# Patent

## Title
Antipodal demodulation method and antipodal demodulator for non-coherent unitary space-time modulation in MIMO wireless communication

## Abstract

Provided is an antipodal demodulation method and an antipodal demodulator for non-coherent unitary space-time modulation in MIMO wireless communication. The invention comprises: traversing L/2 constellation points in each sub-constellation of a non-coherent unitary space-time diagram for maximum likelihood demodulation calculation, determining a maximum trace ψmax and a minimum trace ψmin from traces of L/2 matrix products, calculating a maximum trace ψmax of a matrix product corresponding to the constellation matrix in the other sub-constellation according to ψmax=tr(YH Φj ΦhHY)=tr(YHY)−tr(YHΦjΦjHY)=σ−ψmin, and outputting a constellation point corresponding to the greater one of ψmax and ψmax as a demodulation signal. The antipodal demodulation method of the invention reduces calculation workload by 1⁄2 and features lower calculation complexity over the conventional maximum likelihood demodulation method without degrading demodulation performance.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
Pursuant to 35 U.S.C. §119 and the Paris Convention Treaty, this application claims the benefit of Chinese Patent Application No. 201310409889.4 filed on Sep. 10, 2013, the contents of which are incorporated herein by reference.
FIELD
The invention relates to the communication technology field, and more particularly to an antipodal demodulation method and an antipodal demodulator for non-coherent unitary space-time modulation in MIMO wireless communication.
BACKGROUND
With fast development of wireless communication, it has become a core problem for next generation wireless communication systems to increase data transmission speeds without degrading the quality of service (QoS). Since Telatar found that multiple-input multiple-output (MIMO) systems are capable of linearly increasing channel capacity in 1995, research fever on wireless MIMO communication systems has been activated, and the MIMO technology has become a key technology in the next generation wireless communication systems. In addition, space-time codes are one of the main transmission technologies for long-term evolution (LTE) of the third-generation (3G) communication.
The MIMO communication system is divided into a coherent communication system and a non-coherent communication system based on requirement for channel estimation during demodulation. The non-coherent space-time code is divided into a differential space-time code and a unitary space-time code, and this invention is aimed at the unitary space-time code since there is very little research achievement for non-coherent unitary space-time demodulation methods. At present, experimental simulation platforms for designing the non-coherent space-time code mainly use a maximum likelihood algorithm as a demodulation algorithm. Maximum likelihood demodulation comprises calculating likelihood probabilities of all constellation points, and selecting a constellation point with the greatest likelihood probability as an output signal of a demodulator. However, a problem with the demodulation method traversing all the constellation points is that, calculation workload and complexity linearly increase as a constellation becomes larger.
SUMMARY
It is an objective of the invention to provide an antipodal demodulation method for non-coherent unitary space-time modulation in MIMO wireless communication, the method finds an antipodal structure of a high-performance unitary space-time constellation and relationship between different antipodes by analyzing conventional non-coherent unitary space-time diagrams, and features the same demodulation performance as a maximum likelihood demodulation method with the number of constellation points half of that thereof during a demodulation process.
Provided is an antipodal demodulation method for non-coherent unitary space-time modulation in MIMO wireless communication, comprising steps of:
(1) dividing an antipode-based unitary space-time constellation




  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    L
  




into two sub-constellation





  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




and





  
    
      
        C
        _
      
      1
    
    =
    
      
        {
        
          
            Φ
            _
          
          l
        
        }
      
      
        l
        =
        1
      
      
        L
        /
        2
      
    
  
  ,




where L represents the number of constellation points in the constellation, Φl and Φl represents two T×M complex matrices, T represents a coherent time interval, M represents the number of transmission antennas, Φαβ and Φαβ represents signals transmitted by the βth transmission antenna at time α, there is no antipode pair in the sub-constellation, and there is one-to-one correspondence between two antipodes in different sub-constellations;

(2) obtaining traces of a matrix product of L/2 constellation matrices in the sub-constellation




  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




and a receiving signal matrix Y: ψl=tr(YHΦlΦlHY), l=1,2, . . . L/2, determining a maximum trace ψmax and a minimum trace ψmin therefrom, calculating the trace of a matrix product of said receiving signal matrix Y: σ=tr(YHY), and corresponding constellation matrices Φi and Φj in the sub-constellation C1={Φl}l=1L/2 according to the maximum trace ψmax and the minimum trace ψmin, obtaining an antipode matrix Φj antipodal to Φj in another sub-constellation





