# Patent

## Title
Method for estimating a radioelectric propagation channel

## Abstract

A method estimates a channel for radioelectric propagation between a transmitter and a receiver. The transmitter transmits a signal including frames that each use N1 frequency subcarriers, over each of which N1 symbols are transmitted, wherein, among the set of symbols, certain symbols, referred to as pilot symbols, are known to the receiver. The method implemented in the receiver includes; determining an overall intermediate covariance matrix M2 of the channel that embodies a time profile of the channel, which profile is symmetrical and centered on the time synchronization position, and a frequency profile of the channel, which profile is symmetrical and centered on the frequency synchronization position; calculating a vector for an intermediate channel C on the basis of the predetermined overall intermediate covariance matrix M2; and estimating the channel on the basis of the calculated vector for the intermediate channel C′.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This is the U.S. National Stage of PCT/EP2015/063583, filed Jun. 17, 2015, which in turn claims priority to French Application No. 1401367, filed Jun. 17, 2014, the entire contents of all applications are incorporated herein by reference in their entireties.
TECHNICAL FIELD
The present invention relates to a method for estimating a radio propagation channel between a transmitter and a receiver. It also relates to a corresponding receiving device and a corresponding computer program.
The invention relates more specifically to multicarrier transmission systems, for example of the OFDM type (“Orthogonal Frequency Division Multiplexing”) or of the SC-FDMA (Single-Carrier/Frequency Division Multiple Access) type, or alternatively of type FB-MC (Filter Bank Multi-Carrier) type, all these techniques being multicarrier-type transmission techniques.
STATE OF THE ART
This type of transmission is used increasingly frequently. It has been adopted in particular in the LTE (“Long Term Evolution”), TEDS (“TETRA Enhanced Data Service”), DAB (“Digital Audio Broadcasting”) and DVB-T (“Digital Video Broadcasting-Terrestrial”) systems.
In multicarrier transmission systems the data is generally encoded in the form of symbols organised into frames sent in a signal by a transmitter towards a receiver through a propagation channel, where each frame uses Nf frequency subcarriers over each of which Nt symbols are transmitted, i.e. n total number of symbols in the time-frequency plane equal to n=Nt×Nf.
The propagation channel is defined as the radio path taken by the transmitted signal from the transmitter to the receiver. The signal received by the receiver is generally written in the form R=E·C+B, where R is a column vector of dimension n consisting of the received symbols, E is a diagonal matrix of dimension (n,n) the diagonal of which consists of the n symbols transmitted in a frame, C is a column vector, called a channel vector, of dimension n representing the propagation channel and B is a column vector of dimension n representing the noise of the channel. In what follows vectors R, C and B will be represented conventionally in the form of a concatenation of Nt vectors, where each is of dimension Nf, the first vector corresponding to the Nf symbols, corresponding to the first symbol of the frame, located in succession on Nf sub-carriers, and the following vectors corresponding in a similar manner to the Nt successive symbols. Similarly, in the following description, the diagonal of matrix E consists of a concatenation, for the Nt successive symbols in the frame, of the Nf successive values of the propagation channel for the successive sub-carriers.
The propagation channel includes, for a signal transmitted by the transmitter, a plurality of paths between the transmitter and the receiver, due in particular to the signal's reflection and/or diffraction on obstacles such as, for example, hills, buildings, vehicles, etc. Each path is thus characterised by a delay and an attenuation, and the delay between the signal received by the receiver over the shortest radio path and the signal received by the receiver over the longest radio path constitutes the channel's temporal spread. All the paths with their power values and their delays constitute the channel's temporal profile. Depending on the characteristics of the propagation environment, a typical propagation temporal profile is expected.
The different paths taken by the signal can also combine destructively with one another, in particular when the signal's reflections occur on obstacles located close to the receiver and/or the transmitter. More specifically, each path can be affected by a fading known as “Rayleigh” fading, known to those skilled in the art, the pseudo-frequency of which is equal to the double of the Doppler frequency, where this Doppler frequency is determined from the speed of the transmitter and/or of the receiver when at least one of the two is mobile, and from the carrier frequency of the transmitted signal. The difference between the lower frequency and the higher frequency between the signals received by the receiver over the different radio paths of a monochrome signal transmitted by the transmitter constitutes the channel's frequency spread. The power spectrum of this received signal is called the channel's frequency profile. Depending on the characteristics of the propagation environment, a typical propagation frequency profile is expected.
A multi-path channel with Rayleigh fading may therefore be selective in terms of time and/or of frequency.
To estimate the propagation channel certain symbols, distributed on the time-frequency plane, are inserted in each frame among the useful information intended for the receiver. These symbols, called “pilot symbols”, are known to the transmitter and to the receiver. They are used for purposes of synchronising and estimating the propagation channel.
In a multi-carrier system the effect of the propagation channel on a data symbol, in the time-frequency plane, is generally modelled simply by a complex multiplying coefficient which the receiver attempts to estimate in order to determine the transmitted symbol with the least possible error. The channel estimation is defined as being the determination of these coefficients for all the transmitted symbols.
In a known manner the receiver generally starts by estimating the channel at the position of the pilot symbols; it then makes an estimation of the channel over the entire frame. The channel estimation for the positions which are not pilot symbols is generally made by means of an interpolation from the channel estimation for the pilot symbols.
Document FR2814011 describes a method for estimating a channel enabling the known physical characteristics of the propagation channel to be taken into account. However, the described method is very constrictive in terms of complexity. To resolve these disadvantages partially, patent application FR2983666 A1 filed by the Applicant describes a method for estimating a channel of lesser complexity, enabling the known physical characteristics of the propagation channel to be taken into account, and in particular implementing the maximum a posteriori, or MAP, criterion.
The resolution of the problem of estimating the channel in the sense of the MAP amounts to maximising term




