# Patent

## Title
Method to increase the bit rate in a communications system

## Abstract

Disclosed is a method and a device to increase the bit rate in a communications system comprising N transmitters (2N) and M receivers (3M), with M greater than or equal to N. The method comprises the following steps.

    
    
        a) simultaneously sending different messages on several of the N (2N) transmitters,
        b) simultaneously receiving the superimposition of the messages sent during the step a) on several of the M (3M) receivers or reception sensors,
        c) estimating the characteristics of the transmission channel for each pair constituted by a transmission sensor and a receiver sensor,
        d) jointly estimating all or at least the majority of the messages received in taking account of the signals as well as the characteristics of the transmission channel.
    
    


Application to GSM signals and to systems of unicast transmission and multicast transmission, namely multipoint-to-point and multipoint-to-multipoint transmission.
FIGS. 2a, 2B.

## Background
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention pertains more generally to the field of communications systems and, more particularly, to wireless communications, for examples cellular networks.
It can be applied to any communications system in which the structure of the data transmitted does not comprise any intrinsic system for differentiating between the different users if they are making simultaneous transmission (as is the case, for example with CDMA codes which are used to used to identify the different transmitters).
The system according to the invention can be applied more particularly to dedicated unicast or multicast communications (in which one point corresponds to a receiver or to a transmitter having one or more antennas).
2. Description of the Prior Art
Most present-day communications systems generally make use of a single transmission antenna. Consequently, the capacity of the transmission channel or the maximum achievable bit rate for the data transmitted is fairly low.
There are also known ways of using spread-spectrum codes such as the CDMA (Code Division Multiple Access) to exploit the (channel) diversity of a communications system such as the UMTS (Universal Mobile Telecommunications System).
The U.S. Pat. No. 6,115,427 discloses a method and a system to augment the data bit rate in a transmission system and provide a diversity of antennas by using several transmit and receive antennas. This method relies mainly on a step for the space-time encoding of the data at transmission in order to differentiate between the different data streams and to detect them in conjunction.
The drawback of these methods, especially, is that their implementation leads to a modification of the transmission or communications systems, for example the modification of existing transmitters or receivers.
SUMMARY OF THE INVENTION
The present invention relies on a novel approach based on a joint processing of all the signals. This approach considers all the signals sent to be useful rather than estimating only one of them and considering the others to be noise for example. It can be applied to both unicast links and multicast links.
The method especially uses the diversity provided by the transmission channel, which is spatially sampled by a number of reception sensors greater than or equal to the number of transmission sensors and an adapted processor or computer.
In normal operation, the method does not make use of a spread-spectrum code associated with a user, which is the known approach in most of the prior art devices. It can be applied without distinction to multicast transmission as well as to unicast transmission.
The object of the invention pertains to a method to increase the bit rate in a communications system comprising N transmitters and M receivers or reception sensors, with M greater than or equal to N, the structure of the data transmitted having no intrinsic system to differentiate between the users. The method comprises at least the following steps.

    
    
        a) simultaneously sending different messages on several of the N transmitters,
        b) simultaneously receiving the superimposition of the messages sent during the step a) on several of the M reception sensors, with M greater than or equal to N,
        c) estimating the characteristics of the transmission channel for each pair constituted by a transmission sensor and a receiver sensor,
        d) jointly estimating all or at least the majority of the messages received in taking account of the signals as well as the characteristics of the transmission channel or channels.
    
    


The step d) is performed, for example, with a receiver adapted to the joint estimation of the reference sequences transmitted in the signal and the propagation channels.
For the step d), the method uses, for example, a linear filter minimizing the mean squared error between the output of the receiver and the real symbols of the signal received at the reception sensors or again a non-linear filter minimizing the mean squared error in taking account of a “feed forward” filtering function and a “feedback” filtering function and of the of the vector bn of the symbols of the received signal.
The method can be applied to GSM signals comprising a reference sequence used for the step d).
The method is used, for example, for a same user simultaneously transmitting several different messages or for several users each transmitting its own message.
The object of the invention also relates to a device to increase the bit rate in a transmission system comprising several transmitters N and several receivers M, wherein the device comprises a device adapted to performing the steps of the method described here above.
The object of the invention especially has the following advantages:

    
    
        It offers a transmission system that provides an increase in the bit rate and robustness of cellular type transmission, described for example in the ETSI standard for GSM communications systems.
        It does not require space-time encoding in normal operation.
        With slight modification of existing standards, it enables:
        
            the multiplication by N of the bit rate of a BTS or node type transmission,
            the multiplication by N of the bit rate of a cellular radiomobile type reception system,
            an increase in robustness with respect to disturbances generated by the transmission channel.
        
        
        It can be applied in confined types of transmission channels such as train tunnels or metropolitan underground rail transit tunnels, whatever the type of transmission medium, and can also be used in urban, mountainous and rural environments where the spatial diversity is sufficient to provide for high-quality transmission.
    