  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




according to relationship between the antipodes, calculating a maximum trace ψmax of a matrix product corresponding to the other sub-constellation





  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




according to a relationship among the constellation matrices Φj and Φj antipodal to each other, and the receiving signal matrix Y: ψmax=σ−ψmin=tr(YH Φj ΦjHY)=tr(YHY)−tr(YHΦjΦjHY), where the receiving signal matrix Y represents a T×N complex matrix, T represents a coherent time interval, N represents the number of receiving antennas, yαγ represents a signal received by the γth receiving antenna at the time α, and tr(□) represents obtaining a trace of a matrix within the brackets; and

(3) comparing the maximum trace ψmax and the maximum trace ψmax corresponding to constellation points in the sub-constellations, determining a greater one therefrom, and selecting a constellation matrix corresponding thereto as a demodulation signal matrix, namely, selecting the transmission signal matrix Φi corresponding to ψmax from the sub-constellation




  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




as a demodulated constellation matrix {circumflex over (ψ)}=Φi as ψmax> ψmax, and selecting the transmission signal matrix Φj corresponding to ψmax from the sub-constellation





  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




as a demodulated constellation matrix {circumflex over (Φ)}= Φj as ψmax< ψmax.

The invention uses a method of dividing the antipodal sub-constellation: firstly, the non-coherent unitary space-time constellation is divided into two antipodal sub-constellations, there is no antipode pair in each sub-constellation, and there is one-to-one correspondence between two constellation points in different sub-constellations, then relationship between antipodal constellation points during the demodulation process is determined tr(YHΦΦHY)+tr(YH Φ ΦHY)=tr(YHY), after that, the maximum value ψmax and the minimum value ψmin therefrom are determined by traversing all constellation points in (one of) the sub-constellation, then the maximum trace ψmax of the matrix product corresponding to the other sub-constellation is derived according to ψmax=tr(YHY)−ψmin, and finally, the constellation matrix corresponding to the greater one of ψmax and ψmax is output as the demodulation signal. This method reduces calculation workload by 1⁄2 and features lower calculation complexity over the conventional maximum likelihood demodulation method without degrading demodulation performance
Provided is an antipodal demodulator for non-coherent unitary space-time modulation in MIMO wireless communication, comprising an input buffer, a read-only memory module, a trace-calculating module, an extreme-value-calculating module, a register group, a maximum-calculating module, a comparing and selecting module, and an output buffer, the input buffer is configured to receive and save a receiving signal matrix Y, and to output the receiving signal matrix Y to the trace-calculating module, the receiving signal matrix Y representing a T×N complex matrix, and yαγ representing a signal received by the γth receiving antenna at time α, the read-only memory module is configured to save all the constellation matrices of two sub-constellations




  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




and





  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




of an antipode-based unitary space-time constellation





  
    C
    =
    
      
        {
        
          Φ
          l
        
        }
      
      
        l
        =
        1
      
      L
    
  
  ,




where L represents the number of constellation points in the constellation, Φl and Φl represents two T×M complex matrices, T represents a coherent time interval, and Φαβ and Φαβ represents signals transmitted by the βth transmission antenna at the time α, the trace-calculating module is configured to receive L/2 constellation matrices in the sub-constellation





  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




from the read-only memory module, and the receiving signal matrix Y from the input buffer, calculating traces ψl=tr(YHΦlΦlHY) and σ=tr(YHY), and transmitting L/2 traces ψl of the matrix YHΦlΦlHY to the extreme-value-calculating module, and the trace σ of the matrix YHY to the maximum-calculating module, where 1≦l≦L/2, and tr(□) represents obtaining a trace of a matrix within the brackets, the extreme-value-calculating module is configured to compare the L/2 traces ψl of the matrix YHΦlΦlHY, and to save a maximum trace ψmax and a minimum trace ψmin thereof, an address i1 of a constellation matrix Φi corresponding to the maximum trace ψmax in the read-only memory module, and an address j1 of an antipode matrix Φj corresponding to the minimum trace ψmin and antipodal to a constellation matrix Φj in another sub-constellation





