
                                    
                                      S
                                      2
                                    
                                  
                                  +
                                  ...
                                  +
                                
                                ⁢
                                
                                  
                                
                              
                            
                          
                          
                            
                              
                                
                                  h
                                  
                                    1
                                    ,
                                    N
                                  
                                
                                ⁢
                                
                                  α
                                  0
                                
                                ⁢
                                
                                  S
                                  N
                                
                              
                            
                          
                        
                        ⁢
                        
                          
                        
                      
                    
                    
                      ...
                    
                    
                      ...
                    
                    
                      
                        
                          
                            
                              
                                
                                  h
                                  
                                    1
                                    ,
                                    1
                                  
                                
                                ⁢
                                
                                  α
                                  0
                                
                                ⁢
                                
                                  S
                                  1
                                
                              
                              +
                            
                          
                        
                        
                          
                            
                              
                                
                                  h
                                  
                                    1
                                    ,
                                    2
                                  
                                
                                ⁢
                                
                                  α
                                  
                                    N
                                    -
                                    1
                                  
                                
                                ⁢
                                
                                  S
                                  2
                                
                              
                              +
                            
                          
                        
                        
                          
                            
                              
                                
                                  h
                                  
                                    1
                                    ,
                                    3
                                  
                                
                                ⁢
                                
                                  α
                                  
                                    N
                                    -
                                    1
                                  
                                
                                ⁢
                                
                                  S
                                  2
                                
                              
                              +
                              ...
                              +
                            
                          
                        
                        
                          
                            
                              
                                
                                  h
                                  
                                    1
                                    ,
                                    
                                      N
                                      -
                                      1
                                    
                                  
                                
                                ⁢
                                
                                  α
                                  
                                    N
                                    -
                                    3
                                  
                                
                                ⁢
                                
                                  S
                                  
                                    N
                                    -
                                    1
                                  
                                
                              
                              +
                            
                          
                        
                        
                          
                            
                              
                                h
                                
                                  1
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                α
                                
                                  N
                                  -
                                  2
                                
                              
                              ⁢
                              
                                S
                                N
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              
                                
                                  h
                                  
                                    2
                                    ,
                                    1
                                  
                                
                                ⁢
                                
                                  α
                                  0
                                
                                ⁢
                                
                                  S
                                  1
                                
                              
                              +
                            
                          
                        
                        
                          
                            
                              
                                
                                  h
                                  
                                    2
                                    ,
                                    2
                                  
                                
                                ⁢
                                
                                  α
                                  0
                                
                                ⁢
                                
                                  S
                                  2
                                
                              
                              +
                              ...
                              +
                            
                          
                        
                        
                          
                            
                              
                                h
                                
                                  2
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                α
                                0
                              
                              ⁢
                              
                                S
                                N
                              
                            
                          
                        
                      
                    
                    
                      ...
                    
                    
                      ...
                    
                    
                      
                        
                          
                            
                              
                                
                                  h
                                  
                                    2
                                    ,
                                    1
                                  
                                
                                ⁢
                                
                                  α
                                  0
                                
                                ⁢
                                
                                  S
                                  1
                                
                              
                              +
                            
                          
                        
                        
                          
                            
                              
                                
                                  h
                                  
                                    2
                                    ,
                                    2
                                  
                                
                                ⁢
                                
                                  α
                                  
                                    N
                                    -
                                    1
                                  
                                
                                ⁢
                                
                                  S
                                  2
                                
                              
                              +
                            
                          
                        
                        
                          
                            
                              
                                
                                  h
                                  
                                    2
                                    ,
                                    3
                                  
                                
                                ⁢
                                
                                  α
                                  
                                    N
                                    -
                                    1
                                  
                                
                                ⁢
                                
                                  S
                                  2
                                
                              
                              +
                              ...
                              +
                            
                          
                        
                        
                          
                            
                              
                                
                                  h
                                  
                                    2
                                    ,
                                    
                                      N
                                      -
                                      1
                                    
                                  
                                
                                ⁢
                                
                                  α
                                  
                                    N
                                    -
                                    3
                                  
                                
                                ⁢
                                
                                  S
                                  
                                    N
                                    -
                                    1
                                  
                                
                              
                              +
                            
                          
                        
                        
                          
                            
                              
                                h
                                
                                  2
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                α
                                
                                  N
                                  -
                                  2
                                
                              
                              ⁢
                              
                                S
                                N
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      ⋮
                    
                    
                      ⋮
                    
                    
                      ⋮
                    
                    
                      ⋮
                    
                  
                  
                    
                      
                        
                          
                            
                              
                                
                                  h
                                  
                                    N
                                    ,
                                    1
                                  
                                
                                ⁢
                                
                                  α
                                  0
                                
                                ⁢
                                
                                  S
                                  1
                                
                              
                              +
                            
                          
                        
                        
                          
                            
                              
                                
                                  h
                                  
                                    N
                                    ,
                                    2
                                  
                                
                                ⁢
                                
                                  α
                                  0
                                
                                ⁢
                                
                                  S
                                  2
                                
                              
                              +
                              ...
                              +
                            
                          
                        
                        
                          
                            
                              
                                h
                                
                                  N
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                α
                                0
                              
                              ⁢
                              
                                S
                                N
                              
                            
                          
                        
                      
                    
                    
                      ...
                    
                    
                      ...
                    
                    
                      
                        
                          
                            
                              
                                
                                  h
                                  
                                    N
                                    ,
                                    1
                                  
                                
                                ⁢
                                
                                  α
                                  0
                                
                                ⁢
                                
                                  S
                                  1
                                
                              
                              +
                            
                          
                        
                        
                          
                            
                              
                                
                                  h
                                  
                                    N
                                    ,
                                    2
                                  
                                
                                ⁢
                                
                                  α
                                  
                                    N
                                    -
                                    1
                                  
                                
                                ⁢
                                
                                  S
                                  2
                                
                              
                              +
                            
                          
                        
                        
                          
                            
                              
                                
                                  h
                                  
                                    N
                                    ,
                                    3
                                  
                                
                                ⁢
                                
                                  α
                                  
                                    N
                                    -
                                    1
                                  
                                
                                ⁢
                                
                                  S
                                  2
                                
                              
                              +
                              ...
                              +
                            
                          
                        
                        
                          
                            
                              
                                
                                  h
                                  
                                    N
                                    ,
                                    
                                      N
                                      -
                                      1
                                    
                                  
                                
                                ⁢
                                
                                  α
                                  
                                    N
                                    -
                                    3
                                  
                                
                                ⁢
                                
                                  S
                                  
                                    N
                                    -
                                    1
                                  
                                
                              
                              +
                            
                          
                        
                        
                          
                            
                              
                                h
                                
                                  N
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                α
                                
                                  N
                                  -
                                  2
                                
                              
                              ⁢
                              
                                S
                                N
                              
                            
                          
                        
                      
                    
                  
                
                ]
              
              +
              
                

              
              ⁢
              
                
              
              ⁢
              
                [
                
                  
                    
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                    
                    
                      
                        n
                        1
                        
                          (
                          2
                          )
                        
                      
                    
                    
                      ...
                    
                    
                      
                        n
                        1
                        
                          (
                          N
                          )
                        
                      
                    
                  
                  
                    
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                    
                    
                      
                        n
                        2
                        
                          (
                          2
                          )
                        
                      
                    
                    
                      ...
                    
                    
                      
                        n
                        2
                        
                          (
                          N
                          )
                        
                      
                    
                  
                  
                    
                      ⋮
                    
                    
                      ⋮
                    
                    
                      ⋱
                    
                    
                      ⋮
                    
                  
                  
                    
                      
                        n
                        N
                        
                          (
                          1
                          )
                        
                      
                    
                    
                      
                        n
                        N
                        
                          (
                          2
                          )
                        
                      
                    
                    
                      ...
                    
                    
                      
                        n
                        N
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
                ]
              
            
          
        
      
    
    
      
        (
        34
        )
      
    
  




After the MIMO processing unit 22 receives the sequence r(1:N) by using the N receiving antennas, the error correction decoding unit 26 of the data reception device 2 multiplies the received sequence r(1:N) by an orthogonal code to deform equation (34), as will be shown below.



  
    
      
    
    ⁢
    
      [
      
        Equation
        ⁢
        
          
            
          
          ⁢
          
            
          
        
        ⁢
        18
      
      ]
    
  




  
    
      
    
    ⁢
    
      (
      35
      )
    
  




  
    
      
        r
        
          (
          
            1
            :
            N
          
          )
        
      
      ⁡
      
        [
        
          
            
              
                α
                0
              
            
            
              
                α
                0
              
            
            
              
                α
                0
              
            
            
              ...
            
            
              
                α
                0
              
            
            
              
                α
                0
              
            
          
          
            
              
                α
                0
              
            
            
              
                α
                
                  -
                  1
                
              
            
            
              
                α
                
                  -
                  2
                
              
            
            
              ...
            
            
              
                α
                
                  -
                  
                    (
                    
                      N
                      -
                      2
                    
                    )
                  
                
              
            
            
              
                α
                
                  -
                  
                    (
                    
                      N
                      -
                      1
                    
                    )
                  
                
              
            
          
          
            
              
                α
                0
              
            
            
              
                α
                
                  -
                  2
                
              
            
            
              
                α
                
                  -
                  3
                
              
            
            
              ...
            
            
              
                α
                
                  -
                  
                    (
                    
                      N
                      -
                      1
                    
                    )
                  
                
              
            
            
              
                α
                
                  -
                  1
                
              
            
          
          
            
              ⋮
            
            
              ⋮
            
            
              ⋮
            
            
              ⋱
            
            
              ⋮
            
            
              ⋮
            
          
          
            
              
                α
                0
              
            
            
              
                α
                
                  -
                  
                    (
                    
                      N
                      -
                      2
                    
                    )
                  
                
              
            
            
              
                α
                
                  -
                  
                    (
                    
                      N
                      -
                      1
                    
                    )
                  
                
              
            
            
              ...
            
            
              
                α
                
                  -
                  
                    (
                    
                      N
                      -
                      4
                    
                    )
                  
                
              
            
            
              
                α
                
                  -
                  
                    (
                    
                      N
                      -
                      3
                    
                    )
                  
                
              
            
          
          
            
              
                α
                0
              
            
            
              
                α
                
                  -
                  
                    (
                    
                      N
                      -
                      1
                    
                    )
                  
                
              
            
            
              
                α
                
                  -
                  1
                
              
            
            
              ...
            
            
              
                α
                
                  -
                  
                    (
                    
                      N
                      -
                      3
                    
                    )
                  
                
              
            
            
              
                α
                
                  -
                  
                    (
                    
                      N
                      -
                      2
                    
                    )
                  
                
              
            
          
        
        ]
      
    
    =
    
      
    
    ⁢
    
      
        N
        ⁡
        
          [
          
            
              
                
                  
                    h
                    
                      1
                      ,
                      1
                    
                  
                  ⁢
                  
                    S
                    1
                  
                
              
              
                
                  
                    h
                    
                      1
                      ,
                      2
                    
                  
                  ⁢
                  
                    S
                    1
                  
                
              
              
                ...
              
              
                
                  
                    h
                    
                      1
                      ,
                      N
                    
                  
                  ⁢
                  
                    S
                    1
                  
                
              
            
            
              
                
                  
                    h
                    
                      2
                      ,
                      1
                    
                  
                  ⁢
                  
                    S
                    2
                  
                
              
              
                
                  
                    h
                    
                      2
                      ,
                      2
                    
                  
                  ⁢
                  
                    S
                    2
                  
                
              
              
                ...
              
              
                
                  
                    h
                    
                      2
                      ,
                      N
                    
                  
                  ⁢
                  
                    S
                    2
                  
                
              
            
            
              
                ⋮
              
              
                ⋮
              
              
                ⋮
              
              
                ⋮
              
            
            
              
                
                  
                    h
                    
                      N
                      ,
                      1
                    
                  
                  ⁢
                  
                    S
                    N
                  
                
              
              
                
                  
                    h
                    
                      N
                      ,
                      2
                    
                  
                  ⁢
                  
                    S
                    N
                  
                
              
              
                ...
              
              
                
                  
                    h
                    
                      N
                      ,
                      N
                    
                  
                  ⁢
                  
                    S
                    N
                  
                
              
            
          
          ]
        
      
      +
      
        
      
      ⁢
      
        

      
      ⁢
      
        
      
      ⁢
      
        [
        
          
            
              
                
                  
                    
                      
                        
                          α
                          0
                        
                        ⁢
                        
                          n
                          1
                          
                            (
                            1
                            )
                          
                        
                      
                      +
                    
                  
                
                
                  
                    
                      
                        
                          α
                          0
                        
                        ⁢
                        
                          n
                          1
                          
                            (
                            2
                            )
                          
                        
                      
                      +
                      ...
                      +
                    
                  
                
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
            
              
                
                  
                    
                      
                        
                          α
                          0
                        
                        ⁢
                        
                          n
                          1
                          
                            (
                            1
                            )
                          
                        
                      
                      +
                    
                  
                
                
                  
                    
                      
                        
                          α
                          
                            -
                            1
                          
                        
                        ⁢
                        
                          n
                          1
                          
                            (
                            2
                            )
                          
                        
                      
                      +
                      ...
                      +
                    
                  
                
                
                  
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              1
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
            
              ...
            
            
              
                
                  
                    
                      
                        
                          α
                          0
                        
                        ⁢
                        
                          n
                          1
                          
                            (
                            1
                            )
                          
                        
                      
                      +
                    
                  
                
                
                  
                    
                      
                        
                          α
                          
                            -
                            
                              (
                              
                                N
                                -
                                1
                              
                              )
                            
                          
                        
                        ⁢
                        
                          n
                          1
                          
                            (
                            2
                            )
                          
                        
                      
                      +
                      ...
                      +
                    
                  
                
                
                  
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              2
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      
                        
                          α
                          0
                        
                        ⁢
                        
                          n
                          2
                          
                            (
                            1
                            )
                          
                        
                      
                      +
                    
                  
                
                
                  
                    
                      
                        
                          α
                          0
                        
                        ⁢
                        
                          n
                          2
                          
                            (
                            2
                            )
                          
                        
                      
                      +
                      ...
                      +
                    
                  
                
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
            
              
                
                  
                    
                      
                        
                          α
                          0
                        
                        ⁢
                        
                          n
                          2
                          
                            (
                            1
                            )
                          
                        
                      
                      +
                    
                  
                
                
                  
                    
                      
                        
                          α
                          
                            -
                            1
                          
                        
                        ⁢
                        
                          n
                          2
                          
                            (
                            2
                            )
                          
                        
                      
                      +
                      ...
                      +
                    
                  
                
                
                  
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              1
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
            
              ...
            
            
              
                
                  
                    
                      
                        
                          α
                          0
                        
                        ⁢
                        
                          n
                          2
                          
                            (
                            1
                            )
                          
                        
                      
                      +
                    
                  
                
                
                  
                    
                      
                        
                          α
                          
                            -
                            
                              (
                              
                                N
                                -
                                1
                              
                              )
                            
                          
                        
                        ⁢
                        
                          n
                          2
                          
                            (
                            2
                            )
                          
                        
                      
                      +
                      ...
                      +
                    
                  
                
                
                  
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              2
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
          
          
            
              ⋮
            
            
              ⋮
            
            
              ⋱
            
            
              ⋮
            
          
          
            
              
                
                  
                    
                      
                        
                          α
                          0
                        
                        ⁢
                        
                          n
                          N
                          
                            (
                            1
                            )
                          
                        
                      
                      +
                    
                  
                
                
                  
                    
                      
                        
                          α
                          0
                        
                        ⁢
                        
                          n
                          N
                          
                            (
                            2
                            )
                          
                        
                      
                      +
                      ...
                      +
                    
                  
                
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
            
              
                
                  
                    
                      
                        
                          α
                          0
                        
                        ⁢
                        
                          n
                          N
                          
                            (
                            1
                            )
                          
                        
                      
                      +
                    
                  
                
                
                  
                    
                      
                        
                          α
                          
                            -
                            1
                          
                        
                        ⁢
                        
                          n
                          N
                          
                            (
                            2
                            )
                          
                        
                      
                      +
                      ...
                      +
                    
                  
                
                
                  
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              1
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
            
              ...
            
            
              
                
                  
                    
                      
                        
                          α
                          0
                        
                        ⁢
                        
                          n
                          N
                          
                            (
                            1
                            )
                          
                        
                      
                      +
                    
                  
                
                
                  
                    
                      
                        
                          α
                          
                            -
                            
                              (
                              
                                N
                                -
                                1
                              
                              )
                            
                          
                        
                        ⁢
                        
                          n
                          N
                          
                            (
                            2
                            )
                          
                        
                      
                      +
                      ...
                      +
                    
                  
                
                
                  
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              2
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
          
        
        ⁢
        
          
        
        ]
      
    
  



The error correction decoding unit 26 of the data reception device 2 also extracts S1, S2, . . . , and SN which construct the symbols S of the codewords by arranging equation (35) to form equation (36) and then calculating equation (36).




  
    
      
        
          
        
        ⁢
        
          [
          
            Equation
            ⁢
            
              
            
            ⁢
            19
          
          ]
        
      
    
    
      
        
      
    
  
  
    
      
        
          
            
              
                Nh
                
                  1
                  ,
                  1
                
              
              ⁢
              
                S
                1
              
              ⁢
              
                h
                
                  1
                  ,
                  1
                
                *
              
            
            +
            
              
                Nh
                
                  1
                  ,
                  2
                
              
              ⁢
              
                S
                1
              
              ⁢
              
                h
                
                  1
                  ,
                  2
                
                *
              
            
            +
            ...
            +
            
              n
              1
              ′
            
          
          =
          
            
              
                N
                (
                
                  
                    
                      
                      
                        h
                        
                          1
                          ,
                          1
                        
                      
                      
                    
                    2
                  
                  +
                  
                    
                      
                      
                        h
                        
                          1
                          ,
                          2
                        
                      
                      
                    
                    2
                  
                  +
                  ...
                
                ⁢
                
                  
                
                )
              
              ·
              
                S
                1
              
            
            +
            
              n
              1
              ′
            
          
        
        ,
        
          

        
        ⁢
        
          
            
              
                Nh
                
                  2
                  ,
                  1
                
              
              ⁢
              
                S
                2
              
              ⁢
              
                h
                
                  2
                  ,
                  1
                
                *
              
            
            +
            
              
                Nh
                
                  2
                  ,
                  2
                
              
              ⁢
              
                S
                2
              
              ⁢
              
                h
                
                  2
                  ,
                  2
                
                *
              
            
            +
            ...
            +
            
              n
              2
              ′
            
          
          =
          
            
              
                N
                (
                
                  
                    
                      
                      
                        h
                        
                          2
                          ,
                          1
                        
                      
                      
                    
                    2
                  
                  +
                  
                    
                      
                      
                        h
                        
                          2
                          ,
                          2
                        
                      
                      
                    
                    2
                  
                  +
                  ...
                
                ⁢
                
                  
                
                )
              
              ·
              
                S
                2
              
            
            +
            
              n
              2
              ′
            
          
        
        ,
        ...
      
    
    
      
        (
        36
        )
      
    
  




where when n′1, n′2, . . . , n′N are defined as follows:





  
    
  
  ⁢
  
    
      [
      
        
          
            
              n
              
                1
                ,
                1
              
              ′
            
          
          
            
              n
              
                1
                ,
                2
              
              ′
            
          
          
            ...
          
          
            
              n
              
                1
                ,
                N
              
              ′
            
          
        
        
          
            
              n
              
                2
                ,
                1
              
              ′
            
          
          
            
              n
              
                2
                ,
                2
              
              ′
            
          
          
            ...
          
          
            
              n
              
                2
                ,
                N
              
              ′
            
          
        
        
          
            ⋮
          
          
            ⋮
          
          
            ⋱
          
          
            ⋮
          
        
        
          
            
              n
              
                N
                ,
                1
              
              ′
            
          
          
            
              n
              
                N
                ,
                2
              
              ′
            
          
          
            ...
          
          
            
              n
              
                N
                ,
                N
              
              ′
            
          
        
      
      ]
    
    =
    
      

    
    ⁢
    
      
    
    ⁢
    
      [
      
        
          
            
              
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                  
                
              
              
                
                  
                    
                      α
                      0
                    
                    ⁢
                    
                      n
                      1
                      
                        (
                        N
                        )
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    
                      
                        α
                        
                          -
                          1
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                  
                
              
              
                
                  
                    
                      α
                      
                        -
                        
                          (
                          
                            N
                            -
                            1
                          
                          )
                        
                      
                    
                    ⁢
                    
                      n
                      1
                      
                        (
                        N
                        )
                      
                    
                  
                
              
            
          
          
            ...
          
          
            
              
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              1
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                  
                
              
              
                
                  
                    
                      α
                      
                        -
                        
                          (
                          
                            N
                            -
                            2
                          
                          )
                        
                      
                    
                    ⁢
                    
                      n
                      1
                      
                        (
                        N
                        )
                      
                    
                  
                
              
            
          
        
        
          
            
              
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                  
                
              
              
                
                  
                    
                      α
                      0
                    
                    ⁢
                    
                      n
                      2
                      
                        (
                        N
                        )
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    
                      
                        α
                        
                          -
                          1
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                  
                
              
              
                
                  
                    
                      α
                      
                        -
                        
                          (
                          
                            N
                            -
                            1
                          
                          )
                        
                      
                    
                    ⁢
                    
                      n
                      2
                      
                        (
                        N
                        )
                      
                    
                  
                
              
            
          
          
            ...
          
          
            
              
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              1
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                  
                
              
              
                
                  
                    
                      α
                      
                        -
                        
                          (
                          
                            N
                            -
                            2
                          
                          )
                        
                      
                    
                    ⁢
                    
                      n
                      2
                      
                        (
                        N
                        )
                      
                    
                  
                
              
            
          
        
        
          
            ⋮
          
          
            ⋮
          
          
            ⋱
          
          
            ⋮
          
        
        
          
            
              
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                  
                
              
              
                
                  
                    
                      α
                      0
                    
                    ⁢
                    
                      n
                      N
                      
                        (
                        N
                        )
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    
                      
                        α
                        
                          -
                          1
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                  
                
              
              
                
                  
                    
                      α
                      
                        -
                        
                          (
                          
                            N
                            -
                            1
                          
                          )
                        
                      
                    
                    ⁢
                    
                      n
                      N
                      
                        (
                        N
                        )
                      
                    
                  
                
              
            
          
          
            ...
          
          
            
              
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              1
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                  
                
              
              
                
                  
                    
                      α
                      
                        -
                        
                          (
                          
                            N
                            -
                            2
                          
                          )
                        
                      
                    
                    ⁢
                    
                      n
                      N
                      
                        (
                        N
                        )
                      
                    
                  
                
              
            
          
        
      
      ]
    
  
  ⁢
  
    

  




they are expressed as follows:





  
    
      
        
          
            n
            1
            ′
          
          =
          
            
              
                h
                1.1
                *
              
              ⁢
              
                n
                1.1
                ′
              
            
            +
            
              
                h
                2.1
                *
              
              ⁢
              
                n
                2.1
                ′
              
            
            +
            ...
            +
            
              
                h
                
                  N
                  ⁢
                  .1
                
                *
              
              ⁢
              
                n
                
                  N
                  ⁢
                  .1
                
                ′
              
            
          
        
        ,
        
          

        
        ⁢
        
          
            n
            2
            ′
          
          =
          
            
              
                h
                1.2
                *
              
              ⁢
              
                n
                1.2
                ′
              
            
            +
            
              
                h
                2.2
                *
              
              ⁢
              
                n
                2.2
                ′
              
            
            +
            ...
            +
            
              
                h
                
                  N
                  ⁢
                  .2
                
                *
              
              ⁢
              
                n
                
                  N
                  ⁢
                  .2
                
                ′
              
            
          
        
        ,
        
          

        
        ⁢
        ⋮
      
    
    
      
        (
        37
        )
      
    
  




In this Embodiment 2, the case in which the error correction decoding unit 26 of the data reception device 2 extracts S1, S2, . . . , and SN which construct the symbols S of the codewords by arranging equation (35) to form equation (36), and calculating equation (36) is shown. As an alternative, the error correction decoding unit can extract S1, S2, . . . , and SN which construct the symbols S of the codewords by simplifying equation (36) into equation (38) and then calculating equation (38).