  
    
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whilst responding to the physical variations of the channel in terms of time and frequency, expressed by means of the channel's global covariance matrix M1. σ2 represents the variance of noise in the channel.

The channel's global covariance matrix M1 is obtained from knowledge of the channel's physical variations, i.e.:

    
    
        the channel's temporal profile, defined in a time window, which causes variations of the propagation channel along the frequency axis, and from which a covariance matrix M1f can be calculated, therefore expressing the channel's frequency variations due to the said temporal profile, and
        the frequency profile, defined in a frequency window, which causes variations of the propagation channel along the time axis, and from which a covariance matrix M1f can be calculated, therefore expressing the channel's time variations due to the said frequency profile.
    
    


Temporal covariance matrix M1t expressing the channel's temporal constraint may be obtained by an inverse Fourier transform of the channel's frequency profile, whereas frequency covariance matrix M1f expressing the channel's frequency constraint may be obtained by a Fourier transform of the channel's temporal profile. Global covariance matrix M1 of the channel is the Kronecker tensor product of the two covariance matrices, temporal covariance matrix M1f and frequency covariance matrix M1f: M1=M1t{circle around (x)}M1f.
The theoretical hypothesis considered to estimate the channel in the frequency field is often a temporal profile of the channel which is symmetric call and centred on a position called the “signal's timing synchronisation position”. Such a timing synchronisation position of the signal is generally predetermined in a known manner, for example by means of a specific timing synchronisation sequence (or by other means), and is used by the receiver to synchronise temporally the signal received from the transmitter, i.e. to determine a precise instant associated with the window of the signal's temporal profile (in this case the middle of the window). In this case the eigenvalues and the eigenvectors of frequency covariance matrix M1f are real.
In practice, however, the channel's temporal profile is not necessarily symmetrical and centred on the timing synchronisation position. It may, for example, be symmetrical but centred on an effective central timing position which differs from the position called the signal's “timing synchronisation position” since timing synchronisation is often accomplished with the first propagation paths of the received signals, which are generally the least attenuated, whereas subsequent paths maybe more attenuated and substantially delayed but also significant. In this case the eigenvalues of frequency covariance matrix M1f are real, but the eigenvectors of frequency covariance matrix M1f are complex.
Similarly, the theoretical constraint considered in the temporal field corresponds to a frequency profile of the channel which is symmetrical and centred on a position known as the “signal's frequency synchronisation position”. Such a frequency synchronisation position of the signal may be predetermined in a known manner, for example by means of a specific frequency synchronisation sequence (or by other means), and is used by the receiver to synchronise frequentially the signal received from the transmitter, i.e. to determine a precise frequency associated with the spread window of the signal's frequency profile (in this case the middle of the window). In this case the eigenvalues and the eigenvectors of frequency covariance matrix M1t are real.
In practice, however, the channel's frequency profile is not necessarily symmetrical and centred on the frequency synchronisation position. It may, for example, be symmetrical but centred on an effective central frequency position which is different to the signal's “frequency synchronisation position”. In this case the eigenvalues of covariance matrix M1t are real, but the eigenvectors of covariance matrix M1t are complex.
The resolution of the problem of estimating the channel in the sense of the MAP with complex eigenvectors in temporal covariance matrix M1f and/or frequency matrix M1t makes the receiver complex and expensive since its memory and the capacity of its processor must be substantial in order to process the received data to estimate the propagation channel, which represents a substantial disadvantage.
GENERAL PRESENTATION OF THE INVENTION
The present invention seeks to resolve this disadvantage by proposing a method for estimating a radio propagation channel between a transmitter and a receiver which enables the complexity and cost of implementation of the receiver to be reduced whilst enabling the estimation of a channel the constraints of which correspond to those of reality.
To this end the invention concerns firstly a method for estimating a radio propagation channel between a transmitter and a receiver, where the said transmitter transmits a signal including frames each of which uses Nf frequency subcarriers over each of which Nt symbols are transmitted, where among all the symbols, certain symbols, called pilot symbols, are known to the said receiver, where the said signal is synchronised by the receiver from a timing synchronisation position and a frequency synchronisation position, where the temporal profile of the channel is symmetrical and centred on an effective central timing position Tmean different to the timing synchronisation position, where the frequency profile of the channel is symmetrical and centred on an effective central frequency position fmean different to the frequency synchronisation position. The method implemented by the receiver is noteworthy due to the fact that it includes the steps of:

    
    
        determination of an intermediate frequency covariance matrix M2f representing the frequency variations of the channel due to a theoretical temporal profile of the channel, which is symmetrical and centred on the timing synchronisation position, where this theoretical temporal profile of the channel is obtained from the temporal profile of the channel translated to a time of (−Tmean) such that it is symmetrical around the timing synchronisation position (zero time position);
        determination of an intermediate temporal covariance matrix M2f representing the temporal variations of the channel due to a theoretical frequency profile of the channel, which is symmetrical and centred on the frequency synchronisation position, where this theoretical frequency profile of the channel is obtained from the frequency profile of the channel translated to a frequency of (−fmean) such that it is symmetrical around the frequency synchronisation position (zero frequency position);
        calculation of an intermediate global covariance matrix M2 according to the Kronecker product: M2=M2fM2f;
        calculation of a matrix E′ according to the relationship E=E·TH, where T=T1Tj and in which E is a diagonal matrix including the pilot symbols transmitted in a frame at the positions of the pilot symbols, where the other symbols are zero, Tf is

a diagonal centring matrix (Nf, Nf) defined by

    
    





  
    
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calculation of a column vector representing an intermediate channel C′ which minimises the relationship





  
    
      
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where R is a column vector of dimension (Nt×Nf) consisting of the received symbols, and;

    
    
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The words “determination of an intermediate frequency covariance matrix M2f representing the frequency variations of the channel due to the channel's temporal profile centred on the timing synchronisation position” are understood to mean that the effects of the signal's temporal profile on the signal's frequency variations are determined when this temporal profile is centred on the signal's timing synchronisation position.
Similarly, the words “determination of an intermediate temporal covariance matrix M2t representing the temporal variations of the channel due to the channel's frequency profile centred on the frequency synchronisation position” are understood to mean that the effects of the signal's frequency profile on the signal's temporal variations are determined when this frequency profile is centred on the signal's frequency synchronisation position.