  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




in the read-only memory module into the register group, where 1≦l≦L/2, the maximum-calculating module is configured to receive the trace σ of the matrix YHY from the trace-calculating module, and the minimum trace ψmin from the register group, to calculate ψmax=σ−ψmin, and to save ψmax into the register group, the comparing and selecting module is configured to obtain ψmax and ψmax from the register group, to compare ψmax with ψmax, and to output a control signal contr operating to control the register group, and an address of a constellation matrix corresponding to a greater one of ψmax and ψmax in the read-only memory module to the read-only memory module, the register group is configured to save ψmax, ψmin, i1, and j1 from the extreme-value-calculating module, and ψmax from the maximum-calculating module, and to output an address of a constellation matrix corresponding to the greater one of ψmax and ψmax in the read-only memory module to the read-only memory module according to the control signal contr output by the comparing and selecting module, whereby controlling the read-only memory module to output a demodulated constellation matrix to the output buffer, and the output buffer is configured to receive and buffer the demodulated constellation matrix {circumflex over (Φ)} from the read-only memory module.

In a class of this embodiment, the read-only memory module is configured to save the two sub-constellations




  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




and





  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




of the antipode-based unitary space-time constellation, there is no antipode pair in each sub-constellation, and there is one-to-one correspondence between two antipodes in different sub-constellations, the read-only memory module is configured to output L/2 constellation matrices in the sub-constellation





  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




to the trace-calculating module, to receive the address from the register group indicating a corresponding constellation matrix in the read-only memory module is the demodulated constellation matrix {circumflex over (Φ)}, and to output {circumflex over (Φ)} to the output buffer.

In a class of this embodiment, the extreme-value-calculating module is configured to receive L/2 traces ψl of matrices YHΦlΦlHY output by ψl computing units in the trace-calculating module, to determine a maximum trace ψmax and a minimum trace ψmin therefrom, to output the maximum trace ψmax and the minimum trace ψmin to the register group, and to output the address it of the constellation matrix Φi corresponding to the maximum trace ψmax in the read-only memory module, and the address j1 of the antipode matrix Φj corresponding to the minimum value ψmin and antipodal to the constellation matrix Φj in another sub-constellation




  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




in the read-only memory module into the register group, where 1≦l≦L/2;

In a class of this embodiment, the maximum-calculating module is configured to receive the trace σ of the matrix YHY from σ computing unit in the trace-calculating module, to obtain the minimum trace ψmin from the register group, to calculate ψmax=σ−ψmin, and to output ψmax to the register group.
In a class of this embodiment, the register group is configured to receive and to save ψmax and ψmin from the extreme-value-calculating module, and the address i1 of the constellation matrix Φi corresponding to the maximum trace ψmax in the read-only memory module, and the address j1 of the antipode matrix Φj corresponding to the minimum value ψmin and antipodal to the constellation matrix Φj in another sub-constellation




  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




in the read-only memory module, to output ψmin to the maximum-calculating module, to receive and save ψmax from the maximum-calculating module, and to output ψmax and ψmax to the comparing and selecting module.

In a class of this embodiment, the comparing and selecting module is configured to compare ψmax with ψmax, and to output the control signal contr operating to control the register group to the register group so that the register group transmits the address i1 of the constellation matrix Φi corresponding to the maximum trace ψmax in the read-only memory module to the read-only memory module if ψmax> ψmax, and transmits the address j1 of the constellation matrix Φj corresponding to the maximum trace ψmax in the read-only memory module to the read-only memory module if ψmax< ψmax.



BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS
FIG. 1 is a block diagram of an antipodal demodulator for non-coherent unitary space-time modulation in MIMO wireless communication.