    





BRIEF DESCRIPTION OF THE DRAWINGS
Other features and advantages shall appear from the following description, given by way of an illustration that in no way restricts the scope of the invention, and from the appended drawings, of which:
FIG. 1 shows an architecture of a transmission system according to the invention,
FIGS. 2A and 2B show the layout of co-localized and de-localized antennas,
FIG. 3 gives a view of the functions used to linearize the GMSK modulation,
FIG. 4 shows several comparative curves implementing the linear approximation and a standard demodulation,
FIG. 5 shows the structure of the standard DFE or decision feedback equalizer,
FIG. 6 shows two contexts of application of the method according to the invention,
FIGS. 7 to 10 show results obtained by implementing the method according to the invention.



MORE DETAILED DESCRIPTION
In order to provide for a clearer understanding of the method and system of transmission according to the invention, the following description is given by way of an illustration that in no way restricts the scope of the invention. The description pertains to a cellular type transmission system, such as the GSM system, in a multiple-user context. The structure of the data transmitted has the characteristic of not comprising an intrinsic system to differentiate between users, at least in normal operation.
FIG. 1 shows a block diagram of a GSM type communications system comprising a transmitter source 1 comprising N transmission antennas 2N and M reception antennas 3M connected to a receiver 4 and to a device such as a processor 5 provided with an algorithm adapted to the execution of the steps of the method according to the invention. The number M of antennas at reception is greater than or equal to the number N of antennas at transmission. If N users are present, they form the network of the N transmission antennas.
The object of the present invention relies especially on the fact that the networks of the M reception antennas and of the N transmission antennas associated with the characteristics of the transmission channel can be used especially to exploit the diversity needed to implement MIMO (Multiple Input Multiple Output) type antennas based on the decorrelation of the different channels for the detection of the data streams transmitted.
The N transmission antennas 2N preferably transmit several data streams corresponding to different messages. The signals are propagated between the source and the receiver along several paths. These are direct paths or multiple paths resulting from reflections on obstacles 5.
Two examples of the layout of the antennas at transmission and at reception are shown in FIGS. 2A and 2B.
According to one alternative embodiment (FIG. 2A), one and the same user can simultaneously transmit several different messages. This corresponds to transmission antennas 2N that are close to one another. In this case, the transmission antennas 2N and reception antennas 3M are kept at a sufficient distance from each other as compared with the spatial decorrelation distance, thus generating decorrelated propagation channels.
According to another alternative embodiment (FIG. 2B), each of the N users, for example, transmits his own message. This corresponds to a layout of delocalized antennas. The reception sensors 3M are sufficiently separated to ensure a decorrelation between the different propagation channels.
The idea of the invention is based especially on the joint processing of all the signals sent, in considering these signals to be useful signals, rather than in seeking to estimate one of them while considering the other signals to be noise.
The processor 5 linked with the reception antennas 3M is provided for example with an algorithm enabling an antenna of co-localized sensors to receive several messages coming from delocalized or co-localized transmission antennas, through an urban, mountainous or tunnel type propagation channel for example.
Various exemplary receivers are given here below in the description.
In short, the method according to the invention comprises especially the following steps:

    
    
        a) Simultaneously transmitting different messages on the N transmission antennas 2N 
        b) Simultaneously receiving the different superimposed messages on M reception antennas 3M, 
        c) Estimating the characteristics of the transmission channel with respect to each reception antenna,
        d) jointly estimating all the messages received in taking account of the information from the sensors (signals received on the sensors) as well as the characteristics of the above-mentioned channel.
    
    


In normal operating conditions, the method does not use any intrinsic system to differentiate between users, as is done for example with the codes used at the CDMA level.
In normal operating conditions, the method does not require any space-time encoding at transmission.
The characteristics of the channel may be estimated according to a method known to those skilled in the art. For example, the estimation is carried out by using reference sequences included in the signals, such as the GSM “training sequence”.
The transmissions may be unicast or multicast (point-to-multipoint as well as multipoint-to-multipoint) communications.
Before providing a detailed description of the various possibilities of processing at reception, corresponding to the step d) of the method, a few points about the signals are recalled.
Model of the Signal
The signal received by the network of sensors is expressed in the case of a single transmission by the relationship (1)

x(t)=h(t,τ)*s(t)+n(t)  (1)

where

    
    
        x(t) is the received signal,
        h(t,τ) is the vector of the transmission channel having a dimension M, t being the time and τ the temporal spread,
        s(t) is the transmitted GMSK (Gaussian Minimum Shift Keying) signal that does not comprise any identifier proper to a user,
        n(t) is the noise vector, with a dimension N, assumed to be spatially and temporally Gaussian white noise having a covariance σ2I.
    
    


In the case of a multiple-transmission context for which the types of propagation give rise to a diversity of transmission and, therefore generate decorrelated propagation channels on an antenna with several sensors that are spatially distant from each other, the received signal is modeled by the following expression:




  
    x
    ⁢
    
      (
      t
      )
    
  
  =
  
    
      
        ∑
        
          u
          =
          1
        
        U
      
      ⁢
      
        
          ∑
          
            p
            =
            1
          
          P
        
        ⁢
        
          
            
              α
              p
              u
            
            ⁢
            
              (
              t
              )
            
          
          ⁢
          
            
              s
              u
            
            ⁢
            
              (
              
                t
                -
                
                  
                    τ
                    p
                    u
                  
                  ⁢
                  
                    (
                    t
                    )
                  
                
              
              )
            
          
        
      
    
    +
    
      n
      ⁢
      
        (
        t
        )
      
    
  




with:

    
    
        su(t) the signal transmitted by the user,
        αup(t) the vector with a dimension N grouping the complex amplitudes of the path P for the signal u transmitted,
        τup the propagation delay of the path P for the transmitted signal U,
        P is the number of propagation paths, assumed to be equal for each transmitter,
        U is the number of simultaneous transmissions.
    