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          20
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        
          
            
              
                Nh
                1.1
              
              ⁢
              
                S
                1
              
              ⁢
              
                h
                1.1
                *
              
            
            +
            
              
                h
                1.1
                *
              
              ⁢
              
                n
                1.1
                ′
              
            
          
          =
          
            
              
                N
                ⁡
                
                  (
                  
                    
                      
                      
                        h
                        1.1
                      
                      
                    
                    2
                  
                  )
                
              
              ·
              
                S
                1
              
            
            +
            
              
                h
                1.1
                *
              
              ⁢
              
                n
                1.1
                ′
              
            
          
        
        ,
        
          

        
        ⁢
        
          
            
              
                Nh
                2.2
              
              ⁢
              
                S
                2
              
              ⁢
              
                h
                2.2
                *
              
            
            +
            
              
                h
                2.2
                *
              
              ⁢
              
                n
                2.2
                ′
              
            
          
          =
          
            
              
                N
                ⁡
                
                  (
                  
                    
                      
                      
                        h
                        2.2
                      
                      
                    
                    2
                  
                  )
                
              
              ·
              
                S
                2
              
            
            +
            
              
                h
                2.2
                *
              
              ⁢
              
                n
                2.2
                ′
              
            
          
        
        ,
        
          

        
        ⁢
        ⋮
      
    
    
      
        (
        38
        )
      
    
  




Embodiment 3
In above-mentioned Embodiment 1, the example in which codewords are transmitted via three communication channels and interference occurs among the three communication channels is shown. In contrast, in accordance with this Embodiment 3, the example is generalized to a case in which codewords are transmitted via N communication channels and interference occurs among the N communication channels, as will be explained below.
In this embodiment, N is a power of two, and, in this Embodiment 3, a case of N=2 will be explained as an example.
First, a communication channel response matrix H is assumed as follows.




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          21
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        H
        =
        
          [
          
            
              
                
                  h
                  
                    1
                    ,
                    1
                  
                
              
              
                
                  h
                  
                    1
                    ,
                    2
                  
                
              
            
            
              
                
                  h
                  
                    2
                    ,
                    1
                  
                
              
              
                
                  h
                  
                    2
                    ,
                    2
                  
                
              
            
          
          ]
        
      
    
    
      
        (
        39
        )
      
    
  




where hi,j is a communication channel response from j-th transmitting antenna to i-th receiving antenna.

Furthermore, the symbols of codewords transmitted from an MIMO processing unit 15 of a data transmission device 1 (symbols which are obtained by modulating an error correcting code expressed by two elements) are expressed as S. For the sake of simplicity, it is assumed that no OFDM modulation is carried out in this example.




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          22
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        S
        =
        
          [
          
            
              
                
                  S
                  1
                
              
            
            
              
                
                  S
                  2
                
              
            
          
          ]
        
      
    
    
      
        (
        40
        )
      
    
  




When the MIMO processing unit 15 of the data transmission device 1 transmits the symbols S of the codewords by using two transmitting antennas 16a and 16b, an MIMO processing unit 22 of a data reception device 2 receives the symbols of the codewords by using two receiving antennas 21a and 21b. When the received signal is expressed as r, the received signal r is shown as follows.




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          23
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        r
        =
        
          
            HS
            +
            n
          
          =
          
            
              
                [
                
                  
                    
                      
                        h
                        1.1
                      
                    
                    
                      
                        h
                        1.2
                      
                    
                  
                  
                    
                      
                        h
                        2.1
                      
                    
                    
                      
                        h
                        2.2
                      
                    
                  
                
                ]
              
              ⁡
              
                [
                
                  
                    
                      
                        S
                        1
                      
                    
                  
                  
                    
                      
                        S
                        2
                      
                    
                  
                
                ]
              
            
            =
            
              
                [
                
                  
                    
                      
                        
                          
                            h
                            1.1
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            1.2
                          
                          ⁢
                          
                            S
                            2
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            h
                            2.1
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            2.2
                          
                          ⁢
                          
                            S
                            2
                          
                        
                      
                    
                  
                
                ]
              
              +
              
                [
                
                  
                    
                      
                        n
                        1
                      
                    
                  
                  
                    
                      
                        n
                        2
                      
                    
                  
                
                ]
              
            
          
        
      
    
    
      
        (
        41
        )
      
    
  




When the symbols S(1) of the codewords which are transmitted for the first time (at the time of the first-time transmission) are not decoded normally by an error correction decoding unit 26 of the data reception device 2, the MIMO processing unit 15 of the data transmission device 1 multiplies the symbols S(1) by a part of an orthogonal code to deform the symbols S(1) into symbols S(2).
After creating the symbols S(2) in the above-mentioned way, the MIMO processing unit 15 of the data transmission device 1 transmits the symbols S(2) by using the two transmitting antennas 16a and 16b after transmitting the symbols S(1).




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          24
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        
          
            S
            
              (
              1
              )
            
          
          =
          
            [
            
              
                
                  
                    S
                    1
                  
                
              
              
                
                  
                    S
                    2
                  
                
              
            
            ]
          
        
        ,
        
          
            S
            
              (
              2
              )
            
          
          =
          
            [
            
              
                
                  
                    S
                    1
                  
                
              
              
                
                  
                    -
                    
                      S
                      2
                    
                  
                
              
            
            ]
          
        
      
    
    
      
        (
        42
        )
      
    
  




After the MIMO processing unit 15 of the data transmission device 1 transmits the sequence S(1, 2) of the symbols S(1) and S(2), the MIMO processing unit 22 of the data reception device 2 receives a sequence r(1, 2) of symbols by using the two receiving antennas 21a and 21b. This sequence r(1, 2) is shown as follows.




  
    
      
        
          
        
        ⁢
        
          [
          
            Equation
            ⁢
            
              
            
            ⁢
            25
          
          ]
        
      
    
    
      
        
      
    
  
  
    
      
        
          r
          
            (
            
              1
              ,
              2
            
            )
          
        
        =
        
          
            
              H
              ⁡
              
                [
                
                  
                    S
                    
                      (
                      1
                      )
                    
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    S
                    
                      (
                      2
                      )
                    
                  
                
                ]
              
            
            +
            
              n
              
                (
                
                  1
                  ,
                  2
                
                )
              
            
          
          =
          
            
              
                
                  [
                  
                    
                      
                        
                          h
                          1.1
                        
                      
                      
                        
                          h
                          1.2
                        
                      
                    
                    
                      
                        
                          h
                          2.1
                        
                      
                      
                        
                          h
                          2.2
                        
                      
                    
                  
                  ]
                
                ⁡
                
                  [
                  
                    
                      
                        
                          S
                          1
                        
                      
                      
                        
                          S
                          1
                        
                      
                    
                    
                      
                        
                          S
                          2
                        
                      
                      
                        
                          -
                          
                            S
                            2
                          
                        
                      
                    
                  
                  ]
                
              
              +
              
                n
                
                  (
                  
                    1
                    ,
                    2
                  
                  )
                
              
            
            =
            
              
                [
                
                  
                    
                      
                        
                          
                            h
                            1.1
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            1.2
                          
                          ⁢
                          
                            S
                            2
                          
                        
                      
                    
                    
                      
                        
                          
                            h
                            1.1
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        -
                        
                          
                            h
                            1.2
                          
                          ⁢
                          
                            S
                            2
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            h
                            2.1
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            2.2
                          
                          ⁢
                          
                            S
                            2
                          
                        
                      
                    
                    
                      
                        
                          
                            h
                            2.1
                          
                          ⁢
                          
                            S
                            1
                          
                        
                        -
                        
                          
                            h
                            2.2
                          
                          ⁢
                          
                            S
                            2
                          
                        
                      
                    
                  
                
                ]
              
              +
              
                [
                
                  
                    
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                    
                    
                      
                        n
                        1
                        
                          (
                          2
                          )
                        
                      
                    
                  
                  
                    
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                    
                    
                      
                        n
                        2
                        
                          (
                          2
                          )
                        
                      
                    
                  
                
                ]
              
            
          
        
      
    
    
      
        (
        43
        )
      
    
  




After the MIMO processing unit 22 receives the sequence r(1, 2) by using the two receiving antennas 21a and 21b, the error correction decoding unit 26 of the data reception device 2 multiplies the received sequence r(1, 2) by an orthogonal code to deform equation (43), as will be shown below.




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          26
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        
          
            r
            
              (
              
                1
                ,
                2
              
              )
            
          
          ⁡
          
            [
            
              
                
                  1
                
                
                  1
                
              
              
                
                  1
                
                
                  
                    -
                    1
                  
                
              
            
            ]
          
        
        =
        
          
            2
            ⁡
            
              [
              
                
                  
                    
                      
                        h
                        1.1
                      
                      ⁢
                      
                        S
                        1
                      
                    
                  
                  
                    
                      
                        h
                        1.2
                      
                      ⁢
                      
                        S
                        2
                      
                    
                  
                
                
                  
                    
                      
                        h
                        2.1
                      
                      ⁢
                      
                        S
                        1
                      
                    
                  
                  
                    
                      
                        h
                        2.2
                      
                      ⁢
                      
                        S
                        2
                      
                    
                  
                
              
              ]
            
          
          +
          
            [
            
              
                
                  
                    
                      n
                      1
                      
                        (
                        1
                        )
                      
                    
                    +
                    
                      n
                      1
                      
                        (
                        2
                        )
                      
                    
                  
                
                
                  
                    
                      n
                      1
                      
                        (
                        1
                        )
                      
                    
                    -
                    
                      n
                      1
                      
                        (
                        2
                        )
                      
                    
                  
                
              
              
                
                  
                    
                      n
                      2
                      
                        (
                        1
                        )
                      
                    
                    +
                    
                      n
                      2
                      
                        (
                        2
                        )
                      
                    
                  
                
                
                  
                    
                      n
                      2
                      
                        (
                        1
                        )
                      
                    
                    -
                    
                      n
                      2
                      
                        (
                        2
                        )
                      
                    
                  
                
              
            
            ]
          
        
      
    
    
      
        (
        44
        )
      
    
  




The error correction decoding unit 26 of the data reception device 2 also extracts S1 and S2 which construct the symbols S of the codewords by arranging equation (44) to form equation (45) and then calculating equation (45).

[Equation 27]

2h1,1S1h*1,1+2h2,1S1h*2,1+n′1=2(|h1,1|2+|h2,1|2)·S1+n′1 

2h1,2S2h*1,2+2h2,2S2h*2,2+n′2=2(|h2,1|2+|h2,2|2)·S2+n′2   (45)

where when n′1, n′2 are defined as follows:





  
    [
    
      
        
          
            n
            
              1
              ,
              1
            
            ′
          
        
        
          
            n
            
              1
              ,
              2
            
            ′
          
        
      
      
        
          
            n
            
              2
              ,
              1
            
            ′
          
        
        
          
            n
            
              2
              ,
              2
            
            ′
          
        
      
    
    ]
  
  =
  
    [
    
      
        
          
            
              n
              1
              
                (
                1
                )
              
            
            +
            
              n
              1
              
                (
                2
                )
              
            
          
        
        
          
            
              n
              1
              
                (
                1
                )
              
            
            -
            
              n
              1
              
                (
                2
                )
              
            
          
        
      
      
        
          
            
              n
              2
              
                (
                1
                )
              
            
            +
            
              n
              2
              
                (
                2
                )
              
            
          
        
        
          
            
              n
              2
              
                (
                1
                )
              
            
            -
            
              n
              2
              
                (
                2
                )
              
            
          
        
      
    
    ]
  




they are expressed as follows:

n′1=h*1.1n′1.1+h*2.1n′2.1,

n′2=h*1.2n′1.2+h*2.2n′2.2.   (46)

In this Embodiment 3, the case in which the error correction decoding unit 26 of the data reception device 2 extracts S1 and S2 which construct the symbols S of the codewords by arranging equation (44) to form equation (45), and calculating equation (45) is shown. As an alternative, the error correction decoding unit can extract S1 and S2 which construct the symbols S of the codewords by simplifying equation (45) into equation (47) and then calculating equation (47).

[Equation 28]

2h1.1S1h*1.1+h*1.1n′1.1=2(|h1.1|2)·S1+h*1.1n′1.1 

2h2.2S2h*2.2+h*2.2n′2.2=2(|h2.2|2)·S2+h*2.2n′2.2   (47)

Embodiment 4
In above-mentioned Embodiment 3, the case of N=2 is shown. In contrast, in this Embodiment 4, a case of N=4 will be shown.
First, a communication channel response matrix H is assumed as follows.




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          29
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        H
        =
        
          [
          
            
              
                
                  h
                  
                    1
                    ,
                    1
                  
                
              
              
                
                  h
                  
                    1
                    ,
                    2
                  
                
              
              
                
                  h
                  
                    1
                    ,
                    3
                  
                
              
              
                
                  h
                  
                    1
                    ,
                    4
                  
                
              
            
            
              
                
                  h
                  
                    2
                    ,
                    1
                  
                
              
              
                
                  h
                  
                    2
                    ,
                    2
                  
                
              
              
                
                  h
                  
                    2
                    ,
                    3
                  
                
              
              
                
                  h
                  
                    2
                    ,
                    4
                  
                
              
            
            
              
                
                  h
                  
                    3
                    ,
                    1
                  
                
              
              
                
                  h
                  
                    3
                    ,
                    2
                  
                
              
              
                
                  h
                  
                    3
                    ,
                    3
                  
                
              
              
                
                  h
                  
                    3
                    ,
                    4
                  
                
              
            
            
              
                
                  h
                  
                    4
                    ,
                    1
                  
                
              
              
                
                  h
                  
                    4
                    ,
                    2
                  
                
              
              
                
                  h
                  
                    4
                    ,
                    3
                  
                
              
              
                
                  h
                  
                    4
                    ,
                    4
                  
                
              
            
          
          ]
        
      
    
    
      
        (
        48
        )
      
    
  




where hi,jis a communication channel response from j-th transmitting antenna to i-th receiving antenna.

Furthermore, the symbols of codewords transmitted from an MIMO processing unit 15 of a data transmission device 1 (symbols which are obtained by modulating an error correcting code expressed by two elements) are expressed as S. For the sake of simplicity, it is assumed that no OFDM modulation is carried out in this example.




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          30
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        S
        =
        
          [
          
            
              
                
                  S
                  1
                
              
            
            
              
                
                  S
                  2
                
              
            
            
              
                
                  S
                  3
                
              
            
            
              
                
                  S
                  4
                
              
            
          
          ]
        
      
    
    
      
        (
        49
        )
      
    
  




When the MIMO processing unit 15 of the data transmission device 1 transmits the symbols S of the codewords by using four transmitting antennas 16a, 16b, 16c, and 16d, an MIMO processing unit 22 of a data reception device 2 receives the symbols of codewords by using four receiving antennas 21a, 21b, 21c, and 21d. When the received signal is expressed as r, the received signal r is shown as follows.




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          31
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        r
        =
        
          
            HS
            +
            n
          
          =
          
            
              [
              
                
                  
                    
                      
                        
                          h
                          
                            1
                            ,
                            1
                          
                        
                        ⁢
                        
                          S
                          1
                        
                      
                      +
                      
                        
                          h
                          
                            1
                            ,
                            2
                          
                        
                        ⁢
                        
                          S
                          2
                        
                      
                      +
                      
                        
                          h
                          
                            1
                            ,
                            3
                          
                        
                        ⁢
                        
                          S
                          3
                        
                      
                      +
                      
                        
                          h
                          
                            1
                            ,
                            4
                          
                        
                        ⁢
                        
                          S
                          4
                        
                      
                    
                  
                
                
                  
                    
                      
                        
                          h
                          
                            2
                            ,
                            1
                          
                        
                        ⁢
                        
                          S
                          1
                        
                      
                      +
                      
                        
                          h
                          
                            2
                            ,
                            2
                          
                        
                        ⁢
                        
                          S
                          2
                        
                      
                      +
                      
                        
                          h
                          
                            2
                            ,
                            3
                          
                        
                        ⁢
                        
                          S
                          3
                        
                      
                      +
                      
                        
                          h
                          
                            2
                            ,
                            4
                          
                        
                        ⁢
                        
                          S
                          4
                        
                      
                    
                  
                
                
                  
                    
                      
                        
                          h
                          
                            3
                            ,
                            1
                          
                        
                        ⁢
                        
                          S
                          1
                        
                      
                      +
                      
                        
                          h
                          
                            3
                            ,
                            2
                          
                        
                        ⁢
                        
                          S
                          2
                        
                      
                      +
                      
                        
                          h
                          
                            3
                            ,
                            3
                          
                        
                        ⁢
                        
                          S
                          3
                        
                      
                      +
                      
                        
                          h
                          
                            3
                            ,
                            4
                          
                        
                        ⁢
                        
                          S
                          4
                        
                      
                    
                  
                
                
                  
                    
                      
                        
                          h
                          
                            4
                            ,
                            1
                          
                        
                        ⁢
                        
                          S
                          1
                        
                      
                      +
                      
                        
                          h
                          
                            4
                            ,
                            2
                          
                        
                        ⁢
                        
                          S
                          2
                        
                      
                      +
                      
                        
                          h
                          
                            4
                            ,
                            3
                          
                        
                        ⁢
                        
                          S
                          3
                        
                      
                      +
                      
                        
                          h
                          
                            4
                            ,
                            4
                          
                        
                        ⁢
                        
                          S
                          4
                        
                      
                    
                  
                
              
              ]
            
            +
            
              [
              
                
                  
                    
                      n
                      1
                    
                  
                
                
                  
                    
                      n
                      2
                    
                  
                
                
                  
                    
                      n
                      3
                    
                  
                
                
                  
                    
                      n
                      4
                    
                  
                
              
              ]
            
          
        
      
    
    
      
        (
        50
        )
      
    
  




When the symbols S(1) of the codewords which are transmitted for the first time (at the time of the first-time transmission) are not decoded normally by an error correction decoding unit 26 of the data reception device 2, the MIMO processing unit 15 of the data transmission device 1 multiplies the symbols S(1) by a part of an orthogonal code to deform the symbols S(1) into symbols S(2). The MIMO processing unit also multiplies the symbols S(1) by a part of the orthogonal code to deform the symbols S(1) into symbols S(3). The MIMO processing unit further multiplies the symbols S(1) by a part of the orthogonal code to deform the symbols S(1) into symbols S(4).
After creating the symbols S(2), S(3), and S(4) in the above-mentioned way, the MIMO processing unit 15 of the data transmission device 1 sequentially transmits the symbols S(2), S(3), and S(4) by using the four transmitting antennas 16a, 16b, 16c, and 16d after transmitting the symbols S(1).




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          32
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        
          
            S
            
              (
              1
              )
            
          
          =
          
            [
            
              
                
                  
                    S
                    1
                  
                
              
              
                
                  
                    S
                    2
                  
                
              
              
                
                  
                    S
                    3
                  
                
              
              
                
                  
                    S
                    4
                  
                
              
            
            ]
          
        
        ,
        
          
            S
            
              (
              2
              )
            
          
          =
          
            [
            
              
                
                  
                    S
                    1
                  
                
              
              
                
                  
                    -
                    
                      S
                      2
                    
                  
                
              
              
                
                  
                    S
                    3
                  
                
              
              
                
                  
                    -
                    
                      S
                      4
                    
                  
                
              
            
            ]
          
        
        ,
        
          
            S
            
              (
              3
              )
            
          
          =
          
            [
            
              
                
                  
                    S
                    1
                  
                
              
              
                
                  
                    S
                    2
                  
                
              
              
                
                  
                    -
                    
                      S
                      3
                    
                  
                
              
              
                
                  
                    -
                    
                      S
                      4
                    
                  
                
              
            
            ]
          
        
        ,
        
          
            S
            
              (
              4
              )
            
          
          =
          
            [
            
              
                
                  
                    S
                    1
                  
                
              
              
                
                  
                    -
                    
                      S
                      2
                    
                  
                
              
              
                
                  
                    -
                    
                      S
                      3
                    
                  
                
              
              
                
                  
                    S
                    4
                  
                
              
            
            ]
          
        
      
    
    
      
        (
        51
        )
      
    
  




After the MIMO processing unit 15 of the data transmission device 1 transmits the sequence S(1, 2, 3, 4) of the symbols S(1), S(2), S(3) and S(4), the MIMO processing unit 22 of the data reception device 2 receives a sequence r(1, 2, 3, 4) of symbols by using the four receiving antennas 21a, 21b, 21c, and 21d. This sequence r(1, 2, 3, 4) is shown as follows.




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          33
        
        ]
      
    
    
      
        
      
    
    
      
        
      
    
  
  
    
      
        
          r
          
            (
            
              1
              ,
              2
              ,
              3
              ,
              4
            
            )
          
        
        =
        
          
            
              H
              ⁡
              
                [
                
                  
                    
                      
                        S
                        
                          (
                          1
                          )
                        
                      
                    
                    
                      
                        S
                        
                          (
                          2
                          )
                        
                      
                    
                    
                      
                        S
                        
                          (
                          3
                          )
                        
                      
                    
                    
                      
                        S
                        
                          (
                          4
                          )
                        
                      
                    
                  
                
                ]
              
            
            +
            
              n
              
                (
                
                  1
                  ,
                  2
                  ,
                  3
                  ,
                  4
                
                )
              
            
          
          =
          
            
              
                [
                
                  
                    
                      
                        h
                        
                          1
                          ,
                          1
                        
                      
                    
                    
                      
                        h
                        
                          1
                          ,
                          2
                        
                      
                    
                    
                      
                        h
                        
                          1
                          ,
                          3
                        
                      
                    
                    
                      
                        h
                        
                          1
                          ,
                          4
                        
                      
                    
                  
                  
                    
                      
                        h
                        
                          2
                          ,
                          1
                        
                      
                    
                    
                      
                        h
                        
                          2
                          ,
                          2
                        
                      
                    
                    
                      
                        h
                        
                          2
                          ,
                          3
                        
                      
                    
                    
                      
                        h
                        
                          2
                          ,
                          4
                        
                      
                    
                  
                  
                    
                      
                        h
                        
                          3
                          ,
                          1
                        
                      
                    
                    
                      
                        h
                        
                          3
                          ,
                          2
                        
                      
                    
                    
                      
                        h
                        
                          3
                          ,
                          3
                        
                      
                    
                    
                      
                        h
                        
                          3
                          ,
                          4
                        
                      
                    
                  
                  
                    
                      
                        h
                        
                          4
                          ,
                          1
                        
                      
                    
                    
                      
                        h
                        
                          4
                          ,
                          2
                        
                      
                    
                    
                      
                        h
                        
                          4
                          ,
                          3
                        
                      
                    
                    
                      
                        h
                        
                          3
                          ,
                          4
                        
                      
                    
                  
                
                ]
              
              ⁡
              
                [
                
                  
                    
                      
                        S
                        1
                      
                    
                    
                      
                        S
                        1
                      
                    
                    
                      
                        S
                        1
                      
                    
                    
                      
                        S
                        1
                      
                    
                  
                  
                    
                      
                        S
                        2
                      
                    
                    
                      
                        -
                        
                          S
                          2
                        
                      
                    
                    
                      
                        S
                        2
                      
                    
                    
                      
                        -
                        
                          S
                          2
                        
                      
                    
                  
                  
                    
                      
                        S
                        3
                      
                    
                    
                      
                        S
                        3
                      
                    
                    
                      
                        -
                        
                          S
                          3
                        
                      
                    
                    
                      
                        -
                        
                          S
                          3
                        
                      
                    
                  
                  
                    
                      
                        S
                        4
                      
                    
                    
                      
                        -
                        
                          S
                          4
                        
                      
                    
                    
                      
                        -
                        
                          S
                          4
                        
                      
                    
                    
                      
                        S
                        4
                      
                    
                  
                
                ]
              
            
            +
            
              
                n
                
                  (
                  
                    1
                    ,
                    2
                    ,
                    3
                    ,
                    4
                  
                  )
                
              
              ⁡
              
                [
                
                  
                    
                      
                        
                          
                            
                              
                                
                                  
                                    h
                                    
                                      1
                                      ,
                                      1
                                    
                                  
                                  ⁢
                                  
                                    S
                                    1
                                  
                                
                                +
                                
                                  
                                    h
                                    
                                      1
                                      ,
                                      2
                                    