SPECIFIC EMBODIMENTS
For clear understanding of the objectives, features and advantages of the invention, detailed description of the invention will be given below in conjunction with accompanying drawings and specific embodiments. It should be noted that the embodiments are only meant to explain the invention, and not to limit the scope of the invention.
Principle of the method of the invention will be described below:
(1) Maximum Likelihood Demodulation
Assume a MIMO wireless communication system comprises M transmission antennas and N receiving antennas, a symbol transmission interval thereof is T, and channel fading coefficient is constant in a cycle T, and varies in different cycles. Assume Φ represents a T×M transmission signal unitary matrix and a transmission symbol, Y represents a T×N receiving signal matrix and a receiving symbol, H is a M×N channel fading coefficient matrix, and W is a T×N additive white Gaussian noise (AWGN) matrix, and all elements in H and W are independently and identically distributed random variables which obey the CN(0,1) distribution, wherein ρ represents a signal-noise ratio (SNR) at each receiving antenna, and a normalization coefficient √{square root over (ρ/M)} ensures an average signal-noise ratio of each receiving antenna is ρ. A Rayleigh fast flat-fading channel model is defined as:




  
    
      
        Y
        =
        
          
            
              
                
                  ρ
                  ⁢
                  
                    
                  
                  ⁢
                  T
                
                M
              
            
            ⁢
            Φ
            ⁢
            
              
            
            ⁢
            H
          
          +
          W
        
      
    
    
      
        (
        1
        )
      
    
  




Assume C={Φl}l=1L represents the non-coherent unitary space-time diagram, tr(•) represents calculating a trace of a matrix within the brackets, (•)H represents a complex conjugate transpose of a matrix or a vector, p(Y|Φl) represents a conditional probability of the receiving symbol Y as the transmission symbol is Φl, {circumflex over (Φ)} represents a demodulated constellation matrix which is also the signal output matrix, arg max tr( ) represents calculating traces of all the constellation matrices and determining the maximum trace, and then obtaining the demodulated constellation matrix {circumflex over (Φ)} corresponding to the maximum trace, where ψl represents a conditional probability or a trace of the matrix product YHΦlΦlHY. A maximum likelihood demodulation algorithm of the receiver without channel estimation is:




  
    
      
        
          
            
              Φ
              ^
            
            =
            
              
                argmax
                
                  
                    Φ
                    l
                  
                  ∈
                  C
                
              
              ⁢
              
                p
                (
                Y
                
              
              ⁢
              
                Φ
                l
              
            
          
          )
        
        =
        
          
            argmax
            
              
                Φ
                l
              
              ∈
              C
            
          
          ⁢
          
            
          
          ⁢
          
            tr
            ⁡
            
              (
              
                
                  Y
                  H
                
                ⁢
                
                  Φ
                  l
                
                ⁢
                
                  Φ
                  l
                  H
                
                ⁢
                Y
              
              )
            
          
        
      
    
    
      
        (
        2
        )
      
    
  




Assume the trace of the matrix product YHΦlΦlHY is:

ψl=tr(YHΦlΦlHY)  (3)

where 1≦l≦L.
(2) Antipodal Constellation
Assume U, V represent two T×M matrices on the complex domain space (where T=2M)), ΣUHV represents a diagonal matrix formed by singular values of a matrix UHV, d(U, V) represents a Frobenius chord distance between U and V:

d(U, V)=√{square root over (2M−2tr(ΣUHV))}  (4)

Two points Φα and Φβ with the biggest Frobenius chord distance are defined as antipodes, and it is obvious that the Frobenius chord distance therebetween is d(Φα,Φβ)=√{square root over (2M)}. The antipodal constellation is defined as follows: if the unitary space-time constellation comprises L/2 pairs of antipodes, this kind of constellation is referred to as the antipodal constellation.
(3) Relationship Between the Antipodal Constellation matrix and the Receiving Signal Matrix
For the antipodal constellation, two constellation matrix Φ and Φ antipodal to each other and the receiving signal matrix Y have the following relationship:

tr(YHΦΦHY)+tr(YH Φ ΦHY)=tr(YHY)  (5)

Assume σ represents a trace of an autocorrelation matrix YHY of the output matrix Y, then

σ=tr(YHY)  (6)

Equation (5) can be proved as follows: Assume Φ=[φ1 φ2 . . . φM], Φ=[ φ1  φ2 . . . φM], where Φ and Φ are an antipode pair, φi and φi are respectively T-dimensional column vectors of Φ and Φ. It can be seen from definition of the antipode that column vectors between Φ and Φ are unit orthogonal to each other, namely φi⊥ φi, i=1,2, . . . , M. Two matrices orthogonal to each other satisfy




  
    
      
        ΦΦ
        H
      
      +
      
        
          Φ
          _
        
        ⁢
        
          
            Φ
            _
          
          H
        
      
    
    =
    
      
        
          [
          
            Φ
            ⁢
            
              
            
            ⁢
            
              Φ
              _
            
          
          ]
        
        ⁡
        
          [
          
            
              
                
                  Φ
                  H
                
              
            
            
              
                
                  
                    Φ
                    _
                  
                  H
                
              
            
          
          ]
        
      
      =
      I
    
  
  ,




where I is a T×T unit matrix.