  
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The Kronecker product of two matrices A and B, where matrix A has components (aij), where i is an integer of between 1 and m and j is an integer of between 1 and n, is the matrix product noted A{circle around (x)}B and defined by the following expression:
When the channel's temporal profile is symmetrical and centred around effective central timing position Tmean but effective central timing position Tmean is not equal to the timing synchronisation position, frequency covariance matrix M1f expressing the variation of the channel along the frequency axis is a matrix with complex eigenvectors. The method according to the invention allows definition, from a given temporal profile, but centred around the timing synchronisation position, for example by a Fourier transform of the channel's temporal profile, of an intermediate frequency covariance matrix M2f, which is equal to frequency covariance matrix M1f of the real channel, but which has real eigenvectors. In other words, intermediate frequency covariance matrix M2f is equal to the constraint due to the channel's temporal profile, but with a temporal offset such that the constraint in terms of the channel's temporal profile is symmetrical and centred not on effective central timing position Tmean but on the timing synchronisation position. The channel's temporal profile constraint is then centred and symmetrical around the timing synchronisation position. In addition, in the special case in which effective central timing position Tmean is equal to the timing synchronisation position is then M2f=M1f.
Similarly, when the channel's frequency profile is symmetrical around effective central frequency position fmean but said effective central frequency position fmean is not equal to the frequency synchronisation position, temporal covariance matrix M1f expressing the variation of the channel along the temporal axis is a matrix with complex eigenvectors. The method according to the invention allows definition, from a given frequency profile, but now centred around the frequency synchronisation position, for example by a inverse Fourier transform of the channel's frequency profile, of an intermediate temporal covariance matrix M2t, which is equal to temporal covariance matrix M1t of the real channel, but which has real eigenvectors. In other words, intermediate temporal covariance matrix M2t is equal to the constraint due to the channel's frequency profile, but with a frequency offset such that the constraint in terms of the channel's frequency profile is symmetrical and centred not on effective central frequency position fmean but on the frequency synchronisation position. The constraint in terms of the channel's frequency profile is then centred and symmetrical around the frequency synchronisation position. In addition, in the special case in which effective central frequency position fmean is equal to the frequency synchronisation position then M2t=M1t.
Global intermediate covariance matrix M2 which is the Kronecker product of intermediate temporal covariance matrix M2t and of intermediate frequency covariance matrix M2f is thus equal to a virtual propagation channel C′ and advantageously has real eigenvectors. To estimate channel C′ corresponding to this intermediate matrix M2, a method may be used based on the maximum a posteriori (MAP) criterion such as, for example, the method described in document FR2983666 A1 or alternatively in document FR2814011. Column vector C corresponding to the real channel is then advantageously obtained from intermediate channel matrix C′ and from centring matrix T defined according to the invention.
Use of the separability of intermediate covariance matrix M2<<, the eigenvectors of which are real, is verifiable in terms of complexity. Thus, for a frame of n symbols, with Nf subcarriers and Nt time symbols, intermediate covariance matrix M2 is of dimension (n,n) with n=Nt×Nt. This matrix is equal to the Kronecker product of a covariance matrix M2t of dimension (Nf, Nf) with a covariance matrix M2t of dimension (Nt, Nf). It is therefore sufficient to record (Nt2+Nt2) values instead of (Nt2×Nt2) values. The method of the present invention thus enables the complexity of the channel estimation to be reduced significantly, particularly in terms of required storage memory, taking account of the real physical constraints of the propagation channel.
Preferably, on the diagonal of matrix E, the transmitted symbols are concatenated such that, for the first symbol of the frame, firstly the symbols corresponding to the successive subcarriers are placed, and then the same is done for the second symbol of the frame, and so forth until the last symbol of the frame. According to one aspect of the invention the method includes a preliminary step of determination of the signal's timing synchronisation position and frequency synchronisation position.
According to another aspect of the invention the method includes a step of determination of the signal's effective central timing position Tmean and effective central frequency position fmean.
The step of calculation of intermediate channel vector C′ preferably includes the sub-steps of:

    
    
        decomposition of covariance matrices M2f and M2t into eigenvectors according to the relationships M2f=WFHNFWF et M2t=WTHNTWT, in which:
        WF is a matrix of eigenvectors of matrix M2f;
        NF is a diagonal matrix including eigenvalues associated with the eigenvectors of matrix M2f;
        WT is a matrix of eigenvectors of matrix M2t;
        NT is a diagonal matrix including eigenvalues associated with the eigenvectors of matrix M2t;
        calculation of the Kronecker product of the matrices of eigenvectors WF and WT, to obtain a global matrix of eigenvectors W;
        calculation of a global diagonal matrix of eigenvectors N equal to the Kronecker product of matrices of eigenvalues NF, and NT; and
        calculation of intermediate channel vector C′ using the pilot symbols given by matrix E′ and of the matrices of eigenvectors W and of eigenvalues N using the maximum a posteriori criterion.
    
