# Patent

## Title
Multi-user iterative detection for CDMA communications systems on the MIMO channel

## Abstract

The invention relates to a reception method for communication over frequency-selective channels with a plurality of send antennas and a plurality of receive antennas, to process data received by the receive antennas that, on sending, was successively modulated and spread.
To this end, reception uses:

    
    
        linear filtering (202, 202′) adapted to process the received data to generate an evaluation (Ŝ) of the sent modulated data before spreading, this filtering taking account in particular of the spatial diversity of the plurality of receive antennas;
        subtracting interference using an estimate of multi-antenna interference (MAI), intersymbol interference (ISI), and multi-user interference (MUI) previously regenerated on the basis of the evaluation (ŝ) of the sent modulated data generated by previous filtering 202; 
        processing to generate an interference estimate for the data received from information computed on the basis of the evaluation (ŝ) of the sent modulated data.
    
    


The invention relates further to a reception system adapted to implement the method and a transmission system including the reception system.

## Background
RELATED APPLICATIONS
This is a U.S. National Phase Application under 35 USC 371 of International Application PCT/EP2005/004408, filed on Apr. 21, 2005.
GENERAL TECHNICAL FIELD
The present invention relates to the field of digital communications. It concerns how to decode efficiently digital data transmitted on a frequency-selective MIMO channel at the same time as optimizing the performance/complexity trade-off. FIG. 1 shows an overall method of transmission on a frequency-selective MIMO channel 300 between a sender 100 with T send antennas, delivering signals x[n] at the time n, and a receiver 200 with R receive antennas, receiving signals y[n] at the time n.
GENERAL DESCRIPTION OF THE PRIOR ART
Any communications system managing the access of multiple users to the same channel by allocating specific spreading codes (CDMA) is limited in capacity by multi-user interference (MUI) between users. In the context of the present invention, transmission is envisaged on a channel liable to generate other kinds of interference such as spatial multi-antenna interference (MAI) caused by multiple send antennas and intersymbol interference (ISI) caused by the frequency selectivity of the channel. On reception, these various kinds of interference are cumulative and make recovering the useful information difficult.
Pioneering work carried out by S. Verdu in the 1980s clearly demonstrated the benefit of exploiting the structural properties of multi-user interference (MUI), multi-antenna interference (MAI) and intersymbol interference (ISI) to improve performance for a fixed load (the number of users per chip) or to improve the load for fixed performance.
Many types of linear detectors have been studied, capable of supporting a greater or lesser load, which load may be evaluated analytically under asymptotic conditions. Without recourse to iterative techniques, the performance of these detectors falls far short of the performance of a maximum likelihood (ML) detector (for a system with or without coding).
The class of non-linear LIC-ID detectors based on linear iterative cancellation of the interference thus offers an excellent trade-off between performance and complexity. LIC-ID detectors use the following functions: linear filtering, weighted regeneration of interference (regardless of its nature), subtraction of the regenerated interference from the received signal. They deliver decisions on the sent modulated data (or symbols) with a reliability that increases in monotonous fashion with each new attempt. LIC-ID detectors which are intended to eliminate ISI (at block level) asymptotically achieve the performance of an optimum ML detector with a computation complexity similar to that of a linear equalizer. LIC-ID detectors intended to combat MUI approximate the performance of the optimum ML detector with a computation complexity comparable to that of a simple linear detector.
A remarkable feature of LIC-ID detectors is that they can easily be combined with hard or weighted decisions delivered by the channel decoder, thus effecting separate and iterative detection and decoding of the data.
For CDMA systems that are overloaded (by hypothesis by MUI) transmitting on frequency-selective MIMO channels, the level of interference is such that using LIC-ID receivers proves essential. If an iterative strategy is selected, the complexity of the receivers can be reduced, and rendered reasonable, only by simplifying the iterative processing as much as possible. LIC-ID detectors are treated separately for ISI and for MUI in reference [1] (see below) and in the case of ISI+MUI in reference [2] (see below).
[1] A. M. Chan, G. W. Wornell, “A New Class of Efficient Block-Iterative Interference Cancellation Techniques for Digital Communication Receivers”, IEEE J. VLSI Signal Processing (Special Issue on Signal Processing for Wireless Communication Systems), vol. 30, pp. 197-215, January-March 2002.

[2] W. Wang, V. H. Poor, “Iterative (Turbo) Soft Interference Cancellation and Decoding for Coded CDMA”, IEEE Trans. Commun., vol. COM-47, no. 9, pp. 2356-2374, September 1999.

Their generalization to MUI+MAI+ISI still constitutes an open subject of research, in particular because of the complexity of the processing to be effected, implying computations on particularly large matrices.
SUMMARY OF THE INVENTION
A first aspect of the invention proposes a receiving method according to any one of claims 1 to 17.
A second aspect of the invention proposes a transmission system according to claim 18.
A third aspect of the invention proposes a receiving method according to any one of claims 19 to 24.
An object of the present invention is to propose a receiver for “multicode” CDMA transmission (K>T) and/or overloaded CDMA transmission (K users, spreading factor N<K) on frequency-selective MIMO channels (T send antennas and R receive antennas), on the general assumption of there being no CSI (i.e. no information as to the state of the channel) at the sender and a perfect knowledge of the CSI at the receiver. The receiver is based on a combination of simple mechanisms and techniques to obtain the best possible quality of service at fixed spectral efficiency and signal-to-noise ratio (SNR) or the best possible usable bit rate at fixed quality of service, band and SNR.
To this end, the invention proposes an iterative decoding and equalization device including a data detector receiving data from the various send antennas comprising:

    
    
        a bank of K linear filters, one for each of the K potential users or streams, for generating statistics on the sent modulated data (also referred to as symbolic data or symbols) taking account of the spatial diversity offered by the N receive antennas;
        means for-subtracting from the received signal the MAI+ISI+MUI interference regenerated for the user processed on the basis of estimates of the available symbolic data sent, before any linear filtering;
        means for processing the output of each linear filter in order to generate probabilistic information at the bit level that can be used for external decoding;
        external decoding with weighted inputs and outputs capable of generating probabilistic information referred to as extrinsic information pertinent to the computation of the estimates of the data sent (in the sense of the criterion minimizing the mean square error (MMSE));
        means for recursively concatenating the output of the external decoder with the MAI+ISI+MUI interference regenerator.
    
    





DESCRIPTION OF THE DRAWINGS
Other features and advantages of the invention will emerge from the following description, which is purely illustrative and non-limiting and should be read with reference to the appended drawings in which:
FIG. 1 illustrates a general concept of transmission on a frequency-selective MIMO channel;
FIG. 2 shows a first part of a sending process, including external channel coding of digital information, bit interleaving, and demultiplexing into K streams (one for each potential user);
FIG. 3 shows the second part of the FIG. 2 sending process, including space-time (space-frequency) spreading followed by multiplexing onto T send antennas;
FIG. 4 shows a first part of a variant sending process including external channel coding of digital information, bit interleaving, first demultiplexing (space demultiplexing) into T streams followed by second demultiplexing (code demultiplexing) into U streams;
FIG. 5 shows the second part of the FIG. 4 sending process, including time (or frequency) spreading and independent multiplexing for each antenna, compatible with the UMTS HSDPA mode;
FIG. 6 shows a flat ergodic or block level fading equivalent channel obtained by decomposition of the frequency-selective MIMO channel into the Fourier base and routinely used as a model for multicarrier modulations;
FIG. 7 shows the architecture of an LIC-ID receiver of the invention, indicating only the functional units necessary to understand the receiving process;
FIGS. 8a and 8b show two equivalent methods of implementing LIC-ID receivers, the FIG. 8a method representing the interference regeneration and filtering parts of the overall detector shown in FIG. 7.