    


Hereinafter in the description of a GSM context that does not restrict the scope of the invention, the complex amplitudes and the propagation delays shall be considered to be invariant over a period of time equivalent to one GSM burst, namely 0.5 ms. This is an example given in order to simply the notations, by way of an illustration that no way restricts the scope of the invention.
Linearization of the Modulation in the Example Given for the GSM
In the case of the non-restrictive application to the GSM system, the modulation used in transmission is of the GMSK (Gaussian Minimum Shift Keying) type. This modulation is a modulation using memorized symbols. The modulation is dependent on three symbols at each instant t. The optimum demodulator in SGWN (standard Gaussian white noise) is implemented for example by a Viterbi decoder known to those skilled in the art. Owing to the number of possible phase states (0, π/2, π, 3π/2) and the number of memory symbols (c), the decoder comprises 16 states (3-1)4 to be examined for each bit received.
In order to simplify the problem induced by the memory symbol and related to the GMSK modulation, a simplification is obtained by means of an equivalent representation using a combination of linear modulations, described for example in the article by P. A. Laurent, “Exact and Approximate Construction of Digital Phase Modulations by Superposition of Amplitude Modulated Pulses (AMP)” in IEEE Trans. Communications, Vol. 34, pp. 150–60, 1986.
This linear combination can be expressed in the following form (3):




  
    
      
        
          s
          ⁡
          
            (
            t
            )
          
        
        =
        
        ⁢
        
          
            ∑
            
              n
              =
              
                -
                ∞
              
            
            ∞
          
          ⁢
          
            
              j
              
                A
                
                  a
                  ,
                  n
                
              
            
            [
            
              
                
                  C
                  0
                
                ⁢
                
                  (
                  
                    t
                    -
                    
                      nT
                      s
                    
                  
                  )
                
              
              +
              
                
                  j
                  
                    
                      -
                      a
                    
                    ,
                    
                      n
                      -
                      1
                    
                  
                
                ⁢
                
                  C
                  1
                
                ⁢
                
                  (
                  
                    t
                    -
                    
                      nT
                      s
                    
                  
                  )
                
              
              +
            
          
        
      
    
  
  
    
      
        
        ⁢
        
          
            
              j
              
                a
                ,
                
                  n
                  -
                  2
                
              
            
            ⁢
            
              
                C
                2
              
              ⁡
              
                (
                
                  t
                  -
                  
                    nT
                    s
                  
                
                )
              
            
          
          +
          
            
              j
              
                a
                ,
                
                  n
                  -
                  1
                  -
                  a
                
                ,
                
                  n
                  -
                  2
                
              
            
            ⁢
            
              C
              3
            
            ⁢
            
              (
              
                t
                -
                
                  nT
                  s
                
              
              )
            
          
        
        ]
      
    
  




with





  
    A
    
      0
      ,
      n
    
  
  =
  
    
      ∑
      
        i
        =
        
          -
          ∞
        
      
      n
    
    ⁢
    
      a
      i
    
  




The functions C0(t), . . . , C3(t) shown in FIG. 3 are obtained from the above-mentioned breakdown.
Given the small contribution of the coefficients C0(t), . . . , C3(t), the GMSK modulation is expressed according to the relationship (4):




  
    s
    ⁢
    
      (
      t
      )
    
  
  =
  
    
      ∑
      
        n
        =
        0
      
      ∞
    
    ⁢
    
      
        j
        
          A
          
            0
            ,
            n
          
        
      
      ⁢
      
        
          C
          0
        
        ⁢
        
          (
          
            t
            -
            
              nT
              s
            
          
          )
        
      
    
  




the function C0(t) being defined on 4 symbols.

In this case, the standard Gaussian white noise (SGWN) demodulation that meets the Nyquist criterion is obtained, for example, through a simple matched filter (MF), followed by a sampler working at the symbol rhythm and a decision-making operation.
FIG. 4 illustrates the low distortion introduced by the linear approximation method as compared with a classic GMSK demodulation using the Viterbi decoder. The curves (I), (II), (III) respectively correspond to the linear approximation method, the theoretical curves and an optimum Viterbi type demodulation. The x-axis corresponds to the ratio Eb/N0 with Eb being the binary energy and N0 being the spectral power density of the noise.
Model of the Signal in Multiple-user Transmission Mode
In the multiple-user context, the propagation or transmission channel is modeled as being specular. This representation is given by way of an illustration; it is in no way restrictive, and any other type of adaptive modeling may be used.
The model of the signal in this example is modified in order to take account of these new assumptions according to the following relationship (5):




  
    x
    ⁢
    
      (
      t
      )
    
  
  =
  
    
      
        ∑
        
          u
          =
          1
        
        U
      
      ⁢
      
        
          ∑
          
            p
            =
            1
          
          P
        
        ⁢
        
          
            α
            p
            u
          
          ⁢
          
            
              s
              u
            
            ⁢
            
              (
              
                t
                -
                
                  τ
                  p
                  u
                
              
              )
            