                                  
                                  ⁢
                                  
                                    S
                                    2
                                  
                                
                                +
                              
                            
                          
                          
                            
                              
                                
                                  
                                    h
                                    
                                      1
                                      ,
                                      3
                                    
                                  
                                  ⁢
                                  
                                    S
                                    3
                                  
                                
                                +
                                
                                  
                                    h
                                    
                                      1
                                      ,
                                      4
                                    
                                  
                                  ⁢
                                  
                                    S
                                    4
                                  
                                
                              
                            
                          
                        
                      
                    
                    
                      
                        
                          
                            
                              
                                
                                  
                                    h
                                    
                                      2
                                      ,
                                      1
                                    
                                  
                                  ⁢
                                  
                                    S
                                    1
                                  
                                
                                +
                                
                                  
                                    h
                                    
                                      2
                                      ,
                                      2
                                    
                                  
                                  ⁢
                                  
                                    S
                                    2
                                  
                                
                                +
                              
                            
                          
                          
                            
                              
                                
                                  
                                    h
                                    
                                      2
                                      ,
                                      3
                                    
                                  
                                  ⁢
                                  
                                    S
                                    3
                                  
                                
                                +
                                
                                  
                                    h
                                    
                                      2
                                      ,
                                      4
                                    
                                  
                                  ⁢
                                  
                                    S
                                    4
                                  
                                
                              
                            
                          
                        
                      
                    
                    
                      
                        
                          
                            
                              
                                
                                  
                                    h
                                    
                                      3
                                      ,
                                      1
                                    
                                  
                                  ⁢
                                  
                                    S
                                    1
                                  
                                
                                +
                                
                                  
                                    h
                                    
                                      3
                                      ,
                                      2
                                    
                                  
                                  ⁢
                                  
                                    S
                                    2
                                  
                                
                                +
                              
                            
                          
                          
                            
                              
                                
                                  
                                    h
                                    
                                      3
                                      ,
                                      3
                                    
                                  
                                  ⁢
                                  
                                    S
                                    3
                                  
                                
                                +
                                
                                  
                                    h
                                    
                                      3
                                      ,
                                      4
                                    
                                  
                                  ⁢
                                  
                                    S
                                    4
                                  
                                
                              
                            
                          
                        
                      
                    
                    
                      
                        
                          
                            
                              
                                
                                  
                                    h
                                    
                                      4
                                      ,
                                      1
                                    
                                  
                                  ⁢
                                  
                                    S
                                    1
                                  
                                
                                +
                                
                                  
                                    h
                                    
                                      4
                                      ,
                                      2
                                    
                                  
                                  ⁢
                                  
                                    S
                                    2
                                  
                                
                                +
                              
                            
                          
                          
                            
                              
                                
                                  
                                    h
                                    
                                      4
                                      ,
                                      3
                                    
                                  
                                  ⁢
                                  
                                    S
                                    3
                                  
                                
                                +
                                
                                  
                                    h
                                    
                                      4
                                      ,
                                      4
                                    
                                  
                                  ⁢
                                  
                                    S
                                    4
                                  
                                
                              
                            
                          
                        
                      
                    
                  
                  ⁢
                  
                    
                      
                        
                          
                            
                              
                                
                                  
                                    h
                                    
                                      1
                                      ,
                                      1
                                    
                                  
                                  ⁢
                                  
                                    S
                                    1
                                  
                                
                                -
                                
                                  
                                    h
                                    
                                      1
                                      ,
                                      2
                                    
                                  
                                  ⁢
                                  
                                    S
                                    2
                                  
                                
                                +
                              
                            
                          
                          
                            
                              
                                
                                  
                                    h
                                    
                                      1
                                      ,
                                      3
                                    
                                  
                                  ⁢
                                  
                                    S
                                    3
                                  
                                
                                -
                                
                                  
                                    h
                                    
                                      1
                                      ,
                                      4
                                    
                                  
                                  ⁢
                                  
                                    S
                                    4
                                  
                                
                              
                            
                          
                        
                      
                      
                        
                          
                            
                              
                                
                                  
                                    h
                                    
                                      1
                                      ,
                                      1
                                    
                                  
                                  ⁢
                                  
                                    S
                                    1
                                  
                                
                                +
                                
                                  
                                    h
                                    
                                      1
                                      ,
                                      2
                                    
                                  
                                  ⁢
                                  
                                    S
                                    2
                                  
                                
                                -
                              
                            
                          
                          
                            
                              
                                
                                  
                                    h
                                    
                                      1
                                      ,
                                      3
                                    
                                  
                                  ⁢
                                  
                                    S
                                    3
                                  
                                
                                -
                                
                                  
                                    h
                                    
                                      1
                                      ,
                                      4
                                    
                                  
                                  ⁢
                                  
                                    S
                                    4
                                  
                                
                              
                            
                          
                        
                      
                      
                        
                          
                            
                              
                                
                                  
                                    h
                                    
                                      1
                                      ,
                                      1
                                    
                                  
                                  ⁢
                                  
                                    S
                                    1
                                  
                                
                                -
                                
                                  
                                    h
                                    
                                      1
                                      ,
                                      2
                                    
                                  
                                  ⁢
                                  
                                    S
                                    2
                                  
                                
                                -
                              
                            
                          
                          
                            
                              
                                
                                  
                                    h
                                    
                                      1
                                      ,
                                      3
                                    
                                  
                                  ⁢
                                  
                                    S
                                    3
                                  
                                
                                +
                                
                                  
                                    h
                                    
                                      1
                                      ,
                                      4
                                    
                                  
                                  ⁢
                                  
                                    S
                                    4
                                  
                                
                              
                            
                          
                        
                      
                    
                    
                      
                        
                          
                            
                              
                                
                                  
                                    h
                                    
                                      2
                                      ,
                                      1
                                    
                                  
                                  ⁢
                                  
                                    S
                                    1
                                  
                                
                                -
                                
                                  
                                    h
                                    
                                      2
                                      ,
                                      2
                                    
                                  
                                  ⁢
                                  
                                    S
                                    2
                                  
                                
                                +
                              
                            
                          
                          
                            
                              
                                
                                  
                                    h
                                    
                                      2
                                      ,
                                      3
                                    
                                  
                                  ⁢
                                  
                                    S
                                    3
                                  
                                
                                -
                                
                                  
                                    h
                                    
                                      2
                                      ,
                                      4
                                    
                                  
                                  ⁢
                                  
                                    S
                                    4
                                  
                                
                              
                            
                          
                        
                      
                      
                        
                          
                            
                              
                                
                                  
                                    h
                                    
                                      2
                                      ,
                                      1
                                    
                                  
                                  ⁢
                                  
                                    S
                                    1
                                  
                                
                                +
                                
                                  
                                    h
                                    
                                      2
                                      ,
                                      2
                                    
                                  
                                  ⁢
                                  
                                    S
                                    2
                                  
                                
                                -
                              
                            
                          
                          
                            
                              
                                
                                  
                                    h
                                    
                                      2
                                      ,
                                      3
                                    
                                  
                                  ⁢
                                  
                                    S
                                    3
                                  
                                
                                -
                                
                                  
                                    h
                                    
                                      2
                                      ,
                                      4
                                    
                                  
                                  ⁢
                                  
                                    S
                                    4
                                  
                                
                              
                            
                          
                        
                      
                      
                        
                          
                            
                              
                                
                                  
                                    h
                                    
                                      2
                                      ,
                                      1
                                    
                                  
                                  ⁢
                                  
                                    S
                                    1
                                  
                                
                                -
                                
                                  
                                    h
                                    
                                      2
                                      ,
                                      2
                                    
                                  
                                  ⁢
                                  
                                    S
                                    2
                                  
                                
                                -
                              
                            
                          
                          
                            
                              
                                
                                  
                                    h
                                    
                                      2
                                      ,
                                      3
                                    
                                  
                                  ⁢
                                  
                                    S
                                    3
                                  
                                
                                +
                                
                                  
                                    h
                                    
                                      2
                                      ,
                                      4
                                    
                                  
                                  ⁢
                                  
                                    S
                                    4
                                  
                                
                              
                            
                          
                        
                      
                    
                    
                      
                        
                          
                            
                              
                                
                                  
                                    h
                                    
                                      3
                                      ,
                                      1
                                    
                                  
                                  ⁢
                                  
                                    S
                                    1
                                  
                                
                                -
                                
                                  
                                    h
                                    
                                      3
                                      ,
                                      2
                                    
                                  
                                  ⁢
                                  
                                    S
                                    2
                                  
                                
                                +
                              
                            
                          
                          
                            
                              
                                
                                  
                                    h
                                    
                                      3
                                      ,
                                      3
                                    
                                  
                                  ⁢
                                  
                                    S
                                    3
                                  
                                
                                -
                                
                                  
                                    h
                                    
                                      3
                                      ,
                                      4
                                    
                                  
                                  ⁢
                                  
                                    S
                                    4
                                  
                                
                              
                            
                          
                        
                      
                      
                        
                          
                            
                              
                                
                                  
                                    h
                                    
                                      3
                                      ,
                                      1
                                    
                                  
                                  ⁢
                                  
                                    S
                                    1
                                  
                                
                                +
                                
                                  
                                    h
                                    
                                      3
                                      ,
                                      2
                                    
                                  
                                  ⁢
                                  
                                    S
                                    2
                                  
                                
                                -
                              
                            
                          
                          
                            
                              
                                
                                  
                                    h
                                    
                                      3
                                      ,
                                      3
                                    
                                  
                                  ⁢
                                  
                                    S
                                    3
                                  
                                
                                -
                                
                                  
                                    h
                                    
                                      3
                                      ,
                                      4
                                    
                                  
                                  ⁢
                                  
                                    S
                                    4
                                  
                                
                              
                            
                          
                        
                      
                      
                        
                          
                            
                              
                                
                                  
                                    h
                                    
                                      3
                                      ,
                                      1
                                    
                                  
                                  ⁢
                                  
                                    S
                                    1
                                  
                                
                                -
                                
                                  
                                    h
                                    
                                      3
                                      ,
                                      2
                                    
                                  
                                  ⁢
                                  
                                    S
                                    2
                                  
                                
                                -
                              
                            
                          
                          
                            
                              
                                
                                  
                                    h
                                    
                                      3
                                      ,
                                      3
                                    
                                  
                                  ⁢
                                  
                                    S
                                    3
                                  
                                
                                +
                                
                                  
                                    h
                                    
                                      3
                                      ,
                                      4
                                    
                                  
                                  ⁢
                                  
                                    S
                                    4
                                  
                                
                              
                            
                          
                        
                      
                    
                    
                      
                        
                          
                            
                              h
                              
                                4
                                ,
                                1
                              
                            
                            ⁢
                            
                              S
                              1
                            
                          
                          -
                          
                            
                              h
                              
                                4
                                ,
                                2
                              
                            
                            ⁢
                            
                              S
                              2
                            
                          
                        
                      
                      
                        
                          
                            
                              h
                              
                                4
                                ,
                                1
                              
                            
                            ⁢
                            
                              S
                              1
                            
                          
                          +
                          
                            
                              h
                              
                                4
                                ,
                                2
                              
                            
                            ⁢
                            
                              S
                              2
                            
                          
                          -
                        
                      
                      
                        
                          
                            
                              h
                              
                                4
                                ,
                                1
                              
                            
                            ⁢
                            
                              S
                              1
                            
                          
                          -
                          
                            
                              h
                              
                                4
                                ,
                                2
                              
                            
                            ⁢
                            
                              S
                              2
                            
                          
                          -
                        
                      
                    
                    
                      
                        
                          
                            
                              +
                              
                                h
                                
                                  4
                                  ,
                                  3
                                
                              
                            
                            ⁢
                            
                              S
                              3
                            
                          
                          -
                          
                            
                              h
                              
                                4
                                ,
                                4
                              
                            
                            ⁢
                            
                              S
                              4
                            
                          
                        
                      
                      
                        
                          
                            
                              h
                              
                                4
                                ,
                                3
                              
                            
                            ⁢
                            
                              S
                              3
                            
                          
                          -
                          
                            
                              h
                              
                                4
                                ,
                                4
                              
                            
                            ⁢
                            
                              S
                              4
                            
                          
                        
                      
                      
                        
                          
                            
                              h
                              
                                4
                                ,
                                3
                              
                            
                            ⁢
                            
                              S
                              3
                            
                          
                          +
                          
                            
                              h
                              
                                4
                                ,
                                4
                              
                            
                            ⁢
                            
                              S
                              4
                            
                          
                        
                      
                    
                  
                
                ]
              
            
            +
            
              [
              
                
              
              ⁢
              
                
                  
                    
                      n
                      1
                      
                        (
                        1
                        )
                      
                    
                  
                  
                    
                      n
                      1
                      
                        (
                        2
                        )
                      
                    
                  
                  
                    
                      n
                      1
                      
                        (
                        3
                        )
                      
                    
                  
                  
                    
                      n
                      1
                      
                        (
                        4
                        )
                      
                    
                  
                
                
                  
                    
                      n
                      2
                      
                        (
                        1
                        )
                      
                    
                  
                  
                    
                      n
                      2
                      
                        (
                        2
                        )
                      
                    
                  
                  
                    
                      n
                      2
                      
                        (
                        3
                        )
                      
                    
                  
                  
                    
                      n
                      2
                      
                        (
                        4
                        )
                      
                    
                  
                
                
                  
                    
                      n
                      3
                      
                        (
                        1
                        )
                      
                    
                  
                  
                    
                      n
                      3
                      
                        (
                        2
                        )
                      
                    
                  
                  
                    
                      n
                      3
                      
                        (
                        3
                        )
                      
                    
                  
                  
                    
                      n
                      3
                      
                        (
                        4
                        )
                      
                    
                  
                
                
                  
                    
                      n
                      4
                      
                        (
                        1
                        )
                      
                    
                  
                  
                    
                      n
                      4
                      
                        (
                        2
                        )
                      
                    
                  
                  
                    
                      n
                      4
                      
                        (
                        3
                        )
                      
                    
                  
                  
                    
                      n
                      4
                      
                        (
                        4
                        )
                      
                    
                  
                
              
              ⁢
              
                
              
              ]
            
          
        
      
    
    
      
        
      
    
    
      
        (
        52
        )
      
    
  




After the MIMO processing unit 22 receives the sequence r(1, 2, 3, 4) by using the four receiving antennas 21a, 21b, 21c, and 21d, the error correction decoding unit 26 of the data reception device 2 multiplies the received sequence r(1, 2, 3, 4) by an orthogonal code to deform equation (52), as will be shown below.




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          34
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        
          
            r
            
              (
              
                1
                ,
                2
                ,
                3
                ,
                4
              
              )
            
          
          ⁡
          
            [
            
              
                
                  1
                
                
                  1
                
                
                  1
                
                
                  1
                
              
              
                
                  1
                
                
                  
                    -
                    1
                  
                
                
                  1
                
                
                  
                    -
                    1
                  
                
              
              
                
                  1
                
                
                  1
                
                
                  
                    -
                    1
                  
                
                
                  
                    -
                    1
                  
                
              
              
                
                  1
                
                
                  
                    -
                    1
                  
                
                
                  
                    -
                    1
                  
                
                
                  1
                
              
            
            ]
          
        
        =
        
          
            4
            ⁡
            
              [
              
                
                  
                    
                      
                        h
                        
                          1
                          ,
                          1
                        
                      
                      ⁢
                      
                        S
                        1
                      
                    
                  
                  
                    
                      
                        h
                        
                          1
                          ,
                          2
                        
                      
                      ⁢
                      
                        S
                        2
                      
                    
                  
                  
                    
                      
                        h
                        
                          1
                          ,
                          3
                        
                      
                      ⁢
                      
                        S
                        3
                      
                    
                  
                  
                    
                      
                        h
                        
                          1
                          ,
                          4
                        
                      
                      ⁢
                      
                        S
                        4
                      
                    
                  
                
                
                  
                    
                      
                        h
                        
                          2
                          ,
                          1
                        
                      
                      ⁢
                      
                        S
                        1
                      
                    
                  
                  
                    
                      
                        h
                        
                          2
                          ,
                          2
                        
                      
                      ⁢
                      
                        S
                        2
                      
                    
                  
                  
                    
                      
                        h
                        
                          2
                          ,
                          3
                        
                      
                      ⁢
                      
                        S
                        3
                      
                    
                  
                  
                    
                      
                        h
                        
                          2
                          ,
                          4
                        
                      
                      ⁢
                      
                        S
                        4
                      
                    
                  
                
                
                  
                    
                      
                        h
                        
                          3
                          ,
                          1
                        
                      
                      ⁢
                      
                        S
                        1
                      
                    
                  
                  
                    
                      
                        h
                        
                          3
                          ,
                          2
                        
                      
                      ⁢
                      
                        S
                        2
                      
                    
                  
                  
                    
                      
                        h
                        
                          3
                          ,
                          3
                        
                      
                      ⁢
                      
                        S
                        3
                      
                    
                  
                  
                    
                      
                        h
                        
                          3
                          ,
                          4
                        
                      
                      ⁢
                      
                        S
                        4
                      
                    
                  
                
                
                  
                    
                      
                        h
                        
                          4
                          ,
                          1
                        
                      
                      ⁢
                      
                        S
                        1
                      
                    
                  
                  
                    
                      
                        h
                        
                          4
                          ,
                          2
                        
                      
                      ⁢
                      
                        S
                        2
                      
                    
                  
                  
                    
                      
                        h
                        
                          4
                          ,
                          3
                        
                      
                      ⁢
                      
                        S
                        3
                      
                    
                  
                  
                    
                      
                        h
                        
                          4
                          ,
                          4
                        
                      
                      ⁢
                      
                        S
                        4
                      
                    
                  
                
              
              ]
            
          
          +
          
             
            
              [
              
                
                  
                    
                      
                        
                          
                            
                              n
                              1
                              
                                (
                                1
                                )
                              
                            
                            +
                            
                              n
                              1
                              
                                (
                                2
                                )
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            
                              n
                              1
                              
                                (
                                3
                                )
                              
                            
                            +
                            
                              n
                              1
                              
                                (
                                4
                                )
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              n
                              1
                              
                                (
                                1
                                )
                              
                            
                            -
                            
                              n
                              1
                              
                                (
                                2
                                )
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            
                              n
                              1
                              
                                (
                                3
                                )
                              
                            
                            -
                            
                              n
                              1
                              
                                (
                                4
                                )
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              n
                              1
                              
                                (
                                1
                                )
                              
                            
                            +
                            
                              n
                              1
                              
                                (
                                2
                                )
                              
                            
                            -
                          
                        
                      
                      
                        
                          
                            
                              n
                              1
                              
                                (
                                3
                                )
                              
                            
                            -
                            
                              n
                              1
                              
                                (
                                4
                                )
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              n
                              1
                              
                                (
                                1
                                )
                              
                            
                            -
                            
                              n
                              1
                              
                                (
                                2
                                )
                              
                            
                            -
                          
                        
                      
                      
                        
                          
                            
                              n
                              1
                              
                                (
                                3
                                )
                              
                            
                            +
                            
                              n
                              1
                              
                                (
                                4
                                )
                              
                            
                          
                        
                      
                    
                  
                
                
                  
                    
                      
                        
                          
                            
                              n
                              2
                              
                                (
                                1
                                )
                              
                            
                            +
                            
                              n
                              2
                              
                                (
                                2
                                )
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            
                              n
                              2
                              
                                (
                                3
                                )
                              
                            
                            +
                            
                              n
                              2
                              
                                (
                                4
                                )
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              n
                              2
                              
                                (
                                1
                                )
                              
                            
                            -
                            
                              n
                              2
                              
                                (
                                2
                                )
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            
                              n
                              2
                              
                                (
                                3
                                )
                              
                            
                            -
                            
                              n
                              2
                              
                                (
                                4
                                )
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              n
                              2
                              
                                (
                                1
                                )
                              
                            
                            +
                            
                              n
                              2
                              
                                (
                                2
                                )
                              
                            
                            -
                          
                        
                      
                      
                        
                          
                            
                              n
                              2
                              
                                (
                                3
                                )
                              
                            
                            -
                            
                              n
                              2
                              
                                (
                                4
                                )
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              n
                              2
                              
                                (
                                1
                                )
                              
                            
                            -
                            
                              n
                              2
                              
                                (
                                2
                                )
                              
                            
                            -
                          
                        
                      
                      
                        
                          
                            
                              n
                              2
                              
                                (
                                3
                                )
                              
                            
                            +
                            
                              n
                              2
                              
                                (
                                4
                                )
                              
                            
                          
                        
                      
                    
                  
                
                
                  
                    
                      
                        
                          
                            
                              n
                              3
                              
                                (
                                1
                                )
                              
                            
                            +
                            
                              n
                              3
                              
                                (
                                2
                                )
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            
                              n
                              3
                              
                                (
                                3
                                )
                              
                            
                            +
                            
                              n
                              3
                              
                                (
                                4
                                )
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              n
                              3
                              
                                (
                                1
                                )
                              
                            
                            -
                            
                              n
                              3
                              
                                (
                                2
                                )
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            
                              n
                              3
                              
                                (
                                3
                                )
                              
                            
                            -
                            
                              n
                              3
                              
                                (
                                4
                                )
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              n
                              3
                              
                                (
                                1
                                )
                              
                            
                            +
                            
                              n
                              3
                              
                                (
                                2
                                )
                              
                            
                            -
                          
                        
                      
                      
                        
                          
                            
                              n
                              3
                              
                                (
                                3
                                )
                              
                            
                            -
                            
                              n
                              3
                              
                                (
                                4
                                )
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              n
                              3
                              
                                (
                                1
                                )
                              
                            
                            -
                            
                              n
                              3
                              
                                (
                                2
                                )
                              
                            
                            -
                          
                        
                      
                      
                        
                          
                            
                              n
                              3
                              
                                (
                                3
                                )
                              
                            
                            +
                            
                              n
                              3
                              
                                (
                                4
                                )
                              
                            
                          
                        
                      
                    
                  
                
                
                  
                    
                      
                        
                          
                            
                              n
                              4
                              
                                (
                                1
                                )
                              
                            
                            +
                            
                              n
                              4
                              
                                (
                                2
                                )
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            
                              n
                              4
                              
                                (
                                3
                                )
                              
                            
                            +
                            
                              n
                              4
                              
                                (
                                4
                                )
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              n
                              4
                              
                                (
                                1
                                )
                              
                            
                            -
                            
                              n
                              4
                              
                                (
                                2
                                )
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            
                              n
                              4
                              
                                (
                                3
                                )
                              
                            
                            -
                            
                              n
                              4
                              
                                (
                                4
                                )
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              n
                              4
                              
                                (
                                1
                                )
                              
                            
                            +
                            
                              n
                              4
                              
                                (
                                2
                                )
                              
                            
                            -
                          
                        
                      
                      
                        
                          
                            
                              n
                              4
                              
                                (
                                3
                                )
                              
                            
                            -
                            
                              n
                              4
                              
                                (
                                4
                                )
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              n
                              4
                              
                                (
                                1
                                )
                              
                            
                            -
                            
                              n
                              4
                              
                                (
                                2
                                )
                              
                            
                            -
                          
                        
                      
                      
                        
                          
                            
                              n
                              4
                              
                                (
                                3
                                )
                              
                            
                            +
                            
                              n
                              4
                              
                                (
                                4
                                )
                              
                            
                          
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    
      
        (
        53
        )
      
    
  




The error correction decoding unit 26 of the data reception device 2 also extracts S1, S2, S3, and S4 which construct the symbols S of the codewords by arranging equation (53) to form equation (54) and then calculating equation (54).