    


A “pilot symbol” is understood to mean all symbols known to the receiver, i.e. the pilot symbols, as designated in the standards of known multicarrier systems such as LTE and TEDS, and/or the synchronisation symbols and/or the symbols which have previously been demodulated and decided by the receiver in a prior processing step.
Since matrix W of the eigenvectors is the Kronecker product of two matrices WF and WT of eigenvectors, only (Nf×Nf+Nt×Nt)=Nf2+Nt2 values are required to represent it. Similarly, since diagonal matrix N of the eigenvalues is the Kronecker product of the two diagonal matrices NF and NT, only Nf+Nt values are required to represent it. This enables the complexity of the estimation of the channel to be reduced significantly, particularly in terms of the required storage memory.
According to one implementation, the step of calculation of intermediate channel vector C′ includes the sub-steps of:

    
    
        calculation of a matrix P according to the relationship P=√{square root over (N)}·W·E′H·E′·WH·√{square root over (N)};
        decomposition of matrix P into eigenvectors according to relationship P=X′′QX in which X is a matrix of eigenvectors of matrix P and Q is a diagonal matrix including eigenvalues associated with the eigenvectors of matrix P; and
        calculation of vector C′ according to the relationship C′′=W′′·√{square root over (N)}·XH·(Q+σ2·I)−1·X·√{square root over (N)}·W·E′H·R in which I is the identity matrix, R is a vector including the received symbols and σ2 represents the power value of the noise in the channel.
    
    


More specifically, matrix √{square root over (N)} is a diagonal matrix the terms of the diagonal of which are the square roots of the terms of the diagonal of diagonal matrix N.
When the pilot symbols are regularly distributed by time and frequency, matrix P can be written in the form of a Kronecker product of two matrices relative, respectively, to the frequency domain and the time domain. In this case the complexity of the channel estimation is reduced still further.
According to one preferred implementation, the step of calculation of matrix C′ includes the sub-steps of:

    
    
        extraction of a matrix W′ from matrix W and of a matrix N′ from matrix N, where matrix N′ includes a determined number n′ of eigenvalues of matrix N and matrix W′ includes the eigenvectors associated with these n′ eigenvalues; and
        calculation of matrix C′ using the pilot symbols and the matrices of eigenvectors W′ and of eigenvalues N′ using the maximum a posteriori criterion.
    
    


The n′ eigenvalues are preferably the highest eigenvalues of matrix N.
This enables the complexity of channel estimation to be reduced whilst minimising loss of performance, due to the fact that the eigenvectors retained in matrix W′ account for most of the energy, represented by the sum of the eigenvalues retained in matrix N′.
Advantageously, the n′ eigenvectors of matrix W′ are the Kronecker products of a limited number n′f of eigenvectors of matrix WF and of a limited number n′t of eigenvectors of matrix WT and the n′ eigenvalues of matrix N′ are the products of the eigenvalues of matrix NF corresponding to the n′f eigenvectors of matrix WF and eigenvalues of matrix NT corresponding to the n′t eigenvectors of matrix WT.
In this case matrix W′ is separable in terms of time and frequency. Only (n′f×Nf+n′t×Nt) values are then required to represent it. The complexity of the method is reduced still further by this means.
n′ is preferably less than or equal to the number of pilot symbols in each frame.
Advantageously, the step of calculation of matrix C′ includes the sub-steps of:

    
    
        calculation of a matrix P according to the relationship P′=√{square root over (N′)}·W′·E′H·E′·W′H·√{square root over (N′)};
        decomposition of matrix P′ into eigenvectors according to relationship P′=X′HQ′X′ in which X′ is a matrix of eigenvectors of matrix P′ and Q′ is a diagonal matrix including eigenvalues associated with the eigenvectors of matrix P′; and
        calculation of matrix C′ according to the relationship C′=W′H·√{square root over (N′)}·X′H·(Q′+σ2·I)−1·X′·√{square root over (N′)}·W′·E′H·R in which I is the identity matrix, R is a vector including the received symbols and σ2 represents the power value of the noise in the channel.
    