          
        
      
    
    +
    
      n
      ⁢
      
        (
        t
        )
      
    
  




After linear approximation, the signal received by the sensors is written as follows (6):




  
    x
    ⁢
    
      (
      t
      )
    
  
  =
  
    
      
        ∑
        
          u
          =
          1
        
        U
      
      ⁢
      
        
          ∑
          
            p
            =
            1
          
          P
        
        ⁢
        
          
            ∑
            
              n
              =
              1
            
            
              N
              a
            
          
          ⁢
          
            
              α
              p
              u
            
            ·
            
              j
              n
            
            ·
            
              b
              n
              u
            
            ·
            
              
                C
                0
              
              ⁢
              
                (
                
                  t
                  -
                  
                    nT
                    s
                  
                  -
                  
                    τ
                    p
                    u
                  
                
                )
              
            
          
        
      
    
    +
    
      n
      ⁢
      
        (
        t
        )
      
    
  




where Na is the number of symbols sent.

After oversampling at the frequency Fe=1/Te with Te=Tsymbol/K (K being the oversampling factor) the received signal becomes (7):




  
    x
    ⁢
    
      (
      
        nT
        e
      
      )
    
  
  =
  
    
      
        ∑
        
          u
          =
          1
        
        U
      
      ⁢
      
        
          ∑
          
            p
            =
            1
          
          P
        
        ⁢
        
          
            α
            p
            u
          
          ⁢
          
            
              ∑
              
                n
                =
                1
              
              
                N
                a
              
            
            ⁢
            
              
                j
                n
              
              ·
              
                b
                n
                u
              
              ·
              
                
                  C
                  0
                
                ⁢
                
                  (
                  
                    
                      nT
                      e
                    
                    -
                    
                      nT
                      s
                    
                    -
                    
                      τ
                      p
                      u
                    
                  
                  )
                
              
            
          
        
      
    
    +
    
      n
      ⁢
      
        (
        
          nT
          e
        
        )
      
    
  




with x(nTe) having dimensions N*Ne,

N is the number of sensors and Ne is the number of samples on the temporal section nTe such that (8):

x=[xT(0), . . . xT((Ne−1)Te)]T 

where Ne is chosen to be equal to:

Na(4·κk+L−1)

with L as the length of the channel verifying (9)

0≦τpu≦(L−1)Te,∀u,p 

The number 4 is related to the temporal duration expressed in symbols of the function C0(t).
The matrix formulation of the signal x leads to (10):

x=Ha+n 

where the vector a with a dimension Na*U is written as follows:




  
    a
    =
    
      
        [
        
          
            a
            1
            T
          
          ,
          ...
          ,
          
            a
            
              N
              a
            
            T
          
        
        ]
      
      T
    
  




  
    
      with
      :
      
        

      
      ⁢
      
        a
        n
      
    
    =
    
      
        j
        n
      
      ·
      
        
          [
          
            
              b
              n
              1
            
            ,
            ...
            ,
            
              b
              n
              U
            
          
          ]
        
        T
      
    
  



The matrix H (N.Ne*Na) represents the convolution of the impulse response of the channel that is oversampled by the function C0(t)

{tilde over (H)}= [C1 . . . CU]  (11)

or:




  
    
      C
      u
    
    =
    
      
        ∑
        
          p
          =
          1
        
        P
      
      ⁢
      
        [
        
          
            
              
                O
                
                  τ
                  p
                  u
                
              
            
          
          
            
              
                c
                
                  τ
                  p
                  u
                
              
            
          
          
            
              
                
                  O
                  _
                
                
                  τ
                  p
                  u
                
              
            
          
        
        ]
      
    
  




  
    
      with
      :
      
        

      
      ⁢
      
        c
        ⁢
        
          
        
        ⁢
        
          τ
          p
          u
        
      
    
    =
    
      
        
          [
          
            
              
                C
                0
              
              ⁢
              
                (
                
                  
                    lT
                    e
                  
                  -
                  
                    τ
                    p
                    u
                  
                
                )
              
            
            ,
            ...
            ,
            
              
                C
                0
              
              ⁢
              
                (
                
                  
                    
                      (
                      
                        l
                        +
                        
                          4
                          ·
                          k
                        
                      
                      )
                    
                    ⁢
                    
                      T
                      e
                    
                  
                  -
                  
                    τ
                    p
                    u
                  
                
                )
              
            
          
          ]
        
        T
      
      ⊗
      
        α
        p
        u
      
    
  







  l
  =
  
    arg
    ⁢
    
      
        min
        l
      
      ⁢
      
        ⌊
        
          
            τ
            p
            u
          
          
            lT
            e
          
        
        ⌋
      
    
  




    
    
         is the Kronecker product.
    