DESCRIPTION OF A PREFERRED EMBODIMENT OF THE PRESENT INVENTION
1. General Structure of the Sender
Reception is intimately linked to the sending mode, which can be defined by a modulation/coding scheme of high spectral efficiency, and high adaptability capacity, based on the use of spread spectrum modulation and on the use of multiple send and receive antennas. The proposed solution is pertinent assuming no knowledge of the send channel (no CSI) and a perfect knowledge of the receive channel (CSI). The communication model is briefly described hereinafter in order to introduce a third embodiment of the present invention.
Referring to FIG. 2, the useful digital data is collected and grouped into a message m of Ko bits constituting the send digital data source 101. In each message m, a linear external code Co having an No×Ko generator matrix Go and constructed on F2 assigns at 102 a code word v of length No bits defined by the matrix equation:

v=Go m

The external coding yield is:




  ρ
  =
  
    
      K
      o
    
    
      N
      o
    
  




The length No of the code words is linked to the various parameters of the system by the equation:

No=K×L×q 

in which K designates the total number of potential users, L the length of the packets (in symbol times) and q the number of bits per modulation symbol. The code may be of any type, for example a convolutional code, a turbocode, an LDPC code, etc. In a multiple access type configuration, the message m consists in a plurality of multiplexed messages from different sources. Coding is effected independently on each component message. The code word v results from the concatenation 103 of the various code words produced.

The code word v is sent to an interleaver 104 operating at the bit level and, where appropriate, having a particular structure. In a multiple access type configuration, the interleaving acts piece by piece on the various code words placed one after the other. The output of this interleaver is broken up into KL sets of q bits called integers.
The stream of integers is demultiplexed 105 onto K separate channels, where K may be chosen arbitrarily to be strictly greater than the number T of send antennas. The output from this operation is a K×L integer matrix D. The L columns d[n] n=0, . . . , L−1 of this matrix D have the following structure:

d[n]=[d1[n]Td2[n]T . . . dK[n]T]T∈F2qK 

in which the component integers dk[n] k=1, . . . , K are themselves structured as follows:

dk[n]=[dk,1[n]dk,2[n]. . . dk,q[n]]T∈F2q 

The integers dk[n] of the matrix D are then individually modulated 107 via a modulation table μ:F2qI to yield modulated data, or more precisely complex symbols sk[n] of a constellation I⊂ with Q=2q elements. This transforms the integer matrix D into a K×L complex matrix S the L columns s[n] n=0, . . . , L−1 whereof are structured as follows:

s[n]μ(d[n])=[s1[n] s2[n] . . . sK[n]]T∈IK 

It is useful to specify the following inverse relationships:

μ−1(s[n])d[n] μ−1(sk[n])dk[n] μj−1(sk[n])dk,j[n]

1.1 Space-time (or Space-frequency) Internal Linear Coding (or Spreading) Under Overload Conditions

Referring to FIG. 3, space-time (or space-frequency) spreading 108 is effected for each matrix S by means of an N×K generator full matrix G (generator matrix of the internal linear coding defined on the body of the complexes), where:

N=T×SFSF∈

This generator matrix is also called a spreading matrix. For example, this matrix may be considered to be constructed from N orthogonal spreading codes with spreading factor N. This internal linear coding therefore corresponds, in this case, to space-time (space-frequency) spreading with spreading factor N. The internal coding yield (or load) of the system is the ratio:




  α
  =
  
    K
    N
  




Two options are always available with respect to the definition of the generator matrix G: periodic spreading 108 in which G is re-used in each symbol time (not shown), or aperiodic spreading 108 in which G depends explicitly on the symbol time (see FIG. 3).
The hypothesis of periodic or aperiodic spreading can change the characteristics of the linear front-ends on reception.
Here aperiodic spreading is assumed.
Referring to FIG. 3, the multiplication at 108 of the symbol vectors s[n] by the generator matrix Gn produces a vector of N chips:

z[n]Gns[n]=[z1[n]z2[n] . . . zN[n]]T∈N 

The chip vectors z[n] are directly multiplexed at 109 onto the T send antennas (there is no posterior interleaving here). The effect of this operation is to transform the N×L chip matrix Z:

Z=[z[0] z[1] . . . z[L−1]]∈N×L 

into a T×LSF chip matrix X:

X=[x[0] x[1] . . . x[LSF−1]]∈T×LSF 

in which the columns x[l] l=0, . . . ,LSF−1 constitute the inputs of the MIMO channel:

x[l]=[x1[l] x2[l] . . . xT[l]]T∈T 

The vector z[n] of the N chips sent at the symbolic time n can always be organized in the form of a chip vector x[n] resulting from the juxtaposition of the chip vectors sent over the T antennas between the chip times l=nSF and l=nSF+SF−1:

x[n] [x[nSF+SF−1]T. . . x[nSF+1]Tx[nSF+0]T]T∈TSF 

Accordingly, as a general rule, the vectors x[n] z[n] and s[n] sent at the symbolic time n=0, . . . ,L−1 are linked by the matrix equations:

x[n]Πz[n]=ΠGns[n]=Wns[n]

in which Π designates an N×N permutation matrix.

1.2 Independent Internal Linear Internal Coding (or Spreading) Per Send Antenna (Code Re-use Principle)

By hypothesis, N is here a multiple of T:

N=T×SF SF∈

There are SF orthogonal codes of length SF. These SF codes are re-used at each send antenna (this is the code re-use principle). The spreading, effected independently for each antenna, is purely in the time domain (or the frequency domain). This imposes that K be also a multiple of T:

K=T×U U∈

This condition yields a new expression for the internal coding yield (load):





  α
  =
  
    U
    
      S
      F
    
  




The generator matrix Gn has a block diagonal structure:





  
    G
    n
  
  =
  
    
      [
      
        
          
            
              G
              n
              
                (
                1
                )
              
            
          
          
            
              
            
          
          
            
              
            
          
          
            0
          
        
        
          
            
              
            
          
          
            
              G
              n
              
                (
                2
                )
              
            
          
          
            
              
            
          
          
            
              
            
          
        
        
          
            
              
            
          
          
            
              
            
          
          
            ⋱
          
          
            
              
            
          
        
        
          
            0
          
          
            
              
            
          
          
            
              
            
          
          
            
              G
              n
              
                (
                T
                )
              
            
          
        
      
      ]
    
    ∈
    
      •
      
        N
        ×
        K
      
    
  




the block Gn(t) of the generator matrix being associated with the antenna t with dimension SF×U.

Referring to FIG. 4, the integer vector d[n] sent at the time n has the following particular structure:

d[n]=[d(1)[n]T d(2)[n]T. . . d(T)[n]T]T∈F2qK 

in which the symbol vectors d(t)[n]t=1, . . . ,T are themselves defined as follows:

d(t)[n]=[d1(t)[n]T d2(t)[n]T. . . dU(t)[n]T]T∈F2qU 

Referring to FIG. 5, the modulation 107 of this data d[n] yields a modulated data (or symbols) vector sent at the time n having the following particular structure:

s[n]=[s(1)[n]T s(2)[n]T. . . s(T)[n]T]T∈k 

in which the symbol vectors s(t)[n] t=1, . . . ,T are themselves defined as follows:

s(t)[n]=[s1(t)[n] s2(t)[n ]. . . sU(t)[n]]T∈U 

The multiplication 108 of the symbol vector s[n] by the generator matrix Gn produces a vector of N chips, which also has a particular structure:

z[n]Gns[n]=[z(1)[n]T z(2)[n]T . . . z(T)[n]T]T∈N 

in which the chip vectors z(t)[n] t=1, . . . , T are themselves defined as follows:

z(t)[n]Gn(t)s(t)[n]=[z1(t)[n]z2(t)[n]. . . zSF(t)[n]]T∈SF 

Each chip vector z(t)[n] is then multiplexed onto the send antenna t.
The vector z[n] of the N chips sent at the symbolic time n can always be organized in the form of a chip vector x[n] resulting from the juxtaposition of the chip vectors sent over the T antennas between the chip times l=nSF and l=nSF+SF−1:

x[n][x[nSF+SF−1]T . . . x[nSF+1]T x[nSF+0]T]T∈TSF 

Accordingly, as a general rule, the vectors x[n] z[n] and s[n] sent at the symbolic time n=0, . . . ,L−1 are linked by the matrix equations:

x[n]Πz[n]=ΠGns[n]=Wns[n]

in which Π designates an N×N permutation matrix.