    


More specifically, matrix √{square root over (N′)} is a diagonal matrix the terms of the diagonal of which are the square roots of the terms of the diagonal of diagonal matrix N′.
When the pilot symbols are regularly distributed in terms of time and frequency, matrix P′ can be written in the form of a Kronecker product of two matrices relative, respectively, to the frequency domain and the time domain. In this case the complexity of the channel estimation is reduced still further.
Advantageously, the signal is a multicarrier signal, and in particular an OFDM signal.
The invention can also be applied to single-carrier systems. In this case there is then M2t=M1f=[1], where [1] represents the identity matrix of dimension (1, 1), this matrix is degenerate in a scalar equal to 1.
The invention also concerns a receiver device able to receive from a transmitter at least one signal transmitted through a radio propagation channel, where the said signal includes frames each using Nf frequency subcarriers over each of which Nt symbols are transmitted, where from among all the symbols certain symbols, called pilot symbols, are known to the said receiver device, where the signal is synchronised by the receiver from a timing synchronisation position and from a frequency synchronisation position, where the channel's temporal profile is symmetrical and centred around an effective central timing position Tmean separate from the timing synchronisation position, and where the channel's frequency profile is symmetrical and centred around an effective central frequency position fmean separate from the frequency synchronisation position. The method implemented in the receiver is noteworthy due to the fact that it includes:

    
    
        means for determining an intermediate frequency covariance matrix M2f representing the channel's frequency variations, due to a theoretical temporal profile of the channel, which is symmetrical and centred on the timing synchronisation position, where this theoretical temporal profile of the channel is obtained from the channel's temporal profile translated to a time of (−Tmean) so as to be symmetrical around the timing synchronisation position;
        means for determining an intermediate temporal covariance matrix M2t representing the channel's temporal variations, due to a theoretical frequency profile of the channel, which is symmetrical and centred on the frequency synchronisation position, where this theoretical frequency profile of the channel is obtained from the channel's frequency profile translated to a frequency of (−fmean) so as to be symmetrical around the frequency synchronisation position;
        means for calculating an intermediate global covariance matrix M2 according to the Kronecker product: M2=M2tM2f;
        means for calculating a matrix E′ according to the relationship E′=E·TH, where T=TtTf and in which E is a diagonal matrix including the pilot symbols transmitted in a frame at the positions of the pilot symbols, where the other symbols are zero, TF is a diagonal centring matrix (Nf, Nf) defined by
    
    






  
    
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                  ⁡
                  
                    (
                    
                      Nf
                      -
                      1
                    
                    )
                  
                
                ⁢
                φ
              
            
          
        
      
      ⁢
      
        
      
      ]
    
  
  ,
  
    
      where
      ⁢
      
        
      
      ⁢
      φ
    
    =
    
      2
      ⁢
      
        π
        ·
        
          
            τ
            moyen
          
          
            N
            f
          
        
      
    
  




and Tt is a diagonal centring matrix (Nt, Nt) defined by




  
    
      rT
      t
    
    =
    
      [
      
        
      
      ⁢
      
        
          
            1
          
          
            0
          
          
            ...
          
          
            ...
          
          
            0
          
        
        
          
            0
          
          
            
              e
              
                i
                ⁢
                
                  
                
                ⁢
                ψ
              
            
          
          
            ...
          
          
            
              
            
          
          
            
              
            
          
        
        
          
            ...
          
          
            ...
          
          
            
              e
              
                i
                ⁢
                
                  
                
                ⁢
                2
                ⁢
                ψ
              
            
          
          
            ...
          
          
            
              
            
          
        
        
          
            ...
          
          
            
              
            
          
          
            ...
          
          
            ...
          
          
            0
          
        
        
          
            0
          
          
            ...
          
          
            ...
          
          
            0
          
          
            
              e
              
                
                  i
                  ⁡
                  
                    (
                    
                      Nt
                      -
                      1
                    
                    )
                  
                
                ⁢
                ψ
              
            
          
        
      
      ⁢
      
        
      
      ]
    
  




  
    
      
        where
        ⁢
        
          
        
        ⁢
        ψ
      
      =
      
        
          -
          2
        
        ⁢
        
          π
          ·
          
            
              J
              moyen
            
            
              N
              t
            
          
        
      
    
    ;
  



    
    
        means for calculating a column vector representing an intermediate channel C′ which minimises the relationship
    
    






  
    
      
        
        
          R
          -
          
            
              E
              ′
            
            ·
            
              C
              ′
            
          
        
        
      
      2
    
    
      σ
      2
    
  
  +
  
    
      
        C
        ′
      
      H
    
    ·
    
      M
      2
      
        -
        1
      
    
    ·
    
      C
      ′
    
  




where R is a column vector of dimension (Nt xNf) consisting of the received symbols, and;

    
    
        means for estimating the propagation channel according to the relationship C=TH·C′, from calculated vector C′.
    