    


This model is used in remaining part of the method according to the invention.
Detailed Explanation of the Processing step d) at Reception
The method and the system according to the invention use an algorithm for the reception of several signals on an antenna of co-localized sensors of several messages coming from delocalized or co-localized transmission antennas and through an urban, mountainous or tunnel type of propagation channel for example.
The following description gives three exemplary receivers used to execute especially the step d).
Optimal Receivers
An optimal receiver jointly estimates the transmitted sequences and the propagation channels. These receivers nevertheless have the drawback of becoming rapidly complex.
Various types of equalizers may be chosen such as the MF (Matched Filter), DFE ZF (Decision Feedback Equalizer-Zero Forcing filter) and the DFE MMSE (Decision Feedback-Minimum Mean Squared Error filter).
The results obtained in simulations have shown that only the linear MMSE sub-optimal receivers as well as the non-linear DFE-MMSE type equalizers perform best in terms of residual bit error rate (BER).
Linear Sub-optimal MMSE Receivers
After the matched filter H, which may or may not be a whitening filter, is applied to the received signals x, we obtain

y=HHx  (12)

In the application to the GSM context, the MMSE detector is a filter applied to the output of the MF minimizing the mean squared error between the output of the receiver and the real symbols such that (13):





  E
  ⁡
  
    [
    
      
        
        
          
            
              M
              MMSE
            
            ·
            
              [
              
                
                  
                    y
                  
                
                
                  
                    
                      y
                      †
                    
                  
                
              
              ]
            
          
          -
          a
        
        
      
      2
    
    ]
  




a is defined by ei=[0,0, . . . 0,1,0, . . . , 0] with the 1 in position i

the minimization step leads to the expression (14):





  
    E
    ⁡
    
      [
      
        
          
            e
            j
            T
          
          ·
          
            [
            
              
                
                  y
                
              
              
                
                  
                    y
                    *
                  
                
              
            
            ]
          
          ·
          
            [
            
              
                y
                †
              
              ⁢
              
                y
                T
              
            
            ]
          
          ·
          
            M
            MMSE
            †
          
        
        ⁢
        
          e
          i
        
      
      ]
    
  
  =
  
    E
    ⁡
    
      [
      
        
          e
          j
          T
        
        ·
        
          [
          
            
              
                y
              
            
            
              
                
                  y
                  *
                
              
            
          
          ]
        
        ·
        
          a
          †
        
        ·
        
          e
          i
        
      
      ]
    
  




with:

E[yy†]={overscore (H)}{overscore (H)}†+σ2{overscore (H)}

E[yyT]={overscore (H)}Ĩ{overscore (H)}T 

the criterion becomes:





  
    
      
        
          
            [
            
              
                [
                
                  
                    
                      
                        
                          H
                          _
                        
                        ⁢
                        
                          
                            H
                            _
                          
                          †
                        
                      
                    
                    
                      
                        
                          H
                          _
                        
                        ⁢
                        
                          I
                          ~
                        
                        ⁢
                        
                          
                            H
                            _
                          
                          T
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            H
                            _
                          
                          *
                        
                        ⁢
                        
                          I
                          ~
                        
                        ⁢
                        
                          
                            H
                            _
                          
                          †
                        
                      
                    
                    
                      
                        
                          
                            H
                            _
                          
                          ⋆
                        
                        ⁢
                        
                          
                            H
                            _
                          
                          T
                        
                      
                    
                  
                
                ]
              
              +
              
                
                  σ
                  2
                
                ⁡
                
                  [
                  
                    
                      
                        
                          H
                          _
                        
                      
                      
                        0
                      
                    
                    
                      
                        0
                      
                      
                        
                          
                            H
                            _
                          
                          *
                        
                      
                    
                  
                  ]
                
              
            
            ]
          
          ·
          
            M
            MMSE
            †
          
        
        =
        
          [
          
            
              
                
                  
                    H
                    _
                  
                  ⁢
                  I
                
              
            
            
              
                
                  
                    
                      H
                      _
                    
                    *
                  
                  ⁢
                  
                    I
                    ~
                  
                
              
            
          
          ]
        
      
    
    
      
        (
        15
        )
      
    
  




Giving the relationship (16):





  
    M
    MMSE
    †
  
  =
  
    
      
        [
        
          
            
              
                
                  
                    H
                    n
                  
                  ⁢
                  
                    H
                    n
                    †
                  
                
                +
                
                  
                    σ
                    2
                  
                  ⁢
                  
                    H
                    n
                  
                
              
            
            
              
                
                  H
                  n
                
                ⁢
                
                  
                    I
                    ~
                  
                  n
                
                ⁢
                
                  H
                  n
                  T
                
              
            
          
          
            
              
                
                  H
                  n
                  *
                
                ⁢
                
                  
                    I
                    ~
                  
                  n
                
                ⁢
                
                  H
                  n
                  †
                
              
            
            
              
                
                  
                    H
                    n
                    *
                  
                  ⁢
                  
                    H
                    n
                    T
                  
                
                +
                
                  
                    σ
                    2
                  
                  ⁢
                  
                    H
                    n
                  
                
              
            
          
        
        ]
      
      #
    
    ·
    
      [
      
        
          
            
              
                H
                n
              
              ⁢
              
                I
                7
              
            
          
        
        
          
            
              
                H
                n
              
              ⁢
              
                I
                8
              
            
          
        
      
      ]
    
  




where # corresponds to the pseudo-inverse value.