[Equation 35]

4h1,1S1h*1,1+4h2,1S1h*2,1+4h3,1S1h*3,1+4h4,1S1h*4,1+n′1=4(|h1,1|2+|h2,1|2+|h3,1|2+|h4,1|2)·S1+n′1 

4h1,2S2h*1,2+4h2,2S2h*2,2+4h3,2S2h*3,2+4h4,2S2h*4,2+n′2=4(|h1,2|2+|h2,2|2+|h3,2|2+|h4,2|2)·S2+n′2 

4h1,3S3h*1,3+4h2,3S3h*2,3+4h3,3S3h*3,3+4h4,3S3h*4,3+n′3=4(|h1,3|2+|h2,3|2+|h3,3|2+|h4,3|2)·S3+n′3 

4h1,4S4h*1,4+4h2,4S4h*2,4+4h3,4S4h*3,4+4h4,4S4h*4,4+n′4=4(|h1,4|2+|h2,4|2+|h3,4|2+|h4,4|2)·S4+n′4   (54)

where when n′1, n′2, n′3, n′4 are defined as follows:





  
    [
    
      
        
          
            n
            
              1
              ,
              1
            
            ′
          
        
        
          
            n
            
              1
              ,
              2
            
            ′
          
        
        
          
            n
            
              1
              ,
              3
            
            ′
          
        
        
          
            n
            
              1
              ,
              4
            
            ′
          
        
      
      
        
          
            n
            
              2
              ,
              1
            
            ′
          
        
        
          
            n
            
              2
              ,
              2
            
            ′
          
        
        
          
            n
            
              2
              ,
              3
            
            ′
          
        
        
          
            n
            
              2
              ,
              4
            
            ′
          
        
      
      
        
          
            n
            
              3
              ,
              1
            
            ′
          
        
        
          
            n
            
              3
              ,
              2
            
            ′
          
        
        
          
            n
            
              3
              ,
              3
            
            ′
          
        
        
          
            n
            
              3
              ,
              4
            
            ′
          
        
      
      
        
          
            n
            
              4
              ,
              1
            
            ′
          
        
        
          
            n
            
              4
              ,
              2
            
            ′
          
        
        
          
            n
            
              4
              ,
              3
            
            ′
          
        
        
          
            n
            
              4
              ,
              4
            
            ′
          
        
      
    
    ⁢
    
      
    
    ]
  
  =
  
     
    
      [
      
        
          
            
              
                
                  
                    
                      n
                      1
                      
                        (
                        1
                        )
                      
                    
                    +
                    
                      n
                      1
                      
                        (
                        2
                        )
                      
                    
                    +
                  
                
              
              
                
                  
                    
                      n
                      1
                      
                        (
                        3
                        )
                      
                    
                    +
                    
                      n
                      1
                      
                        (
                        4
                        )
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      n
                      1
                      
                        (
                        1
                        )
                      
                    
                    -
                    
                      n
                      1
                      
                        (
                        2
                        )
                      
                    
                    +
                  
                
              
              
                
                  
                    
                      n
                      1
                      
                        (
                        3
                        )
                      
                    
                    -
                    
                      n
                      1
                      
                        (
                        4
                        )
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      n
                      1
                      
                        (
                        1
                        )
                      
                    
                    +
                    
                      n
                      1
                      
                        (
                        2
                        )
                      
                    
                    -
                  
                
              
              
                
                  
                    
                      n
                      1
                      
                        (
                        3
                        )
                      
                    
                    -
                    
                      n
                      1
                      
                        (
                        4
                        )
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      n
                      1
                      
                        (
                        1
                        )
                      
                    
                    -
                    
                      n
                      1
                      
                        (
                        2
                        )
                      
                    
                    -
                  
                
              
              
                
                  
                    
                      n
                      1
                      
                        (
                        3
                        )
                      
                    
                    +
                    
                      n
                      1
                      
                        (
                        4
                        )
                      
                    
                  
                
              
            
          
        
        
          
            
              
                
                  
                    
                      n
                      2
                      
                        (
                        1
                        )
                      
                    
                    +
                    
                      n
                      2
                      
                        (
                        2
                        )
                      
                    
                    +
                  
                
              
              
                
                  
                    
                      n
                      2
                      
                        (
                        3
                        )
                      
                    
                    +
                    
                      n
                      2
                      
                        (
                        4
                        )
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      n
                      2
                      
                        (
                        1
                        )
                      
                    
                    -
                    
                      n
                      2
                      
                        (
                        2
                        )
                      
                    
                    +
                  
                
              
              
                
                  
                    
                      n
                      2
                      
                        (
                        3
                        )
                      
                    
                    -
                    
                      n
                      2
                      
                        (
                        4
                        )
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      n
                      2
                      
                        (
                        1
                        )
                      
                    
                    +
                    
                      n
                      2
                      
                        (
                        2
                        )
                      
                    
                    -
                  
                
              
              
                
                  
                    
                      n
                      2
                      
                        (
                        3
                        )
                      
                    
                    -
                    
                      n
                      2
                      
                        (
                        4
                        )
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      n
                      2
                      
                        (
                        1
                        )
                      
                    
                    -
                    
                      n
                      2
                      
                        (
                        2
                        )
                      
                    
                    -
                  
                
              
              
                
                  
                    
                      n
                      2
                      
                        (
                        3
                        )
                      
                    
                    +
                    
                      n
                      2
                      
                        (
                        4
                        )
                      
                    
                  
                
              
            
          
        
        
          
            
              
                
                  
                    
                      n
                      3
                      
                        (
                        1
                        )
                      
                    
                    +
                    
                      n
                      3
                      
                        (
                        2
                        )
                      
                    
                    +
                  
                
              
              
                
                  
                    
                      n
                      3
                      
                        (
                        3
                        )
                      
                    
                    +
                    
                      n
                      3
                      
                        (
                        4
                        )
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      n
                      3
                      
                        (
                        1
                        )
                      
                    
                    -
                    
                      n
                      3
                      
                        (
                        2
                        )
                      
                    
                    +
                  
                
              
              
                
                  
                    
                      n
                      3
                      
                        (
                        3
                        )
                      
                    
                    -
                    
                      n
                      3
                      
                        (
                        4
                        )
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      n
                      3
                      
                        (
                        1
                        )
                      
                    
                    +
                    
                      n
                      3
                      
                        (
                        2
                        )
                      
                    
                    -
                  
                
              
              
                
                  
                    
                      n
                      3
                      
                        (
                        3
                        )
                      
                    
                    -
                    
                      n
                      3
                      
                        (
                        4
                        )
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      n
                      3
                      
                        (
                        1
                        )
                      
                    
                    -
                    
                      n
                      3
                      
                        (
                        2
                        )
                      
                    
                    -
                  
                
              
              
                
                  
                    
                      n
                      3
                      
                        (
                        3
                        )
                      
                    
                    +
                    
                      n
                      3
                      
                        (
                        4
                        )
                      
                    
                  
                
              
            
          
        
        
          
            
              
                
                  
                    
                      n
                      4
                      
                        (
                        1
                        )
                      
                    
                    +
                    
                      n
                      4
                      
                        (
                        2
                        )
                      
                    
                    +
                  
                
              
              
                
                  
                    
                      n
                      4
                      
                        (
                        3
                        )
                      
                    
                    +
                    
                      n
                      4
                      
                        (
                        4
                        )
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      n
                      4
                      
                        (
                        1
                        )
                      
                    
                    -
                    
                      n
                      4
                      
                        (
                        2
                        )
                      
                    
                    +
                  
                
              
              
                
                  
                    
                      n
                      4
                      
                        (
                        3
                        )
                      
                    
                    -
                    
                      n
                      4
                      
                        (
                        4
                        )
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      n
                      4
                      
                        (
                        1
                        )
                      
                    
                    +
                    
                      n
                      4
                      
                        (
                        2
                        )
                      
                    
                    -
                  
                
              
              
                
                  
                    
                      n
                      4
                      
                        (
                        3
                        )
                      
                    
                    -
                    
                      n
                      4
                      
                        (
                        4
                        )
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      n
                      4
                      
                        (
                        1
                        )
                      
                    
                    -
                    
                      n
                      4
                      
                        (
                        2
                        )
                      
                    
                    -
                  
                
              
              
                
                  
                    
                      n
                      4
                      
                        (
                        3
                        )
                      
                    
                    +
                    
                      n
                      4
                      
                        (
                        4
                        )
                      
                    
                  
                
              
            
          
        
      
      ]
    
  




they are expressed as follows:

n′1=h*1.1n′1.1+h*2.1n′2.1+h*3.1n′3.1+h*4.1n′4.1,

n′2=h*1.2n′1.2+h*2.2n′2.2+h*3.2n′3.2+h*4.2n′4.2,

n′3=h*1.3n′1.3+h*2.3n′2.3+h*3.3n′3.3+h*4.3n′4.3,

n′4=h*1.4n′1.4+h*2.4n′2.4+h*3.4n′3.4+h*4.4n′4.4,   (55)

In this Embodiment 4, the case in which the error correction decoding unit 26 of the data reception device 2 extracts S1, S2, S3, and S4 which construct the symbols S of the codewords by arranging equation (53) to form equation (54), and calculating equation (54) is shown. As an alternative, the error correction decoding unit can extract S1, S2, S3, and S4 which construct the symbols S of the codewords by simplifying equation (54) into equation (56) and then calculating equation (56).

[Equation 36]

4h1.1S1h*1.1+h*1.1n′1.1=4(|h1.1|2)·S1+h*1.1n′1.1 

4h2.2S2h*2.2+h*2.2n′2.2=4(|h2.2|2)·S2+h*2.2n′2.2 

4h3.3S3h*3.3+h*3.3n′3.3=4(|h3.3|2)·S3+h*3.3n′3.3 

4h4.4S4h*4.4+h*4.4n′4.4=4(|h4,4|2)·S4+h*4.4n′4.4   (56)

Embodiment 5
In above-mentioned Embodiments 3 and 4, the case of N=2 and the case of N=4 are shown respectively. In contrast, in accordance with this Embodiment 2, the example is generalized to a case in which codewords are transmitted via N communication channels and interference occurs among the N communication channels, as will be explained below. In this embodiment, N is a power of two.
First, a communication channel response matrix H is assumed as follows.




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          37
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        H
        =
        
          [
          
            
              
                
                  h
                  
                    1
                    ,
                    1
                  
                
              
              
                
                  h
                  
                    1
                    ,
                    2
                  
                
              
              
                ...
              
              
                ...
              
              
                
                  h
                  
                    1
                    ,
                    N
                  
                
              
            
            
              
                
                  h
                  
                    2
                    ,
                    1
                  
                
              
              
                ⋱
              
              
                ⋱
              
              
                ⋱
              
              
                ⋮
              
            
            
              
                ⋮
              
              
                ⋱
              
              
                
                  h
                  
                    i
                    ,
                    j
                  
                
              
              
                ⋱
              
              
                ⋮
              
            
            
              
                ⋮
              
              
                ⋱
              
              
                ⋱
              
              
                ⋱
              
              
                ⋮
              
            
            
              
                
                  h
                  
                    N
                    ,
                    1
                  
                
              
              
                ...
              
              
                ...
              
              
                ...
              
              
                
                  h
                  
                    N
                    ,
                    N
                  
                
              
            
          
          ]
        
      
    
    
      
        (
        57
        )
      
    
  




where hi,j is a communication channel response from j-th transmitting antenna to i-th receiving antenna.

Furthermore, the symbols of codewords transmitted from an MIMO processing unit 15 of a data transmission device 1 (symbols which are obtained by modulating an error correcting code expressed by two elements) are expressed as S. For the sake of simplicity, it is assumed that no OFDM modulation is carried out in this example.




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          38
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        S
        =
        
          [
          
            
              
                
                  S
                  1
                
              
            
            
              
                
                  S
                  2
                
              
            
            
              
                ⋮
              
            
            
              
                
                  S
                  N
                
              
            
          
          ]
        
      
    
    
      
        (
        58
        )
      
    
  




When the MIMO processing unit 15 of the data transmission device 1 transmits the symbols S of the codewords by using N transmitting antennas, an MIMO processing unit 22 of a data reception device 2 receives the symbols of the codewords by using N receiving antennas. When the received signal is expressed as r, the received signal r is shown as follows.




  
    
      
        
          
        
        ⁢
        
          [
          
            Equation
            ⁢
            
              
            
            ⁢
            39
          
          ]
        
      
    
    
      
        
      
    
  
  
    
      
        
          
        
        ⁢
        
          r
          =
          
            
              HS
              +
              n
            
            =
            
              
                
                  
                    [
                    
                      
                        
                          
                            h
                            
                              1
                              ,
                              1
                            
                          
                        
                        
                          
                            h
                            
                              1
                              ,
                              2
                            
                          
                        
                        
                          ...
                        
                        
                          ...
                        
                        
                          
                            h
                            
                              1
                              ,
                              N
                            
                          
                        
                      
                      
                        
                          
                            h
                            
                              2
                              ,
                              1
                            
                          
                        
                        
                          ⋱
                        
                        
                          ⋱
                        
                        
                          ⋱
                        
                        
                          ⋮
                        
                      
                      
                        
                          ⋮
                        
                        
                          ⋱
                        
                        
                          
                            h
                            
                              i
                              ,
                              j
                            
                          
                        
                        
                          ⋱
                        
                        
                          ⋮
                        
                      
                      
                        
                          ⋮
                        
                        
                          ⋱
                        
                        
                          ⋱
                        
                        
                          ⋱
                        
                        
                          ⋮
                        
                      
                      
                        
                          
                            h
                            
                              N
                              ,
                              1
                            
                          
                        
                        
                          ...
                        
                        
                          ...
                        
                        
                          ...
                        
                        
                          
                            h
                            
                              N
                              ,
                              N
                            
                          
                        
                      
                    
                    ]
                  
                  ⁢
                  
                    

                  
                  ⁢
                  
                    
                  
                  [
                  
                    
                      
                        
                          S
                          1
                        
                      
                    
                    
                      
                        
                          S
                          2
                        
                      
                    
                    
                      
                        ⋮
                      
                    
                    
                      
                        
                          S
                          N
                        
                      
                    
                  
                  ]
                
                +
                
                  [
                  
                    
                      
                        
                          n
                          1
                        
                      
                    
                    
                      
                        
                          n
                          2
                        
                      
                    
                    
                      
                        ⋮
                      
                    
                    
                      
                        
                          n
                          N
                        
                      
                    
                  
                  ]
                
              
              =
              
                
                  [
                  
                    
                      
                        
                          
                            
                              h
                              
                                1
                                ,
                                1
                              
                            
                            ⁢
                            
                              S
                              1
                            
                          
                          +
                          
                            
                              h
                              
                                1
                                ,
                                2
                              
                            
                            ⁢
                            
                              S
                              2
                            
                          
                          +
                          ...
                          +
                          
                            
                              h
                              
                                1
                                ,
                                N
                              
                            
                            ⁢
                            
                              S
                              N
                            
                          
                        
                      
                    
                    
                      
                        
                          
                            
                              h
                              
                                2
                                ,
                                1
                              
                            
                            ⁢
                            
                              S
                              1
                            
                          
                          +
                          
                            
                              h
                              
                                2
                                ,
                                2
                              
                            
                            ⁢
                            
                              S
                              2
                            
                          
                          +
                          ...
                          +
                          
                            
                              h
                              
                                2
                                ,
                                N
                              
                            
                            ⁢
                            
                              S
                              N
                            
                          
                        
                      
                    
                    
                      
                        ⋮
                      
                    
                    
                      
                        
                          
                            
                              h
                              
                                N
                                ,
                                1
                              
                            
                            ⁢
                            
                              S
                              1
                            
                          
                          +
                          
                            
                              h
                              
                                N
                                ,
                                2
                              
                            
                            ⁢
                            
                              S
                              2
                            
                          
                          +
                          ...
                          +
                          
                            
                              h
                              
                                N
                                ,
                                N
                              
                            
                            ⁢
                            
                              S
                              N
                            
                          
                        
                      
                    
                  
                  ]
                
                +
                
                  [
                  
                    
                      
                        
                          n
                          1
                        
                      
                    
                    
                      
                        
                          n
                          2
                        
                      
                    
                    
                      
                        ⋮
                      
                    
                    
                      
                        
                          n
                          N
                        
                      
                    
                  
                  ]
                
              
            
          
        
      
    
    
      
        (
        59
        )
      
    
  




When the symbols S(1) of the codewords which are transmitted for the first time (at the time of the first-time transmission) are not decoded normally by an error correction decoding unit 26 of the data reception device 2, the MIMO processing unit 15 of the data transmission device 1 multiplies the symbols S(1) by a part of an orthogonal code to deform the symbols S(1) into symbols S(2). The MIMO processing unit similarly multiplies the symbols S(1) by a part of the orthogonal code to deform the symbols S(1) into symbols S(N).
After creating the symbols S(2), . . . , and S(N) in the above-mentioned way, the MIMO processing unit 15 of the data transmission device 1 sequentially transmits the symbols S(2), . . . , and S(N) by using the N transmitting antennas every time when a transmission request is sent to the data transmission device from the receiver after transmitting the symbols S(1).




  
    
      
        
          
        
        ⁢
        
          [
          
            Equation
            ⁢
            
              
            
            ⁢
            40
          
          ]
        
      
    
    
      
        
      
    
  
  
    
      
        
          
            S
            
              (
              
                1
                ⁢
                
                  :
                
                ⁢
                N
              
              )
            
          
          =
          
            
              [
              
                
                  S
                  
                    (
                    1
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  S
                  
                    (
                    2
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                ...
                ⁢
                
                  
                
                ⁢
                
                  S
                  
                    (
                    N
                    )
                  
                
              
              ]
            
            =
            
              [
              
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          1
                        
                      
                      ⁢
                      
                        S
                        1
                      
                    
                  
                  
                    
                      
                        γ
                        
                          1
                          ,
                          2
                        
                      
                      ⁢
                      
                        S
                        1
                      
                    
                  
                  
                    ...
                  
                  
                    
                      
                        γ
                        
                          1
                          ,
                          N
                        
                      
                      ⁢
                      
                        S
                        1
                      
                    
                  
                
                
                  
                    
                      
                        γ
                        
                          2
                          ,
                          1
                        
                      
                      ⁢
                      
                        S
                        2
                      
                    
                  
                  
                    
                      
                        γ
                        
                          2
                          ,
                          2
                        
                      
                      ⁢
                      
                        S
                        2
                      
                    
                  
                  
                    ...
                  
                  
                    
                      
                        γ
                        
                          2
                          ,
                          N
                        
                      
                      ⁢
                      
                        S
                        2
                      
                    
                  
                
                
                  
                    ⋮
                  
                  
                    ⋮
                  
                  
                    ⋱
                  
                  
                    ⋮
                  
                
                
                  
                    
                      
                        γ
                        
                          N
                          ,
                          1
                        
                      
                      ⁢
                      
                        S
                        N
                      
                    
                  
                  
                    
                      
                        γ
                        
                          N
                          ,
                          2
                        
                      
                      ⁢
                      
                        S
                        N
                      
                    
                  
                  
                    ...
                  
                  
                    
                      
                        γ
                        
                          N
                          ,
                          N
                        
                      
                      ⁢
                      
                        S
                        N
                      
                    
                  
                
              
              ]
            
          
        
        ,
      
    
    
      
        (
        60
        )
      
    
  




where γi,j is a component of an Hadamard matrix (a component of an orthogonal code), and, in the case of N=4, is expressed as follows:





  
    [
    
      
        
          
            γ
            
              1
              ,
              1
            
          
        
        
          
            γ
            
              1
              ,
              2
            
          
        
        
          
            γ
            
              1
              ,
              3
            
          
        
        
          
            γ
            
              1
              ,
              4
            
          
        
      
      
        
          
            γ
            
              2
              ,
              1
            
          
        
        
          
            γ
            
              2
              ,
              2
            
          
        
        
          
            γ
            
              2
              ,
              3
            
          
        
        
          
            γ
            
              2
              ,
              4
            
          
        
      
      
        
          
            γ
            
              3
              ,
              1
            
          
        
        
          
            γ
            
              3
              ,
              1
            
          
        
        
          
            γ
            
              3
              ,
              3
            
          
        
        
          
            γ
            
              3
              ,
              4
            
          
        
      
      
        
          
            γ
            
              4
              ,
              1
            
          
        
        
          
            γ
            
              4
              ,
              2
            
          
        
        
          
            γ
            
              4
              ,
              3
            
          
        
        
          
            γ
            
              4
              ,
              4
            
          
        
      
    
    ]
  
  =
  
    [
    
      
        
          1
        
        
          1
        
        
          1
        
        
          1
        
      
      
        
          1
        
        
          
            -
            1
          
        
        
          1
        
        
          
            -
            1
          
        
      
      
        
          1
        
        
          1
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
      
      
        
          1
        
        
          
            -
            1
          
        
        
          
            -
            1
          
        
        
          1
        
      
    
    ]
  




After the MIMO processing unit 15 of the data transmission device 1 transmits the sequence S(1:N) of the symbols S(2), . . . , and S(N), the MIMO processing unit 22 of the data reception device 2 receives a sequence r(1:N) of symbols by using the N receiving antennas. This sequence r(1:N) is shown as follows.

[Equation 41]

r(1:N)=HS(1:N)+n(1:N)   (61)

After the MIMO processing unit 22 receives the sequence r(1:N) by using the N receiving antennas, the error correction decoding unit 26 of the data reception device 2 multiplies the received sequence r(1:N) by an Hadamard matrix which is an orthogonal code to deform equation (61), as will be shown below.




  
    
      
        
          
        
        ⁢
        
          [
          
            Equation
            ⁢
            
              
            
            ⁢
            42
          
          ]
        
      
    
    
      
        
      
    
  
  
    
      
        
          
            r
            
              (
              
                1
                :
                N
              
              )
            
          
          ⁡
          
            [
            
              
                
                  
                    γ
                    
                      1
                      ,
                      1
                    
                  
                
                
                  
                    γ
                    
                      1
                      ,
                      2
                    
                  
                
                
                  ...
                
                
                  
                    γ
                    
                      1
                      ,
                      N
                    
                  
                
              
              
                
                  
                    γ
                    
                      2
                      ,
                      1
                    
                  
                
                
                  
                    γ
                    
                      2
                      ,
                      2
                    
                  
                
                
                  ...
                
                
                  
                    γ
                    
                      2
                      ,
                      N
                    
                  
                
              
              
                
                  ⋮
                
                
                  ⋮
                
                
                  ⋱
                
                
                  ⋮
                
              
              
                
                  
                    γ
                    
                      N
                      ,
                      1
                    
                  
                
                
                  
                    γ
                    
                      N
                      ,
                      2
                    
                  
                
                
                  ...
                
                
                  
                    γ
                    
                      N
                      ,
                      N
                    
                  
                
              
            
            ]
          
        
        =
        
          
            N
            ⁡
            
              [
              
                
                  
                    
                      
                        h
                        
                          1
                          ,
                          1
                        
                      
                      ⁢
                      
                        S
                        1
                      
                    
                  
                  
                    
                      
                        h
                        
                          1
                          ,
                          2
                        
                      
                      ⁢
                      
                        S
                        1
                      
                    
                  
                  
                    ...
                  
                  
                    
                      
                        h
                        
                          1
                          ,
                          N
                        
                      
                      ⁢
                      
                        S
                        1
                      
                    
                  
                
                
                  
                    
                      
                        h
                        
                          2
                          ,
                          1
                        
                      
                      ⁢
                      
                        S
                        2
                      
                    
                  
                  
                    
                      
                        h
                        
                          2
                          ,
                          2
                        
                      
                      ⁢
                      
                        S
                        2
                      
                    
                  
                  
                    ...
                  
                  
                    
                      
                        h
                        
                          2
                          ,
                          N
                        
                      
                      ⁢
                      
                        S
                        2
                      
                    
                  
                
                
                  
                    ⋮
                  
                  
                    ⋮
                  
                  
                    ⋮
                  
                  
                    ⋮
                  
                
                
                  
                    
                      
                        h
                        
                          N
                          ,
                          1
                        
                      
                      ⁢
                      
                        S
                        N
                      
                    
                  
                  
                    
                      
                        h
                        
                          N
                          ,
                          2
                        
                      
                      ⁢
                      
                        S
                        N
                      
                    
                  
                  
                    ...
                  
                  
                    
                      
                        h
                        
                          N
                          ,
                          N
                        
                      
                      ⁢
                      
                        S
                        N
                      
                    
                  
                
              
              ]
            
          
          +
          
             
            
              [
              
                
                  
                    
                      
                        
                          
                            
                              
                                γ
                                
                                  1
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                n
                                1
                                
                                  (
                                  1
                                  )
                                
                              
                            
                            +
                            
                              
                                γ
                                
                                  2
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                n
                                1
                                
                                  (
                                  2
                                  )
                                
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            ...
                            +
                            
                              
                                γ
                                
                                  N
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                n
                                1
                                
                                  (
                                  N
                                  )
                                
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              
                                γ
                                
                                  1
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                n
                                1
                                
                                  (
                                  1
                                  )
                                
                              
                            
                            +
                            
                              
                                γ
                                
                                  2
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                n
                                1
                                
                                  (
                                  2
                                  )
                                
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            ...
                            +
                            
                              
                                γ
                                
                                  N
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                n
                                1
                                
                                  (
                                  N
                                  )
                                
                              
                            
                          
                        
                      
                    
                  
                  
                    ...
                  