It will be noted that in this sending variant, the recovery of the spatial diversity is effected via the code G0 (at 102) and the external bit interleaving (at 104). The overload capacity, which is known to increase with the length of the spreading codes, is lower.
The sending method fits naturally into the general class of space-time codes. The spectral efficiency of the system (in bits per use of the channel), assuming a limited band ideal Nyquist filter, is equal to:

η=T×ρ0×q×α

In practice, the send shaping filter has a non-null overflow factor (roll-off) ε. At the receiver, a filter matched to this send filter is used for all the receive antennas. It is assumed that the channel estimation and timing and carrier synchronization functions are implemented so that the coefficients of the impulse response of the channel are regularly spaced by an amount equal to the chip time (channel equivalent in the discrete baseband to the discrete time). This hypothesis is legitimate, the Shannon sampling theorem imposing sampling at the rate (1+ε)/Tc which may be approximated by 1/Tc when ε is small. Direct generalization is possible for expressions given hereinafter for a sampling rate equal to a multiple of 1/Tc.
2. Channel Model
Transmission is effected on a frequency-selective B-block channel with multiple inputs and outputs (MIMO):

H{H(1), H(2), . . . , H(B)}

The channel H(b) is assumed constant over Lx chips with the convention:

L×SF=B×LX B∈

The chip matrix X may be segmented into B separate T×LX chip matrices X(1), . . . ,X(B) (padded on the right and left with physical zeros or guard times if necessary), each matrix X(b) seeing the channel H(b). For what follows, it is useful to introduce a length of the blocks in symbols, defined as:




  
    L
    S
  
  ⁢
  •
  ⁢
  
    ⌈
    
      
        L
        X
      
      
        S
        F
      
    
    ⌉
  




such that:

L=B×LS 

The extreme cases of the B-block model are as follows:

B=1 and LX=LSFLS=L quasi−static model

B=LSF and LX=1LS=1 ergodic (chip) model

A renumbering of the symbols and the chips is applied within each block.
2.1 Convolutional Channel Model
For any block index b, the discrete time baseband equivalent channel model (chip timing) is used to write the receive vector y(b)[l]∈R at the chip time 1 in the form:




  
    
      y
      
        (
        b
        )
      
    
    ⁡
    
      [
      l
      ]
    
  
  =
  
    
      
        ∑
        
          p
          =
          0
        
        
          P
          -
          1
        
      
      ⁢
      
        
          H
          p
          
            (
            b
            )
          
        
        ⁢
        
          
            x
            
              (
              b
              )
            
          
          ⁡
          
            [
            
              l
              -
              p
            
            ]
          
        
      
    
    +
    
      
        v
        
          (
          b
          )
        
      
      ⁡
      
        [
        l
        ]
      
    
  




where P is the constraint length of the channel (in chips), x(b)[l]∈T is the complex vector of T chips sent at the chip time 1, where Hp(b)∈R×T is the matrix coefficient indexed p of the impulse response of the block MIMO channel indexed b and v(b)[l]∈R is the complex additive noise vector. The complex additive noise vectors v(b)[l] are assumed to be independent and identically distributed in accordance with an R-dimensional Gaussian law of circular symmetry with zero mean and covariance matrix σ2I. The P coefficients of the impulse response are R×T complex matrices, the inputs of which are identically distributed independent Gaussian inputs, with zero mean and with a covariance matrix satisfying the global power normalization constraint:





  
    E
    ⁡
    
      [
      
        diag
        ⁢
        
          {
          
            
              ∑
              
                p
                =
                0
              
              
                P
                -
                1
              
            
            ⁢
            
              
                H
                p
                
                  (
                  b
                  )
                
              
              ⁢
              
                H
                p
                
                  
                    (
                    b
                    )
                  
                  ⁢
                  †
                
              
            
          
          }
        
      
      ]
    
  
  =
  TI




in the case of a system with power equally distributed between the send antennas. Given these hypotheses, the eigen values of the correlation matrices of the coefficients of the MIMO channel conform to a Wishart distribution. It is emphasized that equal distribution of the power to the send antennas is a legitimate power allocation policy in the case of an absence of knowledge of the sending channel (no CSI).

2.2 Block Matrix Channel Model

To introduce the data decoding algorithm, one must show a matrix system on the set of the type:

y(b)=H(b)x(b)+v(b) 

where:

y(b)[y(b)[LS−1+M]T y(b)[LS−2+M]T . . . y(b)[0]T]T∈(LS+M)RSF 

v(b)[v(b)[LS−1+M]T v(b)[LS−2+M]T . . . v(b)[0]T]T∈(LS+M)RSF 

where M is the memory of the channel in symbol times defined as:





  M
  =
  
    ⌈
    
      
        P
        -
        1
      
      
        S
        F
      
    
    ⌉
  




with:

y(b)[n][y(b)[nSF+SF−1]T . . . y(b)[nSF+1]T y(b)[nSF+0]T]T∈RSF 

v(b)[n][v(b)[nSF+SF−1]T . . . v(b)[nSF+1]T v(b)[nSF+0]T]T∈RSF 

where:

x(b)[x(b)[LS−1]T x(b)[LS−2]T . . . x(b)[0]T]T∈LSTSF 

with:

x(b)[n][x(b)[nSF+SF−1]T . . . x(b)[nSF+1]T x(b)[nSF+0]T]T∈TSF 

and where H(b) is the Sylvester matrix for the channel:




  
    
      
        H
        
          _
          _
        
      
      
        (
        b
        )
      
    
    =
    
      
        [
        
          
            
              
                H
                
                  P
                  -
                  1
                
                
                  (
                  b
                  )
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
          
          
            
              
                H
                
                  P
                  -
                  2
                
                
                  (
                  b
                  )
                
              
            
            
              
                H
                
                  P
                  -
                  1
                
                
                  (
                  b
                  )
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
          
          
            
              
                
              
            
            
              
                
              
            
            
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                H
                0
                
                  (
                  b
                  )
                
              
            
            
              
                H
                1
                
                  (
                  b
                  )
                
              
            
            
              ...
            
            
              
                H
                
                  P
                  -
                  1
                
                
                  (
                  b
                  )
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
          
          
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                H
                0
                
                  (
                  b
                  )
                
              
            
            
              
                H
                1
                
                  (
                  b
                  )
                
              
            
            
              ...
            
            
              
                
                  H
                  
                    P
                    -
                    1
                  
                  
                    (
                    b
                    )
                  
                
                ⁢
                
                  
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
          
          
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
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                H
                0
                
                  (
                  b
                  )
                
              
            
            
              
                H
                1
                
                  (
                  b
                  )
                
              
            
            
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                H
                
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                H
                0
                
                  (
                  b
                  )
                
              
            
            
              
                H
                1
                
                  (
                  b
                  )
                
              
            
          
          
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                H
                0
                
                  (
                  b
                  )
                
              
            
          
        
        ]
      
      ∈
      
        •
        
          
            (
            
              
                L
                S
              
              +
              M
            
            )
          
          ⁢
          
            RS
            F
          
          ×
          
            L
            S
          
          ⁢
          
            TS
            F
          
        
      
    
  




  
    Moreover
    ⁢
    
      :
    
  




  
    
      
        x
        
          _
          _
        
      
      
        (
        b
        )
      
    
    =
    
      
        [
        
          
            
              
                
                  
                    x
                    _
                  
                  
                    (
                    b
                    )
                  
                
                ⁡
                
                  [
                  
                    
                      L
                      S
                    
                    -
                    1
                  
                  ]
                