This linear receiver is optimal, with respect to its criterion, on the blocks (or slots) of the GSM transmission and takes account of the fine structure of the FDD/TDMA (Frequency Division Duplex/Time Division Multiple Access) frames.
Non-linear Sub-optimal MMSE Receiver
They have the advantage of minimizing the size of the matrix inversions.
The structure of a standard DFE equalizer is defined in FIG. 5
The filtering function G is commonly called a “Feed Forward” function and the function B is called a “Feedback” function.
Two types of DFE equalizers may be considered: the ZF (Zero Forcing) equalizer and the MMSE (Minimum Mean Square Error) equalizer.
It is recalled that the ZF type equalizers do not take the presence of noise into account. This limits the performance obtained for them for low signal-to-noise ratios.
Consequently, only the MMSE Equalizer is described in the following method.
The optimization criterion minimizing the mean squared error at output of the equalizer is written as follows (17):




  E
  ⁡
  
    [
    
      
        
        
          
            
              [
              
                G
                -
                B
              
              ]
            
            ⁡
            
              [
              
                
                  
                    
                      y
                      n
                    
                  
                
                
                  
                    
                      y
                      n
                      *
                    
                  
                
                
                  
                    
                      d
                      n
                    
                  
                
                
                  
                    
                      d
                      n
                      *
                    
                  
                
              
              ]
            
          
          -
          
            b
            n
          
        
        
      
      2
    
    ]
  




where:

with:





  
    
      
        
          y
          n
        
        =
        
          
            [
            
              
                
                  y
                  _
                
                
                  n
                  -
                  
                    L
                    G
                  
                
                T
              
              ⁢
              
                
              
              ⁢
              ⋯
              ⁢
              
                
              
              ⁢
              
                
                  y
                  _
                
                n
                T
              
              ⁢
              
                
              
              ⁢
              ⋯
              ⁢
              
                
              
              ⁢
              
                
                  y
                  _
                
                
                  n
                  +
                  
                    L
                    G
                  
                
                T
              
            
            ]
          
          T
        
      
    
  
  
    
      
        y
        =
        
          
            [
            
              
                
                  y
                  _
                
                1
                T
              
              ⁢
              
                
              
              ⁢
              ⋯
              ⁢
              
                
              
              ⁢
              
                
                  y
                  _
                
                
                  N
                  a
                
                T
              
            
            ]
          
          T
        
      
    
  




and:





  
    b
    n
  
  =
  
    
      [
      
        
          a
          
            n
            -
            
              L
              G
            
          
          T
        
        ⁢
        
          
        
        ⁢
        ⋯
        ⁢
        
          
        
        ⁢
        
          a
          n
          T
        
        ⁢
        
          
        
        ⁢
        ⋯
        ⁢
        
          
        
        ⁢
        
          a
          
            n
            +
            
              L
              G
            
          
          T
        
      
      ]
    
    T
  




represents a vector of symbols

and:





  
    d
    n
  
  =
  
    
      [
      
        
          a
          
            n
            -
            
              L
              B
            
          
          T
        
        ⁢
        
          
        
        ⁢
        ⋯
        ⁢
        
          
        
        ⁢
        
          a
          
            n
            -
            1
          
          T
        
      
      ]
    
    T
  




The matrix Hn contains the impulse response corresponding to the observation yn:

yn=Hnbn+nn 

with nn being the correlated noise vector corresponding to the observation yn. The filters G and B are obtained according to the following relationships (18):





  
    [
    
      
        
          
            G
            
              DFE
              -
              MMSE
            
            †
          
        
      
      
        
          
            -
            
              B
              
                DFE
                -
                MMSE
              
              †
            
          
        
      
    
    ]
  
  =
  
    
      
        [
        
          
            
              
                
                  
                    H
                    n
                  
                  ⁢
                  
                    H
                    n
                    †
                  
                
                +
                
                  
                    σ
                    2
                  
                  ⁢
                  
                    H
                    n
                  
                
              
            
            
              
                
                  H
                  n
                
                ⁢
                
                  
                    I
                     ̆
                  
                  n
                
                ⁢
                
                  H
                  n
                  T
                
              
            
            
              
                
                  H
                  n
                
                ⁢
                
                  I
                  3
                
              
            
            
              
                
                  H
                  n
                
                ⁢
                
                  I
                  4
                
              
            
          
          
            
              
                
                  H
                  n
                  *
                
                ⁢
                
                  
                    I
                     ̆
                  
                  n
                
                ⁢
                
                  H
                  n
                  7
                
              
            
            
              
                
                  
                    H
                    n
                    *
                  
                  ⁢
                  
                    H
                    n
                    T
                  
                
                +
                
                  
                    σ
                    2
                  
                  ⁢
                  
                    H
                    n
                  
                
              
            
            
              
                
                  H
                  n
                  *
                
                ⁢
                
                  I
                  4
                
              
            
            
              
                
                  H
                  n
                  *
                
                ⁢
                
                  I
                  3
                
              
            
          
          
            
              
                
                  I
                  3
                  T
                
                ⁢
                
                  H
                  n
                  †
                
              
            
            
              
                
                  I
                  4
                  T
                
                ⁢
                
                  H
                  n
                  T
                
              
            
            
              
                I
                5
              
            
            
              
                I
                6
              
            
          
          
            
              
                
                  I
                  1
                  T
                
                ⁢
                
                  H
                  n
                  7
                
              
            
            
              
                
                  I
                  3
                  T
                
                ⁢
                
                  H
                  n
                  T
                
              
            
            
              
                I
                6
              
            
            
              
                I
                5
              
            
          
        
        ]
      
      £
    
    .
    