It can be deduced from the left part of equation (5) that:

tr(YHΦΦHY)+tr(YH Φ ΦHY)=tr(YH(ΦΦH+ Φ ΦH)Y)=tr(YHIY)=σ

(4) Antipodal Demodulation Method
An antipodal demodulation method for non-coherent unitary space-time modulation in MIMO wireless communication of the invention comprises steps of:
(1) dividing an antipode-based unitary space-time constellation




  C
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    L
  




into two sub-constellation





  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




and





  
    
      
        C
        _
      
      1
    
    =
    
      
        {
        
          
            Φ
            _
          
          l
        
        }
      
      
        l
        =
        1
      
      
        L
        /
        2
      
    
  
  ,




there is no antipode pair in each sub-constellation, and there is one-to-one correspondence between two antipodes in different sub-constellations;

(2) using equation (3) to traverse and calculate traces of a product of L/2 constellation matrices in the sub-constellation




  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




and a receiving signal matrix Y: ψl=tr(YHΦlΦlHY), l=1,2, . . . L/2, determining a maximum trace ψmax and a minimum trace ψmin therefrom, and corresponding constellation matrices Φi and Φj in the sub-constellation





  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




according to the maximum trace ψmax and the minimum trace ψmin respectively, obtaining an antipode matrix Φj antipodal to Φj in another sub-constellation





  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




according to relationship between the antipodes, calculating a maximum trace ψmax of a matrix product corresponding to the other sub-constellation





  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




according to a relationship among the constellation matrices Φj and Φj antipodal to each other, and the receiving signal matrix Y:

 ψmax=tr(YH Φj ΦjHY)=tr(YHY)−tr(YHΦjΦjHY)=σ−ψmin  (7);

and
(3) comparing the maximum trace ψmax and the maximum trace ψmax corresponding to constellation points in the sub-constellations, determining a greater one therefrom, and selecting a constellation matrix corresponding thereto as a demodulation signal matrix, namely, selecting the transmission signal matrix Φi corresponding to ψmax from the sub-constellation




  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




as a demodulated constellation matrix {circumflex over (Φ)}=Φi as ψmax> ψmax, and selecting the transmission signal matrix Φj corresponding to ψmax from the sub-constellation





  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




as a demodulated constellation matrix {circumflex over (Φ)}= Φj as ψmax< ψmax.

So far, a maximum likelihood demodulation method traversing L constellation points is converted to an optimized maximum likelihood demodulation method traversing L/2 constellation points.
Based on the above-mentioned antipodal demodulation method, an antipodal demodulator for non-coherent unitary space-time modulation in MIMO wireless communication is provided for performing optimized maximum likelihood demodulation on the antipode-based non-coherent unitary space-time code, as shown in FIG. 1, the demodulator comprises an input buffer, a read-only memory module, a trace-calculating module, an extreme-value-calculating module, a register group, a maximum-calculating module, a comparing and selecting module, and an output buffer.
The input buffer is configured to receive and save a receiving signal matrix Y, and to output the receiving signal matrix Y to the trace-calculating module, the receiving signal matrix Y representing a T×N complex matrix, and yαγ representing a signal received by the γth receiving antenna at time α, the read-only memory module is configured to save all the constellation matrices of two sub-constellation C1={Φl}l=1L/2 and C1={ Φl}l=1L/2 of an antipode-based unitary space-time constellation




  
    C
    =
    
      
        {
        
          Φ
          l
        
        }
      
      
        l
        =
        1
      
      L
    
  
  ,




where L represents the number of constellation points in the constellation, Φi and Φi represents two T×M complex matrices, T represents a coherent time interval, and Φαβ and Φαβ represents signals transmitted by the βth transmission antenna at the time α, the trace-calculating module is configured to receive L/2 constellation matrices in the sub-constellation