              
            
          
          
            
              
                
                  
                    x
                    _
                  
                  
                    (
                    b
                    )
                  
                
                ⁡
                
                  [
                  
                    
                      L
                      S
                    
                    -
                    2
                  
                  ]
                
              
            
          
          
            
              ⋮
            
          
          
            
              
                
                  
                    x
                    _
                  
                  
                    (
                    b
                    )
                  
                
                ⁡
                
                  [
                  0
                  ]
                
              
            
          
        
        ]
      
      =
      
        
          
            [
            
              
                
                  
                    W
                    
                      L
                      -
                      1
                    
                  
                
                
                  
                    
                  
                
                
                  
                    
                  
                
                
                  
                    
                  
                
              
              
                
                  
                    
                  
                
                
                  
                    W
                    
                      L
                      -
                      2
                    
                  
                
                
                  
                    
                  
                
                
                  
                    
                  
                
              
              
                
                  
                    
                  
                
                
                  
                    
                  
                
                
                  ⋱
                
                
                  
                    
                  
                
              
              
                
                  
                    
                  
                
                
                  
                    
                  
                
                
                  
                    
                  
                
                
                  
                    W
                    0
                  
                
              
            
            ]
          
          ⁡
          
            [
            
              
                
                  
                    
                      s
                      
                        (
                        b
                        )
                      
                    
                    ⁡
                    
                      [
                      
                        
                          L
                          S
                        
                        -
                        1
                      
                      ]
                    
                  
                
              
              
                
                  
                    
                      s
                      
                        (
                        b
                        )
                      
                    
                    ⁡
                    
                      [
                      
                        
                          L
                          S
                        
                        -
                        2
                      
                      ]
                    
                  
                
              
              
                
                  ⋮
                
              
              
                
                  
                    
                      s
                      
                        (
                        b
                        )
                      
                    
                    ⁡
                    
                      [
                      0
                      ]
                    
                  
                
              
            
            ]
          
        
        =
        
          
            W
            
              _
              _
            
          
          ⁢
          
            
              s
              
                _
                _
              
            
            
              (
              b
              )
            
          
        
      
    
  



Wn(n=0, . . . ,L−1) having been introduced above from the spreading matrix Gn during the description of preferred sending forms (end of sections 1.1 and 1.2).

Whence, finally, the system:

y(b)=H(b)Ws(b)+v(b)=Θ(b)s(b)+v(b) 

where Θ(b) represents the matrix of convolution of the channel with the spreading codes:

Θ(b)H(b)W∈(LS+M)RSF×LSK 

2.3 Sliding Window Matrix Channel Model

In practice, to reduce the dimensions, a sliding window model is used of length:

LW=L1+L2+1 LS 

The following new system is obtained:

y(b)[n]=H(b)x(b)[n]+v(b)[n]

where:

y(b)[n]=[y(b)[n+L1]T . . . y(b)[n−L2]T]T∈LWRSF 

x(b)[n]=[x(b)[n+L1]T . . . x(b)[n−L2−M]T]T∈(LW+M)TSF 

v(b)[n]=[v(b)[n+L1]T . . . v(b)[n−L2]T]T∈LWRSF 

and where H(b) is the Sylvester matrix for the channel:




  
    
      
        H
        
          _
          _
        
      
      
        (
        b
        )
      
    
    =
    
      
        [
        
          
            
              
                H
                0
                
                  (
                  b
                  )
                
              
            
            
              
                H
                1
                
                  (
                  b
                  )
                
              
            
            
              ...
            
            
              
                H
                
                  P
                  -
                  1
                
                
                  (
                  b
                  )
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
          
          
            
              
                
              
            
            
              
                H
                0
                
                  (
                  b
                  )
                
              
            
            
              
                H
                1
                
                  (
                  b
                  )
                
              
            
            
              ...
            
            
              
                
                  H
                  
                    P
                    -
                    1
                  
                  
                    (
                    b
                    )
                  
                
                ⁢
                
                  
                
              
            
            
              
                
              
            
            
              
                
              
            
          
          
            
              
                
              
            
            
              
                
              
            
            
              ⋱
            
            
              ⋱
            
            
              ⋱
            
            
              ⋱
            
            
              
                
              
            
          
          
            
              
                
              
            
            
              
                
              
            
            
              
                
              
            
            
              
                H
                0
                
                  (
                  b
                  )
                
              
            
            
              
                H
                1
                
                  (
                  b
                  )
                
              
            
            
              ...
            
            
              
                H
                
                  P
                  -
                  1
                
                
                  (
                  b
                  )
                
              
            
          
        
        ]
      
      ∈
      
        •
        
          
            L
            W
          
          ⁢
          
            RS
            F
          
          ×
          
            (
            
              
                L
                W
              
              +
              M
            
            )
          
          ⁢
          
            TS
            F
          
        
      
    
  




  
    Moreover
    ⁢
    
      :
    
  




  
    
      
        
          x
          
            _
            _
          
        
        
          (
          b
          )
        
      
      [
      
        
      
      ⁢
      n
      ]
    
    =
    
      
        [
        
          
            
              
                
                  
                    x
                    _
                  
                  
                    (
                    b
                    )
                  
                
                ⁡
                
                  [
                  
                    n
                    +
                    
                      L
                      1
                    
                  
                  ]
                
              
            
          
          
            
              ⋮
            
          
          
            
              
                
                  
                    x
                    _
                  
                  
                    (
                    b
                    )
                  
                
                ⁡
                
                  [
                  
                    n
                    -
                    
                      L
                      2
                    
                    -
                    M
                  
                  ]
                
              
            
          
        
        ]
      
      =
      
        
          
            [
            
              
                
                  
                    W
                    
                      n
                      +
                      
                        L
                        1
                      
                    
                  
                
                
                  
                    
                  
                
                
                  
                    
                  
                
              
              
                
                  
                    
                  
                
                
                  ⋱
                
                
                  
                    
                  
                
              
              
                
                  
                    
                  
                
                
                  
                    
                  
                
                
                  
                    W
                    
                      n
                      -
                      
                        L
                        2
                      
                      -
                      M
                    
                  
                
              
            
            ]
          
          ⁢
          
            

          
          ⁢
          
            
          
          [
          
            
          
          ⁢
          
            
              
                
                  
                    s
                    
                      (
                      b
                      )
                    
                  
                  ⁡
                  
                    [
                    
                      n
                      +
                      
                        L
                        1
                      
                    
                    ]
                  
                
              
            
            
              
                ⋮
              
            
            
              
                
                  
                    s
                    
                      (
                      b
                      )
                    
                  
                  ⁡
                  
                    [
                    
                      n
                      -
                      
                        L
                        2
                      
                      -
                      M
                    
                    ]
                  
                
              
            
          
          ⁢
          
            
          
          ]
        
        ⁢
        
          
        
        =
        
          
            
              W
              
                _
                _
              
            
            n
          
          ⁢
          
            
              
                s
                
                  _
                  _
                
              
              
                (
                b
                )
              
            
            ⁡
            
              [
              n
              ]
            
          
        
      
    
  



Whence, finally, the system:

y(b)[n]=H(b)Wns(b)[n]+v(b)[n]=Θn(b)s(b)[n]+v(b)[n]

where Θn(b) represents the matrix of convolution of the channel with the spreading codes:

Θn(b)H(b)Wn∈LWRSF×(LW+M)K 

3. Multipath MIMO Channel Single-carrier Transmission (HSDPA)

It is assumed here that the bit rate is very high and that the coherence time of the channel is long, so that LXSFLS1. For the HSDPA mode of the UMTS standard, the channel is quasi-static, i.e. B=1.
4. Multipath MIMO Channel Multicarrier Transmission (MC-CDMA)
The spreading (or the internal linear code) is space-frequency spreading or frequency spreading. With reference to FIG. 6, it is well known to the person skilled in the art that the introduction of a send IFFT 120 and a receive FFT 220 yields (ignoring interleaving) an equivalent channel that is not frequency selective (channel modeled by a circulating matrix using cyclic prefixes, then rendered diagonal in the Fourier base). Accordingly, each carrier sees a flat MIMO channel. Using the formalism previously described, the channel after FFT may be seen as a non-selective B-block channel (P=1, M=0). It is specified that LX≦SFLS=1: the channel is a B-block channel at the chip time but everything happens as if it were “ergodic” at the symbol time for the symbolic model considered. The width of the sliding window for calculating the filters is LW=1.
5. General Structure of the Receiver 200
The receiver 200 uses LIC-ID detection. Two types of linear front end are derived by way of example: unconditional MMSE and SUMF. In the remainder of the description the definition of the index b of the block concerned of the channel model is omitted, the processing being exactly the same for all of them.
5.1 Sent Symbol MMSE Estimation
On any iteration i, there is assumed an a priori knowledge of the data expressed via logarithmic ratios on the bits of the sent symbols:




  
    
      π
      
        k
        ,
        j
      
      i
    
    ⁡
    
      [
      n
      ]
    
  
  ⁢
  •ln
  ⁢
  
    
      
        Pr
        i
      
      ⁡
      
        [
        
          
            
              d
              
                k
                ,
                j
              
            
            ⁡
            
              [
              n
              ]
            
          
          =
          1
        
        ]
      
    
    
      
        Pr
        i
      
      ⁡
      
        [
        
          
            
              d
              
                k
                ,
                j
              
            
            ⁡
            
              [
              n
              ]
            
          
          =
          0
        
        ]
      
    
  




By convention, these ratios have the value 0 on the first iteration.
Referring to FIG. 7, on the basis of this a priori information, there can be found at 209 the value  si of the estimates, in the sense of the MMSE criterion, of the symbols sk[n] sent by the users k=1, . . . , K distributed between the antennas at the times n=0, . . . ,L−1. The estimate of a symbol is expressed as follows:




  
    
      
        s
        _
      
      k
      i
    
    ⁡
    
      [
      n
      ]
    
  
  ⁢
  •
  ⁢
  
    
      ∑
      
        s
        ∈
        J
      
      
        
      
    
    ⁢
    
      
    
    ⁢
    
      s
      ×
      
        
          Pr
          i
        
        ⁡
        
          [
          
            
              
                s
                k
              
              ⁡
              
                [
                n
                ]
              
            
            =
            s
          
          ]
        
      
    
  




With deep space-time interleaving, the a priori probability for a symbol may be approximated by the product of the marginal probabilities of the bits that constitute it:




  
    
      Pr
      i
    
    ⁡
    
      [
      
        
          
            s
            k
          
          ⁡
          
            [
            n
            ]
          
        
        =
        s
      
      ]
    
  
  ≈
  
    
      ∏
      
        j
        =
        1
      
      q
    
    ⁢
    
      
    
    ⁢
    
      
        Pr
        i
      
      ⁡
      
        [
        
          
            
              d
              
                k
                ,
                j
              
            
            ⁡
            
              [
              n
              ]
            
          
          =
          
            
              μ
              j
              
                -
                1
              
            
            ⁡
            
              (
              s
              )
            
          
        
        ]
      
    
  




equality being obtained for an infinite interleaving depth.

To introduce the logarithmic ratio πk,ji[n] of the bit a priori probabilities previously defined, we may write:




  
    
      Pr
      i
    
    ⁡
    
      [
      
        
          
            s
            k
          
          ⁡
          
            [
            n
            ]
          
        
        =
        s
      
      ]
    
  
  =
  
    
      1
      
        2
        q
      
    
    ⁢
    
      
        ∏
        
          j
          =
          1
        
        q
      
      ⁢
      
        
      
      ⁢
      
        {
        
          1
          +
          
            
              (
              
                
                  2
                  ⁢
                  
                    
                      μ
                      j
                      
                        -
                        1
                      
                    
                    ⁡
                    
                      (
                      s
                      )
                    
                  
                
                -
                1
              
              )
            
            ⁢
            
              tanh
              ⁡
              
                (
                
                  
                    
                      π
                      
                        k
                        ,
                        j
                      
                      i
                    
                    ⁡
                    
                      [
                      n
                      ]
                    
                  
                  2
                
                )
              
            
          
        
        }
      
    
  




and finally find:





  
    
      
        s
        _
      
      k
      i
    
    ⁡
    
      [
      n
      ]
    
  
  =
  
    
      1
      
        2
        q
      
    
    ⁢
    
      
        ∑
        
          s
          ∈
          J
        
        
          
        
      
      ⁢
      
        
      
      ⁢
      
        s
        ×
        
          
            
              ∏
              q
            
            
              j
              =
              1
            
          
          ⁢
          
            
          
          ⁢
          
            {
            
              1
              +
              
                
                  (
                  
                    
                      2
                      ⁢
                      
                        
                          μ
                          j
                          
                            -
                            1
                          
                        
                        ⁡
                        
                          (
                          s
                          )
                        
                      
                    
                    -
                    1
                  
                  )
                
                ⁢
                
                  tanh
                  ⁡
                  
                    (
                    
                      
                        
                          π
                          
                            k
                            ,
                            j
                          
                          i
                        
                        ⁡
                        
                          [
                          n
                          ]
                        
                      
                      2
                    
                    )
                  
                
              
            
            }
          
        
      
    
  




5.2 Unconditional MMSE Multi-user Detection

The invention suggests replacing the optimum detection of the symbols sk[n] in the sense of the MAP criterion by an estimate in the sense of the unbiased MMSE criterion derived on the basis of the sliding window model, the complexity whereof is polynomial in terms of the parameters of the system, and no longer exponential.
On each iteration i, for each potential user k, there is calculated at 202 the filter fk,ni∈LWRSF which, on the basis of an updated observation (relating to a portion of the block of the particular channel) eliminates the ISI, MAI, and MUI corrupting the symbols sk[n] and produces an evaluation ŝk[n] of the sent modulated data (or symbols) that minimizes the mean square error (MSE):

E[|ŝk[n]−sk[n]|2]

subject to the constraint of an absence of bias.

On the basis of the vector of the estimates of the symbols on the iteration i:

 si[n]=[ s1i[n+L1]. . . ski[n]. . . sKi[n−L2−M]]T∈(LW+M)K 

there is defined at 210 the modified version, including a 0 at position L1K+k, which serves for the regeneration of the interface 210 for the symbols sk[n]:

 ski[n]=[ s1i[n+L1] . . . sk−1i[n] 0  sk+1i[n] . . . sKi[n−L2−M]]T∈(LW+M)K 

An interference estimate is therefore regenerated at 210, by multiplying this vector by said “matrix of convolution of the channel with the spreading codes” Θn (computed in section 2.2 or 2.3):

Θn ski[n]

The Wiener filter is applied at 202 to the observation vector obtained after subtraction at 201 of the regenerated interference:

{tilde over (y)}ki[n]=y[n]−Θn ski[n]

For reasons of complexity, an unconditional MSE and periodic spreading are used instead such that:

Θn=Θ∀n=0, . . . , LS−1

This makes the filter fki invariant in time for the block considered of the particular channel.
It is preferable not to use this MMSE estimate, in favor of a simpler linear front end (polynomial or SUMF, as described in the next section) if the spreading is aperiodic.
This filter minimizes the unconditional MSE on the (biased) estimate of the symbol sk[n] and may easily be derived from the theory of orthogonal projection:

fki=ek†Θ†[ΘΞkiΘ†+σ2I]−1 

in which ek is the vector of dimension (LW+M)K having a 1 at position L1K+k and a 0 everywhere else and where:

ΞkiE{(s[n]− ski[n])(s[n]− ski[n])†}∈(LW+M)K×(LW+M)K 

Ξki=diag {σs2−σ si2, . . . , σs2−σ si2, σs2, σs2−σ si2, . . . , σs2−σ si2}

with σs2situated at the position L1K+k on the diagonal and σ si2 evaluated using the estimator consisting in:





  
    
  
  ⁢
  
    
      σ
      
        s
        _
      
      
        i
        ⁢
        
          
        
        ⁢
        2
      
    
    ≈
    
      
        
          σ
          ^
        
        
          s
          _
        
        
          i
          ⁢
          
            
          
          ⁢
          2
        
      
      ⁢
      •
      ⁢
      
        1
        
          K
          ⁢
          
            
          
          ⁢
          
            L
            S
          
        
      
      ⁢
      
        
          ∑
          
            k
            =
            1
          
          K
        
        ⁢
        
          
        
        ⁢
        
          
            ∑
            
              n
              =
              0
            
            
              
                L
                S
              
              -
              1
            
          
          ⁢
          
            
          
          ⁢
          
            
              
              
                
                  
                    s
                    _
                  
                  k
                  i
                
                ⁡
                
                  [
                  n
                  ]
                
              
              
            
            2
          
        
      
    
  




To satisfy the absence of bias constraint, the filter must be multiplied on the left by the corrective factor:

{ek†Θ†[ΘΞkiΘ†+σ2I]−1Θek}−1 

There is obtained the final expression for the filter:

fki={ek†Θ†[ΘΞkiΘ†+σ2I]−1Θek}−1ek†Θ†[ΘΞkiΘ†+σ2I]−1 

The evaluated ŝki at the output of the filter 202 then corresponds to:

ŝki[n]fki{tilde over (y)}ki[n]=sk[n]+ζki[n]

The variance of the residual interference plus noise term may be evaluated via the following estimator:




  
    
  
  ⁢
  
    
      σ
      
        ζ
        k
      
      
        i
        ⁢
        
          
        
        ⁢
        2
      
    
    ≈
    
      
        
          
            σ
            ^
          
          
            ζ
            k
          
          
            i
            ⁢
            
              
            
            ⁢
            2
          
        
        ⁢
        •
        ⁢
        
          1
          
            L
            S
          
        
        ⁢
        
          
        
        ⁢
        
          
            ∑
            
              n
              =
              0
            
            
              
                L
                S
              
              -
              1
            
          
          ⁢
          
            
          
          ⁢
          
            
              
              
                
                  
                    s
                    ^
                  
                  k
                  i
                
                ⁡
                
                  [
                  n
                  ]
                
              
              
            
            2
          
        
      
      -
      
        σ
        s
        2
      
    
  




5.3 SUMF (Single Use Matched-filter) Multi-user Detection

In a simplified version, the MMSE front end may be totally or partly replaced at 202 by a single use matched filter (SUMF), from any iteration i, which can be calculated at any time:

fk,ni={ek†Θn†Θnek}−1ek†Θn†

This filter is of interest for its simple implementation and its possible compatibility with the HSDPA mode of the UMTS standard because it does not impose periodic spreading, as in the previous situation.
Other Possible Detection Variant:
FIG. 8b represents a variant of either of the detection types described in sections 5.2 and 5.3. This variant relates to a different way of implementing the filter 202′ and the interference regenerator 210′ compared to the filter 202 and the interference regenerator 210 of FIG. 8a (representing two detection steps corresponding to a portion of the overall detection process shown in the FIG. 7 diagram).
Referring to FIG. 8b, the filtering 202′ is here effected upstream of the subtraction of regenerated interference 201 at 210′, and not downstream thereof as was the case in FIG. 8a. 
The filter f′ used and the interference reconstruction matrix b′ used may be deduced trivially from the filter f and the interference reconstruction matrix b previously computed (see above description with reference to FIGS. 7 and 8a), from the following condition of equality:

ŝ=f(y−b s)=f′y−b′ s

From which we deduce:

f′=f;b′=fb

5.4 Exchange of Probabilistic Information with the Channel Decoder 206

On the basis of the output of the linear filtering 202 with K filters, q logarithmic a posteriori probability (APP) ratios are computed at 203 for each symbol, at each time, for each user and each antenna. These probabilistic quantities are defined as follows:




  
    
      λ
      
        k
        ,
        j
      
      i
    
    ⁡
    
      [
      n
      ]
    
  
  ⁢
  •ln
  ⁢
  
    
      Pr
      ⁡
      
        [
        
          
            
              d
              
                k
                ,
                j
              
            
            ⁡
            
              [
              n
              ]
            
          
          =
          
            1
            ❘
            
              
                
                  s
                  ^
                
                k
                i
              
              ⁡
              
                [
                n
                ]
              
            
          
        
        ]
      
    
    
      Pr
      ⁡
      
        [
        
          
            
              d
              
                k
                ,
                j
              
            
            ⁡
            
              [
              n
              ]
            
          
          =
          
            0
            ❘
            
              
                
                  s
                  ^
                
                k
                i
              
              ⁡
              
                [
                n
                ]
              
            
          
        
        ]
      
    
  




and are referenced Λ in FIG. 7;

or:





  
    
      λ
      
        k
        ,
        j
      
      i
    
    ⁡
    
      [
      n
      ]
    
  
  =
  
    ln
    ⁢
    
      
        
          ∑
          
            d
            ∈
            
              א
              j
              
                (
                1
                )
              
            
          
          
            
          
        
        ⁢
        
          
        
        ⁢
        
          Pr
          ⁡
          
            [
            
              
                
                  d
                  k
                
                ⁡
                
                  [
                  n
                  ]
                
              
              =
              
                d
                ❘
                
                  
                    
                      s
                      ^
                    
                    k
                    i
                  
                  ⁡
                  
                    [
                    n
                    ]
                  
                
              
            
            ]
          
        
      
      
        
          ∑
          
            d
            ∈
            
              א
              j
              
                (
                0
                )
              
            
          
          
            
          
        
        ⁢
        
          
        
        ⁢
        
          Pr
          ⁡
          
            [
            
              
                
                  d
                  k
                
                ⁡
                
                  [
                  n
                  ]
                
              
              =
              
                d
                ❘
                
                  
                    
                      s
                      ^
                    
                    k
                    i
                  
                  ⁡
                  
                    [
                    n
                    ]
                  
                
              
            
            ]
          
        
      
    
  




into which we introduce:

j(ε)={d∈F2q|dj=ε}

Expanding the numerator and the denominator gives:




  
    
      λ
      
        k
        ,
        j
      
      i
    
    ⁡
    
      [
      n
      ]
    
  
  =
  
    ln
    ⁢
    
      
        
          
            ∑
            
              d
              ∈
              
                א
                j
                
                  (
                  1
                  )
                
              
            
            
              
            
          
          ⁢
          
            
          
          ⁢
          
            
              p
              ⁡
              
                (
                
                  
                    
                      
                        
                          s
                          ^
                        
                        k
                        i
                      
                      ⁡
                      
                        [
                        n
                        ]
                      
                    
                    ❘
                    
                      
                        s
                        k
                      
                      ⁡
                      
                        [
                        n
                        ]
                      
                    
                  
                  =
                  
                    μ
                    ⁡
                    
                      (
                      d
                      )
                    
                  
                
                )
              
            
            ⁢
            
              
                Pr
                i
              
              ⁡
              
                [
                
                  
                    
                      d
                      k
                    
                    ⁡
                    
                      [
                      n
                      ]
                    
                  
                  =
                  d
                
                ]
              
            
          
        
        ⁢
        
          
        
      
      
        
          ∑
          
            d
            ∈
            
              א
              j
              
                (
                0
                )
              
            
          
          
            
          
        
        ⁢
        
          
        
        ⁢
        
          
            p
            ⁡
            
              (
              
                
                  
                    
                      
                        s
                        ^
                      
                      k
                      i
                    
                    ⁡
                    
                      [
                      n
                      ]
                    
                  
                  ❘
                  
                    
                      s
                      k
                    
                    ⁡
                    
                      [
                      n
                      ]
                    