                  
                    
                      
                        
                          
                            
                              
                                γ
                                
                                  1
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                n
                                1
                                
                                  (
                                  1
                                  )
                                
                              
                            
                            +
                            
                              
                                γ
                                
                                  2
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                n
                                1
                                
                                  (
                                  2
                                  )
                                
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            ...
                            +
                            
                              
                                γ
                                
                                  N
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                n
                                1
                                
                                  (
                                  N
                                  )
                                
                              
                            
                          
                        
                      
                    
                  
                
                
                  
                    
                      
                        
                          
                            
                              
                                γ
                                
                                  1
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                n
                                2
                                
                                  (
                                  1
                                  )
                                
                              
                            
                            +
                            
                              
                                γ
                                
                                  2
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                n
                                2
                                
                                  (
                                  2
                                  )
                                
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            ...
                            +
                            
                              
                                γ
                                
                                  N
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                n
                                2
                                
                                  (
                                  N
                                  )
                                
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              
                                γ
                                
                                  1
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                n
                                2
                                
                                  (
                                  1
                                  )
                                
                              
                            
                            +
                            
                              
                                γ
                                
                                  2
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                n
                                2
                                
                                  (
                                  2
                                  )
                                
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            ...
                            +
                            
                              
                                γ
                                
                                  N
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                n
                                2
                                
                                  (
                                  N
                                  )
                                
                              
                            
                          
                        
                      
                    
                  
                  
                    ...
                  
                  
                    
                      
                        
                          
                            
                              
                                γ
                                
                                  1
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                n
                                2
                                
                                  (
                                  1
                                  )
                                
                              
                            
                            +
                            
                              
                                γ
                                
                                  2
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                n
                                2
                                
                                  (
                                  2
                                  )
                                
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            ...
                            +
                            
                              
                                γ
                                
                                  N
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                n
                                2
                                
                                  (
                                  N
                                  )
                                
                              
                            
                          
                        
                      
                    
                  
                
                
                  
                    ⋮
                  
                  
                    ⋮
                  
                  
                    ⋱
                  
                  
                    ⋮
                  
                
                
                  
                    
                      
                        
                          
                            
                              
                                γ
                                
                                  1
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                n
                                N
                                
                                  (
                                  1
                                  )
                                
                              
                            
                            +
                            
                              
                                γ
                                
                                  2
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                n
                                N
                                
                                  (
                                  2
                                  )
                                
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            ...
                            +
                            
                              
                                γ
                                
                                  N
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                n
                                N
                                
                                  (
                                  N
                                  )
                                
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            
                              
                                γ
                                
                                  1
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                n
                                N
                                
                                  (
                                  1
                                  )
                                
                              
                            
                            +
                            
                              
                                γ
                                
                                  2
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                n
                                N
                                
                                  (
                                  2
                                  )
                                
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            ...
                            +
                            
                              
                                γ
                                
                                  N
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                n
                                N
                                
                                  (
                                  N
                                  )
                                
                              
                            
                          
                        
                      
                    
                  
                  
                    ...
                  
                  
                    
                      
                        
                          
                            
                              
                                γ
                                
                                  1
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                n
                                N
                                
                                  (
                                  1
                                  )
                                
                              
                            
                            +
                            
                              
                                γ
                                
                                  2
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                n
                                N
                                
                                  (
                                  2
                                  )
                                
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            ...
                            +
                            
                              
                                γ
                                
                                  N
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                n
                                N
                                
                                  (
                                  N
                                  )
                                
                              
                            
                          
                        
                      
                    
                  
                
              
              ]
            
          
        
      
    
    
      
        (
        62
        )
      
    
  




The error correction decoding unit 26 of the data reception device 2 also extracts S1, S2, . . . , and SN which construct the symbols S of the codewords by arranging equation (62) to form equation (63) and then calculating equation (63).




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          43
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        
          
            
              
                
                  Nh
                  
                    1
                    ,
                    1
                  
                
                ⁢
                
                  S
                  1
                
                ⁢
                
                  h
                  
                    1
                    ,
                    1
                  
                  *
                
              
              +
              
                
                  Nh
                  
                    1
                    ,
                    2
                  
                
                ⁢
                
                  S
                  1
                
                ⁢
                
                  h
                  
                    1
                    ,
                    2
                  
                  *
                
              
              +
              ...
              +
              
                n
                1
                ′
              
            
            =
            
              
                
                  N
                  (
                  
                    
                      
                        
                        
                          h
                          
                            1
                            ,
                            1
                          
                        
                        
                      
                      2
                    
                    +
                    
                      
                        
                        
                          h
                          
                            1
                            ,
                            2
                          
                        
                        
                      
                      2
                    
                    +
                    ...
                  
                  ⁢
                  
                    
                  
                  )
                
                ·
                
                  S
                  1
                
              
              +
              
                n
                1
                ′
              
            
          
          ,
          
            

          
          ⁢
          
            
              
                
                  Nh
                  
                    2
                    ,
                    1
                  
                
                ⁢
                
                  S
                  2
                
                ⁢
                
                  h
                  
                    2
                    ,
                    1
                  
                  *
                
              
              +
              
                
                  Nh
                  
                    2
                    ,
                    2
                  
                
                ⁢
                
                  S
                  2
                
                ⁢
                
                  h
                  
                    2
                    ,
                    2
                  
                  *
                
              
              +
              ...
              +
              
                n
                2
                ′
              
            
            =
            
              
                
                  N
                  (
                  
                    
                      
                        
                        
                          h
                          
                            2
                            ,
                            1
                          
                        
                        
                      
                      2
                    
                    +
                    
                      
                        
                        
                          h
                          
                            2
                            ,
                            2
                          
                        
                        
                      
                      2
                    
                    +
                    ...
                  
                  ⁢
                  
                    
                  
                  )
                
                ·
                
                  S
                  2
                
              
              +
              
                n
                2
                ′
              
            
          
          ,
          ...
        
        ⁢
        
          

        
        ⁢
        ⋮
      
    
    
      
        (
        63
        )
      
    
  




where when n′1, n′2, . . . , n′N are defined as follows:





  
    [
    
      
        
          
            n
            
              1
              ,
              1
            
            ′
          
        
        
          
            n
            
              1
              ,
              2
            
            ′
          
        
        
          ...
        
        
          
            n
            
              1
              ,
              N
            
            ′
          
        
      
      
        
          
            n
            
              2
              ,
              1
            
            ′
          
        
        
          
            n
            
              2
              ,
              2
            
            ′
          
        
        
          ...
        
        
          
            n
            
              2
              ,
              N
            
            ′
          
        
      
      
        
          ⋮
        
        
          ⋮
        
        
          ⋱
        
        
          ⋮
        
      
      
        
          
            n
            
              N
              ,
              1
            
            ′
          
        
        
          
            n
            
              N
              ,
              2
            
            ′
          
        
        
          ...
        
        
          
            n
            
              N
              ,
              N
            
            ′
          
        
      
    
    ⁢
    
      
    
    ]
  
  =
  
     
    
      [
      
        
          
            
              
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
          
          
            ...
          
          
            
              
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
          
        
        
          
            
              
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
          
          
            ...
          
          
            
              
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
          
        
        
          
            ⋮
          
          
            ⋮
          
          
            ⋱
          
          
            ⋮
          
        
        
          
            
              
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
          
          
            ...
          
          
            
              
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                  
                
              
              
                
                  
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
          
        
      
      ]
    
  




they are expressed as follows:





  
    
      
        
          
            n
            1
            ′
          
          =
          
            
              
                h
                
                  1
                  ,
                  1
                
                *
              
              ⁢
              
                n
                
                  1
                  ,
                  1
                
                ′
              
            
            +
            
              
                h
                
                  2
                  ,
                  1
                
                *
              
              ⁢
              
                n
                
                  2
                  ,
                  1
                
                ′
              
            
            +
            ...
            +
            
              
                h
                
                  N
                  ,
                  1
                
                *
              
              ⁢
              
                n
                
                  N
                  ,
                  1
                
                ′
              
            
          
        
        ,
        
          

        
        ⁢
        
          
            n
            2
            ′
          
          =
          
            
              
                h
                
                  1
                  ,
                  2
                
                *
              
              ⁢
              
                n
                
                  1
                  ,
                  2
                
                ′
              
            
            +
            
              
                h
                
                  2
                  ,
                  2
                
                *
              
              ⁢
              
                n
                
                  2
                  ,
                  2
                
                ′
              
            
            +
            ...
            +
            
              
                h
                
                  N
                  ,
                  2
                
                *
              
              ⁢
              
                n
                
                  N
                  ,
                  2
                
                ′
              
            
          
        
        ,
        
          

        
        ⁢
        ⋮
      
    
    
      
        (
        64
        )
      
    
  




In this Embodiment 5, the case in which the error correction decoding unit 26 of the data reception device 2 extracts S1, S2, . . . , and SN which construct the symbols S of the codewords by arranging equation (62) to form equation (63), and calculating equation (63) is shown. As an alternative, the error correction decoding unit can extract S1, S2, . . . , and SN which construct the symbols S of the codewords by simplifying equation (63) into equation (65) and then calculating equation (65).




  
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          44
        
        ]
      
    
    
      
        
      
    
  
  
    
      
        
          
            
              
                
                  
                    
                      
                        
                          
                            Nh
                            
                              1
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            1
                          
                          ⁢
                          
                            h
                            
                              1
                              ,
                              1
                            
                            *
                          
                        
                        +
                        
                          
                            h
                            
                              1
                              ,
                              1
                            
                            *
                          
                          ⁢
                          
                            n
                            
                              1
                              ,
                              1
                            
                            ′
                          
                        
                      
                      =
                      
                        
                          
                            N
                            ⁡
                            
                              (
                              
                                
                                  
                                  
                                    h
                                    
                                      1
                                      ,
                                      1
                                    
                                  
                                  
                                
                                2
                              
                              )
                            
                          
                          ·
                          
                            S
                            1
                          
                        
                        +
                        
                          
                            h
                            
                              1
                              ,
                              1
                            
                            *
                          
                          ⁢
                          
                            n
                            
                              1
                              ,
                              1
                            
                            ′
                          
                        
                      
                    
                    ,
                  
                
              
              
                
                  
                    
                      
                        
                          
                            Nh
                            
                              2
                              ,
                              2
                            
                          
                          ⁢
                          
                            S
                            2
                          
                          ⁢
                          
                            h
                            
                              2
                              ,
                              2
                            
                            *
                          
                        
                        +
                        
                          
                            h
                            
                              2
                              ,
                              2
                            
                            *
                          
                          ⁢
                          
                            n
                            
                              2
                              ,
                              2
                            
                            ′
                          
                        
                      
                      =
                      
                        
                          
                            N
                            ⁡
                            
                              (
                              
                                
                                  
                                  
                                    h
                                    
                                      2
                                      ,
                                      2
                                    
                                  
                                  
                                
                                2
                              
                              )
                            
                          
                          ·
                          
                            S
                            2
                          
                        
                        +
                        
                          
                            h
                            
                              2
                              ,
                              2
                            
                            *
                          
                          ⁢
                          
                            n
                            
                              2
                              ,
                              2
                            
                            ′
                          
                        
                      
                    
                    ,
                  
                
              
            
          
        
        
          
            ⋮
          
        
      
    
    
      
        (
        65
        )
      
    
  




In above-mentioned Embodiments 1 to 5, the method of deforming the modulated waves of the codewords in the case of using HARQ-CC is shown. The same deformation can be carried out for one-time transmission when, for example, it can be presumed beforehand that a large interference wave occurs.
For example, according to equation (24) shown in Embodiment 1, three transmissions including two retransmissions are carried out in total. Instead of carrying out the three transmissions, a one-time transmission of the three symbols can be carried out.
More specifically, the three symbols which are currently transmitted in three steps according to the above equation can be transmitted at one time as follows.




  
    
      
        
          S
          =
          
            [
            
              
                
                  
                    S
                    1
                  
                
                
                  
                    S
                    1
                  
                
                
                  
                    S
                    1
                  
                
              
              
                
                  
                    S
                    2
                  
                
                
                  
                    
                      e
                      
                        
                          -
                          j2π
                        
                        ⁢
                        
                          1
                          3
                        
                      
                    
                    ·
                    
                      S
                      2
                    
                  
                
                
                  
                    
                      e
                      
                        
                          -
                          j2π
                        
                        ⁢
                        
                          2
                          3
                        
                      
                    
                    ·
                    
                      S
                      2
                    
                  
                
              
              
                
                  
                    S
                    3
                  
                
                
                  
                    
                      e
                      
                        
                          -
                          j2π
                        
                        ⁢
                        
                          2
                          3
                        
                      
                    
                    ·
                    
                      S
                      3
                    
                  
                
                
                  
                    
                      e
                      
                        
                          -
                          j2π
                        
                        ⁢
                        
                          1
                          3
                        
                      
                    
                    ·
                    
                      S
                      3
                    
                  
                
              
            
            ]
          
        
        ,
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          45
        
        ]
      
    
  




instead of





  
    
      
        
          
            S
            
              (
              1
              )
            
          
          =
          
            [
            
              
                
                  
                    S
                    1
                  
                
              
              
                
                  
                    S
                    2
                  
                
              
              
                
                  
                    S
                    3
                  
                
              
            
            ]
          
        
        ,
        
          
            S
            
              (
              2
              )
            
          
          =
          
            [
            
              
                
                  
                    S
                    1
                  
                
              
              
                
                  
                    
                      e
                      
                        
                          -
                          j2π
                        
                        ⁢
                        
                          1
                          3
                        
                      
                    
                    ·
                    
                      S
                      2
                    
                  
                
              
              
                
                  
                    
                      e
                      
                        
                          -
                          j2π
                        
                        ⁢
                        
                          2
                          3
                        
                      
                    
                    ·
                    
                      S
                      3
                    
                  
                
              
            
            ]
          
        
        ,
        
          
            S
            
              (
              3
              )
            
          
          =
          
            [
            
              
                
                  
                    S
                    1
                  
                
              
              
                
                  
                    
                      e
                      
                        
                          -
                          j2π
                        
                        ⁢
                        
                          2
                          3
                        
                      
                    
                    ·
                    
                      S
                      2
                    
                  
                
              
              
                
                  
                    
                      e
                      
                        
                          -
                          j2π
                        
                        ⁢
                        
                          1
                          3
                        
                      
                    
                    ·
                    
                      S
                      3
                    
                  
                
              
            
            ]
          
        
      
    
    
      
        (
        24
        )
      
    
  




In this case, by using this transmission symbol when the ratio of the interference wave is large, the interference wave can be easily removed through the one-time transmission.

This method can be similarly applied to each of Embodiments 2, 3, 4, and 5.
Embodiment 6
In above-mentioned Embodiments 1 to 5, the method (based on HARQ-CC) of, when the error correction decoding unit 26 of the data reception device 2 fails in the error correction decoding of the codeword, making the MIMO processing unit 15 of the data transmission device 1 deform the transmitted codeword according to the predetermined rule and transmit the deformed codeword is shown. As an alternative, the MIMO processing unit 15 of the data transmission device 1 can switch between transmission methods as follows.
More specifically, when the error correction decoding unit 26 of the data reception device 2 fails in the error correction decoding of the codeword, the MIMO processing unit 15 of the data transmission device 1 can use a method of transmitting additional parity information (a method using HARQ-IR) if the coding rate in the error correction encoding unit 11 is a high one between a first coding rate (e.g., a coding rate of about 1 to 2⁄3) and a second coding rate (e.g. , a coding rate of about 1⁄2 to 1⁄5), whereas the MIMO processing unit 15 of the data transmission device 1 can use a method of deforming the transmitted codeword and transmitting the transmitted codeword according to the predetermined rule (a method using HARQ-CC) if the coding rate in the error correction encoding unit 11 is a low one lower than the above-mentioned high coding rate.
Concretely, the MIMO processing unit does as follows.
Hereafter, it is assumed that the error correction coding unit 11 of the data transmission device 1 creates a codeword b=(b1, b2, . . . , bL) having a length L expressed by two elements {0, 1}.
It is also assumed that this codeword b is subjected to Mth-order QAM modulation by the modulating unit 12 of the data transmission device 1, and modulated symbols S=(S1, S2, . . . , SL/M) are created.
For example, QPSK is assumed to be 2nd-order QAM, and one modulated symbol is expressed by 2 bits in the codeword sequence, like in the case of (b1, b2)→S1.
Similarly, 16QAM is assumed to be a 4 th (24)-order QAM, and one modulated symbol is expressed by 4 bits in the codeword sequence, like in the case of (b1, b2, b3, b4)→S1.
Conventionally, the HARQ-CC is the method of allocating the symbols of this modulated symbol sequence to three antennas in order shown by, for example, the following equation in which the rows correspond the three antennas respectively, to transmit them,



  
    [
    
      Equation
      ⁢
      
        
      
      ⁢
      46
    
    ]
  




  
    
      
        
          S
          =
          
            [
            
              
                
                  
                    S
                    1
                  
                
                
                  
                    S
                    4
                  
                
                
                  ⋯
                
                
                  
                    S
                    
                      
                        L
                        /
                        M
                      
                      -
                      2
                    
                  
                
              
              
                
                  
                    S
                    2
                  
                
                
                  
                    S
                    5
                  
                
                
                  ⋯
                
                
                  
                    S
                    
                      
                        L
                        /
                        M
                      
                      -
                      1
                    
                  
                
              
              
                
                  
                    S
                    3
                  
                
                
                  
                    S
                    6
                  
                
                
                  ⋯
                
                
                  
                    S
                    
                      L
                      /
                      M
                    
                  
                
              
            
            ]
          
        
      
      
        
          (
          66
          )
        
      
    
  



and, when the receive side fails to receive the modulated symbols during one transmission of them, retransmitting the modulated symbols in the same order.

Furthermore, assuming that in the case of using HARQ-IR, modulated symbols which are transmitted during a first-time transmission, a second-time transmission, and . . . are expressed as S(1), S(2), and . . . , and the modulated symbols of one codeword b=(b1, b2, . . . , bL) can be transmitted during three transmissions, they are transmitted according to the following rule.



  
    [
    
      Equation
      ⁢
      
        
      
      ⁢
      47
    
    ]
  




  
    
      
        
          
            
              S
              
                (
                1
                )
              
            
            =
            
              [
              
                
                  
                    
                      S
                      1
                    
                  
                  
                    
                      S
                      4
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        -
                        2
                      
                    
                  
                
                
                  
                    
                      S
                      2
                    
                  
                  
                    
                      S
                      5
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        -
                        1
                      
                    
                  
                
                
                  
                    
                      S
                      3
                    
                  
                  
                    
                      S
                      6
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        L
                        /
                        
                          (
                          
                            3
                            ⁢
                            M
                          
                          )
                        
                      
                    
                  
                
              
              ]
            
          
          ,
          
            

          
          ⁢
          
            
              S
              
                (
                2
                )
              
            
            =
            
              [
              
                
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        +
                        1
                      
                    
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        +
                        4
                      
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        
                          2
                          ⁢
                          
                            L
                            /
                            
                              (
                              
                                3
                                ⁢
                                M
                              
                              )
                            
                          
                        
                        -
                        2
                      
                    
                  
                
                
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        +
                        2
                      
                    
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        +
                        5
                      
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        
                          2
                          ⁢
                          
                            L
                            /
                            
                              (
                              
                                3
                                ⁢
                                M
                              
                              )
                            
                          
                        
                        -
                        1
                      
                    
                  
                
                
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        +
                        3
                      
                    
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        +
                        6
                      
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        2
                        ⁢
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                      
                    
                  
                
              
              ]
            
          
          ,
          
            

          
          ⁢
          
            
              S
              
                (
                3
                )
              
            
            =
            
              [
              
                
                  
                    
                      S
                      
                        
                          2
                          ⁢
                          
                            L
                            /
                            
                              (
                              
                                3
                                ⁢
                                M
                              
                              )
                            
                          
                        
                        +
                        1
                      
                    
                  
                  
                    
                      S
                      
                        
                          2
                          ⁢
                          
                            L
                            /
                            
                              (
                              
                                3
                                ⁢
                                M
                              
                              )
                            
                          
                        
                        +
                        4
                      
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          M
                        
                        -
                        2
                      
                    
                  
                
                
                  
                    
                      S
                      
                        
                          2
                          ⁢
                          
                            L
                            /
                            
                              (
                              
                                3
                                ⁢
                                M
                              
                              )
                            
                          
                        
                        +
                        2
                      
                    
                  
                  
                    
                      S
                      
                        
                          2
                          ⁢
                          
                            L
                            /
                            
                              (
                              
                                3
                                ⁢
                                M
                              
                              )
                            
                          
                        
                        +
                        5
                      
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          M
                        
                        -
                        1
                      
                    
                  
                
                
                  
                    
                      S
                      
                        
                          2
                          ⁢
                          
                            L
                            /
                            
                              (
                              
                                3
                                ⁢
                                M
                              
                              )
                            
                          
                        
                        +
                        3
                      
                    
                  
                  
                    
                      S
                      
                        
                          2
                          ⁢
                          
                            L
                            /
                            
                              (
                              
                                3
                                ⁢
                                M
                              
                              )
                            
                          
                        
                        +
                        6
                      
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          3
                        
                        ⁢
                        M
                      
                    
                  
                
              
              ]
            
          
        
      
      
        
          (
          67
          )
        
      
    
  



After this one codeword has been retransmitted a number of times, the data transmission device can switch to HARQ-CC and implement very long HARQ theoretically according to the following rule.



  
    [
    
      Equation
      ⁢
      
        
      
      ⁢
      48
    
    ]
  




  
    
      
        
          
            
              S
              
                (
                4
                )
              
            
            =
            
              [
              
                
                  
                    
                      S
                      1
                    
                  
                  
                    
                      S
                      4
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        -
                        2
                      
                    
                  
                
                
                  
                    
                      S
                      2
                    
                  
                  
                    
                      S
                      5
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        -
                        1
                      
                    
                  
                
                
                  
                    
                      S
                      3
                    
                  
                  
                    
                      S
                      6
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        L
                        /
                        
                          (
                          
                            3
                            ⁢
                            M
                          
                          )
                        
                      
                    
                  
                
              
              ]
            
          
          ,
          
            

          
          ⁢
          
            
              S
              
                (
                5
                )
              
            
            =
            
              [
              
                
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        +
                        1
                      
                    
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        +
                        4
                      
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        
                          2
                          ⁢
                          
                            L
                            /
                            
                              (
                              
                                3
                                ⁢
                                M
                              
                              )
                            
                          
                        
                        -
                        2
                      
                    
                  
                
                
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        +
                        2
                      
                    
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        +
                        5
                      
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        
                          2
                          ⁢
                          
                            L
                            /
                            
                              (
                              
                                3
                                ⁢
                                M
                              
                              )
                            
                          
                        
                        -
                        1
                      
                    
                  
                
                
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        +
                        3
                      
                    
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        +
                        6
                      
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        2
                        ⁢
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                      
                    
                  
                
              
              ]
            
          
          ,
          
            

          
          ⁢
          
            
              S
              
                (
                6
                )
              
            
            =
            
              [
              
                
                  
                    
                      S
                      
                        
                          2
                          ⁢
                          
                            L
                            /
                            
                              (
                              
                                3
                                ⁢
                                M
                              
                              )
                            
                          
                        
                        +
                        1
                      
                    
                  
                  
                    
                      S
                      
                        
                          2
                          ⁢
                          
                            L
                            /
                            
                              (
                              
                                3
                                ⁢
                                M
                              
                              )
                            
                          
                        
                        +
                        4
                      
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          M
                        
                        -
                        2
                      
                    
                  
                
                
                  
                    
                      S
                      
                        
                          2
                          ⁢
                          
                            L
                            /
                            
                              (
                              
                                3
                                ⁢
                                M
                              
                              )
                            
                          
                        
                        +
                        2
                      
                    
                  
                  
                    
                      S
                      
                        
                          2
                          ⁢
                          
                            L
                            /
                            
                              (
                              
                                3
                                ⁢
                                M
                              
                              )
                            
                          
                        
                        +
                        5
                      
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          M
                        
                        -
                        1
                      
                    
                  
                
                
                  
                    
                      S
                      
                        
                          2
                          ⁢
                          
                            L
                            /
                            
                              (
                              
                                3
                                ⁢
                                M
                              
                              )
                            
                          
                        
                        +
                        3
                      
                    
                  
                  
                    
                      S
                      
                        
                          2
                          ⁢
                          
                            L
                            /
                            
                              (
                              
                                3
                                ⁢
                                M
                              
                              )
                            
                          
                        
                        +
                        6
                      
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          3
                        
                        ⁢
                        M
                      
                    
                  
                
              
              ]
            
          
          ,
          
            

          
          ⁢
          
            
              S
              
                (
                7
                )
              
            
            =
            
              [
              
                
                  
                    
                      S
                      1
                    
                  
                  
                    
                      S
                      4
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        -
                        2
                      
                    
                  
                
                
                  
                    
                      S
                      2
                    
                  
                  
                    
                      S
                      5
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        
                          L
                          /
                          
                            (
                            
                              3
                              ⁢
                              M
                            
                            )
                          
                        
                        -
                        1
                      
                    
                  
                
                
                  
                    
                      S
                      3
                    
                  
                  
                    
                      S
                      6
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        L
                        /
                        
                          (
                          
                            3
                            ⁢
                            M
                          
                          )
                        
                      
                    
                  
                
              
              ]
            
          
          ,
          ...
        