      [
      
        
          
            
              
                H
                n
              
              ⁢
              
                I
                7
              
            
          
        
        
          
            
              
                H
                n
              
              ⁢
              
                I
                8
              
            
          
        
        
          
            0
          
        
        
          
            0
          
        
      
      ]
    
  




The length of the filter B is equal to LB and that of the filter G is equal to 2 (2LG+1)

With:





  
    
      
        
          
            I
            ~
          
          n
        
        =
        
          E
          ⁡
          
            [
            
              
                b
                n
                *
              
              ⁢
              
                b
                n
                †
              
            
            ]
          
        
      
    
  
  
    
      
        
          I
          3
        
        =
        
          E
          ⁡
          
            [
            
              
                b
                n
              
              ⁢
              
                d
                n
                †
              
            
            ]
          
        
      
    
  
  
    
      
        
          I
          4
        
        =
        
          E
          ⁡
          
            [
            
              
                b
                n
              
              ⁢
              
                d
                n
                T
              
            
            ]
          
        
      
    
  
  
    
      
        
          I
          5
        
        =
        
          E
          ⁡
          
            [
            
              
                d
                n
              
              ⁢
              
                d
                n
                †
              
            
            ]
          
        
      
    
  
  
    
      
        
          I
          6
        
        =
        
          E
          ⁡
          
            [
            
              
                d
                n
                *
              
              ⁢
              
                d
                n
                †
              
            
            ]
          
        
      
    
  
  
    
      
        
          I
          7
        
        =
        
          E
          ⁡
          
            [
            
              
                b
                n
              
              ⁢
              
                a
                n
                †
              
            
            ]
          
        
      
    
  
  
    
      
        
          I
          8
        
        =
        
          E
          ⁡
          
            [
            
              
                b
                n
                *
              
              ⁢
              
                a
                n
                †
              
            
            ]
          
        
      
    
  




The method described here above can be applied especially well in the context of urban or mountainous environments, or again for metropolitan underground rail transit or railway tunnels as shown diagrammatically in FIG. 6.
The former case gives rise to a multiple-path context that generates a sum of several correlated and delayed signals. The latter case is categorized chiefly by a major attenuation in the first decameters traveled and a sum of different parts giving rise, at the reception sensors, to a major space-time correlation. The two types of propagation generate a diversity of transmission. They therefore generate decorrelated propagation channels on an antenna with several sensors spatially distant from each other.
Urban, mountainous or tunnel type propagation induces multiple paths converging toward the concerned receiver. Consequently, a Doppler spread is generated by randomly modifying the complex characteristics of the signal received by each of the sensors and thus creating propagation diversity.
FIGS. 7 to 11 represent results obtained by implementing the method according to the invention.
The performance characteristics of the block equalizers and non-block equalizers are presented and compared. The values of the filters computed depend on the chosen length of the transverse filter.
Model of the Transmission Channel
FIG. 7 represents the frequency response of the transmission channel.
The results have been obtained for a channel with the following characteristics:

    4 paths in a channel τ=[1, 14, 17, 11]
    complex amplitudes of the paths: α=[−0.6632+0.0188i, 0.0622−0.0549i, −0.3343+0.2573, i0.1366−0.6557i]
    symbol oversampling factor: 4

Results Obtained in the Case of Multiple Sending, Multiple Reception and Multiple Paths

Two transmission scenarios are considered here:
    
        1. MIMO unicast transmission
        2. MIMO multicast transmission
    
    


In the first case, the transmitters are separated by a distance greater than the correlation distance of the channel considered. In this case, the profile of the channel is the same for all the paths (DOA and induced delays). This is a classic case in tunnel type propagation.
FIG. 9 shows the performance obtained in the case of two delocalized transmission operations, three reception sensors, two paths per channel and non-block receivers.
The DFE-MMSE (Decision Feedback Equalizer-Zero Forcing) system offers the best performance and is not excessively sensitive to inter-symbol interference (ISI) introduced by the second path.
In the second case, the propagation channels are totally decorrelated (outdoor transmission). This makes it possible especially to validate the feasibility of transmission in the context of a metropolitan underground rail transit tunnel in a ratio of 4 with respect to standard GSM transmission. The performance obtained in this type of scenario is shown in FIG. 10 whose notations are identical to those of FIG. 9, taken by way of an example.
The conditions are the following: 4 transmission operations, 5 reception sensors, one path per channel with the same delay and one non-block receiver.
The figure shows that the performance is better than in the case of FIG. 9. This is related to the fact that the capacity of the transmission channel increases when the number of transmission and reception antennas increases.
The above results are obtained without any error correction system and give error rates of to 10−3 to 10−4 for signal-to-noise (S/N) ratios of over 5 dB.