                  
                
                =
                
                  μ
                  ⁡
                  
                    (
                    d
                    )
                  
                
              
              )
            
          
          ⁢
          
            
              Pr
              i
            
            ⁡
            
              [
              
                
                  
                    d
                    k
                  
                  ⁡
                  
                    [
                    n
                    ]
                  
                
                =
                d
              
              ]
            
          
        
      
    
  




The likelihoods are expressed as follows:




  
    p
    ⁡
    
      (
      
        
          
            
              
                s
                ^
              
              k
              i
            
            ⁡
            
              [
              n
              ]
            
          
          ❘
          
            
              s
              k
            
            ⁡
            
              [
              n
              ]
            
          
        
        =
        
          μ
          ⁡
          
            (
            d
            )
          
        
      
      )
    
  
  ∝
  
    exp
    ⁡
    
      (
      
        -
        
          
            
              
              
                
                  
                    
                      s
                      ^
                    
                    k
                    i
                  
                  ⁡
                  
                    [
                    n
                    ]
                  
                
                -
                
                  μ
                  ⁡
                  
                    (
                    d
                    )
                  
                
              
              
            
            2
          
          
            
              σ
              ^
            
            
              ζ
              k
            
            
              i
              ⁢
              
                
              
              ⁢
              2
            
          
        
      
      )
    
  




On each iteration i, a priori information on the bits of the various symbols coming from the channel decoder 206 is available and usable in the form of logarithmic APP ratios introduced beforehand and the expression for which is:




  
    
      π
      
        k
        ,
        j
      
      i
    
    ⁡
    
      [
      n
      ]
    
  
  ⁢
  •ln
  ⁢
  
    
      
        Pr
        i
      
      ⁡
      
        [
        
          
            
              d
              
                k
                ,
                j
              
            
            ⁡
            
              [
              n
              ]
            
          
          =
          1
        
        ]
      
    
    
      
        Pr
        i
      
      ⁡
      
        [
        
          
            
              d
              
                k
                ,
                j
              
            
            ⁡
            
              [
              n
              ]
            
          
          =
          0
        
        ]
      
    
  




Assuming space-time interleaving of sufficiently great depth, we may write:




  
    
      Pr
      i
    
    ⁡
    
      [
      
        
          
            d
            k
          
          ⁡
          
            [
            n
            ]
          
        
        =
        d
      
      ]
    
  
  ≈
  
    
      ∏
      
        j
        =
        1
      
      q
    
    ⁢
    
      
    
    ⁢
    
      
        Pr
        i
      
      ⁡
      
        [
        
          
            
              d
              
                k
                ,
                j
              
            
            ⁡
            
              [
              n
              ]
            
          
          =
          
            d
            j
          
        
        ]
      
    
  
  ∝
  
    
      ∏
      
        j
        =
        1
      
      q
    
    ⁢
    
      
    
    ⁢
    
      {
      
        1
        -
        
          
            (
            
              
                2
                ⁢
                
                  d
                  j
                
              
              -
              1
            
            )
          
          ⁢
          
            tanh
            ⁡
            
              (
              
                
                  
                    π
                    
                      k
                      ,
                      j
                    
                    i
                  
                  ⁡
                  
                    [
                    n
                    ]
                  
                
                2
              
              )
            
          
        
      
      }
    
  




The extrinsic information on each bit delivered by weighted output demodulators 203 intended for the channel decoder 206 is defined by the equation:

ξk,ji[n]λk,ji[n]−πk,ji[n]

It is denoted Ξ in FIG. 7.
All the bit extrinsic information logarithmic ratios for all the blocks are then collected and properly multiplexed and de-interleaved at 205, to be sent to the channel decoder 206. The decoder sees a unique vector φi∈No made up of No bit intrinsic probability logarithmic ratios (one for each bit of the code word v). Decoding 206 then uses an algorithm such as the flexible output Viterbi algorithm to deliver the logarithm λ of a ratio of information APP to sent modulated data (or symbols) bits.
This logarithm λ is then the basis on which are computed at 207a and 207b the bit extrinsic information logarithmic ratios, formally defined ∀l=1, . . . , No as follows:




  
    ξ
    l
    i
  
  ⁢
  •ln
  ⁢
  
    
      
        Pr
        i
      
      ⁡
      
        [
        
          
            
              v
              l
            
            =
            
              1
              ❘
              
                C
                o
              
            
          
          ,
          
            
              φ
              i
            
            /
            
              {
              
                φ
                l
                i
              
              }
            
          
        
        ]
      
    
    
      
        Pr
        i
      
      ⁡
      
        [
        
          
            
              v
              l
            
            =
            
              0
              ❘
              
                C
                o
              
            
          
          ,
          
            
              φ
              i
            
            /
            
              {
              
                φ
                l
                i
              
              }
            
          
        
        ]
      
    
  




The code word extrinsic information logarithmic ratios {ξli} calculated in the iteration i are similar, after bit interleaving and demultiplexing 208a and 208b, to the symbol bit APP logarithmic ratios {πk,ji+1[n]} on the next iteration.
Reception in accordance with the invention refers not only to a method for implementing it but also to the system for executing it and any transmission system incorporating that reception system.

## Claims

1. A reception method for communication over frequency-selective channels with a plurality of send antennas and a plurality of receive antennas, wherein said reception method is adapted to process data received by the receive antennas that, on sending, was successively:
(A) modulated onto K channels, the number K being strictly greater than a number T of the plurality of send antennas;
(B) spread in the frequency or time domain, with an N×K periodic spreading matrix or an N×K aperiodic spreading matrix where N is strictly greater than T, over K-dimensional vectors of the modulated data;
wherein the reception method uses iteratively for processing the received data:
filtering by means of K linear filters adapted to process the received data, after subtraction of an interference estimate, to generate an evaluation of the sent modulated data before the spreading of the step (B), the filtering by means of the K linear filters taking account of the spatial diversity of the plurality of receive antennas;
before said filtering, subtracting interference using an estimate of multi-antenna interference (MAI), intersymbol interference (ISI), and multi-user interference (MUI) previously regenerated from information computed on the basis of the evaluation of the sent modulated data generated by a previous filtering operation; and
processing to generate an interference estimate for the received data from information computed on the basis of the evaluation of the sent modulated data, wherein the interference estimate for the received data is sent recursively to the next subtraction step.

2. The reception method according to claim 1, wherein the send spreading of the step (B) is effected with K strictly greater than N.

3. The reception method according to claim 1, wherein the reception method is adapted to process data that, on sending, was spread during the step (B), independently for each transmit antenna and with a number of channels per transmit antenna strictly greater than 1, the spreading matrix is a diagonal block matrix with a number of blocks equal to the number T of transmit antennas, and the blocks are constructed from N/T orthogonal codes.

4. The reception method according to claim 1 wherein the reception method is adapted to process data that, on sending, was spread during the step (B) by means of a spreading full matrix constructed from N orthogonal codes.

5. The reception method according to claim 1, wherein the K linear filters are derived using the criterion of minimizing the mean square error (MMSE).

6. The reception method according to claim 1, wherein the send spreading of the send step (B) is effected periodically, the K linear filters are derived in accordance with the criterion of minimizing the mean square error, and the K linear filters are invariant in time for a given channel.

7. The reception method according to claim 1, wherein the K linear filters are single user matched filters (SUMF).

8. The reception method according to claim 1, wherein the K linear filters are first derived in accordance with the criterion of minimizing the mean square error (MMSE) and from a given iteration become single user matched filters (SUMF).

9. The reception method according to claim 1, wherein the filtering takes account of the spatial diversity of the plurality of receive antennas by maximizing the signal-to-noise ratio (SNR) after filtering.