      
      
        
          (
          68
          )
        
      
    
  



During these transmissions of modulated symbols, there occur situations in which the same combination of some symbols are transmitted repeatedly via the same antennas, as shown in, for example, the following equation, in the case of using simple HARQ-CC and also in the case of using (HARQ-IR+HARQ-CC).




  
    
      
        [
        
          
            
              
                S
                1
              
            
          
          
            
              
                S
                2
              
            
          
          
            
              
                S
                3
              
            
          
        
        ]
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          49
        
        ]
      
    
  




In above-mentioned Embodiments 1 to 6, the example in which no special process is performed on the channel matrix H is shown, though there is a case in which a weight matrix W on which a spatial filtering process (according to a Zero Forcing algorithm or an MMSE (minimum mean squared error) algorithm) is used in order to further improve the data separation performance of each antenna. Even if this weight matrix W is multiplied by the channel matrix H and the channel matrix H in accordance with above-mentioned Embodiments 1 to 6 is replaced by WTH (T is a transposed matrix), and the processing is then carried out, the same advantages are provided.
INDUSTRIAL APPLICABILITY
As mentioned above, when the error correction decoding means of the data reception device fails to carry out the error correction decoding of codewords, the codeword transmitting means of the data transmission device deforms the transmitted codewords according to a predetermined rule, and transmits the deformed codewords, and the error correction decoding means of the data reception device reproduces the data by using the deformed codewords. As a result, the data transmission device, the data reception device, and the wireless communications system in accordance with the present invention can reduce not only the noise but the interference wave components, and improve the success rates of the demodulation and error correction decoding greatly. Therefore, the data transmission device, the data reception device, and the wireless communications system in accordance with the present invention are suitable for use as a data transmission device that transmits a plurality of codewords simultaneously by using a plurality of antennas, a data reception device that receives a plurality of codewords simultaneously by using a plurality of antennas, and a wireless communications system consisting of the data transmission device and the data reception device respectively.

## Claims

1. A data transmission device comprising:
an error correction encoding unit for carrying out error correction encoding of data which is a transmission object to create a codeword;
a modulation unit for modulating the codeword created by said error correction encoding means; and
a codeword transmitting unit for dividing the codeword modulated by said modulation unit into a plurality of codewords, and for simultaneously transmitting the plurality of codewords into which the codeword is divided by using a plurality of antennas, wherein
when a data reception device fails in error correction decoding of the codewords, said codeword transmitting unit deforms the transmitted codewords according to a predetermined rule and transmits said deformed codewords, and
when the data reception device fails in the error correction decoding of the codewords, said codeword transmitting unit transmits additional parity information if a coding rate in the error correction encoding unit is the higher of a first coding rate and a second coding rate, or deforms the transmitted codewords according to the predetermined rule and transmits said deformed codewords if the coding rate in the error correction encoding unit is the lower of said first coding rate and said second coding rate.

2. The data transmission device according to claim 1, wherein
when the data reception device fails in the error correction decoding of the codewords, the codeword transmitting unit deforms the transmitted codewords by using an orthogonal sequence.

3. A data reception device comprising:
a codeword receiving unit for receiving a plurality of codewords simultaneously transmitted from a data transmission device by using a plurality of antennas;
a demodulating unit for unifying the plurality of codewords received by said codeword receiving unit into a codeword, and for demodulating to the codeword into which the plurality of codewords are unified; and
an error correction decoding unit for carrying out error correction decoding of the codeword demodulated by said demodulating unit to reproduce data, wherein
when said error correction decoding unit fails in the error correction decoding of the codeword, and the transmitted codewords are deformed according to a predetermined rule and the deformed codewords are transmitted to the data reception device by said data transmission device, said error correction decoding unit reproduces the data by using the deformed codewords, and
when the error correction decoding unit fails in the error correction decoding of the codeword, the codeword receiving unit receives the deformed codewords from the data transmission device by using an orthogonal sequence.

4. A wireless communications system comprising:
a data transmission device comprising:
an error correction encoding unit for carrying out error correction encoding of data which is a transmission object to create a codeword,
a modulation unit for modulating the codeword created by said error correction encoding unit, and
a codeword transmitting unit for dividing the codeword modulated by said modulation unit into a plurality of codewords, and for simultaneously transmitting the plurality of codewords into which the codeword is divided by using a plurality of antennas; and

a data reception device comprising:
a codeword receiving unit for receiving the plurality of codewords simultaneously transmitted from said data transmission device by using a plurality of antennas,
a demodulating unit for unifying the plurality of codewords received by said codeword receiving unit into a codeword, and for demodulating the codeword into which the plurality of codewords are unified, and
an error correction decoding unit for carrying out error correction decoding of the codeword demodulated by said demodulating unit to reproduce data, wherein

when the error correction decoding unit of said data reception device fails in the error correction decoding of the codeword, the codeword transmitting unit of said data transmission device deforms the transmitted codewords according to a predetermined rule, and transmits the deformed codewords, and the error correction decoding unit of said data reception device reproduces the data by using the deformed codewords, and
when the error correction decoding unit of the data reception device fails in the error correction decoding of the codeword, the codeword transmitting unit of the data transmission device transmits additional parity information if a coding rate in the error correction encoding unit is the higher of a first coding rate and a second coding rate, or deforms the transmitted codewords according to a predetermined rule and transmits said codewords if the coding rate in the error correction encoding unit is the lower of said first coding rate and said second coding rate.

5. The wireless communications system according to claim 4, wherein
when the error correction decoding unit of the data reception device fails in the error correction decoding of the codeword, the codeword transmitting unit of the data transmission device deforms the transmitted codewords by using an orthogonal sequence.

6. The wireless communications system according to claim 5, wherein
in a case in which the codewords are transmitted via N communication channels and interference occurs among the N communication channels, assuming a channel matrix H and expressing symbols of the codewords transmitted from the codeword transmitting unit of the data transmission device and symbols of the codewords received by the codeword receiving unit of the data reception device as S and r respectively, when the error correction decoding unit of the data reception device fails in the error correction decoding of the codeword, and the codeword transmitting unit of said data transmission device then deforms said symbols S of the codewords and transmits a sequence S(1:N) of symbols S(j), the codeword receiving unit of said data reception device receives a sequence r(1:N), and the error correction decoding unit of said data reception device extracts S1, S2, ..., and SN which construct the symbols S of the codewords from said sequence r(1:N), such that the following equations are satisfied:




  
    [
    
      Equation
      ⁢
      
        
      
      ⁢
      1
    
    ]
  




  
    
      
        
          H
          =
          
            [
            
              
                
                  
                    h
                    
                      1
                      ,
                      1
                    
                  
                
                
                  
                    h
                    
                      1
                      ,
                      2
                    
                  
                
                
                  ⋯
                
                
                  ⋯
                
                
                  
                    h
                    
                      1
                      ,
                      N
                    
                  
                
              
              
                
                  
                    h
                    
                      2
                      ,
                      1
                    
                  
                
                
                  ⋱
                
                
                  ⋱
                
                
                  ⋱
                
                
                  ⋮
                
              
              
                
                  ⋮
                
                
                  ⋱
                
                
                  
                    h
                    
                      i
                      ,
                      j
                    
                  
                
                
                  ⋱
                
                
                  ⋮
                
              
              
                
                  ⋮
                
                
                  ⋱
                
                
                  ⋱
                
                
                  ⋱
                
                
                  ⋮
                
              
              
                
                  
                    h
                    
                      N
                      ,
                      1
                    
                  
                
                
                  ⋯
                
                
                  ⋯
                
                
                  ⋯
                
                
                  
                    h
                    
                      N
                      ,
                      N
                    
                  
                
              
            
            ]
          
        
      
      
        
          (
          1
          )
        
      
    
  



where hi,j is a communication channel response from j-th transmitting antenna to i-th receiving antenna




  
    
      
        
          
        
        ⁢
        
          S
          ⁡
          
            [
            
              
                
                  
                    S
                    1
                  
                
              
              
                
                  
                    S
                    2
                  
                
              
              
                
                  ⋮
                
              
              
                
                  
                    S
                    N
                  
                
              
            
            ]
          
        
      
    
    
      
        (
        2
        )
      
    
  
  
    
      
        
          
        
        ⁢
        
          r
          =
          
            
              HS
              +
              n
            
            =
            
              
                [
                
                  
                    
                      
                        h
                        
                          1
                          ,
                          1
                        
                      
                    
                    
                      
                        h
                        
                          1
                          ,
                          2
                        
                      
                    
                    
                      ⋯
                    
                    
                      ⋯
                    
                    
                      
                        h
                        
                          1
                          ,
                          N
                        
                      
                    
                  
                  
                    
                      
                        h
                        
                          2
                          ,
                          1
                        
                      
                    
                    
                      ⋱
                    
                    
                      ⋱
                    
                    
                      ⋱
                    
                    
                      ⋮
                    
                  
                  
                    
                      ⋮
                    
                    
                      ⋱
                    
                    
                      
                        h
                        
                          i
                          ,
                          j
                        
                      
                    
                    
                      ⋱
                    
                    
                      ⋮
                    
                  
                  
                    
                      ⋮
                    
                    
                      ⋱
                    
                    
                      ⋱
                    
                    
                      ⋱
                    
                    
                      ⋮
                    
                  
                  
                    
                      
                        h
                        
                          N
                          ,
                          1
                        
                      
                    
                    
                      ⋯
                    
                    
                      ⋯
                    
                    
                      ⋯
                    
                    
                      
                        h
                        
                          N
                          ,
                          N
                        
                      
                    
                  
                
                ]
              
              ⁢
              
                 
                
                  
                    
                      [
                      
                        
                          
                            
                              S
                              1
                            
                          
                        
                        
                          
                            
                              S
                              2
                            
                          
                        
                        
                          
                            ⋮
                          
                        
                        
                          
                            
                              S
                              N
                            
                          
                        
                      
                      ]
                    
                    +
                    
                      [
                      
                        
                          
                            
                              n
                              1
                            
                          
                        
                        
                          
                            
                              n
                              2
                            
                          
                        
                        
                          
                            ⋮
                          
                        
                        
                          
                            
                              n
                              N
                            
                          
                        
                      
                      ]
                    
                  
                  =
                  
                    
                      [
                      
                        
                          
                            
                              
                                
                                  h
                                  
                                    1
                                    ,
                                    1
                                  
                                
                                ⁢
                                
                                  S
                                  1
                                
                              
                              +
                              
                                
                                  h
                                  
                                    1
                                    ,
                                    2
                                  
                                
                                ⁢
                                
                                  S
                                  2
                                
                              
                              +
                              ...
                              +
                              
                                
                                  h
                                  
                                    1
                                    ,
                                    N
                                  
                                
                                ⁢
                                
                                  S
                                  N
                                
                              
                            
                          
                        
                        
                          
                            
                              
                                
                                  h
                                  
                                    2
                                    ,
                                    1
                                  
                                
                                ⁢
                                
                                  S
                                  1
                                
                              
                              +
                              
                                
                                  h
                                  
                                    2
                                    ,
                                    2
                                  
                                
                                ⁢
                                
                                  S
                                  2
                                
                              
                              +
                              ...
                              +
                              
                                
                                  h
                                  
                                    2
                                    ,
                                    N
                                  
                                
                                ⁢
                                
                                  S
                                  N
                                
                              
                            
                          
                        
                        
                          
                            ⋮
                          
                        
                        
                          
                            
                              
                                
                                  h
                                  
                                    N
                                    ,
                                    1
                                  
                                
                                ⁢
                                
                                  S
                                  1
                                
                              
                              +
                              
                                
                                  h
                                  
                                    N
                                    ,
                                    2
                                  
                                
                                ⁢
                                
                                  S
                                  2
                                
                              
                              +
                              ...
                              +
                              
                                
                                  h
                                  
                                    N
                                    ,
                                    N
                                  
                                
                                ⁢
                                
                                  S
                                  N
                                
                              
                            
                          
                        
                      
                      ]
                    
                    +
                    
                      [
                      
                        
                          
                            
                              n
                              1
                            
                          
                        
                        
                          
                            
                              n
                              2
                            
                          
                        
                        
                          
                            ⋮
                          
                        
                        
                          
                            
                              n
                              N
                            
                          
                        
                      
                      ]
                    
                  
                
              
            
          
        
      
    
    
      
        (
        3
        )
      
    
  
  
    
      
        
          
        
        ⁢
        
          
            S
            
              (
              
                1
                :
                N
              
              )
            
          
          =
          
            
              [
              
                
                  
                    
                      S
                      
                        (
                        1
                        )
                      
                    
                  
                  
                    
                      S
                      
                        (
                        2
                        )
                      
                    
                  
                  
                    ⋯
                  
                  
                    
                      S
                      
                        (
                        N
                        )
                      
                    
                  
                
              
              ]
            
            =
            
               
              
                
                  [
                  
                    
                      
                        
                          
                            α
                            0
                          
                          ⁢
                          
                            S
                            1
                          
                        
                      
                      
                        
                          
                            α
                            0
                          
                          ⁢
                          
                            S
                            1
                          
                        
                      
                      
                        
                          
                            α
                            0
                          
                          ⁢
                          
                            S
                            1
                          
                        
                      
                      
                        ⋯
                      
                      
                        
                          
                            α
                            0
                          
                          ⁢
                          
                            S
                            1
                          
                        
                      
                      
                        
                          
                            α
                            0
                          
                          ⁢
                          
                            S
                            1
                          
                        
                      
                    
                    
                      
                        
                          
                            α
                            0
                          
                          ⁢
                          
                            S
                            2
                          
                        
                      
                      
                        
                          
                            α
                            1
                          
                          ⁢
                          
                            S
                            2
                          
                        
                      
                      
                        
                          
                            α
                            2
                          
                          ⁢
                          
                            S
                            2
                          
                        
                      
                      
                        ⋯
                      
                      
                        
                          
                            α
                            
                              N
                              -
                              2
                            
                          
                          ⁢
                          
                            S
                            2
                          
                        
                      
                      
                        
                          
                            α
                            
                              N
                              -
                              1
                            
                          
                          ⁢
                          
                            S
                            2
                          
                        
                      
                    
                    
                      
                        
                          
                            α
                            0
                          
                          ⁢
                          
                            S
                            3
                          
                        
                      
                      
                        
                          
                            α
                            2
                          
                          ⁢
                          
                            S
                            3
                          
                        
                      
                      
                        
                          
                            α
                            3
                          
                          ⁢
                          
                            S
                            3
                          
                        
                      
                      
                        ⋯
                      
                      
                        
                          
                            α
                            
                              N
                              -
                              1
                            
                          
                          ⁢
                          
                            S
                            3
                          
                        
                      
                      
                        
                          
                            α
                            1
                          
                          ⁢
                          
                            S
                            3
                          
                        
                      
                    
                    
                      
                        ⋮
                      
                      
                        ⋮
                      
                      
                        ⋮
                      
                      
                        ⋱
                      
                      
                        ⋮
                      
                      
                        ⋮
                      
                    
                    
                      
                        
                          
                            α
                            0
                          
                          ⁢
                          
                            S
                            
                              N
                              -
                              1
                            
                          
                        
                      
                      
                        
                          
                            α
                            
                              N
                              -
                              2
                            
                          
                          ⁢
                          
                            S
                            
                              N
                              -
                              1
                            
                          
                        
                      
                      
                        
                          
                            α
                            
                              N
                              -
                              1
                            
                          
                          ⁢
                          
                            S
                            
                              N
                              -
                              1
                            
                          
                        
                      
                      
                        ⋯
                      
                      
                        
                          
                            α
                            
                              N
                              -
                              4
                            
                          
                          ⁢
                          
                            S
                            
                              N
                              -
                              1
                            
                          
                        
                      
                      
                        
                          
                            α
                            
                              N
                              -
                              3
                            
                          
                          ⁢
                          
                            S
                            
                              N
                              -
                              1
                            
                          
                        
                      
                    
                    
                      
                        
                          
                            α
                            0
                          
                          ⁢
                          
                            S
                            N
                          
                        
                      
                      
                        
                          
                            α
                            
                              N
                              -
                              1
                            
                          
                          ⁢
                          
                            S
                            N
                          
                        
                      
                      
                        
                          
                            α
                            1
                          
                          ⁢
                          
                            S
                            N
                          
                        
                      
                      
                        ⋯
                      
                      
                        
                          
                            α
                            
                              N
                              -
                              3
                            
                          
                          ⁢
                          
                            S
                            N
                          
                        
                      
                      
                        
                          
                            α
                            
                              N
                              -
                              2
                            
                          
                          ⁢
                          
                            S
                            N
                          
                        
                      
                    
                  
                  ]
                
                ,
                
                  

                
                ⁢
                
                  
                
                ⁢
                
                  [
                  
                    Equation
                    ⁢
                    
                      
                    
                    ⁢
                    2
                  
                  ]
                
              
            
          
        
      
    
    
      
        (
        4
        )
      
    
  
  
    
      
        
          
        
        ⁢
        
          
            
              α
              i
            
            =
            
              exp
              ⁡
              
                (
                
                  
                    -
                    j2π
                  
                  ·
                  
                    i
                    /
                    N
                  
                
                )
              
            
          
          ⁢
          
            

          
          ⁢
          
            
              r
              
                (
                
                  1
                  :
                  N
                
                )
              
            
            =
            
              
                
                  HS
                  
                    (
                    
                      1
                      :
                      N
                    
                    )
                  
                
                +
                
                  n
                  
                    (
                    
                      1
                      :
                      N
                    
                    )
                  
                
              
              =
              
                 
                
                  
                    [
                    
                      
                        
                          
                            
                              
                                h
                                
                                  1
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                α
                                0
                              
                              ⁢
                              
                                S
                                1
                              
                            
                            +
                            
                              
                                h
                                
                                  1
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                α
                                0
                              
                              ⁢
                              
                                S
                                2
                              
                            
                            +
                            ...
                            +
                            
                              
                                h
                                
                                  1
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                α
                                0
                              
                              ⁢
                              
                                S
                                N
                              
                            
                          
                        
                        
                          ⋯
                        
                        
                          ⋯
                        
                        
                          
                            
                              
                                h
                                
                                  1
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                α
                                0
                              
                              ⁢
                              
                                S
                                1
                              
                            
                            +
                            
                              
                                h
                                
                                  1
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                α
                                
                                  N
                                  -
                                  1
                                
                              
                              ⁢
                              
                                S
                                2
                              
                            
                            +
                            
                              
                                h
                                
                                  1
                                  ,
                                  3
                                
                              
                              ⁢
                              
                                α
                                
                                  N
                                  -
                                  1
                                
                              
                              ⁢
                              
                                S
                                2
                              
                            
                            +
                            ...
                            +
                            
                              
                                h
                                
                                  1
                                  ,
                                  
                                    N
                                    -
                                    1
                                  
                                
                              
                              ⁢
                              
                                α
                                
                                  N
                                  -
                                  3
                                
                              
                              ⁢
                              
                                S
                                
                                  N
                                  -
                                  1
                                
                              
                            
                            +
                            
                              
                                h
                                
                                  1
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                α
                                
                                  N
                                  -
                                  2
                                
                              
                              ⁢
                              
                                S
                                N
                              
                            
                          
                        
                      
                      
                        
                          
                            
                              
                                h
                                
                                  2
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                α
                                0
                              
                              ⁢
                              
                                S
                                1
                              
                            
                            +
                            
                              
                                h
                                
                                  2
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                α
                                0
                              
                              ⁢
                              
                                S
                                2
                              
                            
                            +
                            ...
                            +
                            
                              
                                h
                                
                                  2
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                α
                                0
                              
                              ⁢
                              
                                S
                                N
                              
                            
                          
                        
                        
                          ⋯
                        
                        
                          ⋯
                        
                        
                          
                            
                              
                                h
                                
                                  2
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                α
                                0
                              
                              ⁢
                              
                                S
                                1
                              
                            
                            +
                            
                              
                                h
                                
                                  2
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                α
                                
                                  N
                                  -
                                  1
                                
                              
                              ⁢
                              
                                S
                                2
                              
                            
                            +
                            
                              
                                h
                                
                                  2
                                  ,
                                  3
                                
                              
                              ⁢
                              
                                α
                                
                                  N
                                  -
                                  1
                                
                              
                              ⁢
                              
                                S
                                2
                              
                            
                            +
                            ...
                            +
                            
                              
                                h
                                
                                  2
                                  ,
                                  
                                    N
                                    -
                                    1
                                  
                                
                              
                              ⁢
                              
                                α
                                
                                  N
                                  -
                                  3
                                
                              
                              ⁢
                              
                                S
                                
                                  N
                                  -
                                  1
                                
                              
                            
                            +
                            
                              
                                h
                                
                                  2
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                α
                                
                                  N
                                  -
                                  2
                                
                              
                              ⁢
                              
                                S
                                N
                              
                            
                          
                        
                      
                      
                        
                          ⋮
                        
                        
                          ⋮
                        
                        
                          ⋮
                        
                        
                          ⋮
                        
                      
                      
                        
                          
                            
                              
                                h
                                
                                  N
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                α
                                0
                              
                              ⁢
                              
                                S
                                1
                              
                            
                            +
                            
                              
                                h
                                
                                  N
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                α
                                0
                              
                              ⁢
                              
                                S
                                2
                              
                            
                            +
                            ...
                            +
                            
                              
                                h
                                
                                  N
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                α
                                0
                              
                              ⁢
                              
                                S
                                N
                              
                            
                          
                        
                        
                          ⋯
                        
                        
                          ⋯
                        
                        
                          
                            
                              
                                h
                                
                                  N
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                α
                                0
                              
                              ⁢
                              
                                S
                                1
                              
                            
                            +
                            
                              
                                h
                                
                                  N
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                α
                                
                                  N
                                  -
                                  1
                                
                              
                              ⁢
                              
                                S
                                2
                              
                            
                            +
                            
                              
                                h
                                
                                  N
                                  ,
                                  3
                                
                              
                              ⁢
                              
                                α
                                
                                  N
                                  -
                                  1
                                
                              
                              ⁢
                              
                                S
                                2
                              
                            
                            +
                            ...
                            +
                            
                              
                                h
                                
                                  N
                                  ,
                                  
                                    N
                                    -
                                    1
                                  
                                
                              
                              ⁢
                              
                                α
                                
                                  N
                                  -
                                  3
                                
                              
                              ⁢
                              
                                S
                                
                                  N
                                  -
                                  1
                                
                              
                            
                            +
                            
                              
                                h
                                
                                  N
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                α
                                
                                  N
                                  -
                                  2
                                
                              
                              ⁢
                              
                                S
                                N
                              
                            
                          
                        
                      
                    
                    ]
                  
                  +
                  
                     
                    
                      [
                      
                        
                          