  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




from the read-only memory module, and the receiving signal matrix Y from the input buffer, calculating traces ψl=tr(YHΦlΦlHY) and σ=tr(YHY), and transmitting L/2 traces ψl of the matrix YHΦlΦlHY to the extreme-value-calculating module, and the trace σ of the matrix YHY to the maximum-calculating module, where 1≦l≦L/2, and tr(□) represents obtaining a trace of a matrix within the brackets, the extreme-value-calculating module is configured to compare the L/2 traces ψl of the matrix YHΦlΦlHY, and to save a maximum trace ψmax and a minimum trace ψmin thereof, an address i1 of a constellation matrix Φi corresponding to the maximum trace ψmax in the read-only memory module, and an address j1 of an antipode matrix Φj corresponding to the minimum trace ψmin and antipodal to a constellation matrix Φj in another sub-constellation





  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




in the read-only memory module into the register group, where 1≦l≦L/2, the maximum-calculating module is configured to receive the trace σ of the matrix YHY from the trace-calculating module, and the minimum trace ψmin from the register group, to calculate ψmax=σ−ψmin, and to save ψmax into the register group, the comparing and selecting module is configured to obtain ψmax and ψmax from the register group, to compare ψmax with ψmax, and to output a control signal contr operating to control the register group, and an address of a constellation matrix corresponding to a greater one of ψmax and ψmax in the read-only memory module to the read-only memory module, the register group is configured to save ψmax, ψmin, i1, and j1 from the extreme-value-calculating module, and ψmax from the maximum-calculating module, and to output an address of a constellation matrix corresponding to the greater one of ψmax and ψmax in the read-only memory module to the read-only memory module according to the control signal contr output by the comparing and selecting module, whereby controlling the read-only memory module to output a demodulated constellation matrix to the output buffer, and the output buffer is configured to receive and buffer the demodulated constellation matrix {circumflex over (Φ)} from the read-only memory module.

The read-only memory module is configured to save the two sub-constellation




  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




and





  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




of the antipode-based unitary space-time constellation, there is no antipode pair in each sub-constellation, and there is one-to-one correspondence between two antipodes in different sub-constellations, the read-only memory module is configured to output L/2 constellation matrices in the sub-constellation





  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




to the trace-calculating module, to receive the address from the register group indicating a corresponding constellation matrix in the read-only memory module is the demodulated constellation matrix {circumflex over (Φ)}, and to output {circumflex over (Φ)} to the output buffer.

The extreme-value-calculating module is configured to receive L/2 traces ψl of matrices YHΦlΦlHY output by ψl computing units in the trace-calculating module, to determine a maximum trace ψmax and a minimum trace ψmin therefrom, to output the maximum trace ψmax and the minimum trace ψmin to the register group, and to output the address i1 of the constellation matrix Φi corresponding to the maximum trace ψmax in the read-only memory module, and the address j1 of the antipode matrix Φj corresponding to the minimum value ψmin and antipodal to the constellation matrix Φj in another sub-constellation




  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




in the read-only memory module into the register group, where 1≦l≦L/2;

The maximum-calculating module is configured to receive the trace a of the matrix YHY from σ computing unit in the trace-calculating module, to obtain the minimum trace ψmin from the register group, to calculate ψmax=σ−ψmin, and to output ψmax to the register group.
The register group is configured to receive and to save ψmax and ψmin from the extreme-value-calculating module, and the address i1 of the constellation matrix Φi corresponding to the maximum trace ψmax in the read-only memory module, and the address j1 of the antipode matrix Φj corresponding to the minimum value ψmin and antipodal to the constellation matrix Φj in another sub-constellation




  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




in the read-only memory module, to output ψmin to the maximum-calculating module, to receive and save ψmax from the maximum-calculating module, and to output ψmax and ψmax to the comparing and selecting module.

The comparing and selecting module is configured to compare ψmax with ψmax, and to output the control signal contr operating to control the register group to the register group so that the register group transmits the address i1 of the constellation matrix Φi corresponding to the maximum trace ψmax in the read-only memory module to the read-only memory module if ψmax> ψmax, and transmits the address j1 of the constellation matrix Φj corresponding to the maximum trace ψmax in the read-only memory module to the read-only memory module if ψmax< ψmax.
While preferred embodiments of the invention have been described above, the invention is not limited to disclosure in the embodiments and the accompanying drawings. Any changes or modifications without departing from the spirit of the invention fall within the scope of the invention.