## Claims

1. A receiver apparatus in a communication system including N transmitters and M receivers, with M greater than or equal to N, said receiver being on of said M receivers, said receiver comprising:
a reception agent configured to simultaneously receive a superimposition of different messages sent by the N transmitters;
a demodulating agent configured to decode a signal received by the reception agent;
a channel estimating agent configured to estimate a characteristic of a transmission channel between one of said N transmitters and said receiver, and configured to jointly estimate a characteristic of the transmission channel by using information of all of the different message; and
an equalizer filter configured to minimize a mean squared error between an output of said equalizer filter and a corresponding real symbol, said equalizer filter having a feed forward filtering function and a feed back filtering function,
wherein the equalizer filter is further configured to produce a bit-error-rate (BER) of less than 10−3, when the signal-to-noise (Eb/N0) ratio of the signal is greater than 5 dB, and when no error correction is performed.

2. A receiver apparatus in a communication system including N transmitters and M receivers, with M greater than or equal to N, said receiver being on of said M receivers, said receiver comprising:
a reception agent configured to simultaneously receive a superimposition of different messages sent by the N transmitters;
a demodulating agent configured to decode a signal received by the reception agent;
a channel estimating agent configured to estimate a characteristic of a transmission channel between one of said N transmitters and said receiver, and configured to jointly estimate a characteristic of the transmission channel by using information of all of the different message; and
an equalizer filter configured to minimize a mean squared error between an output of said equalizer filter and a corresponding real symbol, said equalizer filter having a feed forward filtering function and a feed back filtering function,
wherein said means for equalizing is configured to minimize according to:





  E
  ⁡
  
    [
    
      
        
        
          
            
              [
              
                G
                -
                B
              
              ]
            
            ⁡
            
              [
              
                
                  
                    
                      y
                      n
                    
                  
                
                
                  
                    
                      y
                      n
                      *
                    
                  
                
                
                  
                    
                      d
                      n
                    
                  
                
                
                  
                    
                      d
                      n
                      *
                    
                  
                
              
              ]
            
          
          -
          
            b
            n
          
        
        
      
      2
    
    ]
  



where,
G is the feed forward function,
B is the feed back function,
yn is a symbol at input of G,
dn is a symbol at output of B,
bn is a real symbol.

3. A receiver apparatus in a communication system including N transmitters and M receivers, with M greater than or equal to N, said receiver being one of said M receivers, said receiver comprising:
means for receiving simultaneously a superimposition of different messages sent by the N transmitters;
means for demodulating to decode a received signal;
means for estimating a characteristic of a transmission channel between one of said N transmitters and said receiver; and for estimating a characteristic of the transmission channel by using information of all of the different messages; and
means for equalizing to minimize a mean squared error between an output of said equalizing means and a corresponding real symbol, said equalizing means having a feed forward filtering function and a feed back filtering function,
wherein said means for equalizing includes means for minimizing according to:





  E
  ⁡
  
    [
    
      
        
        
          
            
              [
              
                G
                -
                B
              
              ]
            
            ⁡
            
              [
              
                
                  
                    
                      y
                      n
                    
                  
                
                
                  
                    
                      y
                      n
                      *
                    
                  
                
                
                  
                    
                      d
                      n
                    
                  
                
                
                  
                    
                      d
                      n
                      *
                    
                  
                
              
              ]
            
          
          -
          
            b
            n
          
        
        
      
      2
    
    ]
  



where,
G is the feed forward function,
B is the feed back function,
yn is a symbol at input of G,
dn is a symbol at output of B,
bn is a real symbol.

4. A receiving method configured to operate in a communication system including N transmitters and M receivers, with M greater than or equal to N, said receiver being one of said M receivers, said receiving method comprising:
receiving simultaneously a superimposition of different messages sent by the N transmitters;
demodulating to decode a received signal;
estimating a characteristic of a transmission channel between one of said N transmitters and said receiver;
estimating a characteristic of the transmission channel by using information of all of the different messages; and
equalizing to produce a bit-error-rate (BER) of less than 10−3, when the signal-to-noise (Eb/N0) ratio of the received signal is greater than 5dB and when no error correction is performed.

5. A receiving method configured to operate in a communication system including N transmitters and M receivers, with M greater than or equal to N, said receiver being one of said M receivers, said receiving method comprising:
receiving simultaneously a superimposition of different messages sent by the N transmitters;
demodulating to decode a received signal;
estimating a characteristic of a transmission channel between one of said N transmitters and said receiver;
estimating a characteristic of the transmission channel by using information of all of the different messages; and
minimizing a mean squared error between an output of an equalizing means and a corresponding real symbol, said minimizing including filtering with a feed forward filtering function and a feed back filtering function
wherein said minimizing is configured to minimize according to:





  E
  ⁡
  
    [
    
      
        
        
          
            
              [
              
                G
                -
                B
              
              ]
            
            ⁡
            
              [
              
                
                  
                    
                      y
                      n
                    
                  
                
                
                  
                    
                      y
                      n
                      *
                    
                  
                
                
                  
                    
                      d
                      n
                    
                  
                
                
                  
                    
                      d
                      n
                      *
                    
                  
                
              
              ]
            
          
          -
          
            b
            n
          
        
        
      
      2
    
    ]
  



where,
G is the feed forward function,
B is the feed back function,
yn is a symbol at input of G,
dn is a symbol at output of B,
bn is a real symbol.