                            
                              n
                              1
                              
                                (
                                1
                                )
                              
                            
                          
                          
                            
                              n
                              1
                              
                                (
                                2
                                )
                              
                            
                          
                          
                            ⋯
                          
                          
                            
                              n
                              1
                              
                                (
                                N
                                )
                              
                            
                          
                        
                        
                          
                            
                              n
                              2
                              
                                (
                                1
                                )
                              
                            
                          
                          
                            
                              n
                              2
                              
                                (
                                2
                                )
                              
                            
                          
                          
                            ⋯
                          
                          
                            
                              n
                              2
                              
                                (
                                N
                                )
                              
                            
                          
                        
                        
                          
                            ⋮
                          
                          
                            ⋮
                          
                          
                            ⋱
                          
                          
                            ⋮
                          
                        
                        
                          
                            
                              n
                              N
                              
                                (
                                1
                                )
                              
                            
                          
                          
                            
                              n
                              N
                              
                                (
                                2
                                )
                              
                            
                          
                          
                            ⋯
                          
                          
                            
                              n
                              N
                              
                                (
                                N
                                )
                              
                            
                          
                        
                      
                      ]
                    
                  
                
              
            
          
        
      
    
    
      
        (
        5
        )
      
    
  
  
    
      
        
          
            r
            
              (
              
                1
                :
                N
              
              )
            
          
          ⁡
          
            [
            
              
                
                  
                    α
                    0
                  
                
                
                  
                    α
                    0
                  
                
                
                  
                    α
                    0
                  
                
                
                  ⋯
                
                
                  
                    α
                    0
                  
                
                
                  
                    α
                    0
                  
                
              
              
                
                  
                    α
                    0
                  
                
                
                  
                    α
                    
                      -
                      1
                    
                  
                
                
                  
                    α
                    
                      -
                      2
                    
                  
                
                
                  ⋯
                
                
                  
                    α
                    
                      -
                      
                        (
                        
                          N
                          -
                          2
                        
                        )
                      
                    
                  
                
                
                  
                    α
                    
                      -
                      
                        (
                        
                          N
                          -
                          1
                        
                        )
                      
                    
                  
                
              
              
                
                  
                    α
                    0
                  
                
                
                  
                    α
                    
                      -
                      2
                    
                  
                
                
                  
                    α
                    
                      -
                      3
                    
                  
                
                
                  ⋯
                
                
                  
                    α
                    
                      -
                      
                        (
                        
                          N
                          -
                          1
                        
                        )
                      
                    
                  
                
                
                  
                    α
                    
                      -
                      1
                    
                  
                
              
              
                
                  ⋮
                
                
                  ⋮
                
                
                  ⋮
                
                
                  ⋱
                
                
                  ⋮
                
                
                  ⋮
                
              
              
                
                  
                    α
                    0
                  
                
                
                  
                    α
                    
                      -
                      
                        (
                        
                          N
                          -
                          2
                        
                        )
                      
                    
                  
                
                
                  
                    α
                    
                      -
                      
                        (
                        
                          N
                          -
                          1
                        
                        )
                      
                    
                  
                
                
                  ⋯
                
                
                  
                    α
                    
                      -
                      
                        (
                        
                          N
                          -
                          4
                        
                        )
                      
                    
                  
                
                
                  
                    α
                    
                      -
                      
                        (
                        
                          N
                          -
                          3
                        
                        )
                      
                    
                  
                
              
              
                
                  
                    α
                    0
                  
                
                
                  
                    α
                    
                      -
                      
                        (
                        
                          N
                          -
                          1
                        
                        )
                      
                    
                  
                
                
                  
                    α
                    
                      -
                      1
                    
                  
                
                
                  ⋯
                
                
                  
                    α
                    
                      -
                      
                        (
                        
                          N
                          -
                          3
                        
                        )
                      
                    
                  
                
                
                  
                    α
                    
                      -
                      
                        (
                        
                          N
                          -
                          2
                        
                        )
                      
                    
                  
                
              
            
            ]
          
        
        =
        
           
          
            
              N
              ⁡
              
                [
                
                  
                    
                      
                        
                          h
                          
                            1
                            ,
                            1
                          
                        
                        ⁢
                        
                          S
                          1
                        
                      
                    
                    
                      
                        
                          h
                          
                            1
                            ,
                            2
                          
                        
                        ⁢
                        
                          S
                          1
                        
                      
                    
                    
                      ⋯
                    
                    
                      
                        
                          h
                          
                            1
                            ,
                            N
                          
                        
                        ⁢
                        
                          S
                          1
                        
                      
                    
                  
                  
                    
                      
                        
                          h
                          
                            2
                            ,
                            1
                          
                        
                        ⁢
                        
                          S
                          2
                        
                      
                    
                    
                      
                        
                          h
                          
                            2
                            ,
                            2
                          
                        
                        ⁢
                        
                          S
                          2
                        
                      
                    
                    
                      ⋯
                    
                    
                      
                        
                          h
                          
                            2
                            ,
                            N
                          
                        
                        ⁢
                        
                          S
                          2
                        
                      
                    
                  
                  
                    
                      ⋮
                    
                    
                      ⋮
                    
                    
                      ⋮
                    
                    
                      ⋮
                    
                  
                  
                    
                      
                        
                          h
                          
                            N
                            ,
                            1
                          
                        
                        ⁢
                        
                          S
                          N
                        
                      
                    
                    
                      
                        
                          h
                          
                            N
                            ,
                            2
                          
                        
                        ⁢
                        
                          S
                          N
                        
                      
                    
                    
                      ⋯
                    
                    
                      
                        
                          h
                          
                            N
                            ,
                            N
                          
                        
                        ⁢
                        
                          S
                          N
                        
                      
                    
                  
                
                ]
              
            
            +
            
               
              
                
                  [
                  
                    
                      
                        
                          
                            
                              α
                              0
                            
                            ⁢
                            
                              n
                              1
                              
                                (
                                1
                                )
                              
                            
                          
                          +
                          
                            
                              α
                              0
                            
                            ⁢
                            
                              n
                              1
                              
                                (
                                2
                                )
                              
                            
                          
                          +
                          ...
                          +
                          
                            
                              α
                              0
                            
                            ⁢
                            
                              n
                              1
                              
                                (
                                N
                                )
                              
                            
                          
                        
                      
                      
                        
                          
                            
                              α
                              0
                            
                            ⁢
                            
                              n
                              1
                              
                                (
                                1
                                )
                              
                            
                          
                          +
                          
                            
                              α
                              
                                -
                                1
                              
                            
                            ⁢
                            
                              n
                              1
                              
                                (
                                2
                                )
                              
                            
                          
                          +
                          ...
                          +
                          
                            
                              α
                              
                                -
                                
                                  (
                                  
                                    N
                                    -
                                    1
                                  
                                  )
                                
                              
                            
                            ⁢
                            
                              n
                              1
                              
                                (
                                N
                                )
                              
                            
                          
                        
                      
                      
                        ⋯
                      
                      
                        
                          
                            
                              α
                              0
                            
                            ⁢
                            
                              n
                              1
                              
                                (
                                1
                                )
                              
                            
                          
                          +
                          
                            
                              α
                              
                                -
                                
                                  (
                                  
                                    N
                                    -
                                    1
                                  
                                  )
                                
                              
                            
                            ⁢
                            
                              n
                              1
                              
                                (
                                2
                                )
                              
                            
                          
                          +
                          ...
                          +
                          
                            
                              α
                              
                                -
                                
                                  (
                                  
                                    N
                                    -
                                    2
                                  
                                  )
                                
                              
                            
                            ⁢
                            
                              n
                              1
                              
                                (
                                N
                                )
                              
                            
                          
                        
                      
                    
                    
                      
                        
                          
                            
                              α
                              0
                            
                            ⁢
                            
                              n
                              2
                              
                                (
                                1
                                )
                              
                            
                          
                          +
                          
                            
                              α
                              0
                            
                            ⁢
                            
                              n
                              2
                              
                                (
                                2
                                )
                              
                            
                          
                          +
                          ...
                          +
                          
                            
                              α
                              0
                            
                            ⁢
                            
                              n
                              2
                              
                                (
                                N
                                )
                              
                            
                          
                        
                      
                      
                        
                          
                            
                              α
                              0
                            
                            ⁢
                            
                              n
                              2
                              
                                (
                                1
                                )
                              
                            
                          
                          +
                          
                            
                              α
                              
                                -
                                1
                              
                            
                            ⁢
                            
                              n
                              2
                              
                                (
                                2
                                )
                              
                            
                          
                          +
                          ...
                          +
                          
                            
                              α
                              
                                -
                                
                                  (
                                  
                                    N
                                    -
                                    1
                                  
                                  )
                                
                              
                            
                            ⁢
                            
                              n
                              2
                              
                                (
                                N
                                )
                              
                            
                          
                        
                      
                      
                        ⋯
                      
                      
                        
                          
                            
                              α
                              0
                            
                            ⁢
                            
                              n
                              2
                              
                                (
                                1
                                )
                              
                            
                          
                          +
                          
                            
                              α
                              
                                -
                                
                                  (
                                  
                                    N
                                    -
                                    1
                                  
                                  )
                                
                              
                            
                            ⁢
                            
                              n
                              2
                              
                                (
                                2
                                )
                              
                            
                          
                          +
                          ...
                          +
                          
                            
                              α
                              
                                -
                                
                                  (
                                  
                                    N
                                    -
                                    2
                                  
                                  )
                                
                              
                            
                            ⁢
                            
                              n
                              2
                              
                                (
                                N
                                )
                              
                            
                          
                        
                      
                    
                    
                      
                        ⋮
                      
                      
                        ⋮
                      
                      
                        ⋱
                      
                      
                        ⋮
                      
                    
                    
                      
                        
                          
                            
                              α
                              0
                            
                            ⁢
                            
                              n
                              N
                              
                                (
                                1
                                )
                              
                            
                          
                          +
                          
                            
                              α
                              0
                            
                            ⁢
                            
                              n
                              N
                              
                                (
                                2
                                )
                              
                            
                          
                          +
                          ...
                          +
                          
                            
                              α
                              0
                            
                            ⁢
                            
                              n
                              N
                              
                                (
                                N
                                )
                              
                            
                          
                        
                      
                      
                        
                          
                            
                              α
                              0
                            
                            ⁢
                            
                              n
                              N
                              
                                (
                                1
                                )
                              
                            
                          
                          +
                          
                            
                              α
                              
                                -
                                1
                              
                            
                            ⁢
                            
                              n
                              N
                              
                                (
                                2
                                )
                              
                            
                          
                          +
                          ...
                          +
                          
                            
                              α
                              
                                -
                                
                                  (
                                  
                                    N
                                    -
                                    1
                                  
                                  )
                                
                              
                            
                            ⁢
                            
                              n
                              N
                              
                                (
                                N
                                )
                              
                            
                          
                        
                      
                      
                        ⋯
                      
                      
                        
                          
                            
                              α
                              0
                            
                            ⁢
                            
                              n
                              N
                              
                                (
                                1
                                )
                              
                            
                          
                          +
                          
                            
                              α
                              
                                -
                                
                                  (
                                  
                                    N
                                    -
                                    1
                                  
                                  )
                                
                              
                            
                            ⁢
                            
                              n
                              N
                              
                                (
                                2
                                )
                              
                            
                          
                          +
                          ...
                          +
                          
                            
                              α
                              
                                -
                                
                                  (
                                  
                                    N
                                    -
                                    2
                                  
                                  )
                                
                              
                            
                            ⁢
                            
                              n
                              N
                              
                                (
                                N
                                )
                              
                            
                          
                        
                      
                    
                  
                  ]
                
                ⁢
                
                  

                
                ⁢
                
                  
                
                [
                
                  Equation
                  ⁢
                  
                    
                  
                  ⁢
                  3
                
                ]
              
            
          
        
      
    
    
      
        (
        6
        )
      
    
  
  
    
      
        
          
        
        ⁢
        
          
            
              
                
                  
                    Nh
                    
                      1
                      ,
                      1
                    
                  
                  ⁢
                  
                    S
                    1
                  
                  ⁢
                  
                    h
                    
                      1
                      ,
                      1
                    
                    *
                  
                
                +
                
                  
                    Nh
                    
                      1
                      ,
                      2
                    
                  
                  ⁢
                  
                    S
                    1
                  
                  ⁢
                  
                    h
                    
                      1
                      ,
                      2
                    
                    *
                  
                
                +
                ...
                +
                
                  n
                  1
                  ′
                
              
              =
              
                
                  
                    N
                    ⁡
                    
                      (
                      
                        
                          
                            
                            
                              h
                              
                                1
                                ,
                                1
                              
                            
                            
                          
                          2
                        
                        +
                        
                          
                            
                            
                              h
                              
                                1
                                ,
                                2
                              
                            
                            
                          
                          2
                        
                        +
                        ...
                      
                      )
                    
                  
                  ·
                  
                    S
                    1
                  
                
                +
                
                  n
                  1
                  ′
                
              
            
            ,
            
              

            
            ⁢
            
              
            
            ⁢
            
              
                
                  
                    Nh
                    
                      2
                      ,
                      1
                    
                  
                  ⁢
                  
                    S
                    2
                  
                  ⁢
                  
                    h
                    
                      2
                      ,
                      1
                    
                    *
                  
                
                +
                
                  
                    Nh
                    
                      2
                      ,
                      2
                    
                  
                  ⁢
                  
                    S
                    2
                  
                  ⁢
                  
                    h
                    
                      2
                      ,
                      2
                    
                    *
                  
                
                +
                ...
                +
                
                  n
                  2
                  ′
                
              
              =
              
                
                  
                    N
                    ⁡
                    
                      (
                      
                        
                          
                            
                            
                              h
                              
                                2
                                ,
                                1
                              
                            
                            
                          
                          2
                        
                        +
                        
                          
                            
                            
                              h
                              
                                2
                                ,
                                2
                              
                            
                            
                          
                          2
                        
                        +
                        ...
                      
                      )
                    
                  
                  ·
                  
                    S
                    2
                  
                
                +
                
                  n
                  2
                  ′
                
              
            
            ,
            ...
          
          ⁢
          
            

          
          ⁢
          
            
          
          ⁢
          ⋮
        
      
    
    
      
        (
        7
        )
      
    
  




where a* is a complex conjugate number of a, and n′1, n′2, . . . , n′N are expressed as follows:




  
    
      
        
          [
          
            
              
                
                  n
                  
                    1
                    ,
                    1
                  
                  ′
                
              
              
                
                  n
                  
                    1
                    ,
                    2
                  
                  ′
                
              
              
                ⋯
              
              
                
                  n
                  
                    1
                    ,
                    N
                  
                  ′
                
              
            
            
              
                
                  n
                  
                    2
                    ,
                    1
                  
                  ′
                
              
              
                
                  n
                  
                    2
                    ,
                    2
                  
                  ′
                
              
              
                ⋯
              
              
                
                  n
                  
                    2
                    ,
                    N
                  
                  ′
                
              
            
            
              
                ⋮
              
              
                ⋮
              
              
                ⋱
              
              
                ⋮
              
            
            
              
                
                  n
                  
                    N
                    ,
                    1
                  
                  ′
                
              
              
                
                  n
                  
                    N
                    ,
                    2
                  
                  ′
                
              
              
                ⋯
              
              
                
                  n
                  
                    N
                    ,
                    N
                  
                  ′
                
              
            
          
          ]
        
        =
        
           
          
            [
            
              
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        α
                        
                          -
                          1
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              1
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              1
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              2
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
              
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        α
                        
                          -
                          1
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              1
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              1
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              2
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
              
                
                  ⋮
                
                
                  ⋮
                
                
                  ⋱
                
                
                  ⋮
                
              
              
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        α
                        
                          -
                          1
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              1
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      
                        α
                        0
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              1
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        α
                        
                          -
                          
                            (
                            
                              N
                              -
                              2
                            
                            )
                          
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
            ]
          
        
      
    
    
      
        (
        8
        )
      
    
  
  
    
      
        
          
        
        ⁢
        
          
            
              n
              1
              ′
            
            =
            
              
                
                  h
                  1.1
                  *
                
                ⁢
                
                  n
                  1.1
                  ′
                
              
              +
              
                
                  h
                  2.1
                  *
                
                ⁢
                
                  n
                  2.1
                  ′
                
              
              +
              ...
              +
              
                
                  h
                  
                    N
                    ⁢
                    .1
                  
                  *
                
                ⁢
                
                  n
                  
                    N
                    ⁢
                    .1
                  
                  ′
                
              
            
          
          ,
          
            

          
          ⁢
          
            
          
          ⁢
          
            
              n
              2
              ′
            
            =
            
              
                
                  h
                  1.2
                  *
                
                ⁢
                
                  n
                  1.2
                  ′
                
              
              +
              
                
                  h
                  2.2
                  *
                
                ⁢
                
                  n
                  2.2
                  ′
                
              
              +
              ...
              +
              
                
                  h
                  
                    N
                    ⁢
                    .2
                  
                  *
                
                ⁢
                
                  n
                  
                    N
                    ⁢
                    .2
                  
                  ′
                
              
            
          
          ,
          
            

          
          ⁢
          
            
          
          ⁢
          
            ⋮
            ⁢
            
              
            
            .
          
        
      
    
    
      
        (
        9
        )

7. The wireless communications system according to claim 6, wherein
the error correction decoding unit of the data reception device extracts S1, S2, ..., and SN which construct the symbols S of the codewords according to a following equation (10) which is a simplification of an equation (7):




  
    [
    
      Equation
      ⁢
      
        
      
      ⁢
      4
    
    ]
  




  
    
      
        
          
            
              
                
                  Nh
                  
                    1
                    ,
                    1
                  
                
                ⁢
                
                  S
                  1
                
                ⁢
                
                  h
                  
                    1
                    ,
                    1
                  
                  *
                
              
              +
              
                
                  h
                  
                    1
                    ,
                    1
                  
                  *
                
                ⁢
                
                  n
                  
                    1
                    ,
                    1
                  
                  ′
                
              
            
            =
            
              
                
                  N
                  ⁡
                  
                    (
                    
                      
                        
                        
                          h
                          
                            1
                            ,
                            1
                          
                        
                        
                      
                      2
                    
                    )
                  
                
                ·
                
                  S
                  1
                
              
              +
              
                
                  h
                  
                    1
                    ,
                    1
                  
                  *
                
                ⁢
                
                  n
                  
                    1
                    ,
                    1
                  
                  ′
                
              
            
          
          ,
          
            

          
          ⁢
          
            
              
                
                  Nh
                  
                    2
                    ,
                    2
                  
                
                ⁢
                
                  S
                  2
                
                ⁢
                
                  h
                  
                    2
                    ,
                    2
                  
                  *
                
              
              +
              
                
                  h
                  
                    2
                    ,
                    2
                  
                  *
                
                ⁢
                
                  n
                  
                    2
                    ,
                    2
                  
                  ′
                
              
            
            =
            
              
                
                  N
                  ⁡
                  
                    (
                    
                      
                        
                        
                          h
                          
                            2
                            ,
                            2
                          
                        
                        
                      
                      2
                    
                    )
                  
                
                ·
                
                  S
                  2
                
              
              +
              
                
                  h
                  
                    2
                    ,
                    2
                  
                  *
                
                ⁢
                
                  n
                  
                    2
                    ,
                    2
                  
                  ′
                
              
            
          
          ,
          
            

          
          ⁢
          
            ⋮
            ⁢
            
              
            
            .
          
        
      
      
        
          (
          10
          )

8. The wireless communications system according to claim 5, wherein
in a case in which the codewords are transmitted via N communication channels (N is a power of two) and interference occurs among the N communication channels, assuming a channel matrix H and expressing symbols of the codewords transmitted from the codeword transmitting unit of the data transmission device and symbols of the codewords received by the codeword receiving unit of the data reception device as S and r respectively, when the error correction decoding unit of the data reception device fails in the error correction decoding of the codeword, and the codeword transmitting unit of said data transmission device then deforms said symbols S of the codewords and transmits a sequence S(1:N) of symbols S(j), the codeword receiving unit of said data reception device receives a sequence r(1:N), and the error correction decoding unit of said data reception device extracts S1, S2, ..., and SN which construct the symbols S of the codewords from said sequence r(1:N), such that the following equations are satisfied:




  
    [
    
      Equation
      ⁢
      
        
      
      ⁢
      5
    
    ]
  




  
    
      
        
          H
          =
          
            [
            
              
                
                  
                    h
                    
                      1
                      ,
                      1
                    
                  
                
                
                  
                    h
                    
                      1
                      ,
                      2
                    
                  
                
                
                  ⋯
                
                
                  ⋯
                
                
                  
                    h
                    
                      1
                      ,
                      N
                    
                  
                
              
              
                
                  
                    h
                    
                      2
                      ,
                      1
                    
                  
                
                
                  ⋱
                
                
                  ⋱
                
                
                  ⋱
                
                
                  ⋮
                
              
              
                
                  ⋮
                
                
                  ⋱
                
                
                  
                    h
                    
                      i
                      ,
                      j
                    
                  
                
                
                  ⋱
                
                
                  ⋮
                
              
              
                
                  ⋮
                
                
                  ⋱
                
                
                  ⋱
                
                
                  ⋱
                
                
                  ⋮
                
              
              
                
                  
                    h
                    
                      N
                      ,
                      1
                    
                  
                
                
                  ⋯
                
                
                  ⋯
                
                
                  ⋯
                
                
                  
                    h
                    
                      N
                      ,
                      N
                    
                  
                
              
            
            ]
          
        
      
      
        
          (
          11
          )
        
      
    
  



where hi,j is a communication channel response from j-th transmitting antenna to i-th receiving antenna.