## Claims

1. An antipodal demodulation method for non-coherent unitary space-time modulation in MIMO wireless communication, comprising steps of:
(1) dividing an antipode-based unitary space-time constellation





  C
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    L
  




into two sub-constellations




  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




and




  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




and where L represents the number of constellation points in said constellation, Φl and Φl represents two T×M complex matrices, T represents a coherent time interval, M represents the number of transmission antennas, Φαβ and Φαβ represents signals transmitted by the βth transmission antenna at time α, there is no antipode pair in the sub-constellation, and there is one-to-one correspondence between two antipodes in different sub-constellations;
(2) obtaining traces of a matrix product of L/2 constellation matrices in said sub-constellation C1={Φl}l=1L/2 and a receiving signal matrix Y: ψl=tr(YHΦlΦlHY), l=1,2, . . . L/2, determining a maximum trace ψmax and a minimum trace ψmin therefrom, calculating the trace of a matrix product of said receiving signal matrix Y: σ=tr(YHY), and corresponding constellation matrices Φi and Φj in said sub-constellation





  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




according to said maximum trace ψmax and said minimum trace ψmin, obtaining an antipode matrix Φj antipodal to Φj in another sub-constellation




  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




according to relationship between said antipodes, calculating a maximum trace ψmax of a matrix product corresponding to the other sub-constellation




  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      )
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




according to a relationship among said constellation matrices Φj and Φj antipodal to each other, and said receiving signal matrix Y: ψmax=σ−ψmin=tr(YH Φj ΦjHY)=tr(YHY)−tr(YHΦjΦjHY), where said receiving signal matrix Y represents a T×N complex matrix, T represents a coherent time interval, N represents the number of receiving antennas, yαγ represents a signal received by the γth receiving antenna at said time α, and tr(□) represents obtaining a trace of a matrix within the brackets; and
(3) comparing said maximum trace ψmax and said maximum trace ψmax corresponding to constellation points in said sub-constellations, determining a greater one therefrom, and selecting a constellation matrix corresponding thereto as a demodulation signal matrix, namely, selecting said transmission signal matrix Φi corresponding to ψmax from said sub-constellation





  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




as a demodulated constellation matrix {circumflex over (ψ)}=Φi as ψmax> ψmax, and selecting said transmission signal matrix Φj corresponding to ψmax from said sub-constellation




  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




as a demodulated constellation matrix {circumflex over (Φ)}= Φj as ψmax< ψmax.

2. An antipodal demodulator for non-coherent unitary space-time modulation in MIMO wireless communication, comprising an input buffer, a read-only memory module, a trace-calculating module, an extreme-value-calculating module, a register group, a maximum-calculating module, a comparing and selecting module, and an output buffer, wherein
said input buffer is configured to receive and save a receiving signal matrix Y, and to output said receiving signal matrix Y to said trace-calculating module, said receiving signal matrix Y representing a T×N complex matrix, and yαγ representing a signal received by the γth receiving antenna at time α;
said read-only memory module is configured to save all the constellation matrices of two sub-constellations





  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




and




  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




of an antipode-based unitary space-time constellation




  
    C
    =
    
      
        {
        
          Φ
          l
        
        }
      
      
        l
        =
        1
      
      L
    
  
  ,




where L represents the number of constellation points in said constellation, Φl and Φl represents two T×M complex matrices, T represents a coherent time interval, and Φαβ and Φαβ represents signals transmitted by the βth transmission antenna at said time α;
said trace-calculating module is configured to receive L/2 constellation matrices in said sub-constellation





  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




from said read-only memory module, and said receiving signal matrix Y from said input buffer, calculating traces ψl=tr(YHΦlΦlHY) and σ=tr(YHY), and transmitting L/2 traces ψl of said matrix YHΦlΦlHY to said extreme-value-calculating module, and said trace σ of said matrix YHY to said maximum-calculating module, where 1≦l≦L/2, and tr(□) represents obtaining a trace of a matrix within the brackets;
said extreme-value-calculating module is configured to compare said L/2 traces ψl of said matrix YHΦlΦlHY, and to save a maximum trace ψmax and a minimum trace ψmin thereof, an address i1 of a constellation matrix Φi corresponding to said maximum trace ψmax in said read-only memory module, and an address j1 of an antipode matrix Φj corresponding to said minimum trace ψmin and antipodal to a constellation matrix Φj in another sub-constellation