10. The reception method according to claim 1, wherein dimensions of the K filters are computed using sliding windows.

11. The reception method according to claim 1, wherein, on sending, the data was coded before the step (A), on reception, said processing to generate the interference estimate for the received data uses weighted output processing, decoding, and regeneration of interference, the weighted output processing processes the evaluation of the sent modulated data and generates probabilistic information on modulated data bits usable by the decoding process, the decoding process generates a probabilistic quantity from said probabilistic information, the regeneration of interference generates the interference estimate for the received data on the basis of the probabilistic quantity, and the interference estimate for the received data is sent recursively to the next subtraction step.

12. The reception method according to claim 11, wherein the regeneration of interference generates the interference estimate for the received data from an estimate of the sent modulated data, wherein the estimate of the send modulated data is computed using the criterion of minimizing the mean square error (MMSE) on the basis of extrinsic information that is a function of bits sent previously available after decoding.

13. The reception method according to claim 1, wherein, on sending, the data was coded and interleaved before the step (A) and, on reception, said processing to generate the interference estimate for the received data uses:
weighted output processing based on the evaluation of the sent modulated data and decoding statistics resulting from decoding to generate a statistic per modulated data bit;
de-interleaving at the bit level extrinsic statistics found from the probabilistic quantity generated previously;
weighted input and output decoding on the basis of the de-interleaved extrinsic statistics at the bit level to produce a probabilistic quantity over all of the bits;
interleaving at the bit level extrinsic statistics found from the probabilistic quantity, wherein said interleaved extrinsic statistics are sent recursively to the next step of weighted output processing;
regenerating interference to generate the interference estimate for the received data on the basis of an estimate of the sent modulated data computed using the criterion of minimizing the mean square error (MMSE) from said new interleaved statistics, wherein the interference estimate for the received data is sent recursively to the next subtraction step.

14. The reception method according to claim 11, wherein said probabilistic quantity after decoding is the logarithm of a ratio of modulated data bit information a posteriori probabilities.

15. The reception method according to claim 14, wherein the decoding computes said probabilistic quantity by means of a Viterbi algorithm with weighted inputs and outputs.

16. The reception method according to claim 1, wherein the spreading of the sending step (B) is effected in the frequency domain and transmission before reception is of the multicarrier type.

17. The reception method according to claim 1, wherein the spreading of the sending step (B) is effected in the time domain and the transmission before reception is of the single-carrier type.

18. A transmission system, comprising:
a sending system comprising a plurality of send antennas and adapted to modulate onto K channels, the number K being strictly greater than a number T of send antennas, and to spread modulated data over the K-dimensional vectors with an N×K periodic spreading matrix or an N×K aperiodic spreading matrix where N is strictly greater than T;
a frequency-selective transmission channel;
a reception system comprising a plurality of receive antennas and adapted to implement a reception method according to claim 1.

19. A reception system for communication over frequency-selective channels with a plurality of send antennas and a plurality of receive antennas, wherein the system is adapted to process data received via the receive antennas that, on sending, was successively:
(A) modulated onto K channels, the number K being strictly greater than a number T of send antennas;
(B) spread, with an N×K periodic spreading matrix or an N×K aperiodic spreading matrix where N is strictly greater than T, over K-dimensional vectors of the modulated data;
wherein the system comprises for processing the received data:
K linear filters adapted to process the received data, after subtraction of an interference estimate, to generate an evaluation of the sent modulated data before the spreading of the step (B), the K linear filters taking account of the spatial diversity of the plurality of receive antennas;
upstream of said K filters, an interference estimator that subtracts an estimate of multi-antenna interference (MAI), intersymbol interference (ISI), and multi-user interference (MUI) previously regenerated from information computed on the basis of the evaluation of the sent modulated data generated by a previous filtering operation by the K filters;
processing means adapted to generate an interference estimate for the received data from information computed on the basis of the evaluation of the sent modulated data, wherein the interference estimate for the received data is sent recursively to the interference subtractor;
wherein the reception system is adapted to be used iteratively for processing the received data.

20. The reception system according to claim 19, wherein the K linear filters are derived using the criterion of minimizing the mean square error (MMSE).

21. The reception system according to claim 19, wherein the K linear filters are single user matched filters (SUMF).

22. The reception system according to claim 19, wherein the K linear filters are first derived in accordance with the criterion of minimizing the mean square error (MMSE) and from a given iteration become single user matched filters (SUMF).

23. The reception system according to claim 19, wherein said processing means adapted to generate the interference estimate for the received data include weighted output processing means, a decoder, and an interference regenerator, the weighted output processing means are adapted to process the evaluation of the sent modulated data and to generate probabilistic information on modulated data bits usable by the decoder, the decoder is adapted to generate a probabilistic quantity from said probabilistic information, the interference regenerator generates the interference estimate for the received data on the basis of the probabilistic quantity, and the interference estimate for the received data is sent recursively to the subtractor.

24. The reception system according to claim 19, wherein said processing means adapted to generate the interference estimate for the received data use:
weighted output processing means using the latest evaluation of the sent modulated data and decoding statistics resulting from decoding for demodulation and to generate a statistic per modulated data bit;
a de-interleaver of extrinsic statistics at the bit level found from the probabilistic quantity generated previously;
a weighted input and output decoder adapted to decode on the basis of the de-interleaved extrinsic statistics at the bit level to produce a probabilistic quantity over all of the bits;
an interleaver adapted to interleave at the bit level extrinsic statistics found from the probabilistic quantity, wherein said interleaved extrinsic statistics are sent recursively to the weighted output processing means;
an interference regenerator adapted to generate the interference estimate for the received data on the basis of an estimate of the sent modulated data computed using the criterion of minimizing the mean square error (MMSE) from said new interleaved statistics, wherein the interference estimate for the received data is sent recursively to the subtractor.

25. A reception method for communication over frequency-selective channels with a plurality of send antennas and a plurality of receive antennas, wherein said reception method is adapted to process data received by the receive antennas that, on sending, was successively:
(A) modulated onto K channels, the number K being strictly greater than a number T of the plurality of send antennas;
(B) spread in the frequency or time domain, with an N×K periodic spreading matrix or an N×K aperiodic spreading matrix where N is strictly greater than T, over K-dimensional vectors of the modulated data;
wherein the reception method uses iteratively for processing the received data:
filtering by means of K linear filters adapted to process the received data, to generate an evaluation of the sent modulated data before the spreading of the step (B), the filtering by means of the K linear filters taking account of the spatial diversity of the plurality of receive antennas;
after said filtering, subtracting interference using an estimate of multi-antenna interference (MAI), intersymbol interference (ISI), and multi-user interference (MUI) previously regenerated from information computed on the basis of the evaluation of the sent modulated data generated by a previous filtering operation; and
processing to generate an interference estimate for the received data from information computed on the basis of the evaluation of the sent modulated data,
wherein the interference estimate for the received data is sent recursively to the next subtraction step.

26. A reception system for communication over frequency-selective channels with a plurality of send antennas and a plurality of receive antennas, wherein the system is adapted to process data received via the receive antennas that, on sending, was successively:
(A) modulated onto K channels, the number K being strictly greater than a number T of send antennas;
(B) spread, with an N×K periodic spreading matrix or an N×K aperiodic spreading matrix where N is strictly greater than T, over K-dimensional vectors of the modulated data;
wherein the system comprises for processing the received data:
K linear filters adapted to process the received data, to generate an evaluation of the sent modulated data before the spreading of the step (B), the K linear filters taking account in particular of the spatial diversity of the plurality of receive antennas;
downstream of said K filters, an interference subtractor that subtracts an estimate of multi-antenna interference (MAI), intersymbol interference (ISI), and multi-user interference (MUI) previously regenerated from information computed on the basis of the evaluation of the sent modulated data generated by a previous filtering operation by the K filters;
processing means adapted to generate an interference estimate for the received data from information computed on the basis of the evaluation of the sent modulated data, wherein the interference estimate for the received data is sent recursively to the interference subtractor;
wherein the reception system is adapted to be used iteratively for processing the received data.