  
    
      
        
          
        
        ⁢
        
          S
          =
          
            [
            
              
                
                  
                    S
                    1
                  
                
              
              
                
                  
                    S
                    2
                  
                
              
              
                
                  ⋮
                
              
              
                
                  
                    S
                    N
                  
                
              
            
            ]
          
        
      
    
    
      
        (
        12
        )
      
    
  
  
    
      
        r
        =
        
          
            HS
            +
            n
          
          =
          
            
              [
              
                
                  
                    
                      h
                      
                        1
                        ,
                        1
                      
                    
                  
                  
                    
                      h
                      
                        1
                        ,
                        2
                      
                    
                  
                  
                    ⋯
                  
                  
                    ⋯
                  
                  
                    
                      h
                      
                        1
                        ,
                        N
                      
                    
                  
                
                
                  
                    
                      h
                      
                        2
                        ,
                        1
                      
                    
                  
                  
                    ⋱
                  
                  
                    ⋱
                  
                  
                    ⋱
                  
                  
                    ⋮
                  
                
                
                  
                    ⋮
                  
                  
                    ⋱
                  
                  
                    
                      h
                      
                        i
                        ,
                        j
                      
                    
                  
                  
                    ⋱
                  
                  
                    ⋮
                  
                
                
                  
                    ⋮
                  
                  
                    ⋱
                  
                  
                    ⋱
                  
                  
                    ⋱
                  
                  
                    ⋮
                  
                
                
                  
                    
                      h
                      
                        N
                        ,
                        1
                      
                    
                  
                  
                    ⋯
                  
                  
                    ⋯
                  
                  
                    ⋯
                  
                  
                    
                      h
                      
                        N
                        ,
                        N
                      
                    
                  
                
              
              ]
            
            ⁢
            
               
              
                
                  
                    [
                    
                      
                        
                          
                            S
                            1
                          
                        
                      
                      
                        
                          
                            S
                            2
                          
                        
                      
                      
                        
                          ⋮
                        
                      
                      
                        
                          
                            S
                            N
                          
                        
                      
                    
                    ]
                  
                  +
                  
                    [
                    
                      
                        
                          
                            n
                            1
                          
                        
                      
                      
                        
                          
                            n
                            2
                          
                        
                      
                      
                        
                          ⋮
                        
                      
                      
                        
                          
                            n
                            N
                          
                        
                      
                    
                    ]
                  
                
                =
                
                  
                    [
                    
                      
                        
                          
                            
                              
                                h
                                
                                  1
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                S
                                1
                              
                            
                            +
                            
                              
                                h
                                
                                  1
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                S
                                2
                              
                            
                            +
                            ...
                            +
                            
                              
                                h
                                
                                  1
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                S
                                N
                              
                            
                          
                        
                      
                      
                        
                          
                            
                              
                                h
                                
                                  2
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                S
                                1
                              
                            
                            +
                            
                              
                                h
                                
                                  2
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                S
                                2
                              
                            
                            +
                            ...
                            +
                            
                              
                                h
                                
                                  2
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                S
                                N
                              
                            
                          
                        
                      
                      
                        
                          ⋮
                        
                      
                      
                        
                          
                            
                              
                                h
                                
                                  N
                                  ,
                                  1
                                
                              
                              ⁢
                              
                                S
                                1
                              
                            
                            +
                            
                              
                                h
                                
                                  N
                                  ,
                                  2
                                
                              
                              ⁢
                              
                                S
                                2
                              
                            
                            +
                            ...
                            +
                            
                              
                                h
                                
                                  N
                                  ,
                                  N
                                
                              
                              ⁢
                              
                                S
                                N
                              
                            
                          
                        
                      
                    
                    ]
                  
                  +
                  
                    
                      [
                      
                        
                          
                            
                              n
                              1
                            
                          
                        
                        
                          
                            
                              n
                              2
                            
                          
                        
                        
                          
                            ⋮
                          
                        
                        
                          
                            
                              n
                              N
                            
                          
                        
                      
                      ]
                    
                    ⁢
                    
                      

                    
                    ⁢
                    
                      
                    
                    [
                    
                      Equation
                      ⁢
                      
                        
                      
                      ⁢
                      6
                    
                    ]
                  
                
              
            
          
        
      
    
    
      
        (
        13
        )
      
    
  
  
    
      
        
          S
          
            (
            
              1
              :
              N
            
            )
          
        
        =
        
          
            [
            
              
                
                  
                    S
                    
                      (
                      1
                      )
                    
                  
                
                
                  
                    S
                    
                      (
                      2
                      )
                    
                  
                
                
                  ⋯
                
                
                  
                    S
                    
                      (
                      N
                      )
                    
                  
                
              
            
            ]
          
          =
          
             
            
              
                [
                
                  
                    
                      
                        
                          γ
                          
                            1
                            ,
                            1
                          
                        
                        ⁢
                        
                          S
                          1
                        
                      
                    
                    
                      
                        
                          γ
                          
                            1
                            ,
                            2
                          
                        
                        ⁢
                        
                          S
                          1
                        
                      
                    
                    
                      ⋯
                    
                    
                      
                        
                          γ
                          
                            1
                            ,
                            N
                          
                        
                        ⁢
                        
                          S
                          1
                        
                      
                    
                  
                  
                    
                      
                        
                          γ
                          
                            2
                            ,
                            1
                          
                        
                        ⁢
                        
                          S
                          2
                        
                      
                    
                    
                      
                        
                          γ
                          
                            2
                            ,
                            2
                          
                        
                        ⁢
                        
                          S
                          2
                        
                      
                    
                    
                      ⋯
                    
                    
                      
                        
                          γ
                          
                            2
                            ,
                            N
                          
                        
                        ⁢
                        
                          S
                          2
                        
                      
                    
                  
                  
                    
                      ⋮
                    
                    
                      ⋮
                    
                    
                      ⋱
                    
                    
                      ⋮
                    
                  
                  
                    
                      
                        
                          γ
                          
                            N
                            ,
                            1
                          
                        
                        ⁢
                        
                          S
                          N
                        
                      
                    
                    
                      
                        
                          γ
                          
                            N
                            ,
                            2
                          
                        
                        ⁢
                        
                          S
                          N
                        
                      
                    
                    
                      ⋯
                    
                    
                      
                        
                          γ
                          
                            N
                            ,
                            N
                          
                        
                        ⁢
                        
                          S
                          N
                        
                      
                    
                  
                
                ]
              
              ,
            
          
        
      
    
    
      
        (
        14
        )
      
    
  




where yi,j is a component of an Hadamard matrix (a component of an orthogonal code), and, in a case of N=4, is expressed as follows:




  
    
      
        
          
        
        ⁢
        
          
            
              [
              
                
                  
                    
                      γ
                      
                        1
                        ,
                        1
                      
                    
                  
                  
                    
                      γ
                      
                        1
                        ,
                        2
                      
                    
                  
                  
                    
                      γ
                      
                        1
                        ,
                        3
                      
                    
                  
                  
                    
                      γ
                      
                        1
                        ,
                        4
                      
                    
                  
                
                
                  
                    
                      γ
                      
                        2
                        ,
                        1
                      
                    
                  
                  
                    
                      γ
                      
                        2
                        ,
                        2
                      
                    
                  
                  
                    
                      γ
                      
                        2
                        ,
                        3
                      
                    
                  
                  
                    
                      γ
                      
                        2
                        ,
                        4
                      
                    
                  
                
                
                  
                    
                      γ
                      
                        3
                        ,
                        1
                      
                    
                  
                  
                    
                      γ
                      
                        3
                        ,
                        1
                      
                    
                  
                  
                    
                      γ
                      
                        3
                        ,
                        3
                      
                    
                  
                  
                    
                      γ
                      
                        3
                        ,
                        4
                      
                    
                  
                
                
                  
                    
                      γ
                      
                        4
                        ,
                        1
                      
                    
                  
                  
                    
                      γ
                      
                        4
                        ,
                        2
                      
                    
                  
                  
                    
                      γ
                      
                        4
                        ,
                        3
                      
                    
                  
                  
                    
                      γ
                      
                        4
                        ,
                        4
                      
                    
                  
                
              
              ]
            
            =
            
              [
              
                
                  
                    1
                  
                  
                    1
                  
                  
                    1
                  
                  
                    1
                  
                
                
                  
                    1
                  
                  
                    
                      -
                      1
                    
                  
                  
                    1
                  
                  
                    
                      -
                      1
                    
                  
                
                
                  
                    1
                  
                  
                    1
                  
                  
                    
                      -
                      1
                    
                  
                  
                    
                      -
                      1
                    
                  
                
                
                  
                    1
                  
                  
                    
                      -
                      1
                    
                  
                  
                    
                      -
                      1
                    
                  
                  
                    1
                  
                
              
              ]
            
          
          ⁢
          
            

          
          ⁢
          
            
          
          ⁢
          
            
              r
              
                (
                
                  1
                  :
                  N
                
                )
              
            
            =
            
              
                HS
                
                  (
                  
                    1
                    :
                    N
                  
                  )
                
              
              +
              
                n
                
                  (
                  
                    1
                    ,
                    2
                    ,
                    3
                    ,
                    4
                  
                  )
                
              
            
          
        
      
    
    
      
        (
        15
        )
      
    
  
  
    
      
        
          r
          
            (
            
              1
              :
              N
            
            )
          
        
        ⁢
        
           
          
            
              [
              
                
                  
                    
                      γ
                      
                        1
                        ,
                        1
                      
                    
                  
                  
                    
                      γ
                      
                        1
                        ,
                        2
                      
                    
                  
                  
                    ⋯
                  
                  
                    
                      γ
                      
                        1
                        ,
                        N
                      
                    
                  
                
                
                  
                    
                      γ
                      
                        2
                        ,
                        1
                      
                    
                  
                  
                    
                      γ
                      
                        2
                        ,
                        2
                      
                    
                  
                  
                    ⋯
                  
                  
                    
                      γ
                      
                        2
                        ,
                        N
                      
                    
                  
                
                
                  
                    ⋮
                  
                  
                    ⋮
                  
                  
                    ⋱
                  
                  
                    ⋮
                  
                
                
                  
                    
                      γ
                      
                        N
                        ,
                        1
                      
                    
                  
                  
                    
                      γ
                      
                        N
                        ,
                        2
                      
                    
                  
                  
                    ⋯
                  
                  
                    
                      γ
                      
                        N
                        ,
                        N
                      
                    
                  
                
              
              ]
            
            =
            
              
                N
                ⁡
                
                  [
                  
                    
                      
                        
                          
                            h
                            
                              1
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                      
                      
                        
                          
                            h
                            
                              1
                              ,
                              2
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                      
                      
                        ⋯
                      
                      
                        
                          
                            h
                            
                              1
                              ,
                              N
                            
                          
                          ⁢
                          
                            S
                            1
                          
                        
                      
                    
                    
                      
                        
                          
                            h
                            
                              2
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            2
                          
                        
                      
                      
                        
                          
                            h
                            
                              2
                              ,
                              2
                            
                          
                          ⁢
                          
                            S
                            2
                          
                        
                      
                      
                        ⋯
                      
                      
                        
                          
                            h
                            
                              2
                              ,
                              N
                            
                          
                          ⁢
                          
                            S
                            2
                          
                        
                      
                    
                    
                      
                        ⋮
                      
                      
                        ⋮
                      
                      
                        ⋮
                      
                      
                        ⋮
                      
                    
                    
                      
                        
                          
                            h
                            
                              N
                              ,
                              1
                            
                          
                          ⁢
                          
                            S
                            N
                          
                        
                      
                      
                        
                          
                            h
                            
                              N
                              ,
                              2
                            
                          
                          ⁢
                          
                            S
                            N
                          
                        
                      
                      
                        ⋯
                      
                      
                        
                          
                            h
                            
                              N
                              ,
                              N
                            
                          
                          ⁢
                          
                            S
                            N
                          
                        
                      
                    
                  
                  ]
                
              
              +
              
                 
                
                  
                    
                      [
                      
                        
                          
                            
                              
                                
                                  γ
                                  
                                    1
                                    ,
                                    1
                                  
                                
                                ⁢
                                
                                  n
                                  1
                                  
                                    (
                                    1
                                    )
                                  
                                
                              
                              +
                              
                                
                                  γ
                                  
                                    2
                                    ,
                                    1
                                  
                                
                                ⁢
                                
                                  n
                                  1
                                  
                                    (
                                    2
                                    )
                                  
                                
                              
                              +
                              ...
                              +
                              
                                
                                  γ
                                  
                                    N
                                    ,
                                    1
                                  
                                
                                ⁢
                                
                                  n
                                  1
                                  
                                    (
                                    N
                                    )
                                  
                                
                              
                            
                          
                          
                            
                              
                                
                                  γ
                                  
                                    1
                                    ,
                                    2
                                  
                                
                                ⁢
                                
                                  n
                                  1
                                  
                                    (
                                    1
                                    )
                                  
                                
                              
                              +
                              
                                
                                  γ
                                  
                                    2
                                    ,
                                    2
                                  
                                
                                ⁢
                                
                                  n
                                  1
                                  
                                    (
                                    2
                                    )
                                  
                                
                              
                              +
                              ...
                              +
                              
                                
                                  γ
                                  
                                    N
                                    ,
                                    2
                                  
                                
                                ⁢
                                
                                  n
                                  1
                                  
                                    (
                                    N
                                    )
                                  
                                
                              
                            
                          
                          
                            ⋯
                          
                          
                            
                              
                                
                                  γ
                                  
                                    1
                                    ,
                                    N
                                  
                                
                                ⁢
                                
                                  n
                                  1
                                  
                                    (
                                    1
                                    )
                                  
                                
                              
                              +
                              
                                
                                  γ
                                  
                                    2
                                    ,
                                    N
                                  
                                
                                ⁢
                                
                                  n
                                  1
                                  
                                    (
                                    2
                                    )
                                  
                                
                              
                              +
                              ...
                              +
                              
                                
                                  γ
                                  
                                    N
                                    ,
                                    N
                                  
                                
                                ⁢
                                
                                  n
                                  1
                                  
                                    (
                                    N
                                    )
                                  
                                
                              
                            
                          
                        
                        
                          
                            
                              
                                
                                  γ
                                  
                                    1
                                    ,
                                    1
                                  
                                
                                ⁢
                                
                                  n
                                  2
                                  
                                    (
                                    1
                                    )
                                  
                                
                              
                              +
                              
                                
                                  γ
                                  
                                    2
                                    ,
                                    1
                                  
                                
                                ⁢
                                
                                  n
                                  2
                                  
                                    (
                                    2
                                    )
                                  
                                
                              
                              +
                              ...
                              +
                              
                                
                                  γ
                                  
                                    N
                                    ,
                                    1
                                  
                                
                                ⁢
                                
                                  n
                                  2
                                  
                                    (
                                    N
                                    )
                                  
                                
                              
                            
                          
                          
                            
                              
                                
                                  γ
                                  
                                    1
                                    ,
                                    2
                                  
                                
                                ⁢
                                
                                  n
                                  2
                                  
                                    (
                                    1
                                    )
                                  
                                
                              
                              +
                              
                                
                                  γ
                                  
                                    2
                                    ,
                                    2
                                  
                                
                                ⁢
                                
                                  n
                                  2
                                  
                                    (
                                    2
                                    )
                                  
                                
                              
                              +
                              ...
                              +
                              
                                
                                  γ
                                  
                                    N
                                    ,
                                    2
                                  
                                
                                ⁢
                                
                                  n
                                  2
                                  
                                    (
                                    N
                                    )
                                  
                                
                              
                            
                          
                          
                            ⋯
                          
                          
                            
                              
                                
                                  γ
                                  
                                    1
                                    ,
                                    N
                                  
                                
                                ⁢
                                
                                  n
                                  2
                                  
                                    (
                                    1
                                    )
                                  
                                
                              
                              +
                              
                                
                                  γ
                                  
                                    2
                                    ,
                                    N
                                  
                                
                                ⁢
                                
                                  n
                                  2
                                  
                                    (
                                    2
                                    )
                                  
                                
                              
                              +
                              ...
                              +
                              
                                
                                  γ
                                  
                                    N
                                    ,
                                    N
                                  
                                
                                ⁢
                                
                                  n
                                  2
                                  
                                    (
                                    N
                                    )
                                  
                                
                              
                            
                          
                        
                        
                          
                            ⋮
                          
                          
                            ⋮
                          
                          
                            ⋱
                          
                          
                            ⋮
                          
                        
                        
                          
                            
                              
                                
                                  γ
                                  
                                    1
                                    ,
                                    1
                                  
                                
                                ⁢
                                
                                  n
                                  N
                                  
                                    (
                                    1
                                    )
                                  
                                
                              
                              +
                              
                                
                                  γ
                                  
                                    2
                                    ,
                                    1
                                  
                                
                                ⁢
                                
                                  n
                                  N
                                  
                                    (
                                    2
                                    )
                                  
                                
                              
                              +
                              ...
                              +
                              
                                
                                  γ
                                  
                                    N
                                    ,
                                    1
                                  
                                
                                ⁢
                                
                                  n
                                  N
                                  
                                    (
                                    N
                                    )
                                  
                                
                              
                            
                          
                          
                            
                              
                                
                                  γ
                                  
                                    1
                                    ,
                                    2
                                  
                                
                                ⁢
                                
                                  n
                                  N
                                  
                                    (
                                    1
                                    )
                                  
                                
                              
                              +
                              
                                
                                  γ
                                  
                                    2
                                    ,
                                    2
                                  
                                
                                ⁢
                                
                                  n
                                  N
                                  
                                    (
                                    2
                                    )
                                  
                                
                              
                              +
                              ...
                              +
                              
                                
                                  γ
                                  
                                    N
                                    ,
                                    2
                                  
                                
                                ⁢
                                
                                  n
                                  N
                                  
                                    (
                                    N
                                    )
                                  
                                
                              
                            
                          
                          
                            ⋯
                          
                          
                            
                              
                                
                                  γ
                                  
                                    1
                                    ,
                                    N
                                  
                                
                                ⁢
                                
                                  n
                                  N
                                  
                                    (
                                    1
                                    )
                                  
                                
                              
                              +
                              
                                
                                  γ
                                  
                                    2
                                    ,
                                    N
                                  
                                
                                ⁢
                                
                                  n
                                  N
                                  
                                    (
                                    2
                                    )
                                  
                                
                              
                              +
                              ...
                              +
                              
                                
                                  γ
                                  
                                    N
                                    ,
                                    N
                                  
                                
                                ⁢
                                
                                  n
                                  N
                                  
                                    (
                                    N
                                    )
                                  
                                
                              
                            
                          
                        
                      
                      ]
                    
                    ⁢
                    
                      

                    
                    ⁢
                    
                      
                    
                    [
                    
                      Equation
                      ⁢
                      
                        
                      
                      ⁢
                      7
                    
                    ]
                  
                   
                
              
            
          
        
      
    
    
      
        (
        16
        )
      
    
  
  
    
      
        
          
        
        ⁢
        
          
            
              
                
                  Nh
                  
                    1
                    ,
                    1
                  
                
                ⁢
                
                  S
                  1
                
                ⁢
                
                  h
                  
                    1
                    ,
                    1
                  
                  *
                
              
              +
              
                
                  Nh
                  
                    1
                    ,
                    2
                  
                
                ⁢
                
                  S
                  1
                
                ⁢
                
                  h
                  
                    1
                    ,
                    2
                  
                  *
                
              
              +
              ...
              +
              
                n
                1
                ′
              
            
            =
            
              
                
                  N
                  (
                  
                    
                      
                        
                        
                          h
                          
                            1
                            ,
                            1
                          
                        
                        
                      
                      2
                    
                    +
                    
                      
                        
                        
                          h
                          
                            1
                            ,
                            2
                          
                        
                        
                      
                      2
                    
                    +
                    ...
                  
                  ⁢
                  
                    
                  
                  )
                
                ·
                
                  S
                  1
                
              
              +
              
                n
                1
                ′
              
            
          
          ,
          
            

          
          ⁢
          
            
          
          ⁢
          
            
              
                
                  Nh
                  
                    2
                    ,
                    1
                  
                
                ⁢
                
                  S
                  2
                
                ⁢
                
                  h
                  
                    2
                    ,
                    1
                  
                  *
                
              
              +
              
                
                  Nh
                  
                    2
                    ,
                    2
                  
                
                ⁢
                
                  S
                  2
                
                ⁢
                
                  h
                  
                    2
                    ,
                    2
                  
                  *
                
              
              +
              ...
              +
              
                n
                2
                ′
              
            
            =
            
              
                
                  N
                  (
                  
                    
                      
                        
                        
                          h
                          
                            2
                            ,
                            1
                          
                        
                        
                      
                      2
                    
                    +
                    
                      
                        
                        
                          h
                          
                            2
                            ,
                            2
                          
                        
                        
                      
                      2
                    
                    +
                    ...
                  
                  ⁢
                  
                    
                  
                  )
                
                ·
                
                  S
                  2
                
              
              +
              
                n
                2
                ′
              
            
          
          ,
          
            ...
            ⁢
            
              
            
            .
            
              

            
            ⁢
            
              
            
            ⁢
            ⋮
          
        
      
    
    
      
        (
        17
        )
      
    
  




where n′1, n′2, . . . , n′N are expressed as follows:




  
    
      
        
          [
          
            
              
                
                  n
                  
                    1
                    ,
                    1
                  
                  ′
                
              
              
                
                  n
                  
                    1
                    ,
                    2
                  
                  ′
                
              
              
                ⋯
              
              
                
                  n
                  
                    1
                    ,
                    N
                  
                  ′
                
              
            
            
              
                
                  n
                  
                    2
                    ,
                    1
                  
                  ′
                
              
              
                
                  n
                  
                    2
                    ,
                    2
                  
                  ′
                
              
              
                ⋯
              
              
                
                  n
                  
                    2
                    ,
                    N
                  
                  ′
                
              
            
            
              
                ⋮
              
              
                ⋮
              
              
                ⋱
              
              
                ⋮
              
            
            
              
                
                  n
                  
                    N
                    ,
                    1
                  
                  ′
                
              
              
                
                  n
                  
                    N
                    ,
                    2
                  
                  ′
                
              
              
                ⋯
              
              
                
                  n
                  
                    N
                    ,
                    N
                  
                  ′
                
              
            
          
          ]
        
        =
        
           
          
            [
            
              
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        1
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
              
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        2
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
              
                
                  ⋮
                
                
                  ⋮
                
                
                  ⋱
                
                
                  ⋮
                
              
              
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          1
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          2
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      
                        γ
                        
                          1
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          1
                          )
                        
                      
                    
                    +
                    
                      
                        γ
                        
                          2
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          2
                          )
                        
                      
                    
                    +
                    ...
                    +
                    
                      
                        γ
                        
                          N
                          ,
                          N
                        
                      
                      ⁢
                      
                        n
                        N
                        
                          (
                          N
                          )
                        
                      
                    
                  
                
              
            
            ]
          
        
      
    
    
      
        (
        18
        )
      
    
  
  
    
      
        
          
        
        ⁢
        
          
            
              n
              1
              ′
            
            =
            
              
                
                  h
                  1.1
                  *
                
                ⁢
                
                  n
                  1.1
                  ′
                
              
              +
              
                
                  h
                  2.1
                  *
                
                ⁢
                
                  n
                  2.1
                  ′
                
              
              +
              ...
              +
              
                
                  h
                  
                    N
                    ⁢
                    .1
                  
                  *
                
                ⁢
                
                  n
                  
                    N
                    ⁢
                    .1
                  
                  ′
                
              
            
          
          ,
          
            

          
          ⁢
          
            
          
          ⁢
          
            
              n
              2
              ′
            
            =
            
              
                
                  h
                  1.2
                  *
                
                ⁢
                
                  n
                  1.2
                  ′
                
              
              +
              
                
                  h
                  2.2
                  *
                
                ⁢
                
                  n
                  2.2
                  ′
                
              
              +
              ...
              +
              
                
                  h
                  
                    N
                    ⁢
                    .2
                  
                  *
                
                ⁢
                
                  n
                  
                    N
                    ⁢
                    .2
                  
                  ′
                
              
            
          
          ,
          
            

          
          ⁢
          
            
          
          ⁢
          
            ⋮
            ⁢
            
              
            
            .
          
        
      
    
    
      
        (
        19
        )

9. The wireless communications system according to claim 8, wherein
the error correction decoding unit of the data reception device extracts S1, S2, ..., and SN which construct the symbols S of the codewords according to a following equation (20) which is a simplification of an equation (17):




  
    [
    
      Equation
      ⁢
      
        
      
      ⁢
      8
    
    ]
  




  
    
      
        
          
            
              
                
                  Nh
                  
                    1
                    ,
                    1
                  
                
                ⁢
                
                  S
                  1
                
                ⁢
                
                  h
                  
                    1
                    ,
                    1
                  
                  *
                
              
              +
              
                
                  h
                  1.1
                  *
                
                ⁢
                
                  n
                  1.1
                  ′
                
              
            
            =
            
              
                
                  N
                  ⁡
                  
                    (
                    
                      
                        
                        
                          h
                          
                            1
                            ,
                            1
                          
                        
                        
                      
                      2
                    
                    )
                  
                
                ·
                
                  S
                  1
                
              
              +
              
                
                  h
                  1.1
                  *
                
                ⁢
                
                  n
                  1.1
                  ′
                
              
            
          
          ,
          
            

          
          ⁢
          
            
              
                
                  Nh
                  
                    2
                    ,
                    2
                  
                
                ⁢
                
                  S
                  2
                
                ⁢
                
                  h
                  
                    2
                    ,
                    2
                  
                  *
                
              
              +
              
                
                  h
                  2.2
                  *
                
                ⁢
                
                  n
                  2.2
                  ′
                
              
            
            =
            
              
                
                  N
                  ⁡
                  
                    (
                    
                      
                        
                        
                          h
                          
                            2
                            ,
                            2
                          
                        
                        
                      
                      2
                    
                    )
                  
                
                ·
                
                  S
                  2
                
              
              +
              
                
                  h
                  2.2
                  *
                
                ⁢
                
                  n
                  2.2
                  ′
                
              
            
          
          ,
          
            

          
          ⁢
          
            ⋮
            ⁢
            
              
            
            .
          
        
      
      
        
          (
          20
          )

10. The wireless communications system according to claim 4, wherein
in a case in which it is estimated beforehand that an interference wave is large, when simultaneously transmitting the plurality of divided codewords by using the plurality of antennas, the codeword transmitting unit of the data transmission device deforms said codewords according to the predetermined rule and transmits the deformed codewords together.

11. The data transmission device according to claim 1, wherein the transmitted codewords are deformed in such manner that changes bit values in each transmitted codeword.

12. The data reception device according to claim 3, wherein the transmitted codewords are deformed in such manner that changes bit values in each transmitted codeword.

13. The wireless communication system according to claim 4, wherein the transmitted codewords are deformed in such manner that changes bit values in each transmitted codeword.