  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




in said read-only memory module into said register group, where 1≦l≦L/2;
said maximum-calculating module is configured to receive said trace σ of said matrix YHY from said trace-calculating module, and said minimum trace ψmin from said register group, to calculate ψmax=σ−ψmin, and to save ψmax into said register group;
said comparing and selecting module is configured to obtain ψmax and ψmax from said register group, to compare ψmax and ψmax, and to output a control signal contr operating to control said register group, and an address of a constellation matrix corresponding to a greater one of ψmax and ψmax in said read-only memory module to said read-only memory module;
said register group is configured to save ψmax, ψmin, i1, and j1 from said extreme-value-calculating module, and ψmax from said maximum-calculating module, and to output an address of a constellation matrix corresponding to said greater one of ψmax and ψmax in said read-only memory module to said read-only memory module according to said control signal contr output by said comparing and selecting module, whereby controlling said read-only memory module to output a demodulated constellation matrix to said output buffer; and
said output buffer is configured to receive and buffer said demodulated constellation matrix {circumflex over (Φ)} from said read-only memory module.

3. The antipodal demodulator of claim 2, wherein said read-only memory module is configured to save said two sub-constellations




  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




and




  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




of said antipode-based unitary space-time constellation, there is no antipode pair in each sub-constellation, and there is one-to-one correspondence between two antipodes in different sub-constellations, said read-only memory module is configured to output L/2 constellation matrices in said sub-constellation




  
    C
    1
  
  =
  
    
      {
      
        Φ
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




to said trace-calculating module, to receive said address from said register group indicating a corresponding constellation matrix in said read-only memory module is said demodulated constellation matrix {circumflex over (Φ)}, and to output {circumflex over (Φ)} to said output buffer.

4. The antipodal demodulator of claim 2, wherein said extreme-value-calculating module is configured to receive L/2 traces ψl of matrices YHΦlΦlHY output by ψl computing units in said trace-calculating module, to determine a maximum trace ψmax and a minimum trace ψmin therefrom, to output said maximum trace ψmax and said minimum trace ψmin to said register group, and to output said address i1 of said constellation matrix Φi corresponding to said maximum trace ψmax in said read-only memory module, and said address j1 of said antipode matrix Φj corresponding to said minimum value ψmin and antipodal to said constellation matrix Φj in another sub-constellation




  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




in said read-only memory module into said register group, where 1≦l≦L/2.

5. The antipodal demodulator of claim 2, wherein said maximum-calculating module is configured to receive said trace σ of said matrix YHY from σ computing unit in said trace-calculating module, to obtain said minimum trace ψmin from said register group, to calculate ψmax=σ−ψmin, and to output ψmax to said register group.

6. The antipodal demodulator of claim 2, wherein said register group is configured to receive and to save ψmax and ψmin from said extreme-value-calculating module, and said address i1 of said constellation matrix Φi corresponding to said maximum trace ψmax in said read-only memory module, and said address j1 of said antipode matrix Φj corresponding to said minimum value ψmin and antipodal to said constellation matrix Φj in another sub-constellation




  
    
      C
      _
    
    1
  
  =
  
    
      {
      
        
          Φ
          _
        
        l
      
      }
    
    
      l
      =
      1
    
    
      L
      /
      2
    
  




in said read-only memory module, to output ψmin to said maximum-calculating module, to receive and save ψmax from said maximum-calculating module, and to output ψmax and ψmax to said comparing and selecting module.

7. The antipodal demodulator of claim 2, wherein said comparing and selecting module is configured to compare ψmax with ψmax, and to output said control signal contr operating to control said register group to said register group so that said register group transmits said address i1 of said constellation matrix Φi corresponding to said maximum trace ψmax in said read-only memory module to said read-only memory module if ψmax> ψmax, and transmits said address j1 of said constellation matrix Φj corresponding to said maximum trace ψmax in said read-only memory module to said read-only memory module if ψmax< ψmax.