    


The invention also concerns a computer program including instructions for implementing the method according to the invention when the program is executed by at least one processor.
The flow diagrams of FIGS. 2 to 3 illustrate schematically the functioning of this computer program, for preferred implementations of the invention.



DESCRIPTION OF THE FIGURES
Implementations of the invention will now be described more precisely but not restrictively with reference to the appended illustrations in which:
FIG. 1 is a diagram of a receiver device according to the invention;
FIG. 2 is a flowchart illustrating the operation of the channel estimation method according to a first implementation of the invention; and
FIG. 3 is a flowchart illustrating the operation of the channel estimation method according to a second implementation of the invention.



DETAILED DESCRIPTION OF THE INVENTION
I. Receiver Device 2
FIG. 1 represents a receiver device 2 of a multicarrier transmission system such as, for example, a mobile terminal of a professional mobile radio system PMR (“Professional Mobile Radio”) of the TEDS type. This is in no sense restrictive of the scope of the present invention, which can be applied more generally to all multicarrier transmission systems, or to a single-carrier transmission system.
Receiver 2 includes an antenna 4 for the reception of an OFDM signal transmitted from a transmitter 6 through a radio propagation channel 8.
The OFDM signal transmitted by transmitter 6 is organised into frames of signals distributed over time and over frequency, among which certain symbols, called pilot symbols, are known to receiver 2 and are stored in a memory 10 of said receiver 2. Each frame thus includes n symbols with Nf subcarriers and Nt time symbols, where n is equal to the product of Nf and of Nt.
Receiver 2 includes a channel estimation module 14 using the pilot symbols stored in memory 10 and its knowledge of the physical constraints of channel 8 in the time and frequency domains to estimate propagation channel 8.
Firstly, in the frequency domain, the frequency profile of channel 8, due to the reflections on proximate obstacles, has a limited frequency spread. This frequency spread, also called the Doppler spread, is between −FD and +FD, where FD is the maximum Doppler frequency given by the relationship




  
    
      F
      D
    
    =
    
      
        v
        c
      
      ·
      
        F
        
          p
          t
        
      
    
  
  ,




in which v is the speed of mobile receiver 2, “c” is the speed of light, and FP is the carrier frequency. The components of the frequency spectrum of propagation channel 8 are therefore between fixed limits for given conditions of the maximum speed of mobile receiver 2 and of the carrier frequency. The frequency profile of channel 8 is centred and symmetrical around an effective central frequency position fmean of channel 8 and defines a temporal covariance matrix M1t.

Secondly, the temporal profile of channel 8, due to the reflections on distant obstacles, has a limited temporal spread. This temporal spread depends on the frequency band used and the environment. As examples, at a carrier frequency of 400 MHz, in an urban environment, the temporal spread is of the order of 5 μs whereas in a mountainous environment this spread is of the order of 15 μs. The components of the temporal profile of channel 8 are therefore between fixed limits for given environmental conditions. The temporal profile of channel 8 is centred and symmetrical around an effective central timing position Tmean and defines a frequency covariance matrix M1f of channel 8.
The characteristics of the frequency profile and of the temporal profile of channel 8 are known to receiver 2 and are stored in memory 10.
Receiver 2 is also configured to determine and/or to receive a timing synchronisation position of the signal and a frequency synchronisation position of the signal. The timing synchronisation position may be predetermined in a known manner, for example by means of a specific timing synchronisation sequence (or by any other means). The frequency synchronisation position may be predetermined in a known manner, for example by means of a specific frequency synchronisation sequence (or by any other means).
Receiver 2 is also configured to determine an effective central timing position of the corresponding signal in the middle of the spread window of the received signal's temporal profile, and an effective central frequency position of the corresponding signal in the middle of the spread window of the received signal's frequency profile.
II. Channel Estimation Module 14
a) Determination Means 16
Channel estimation module 14 includes, firstly, determination means 16 configured to determine:

    
    
        intermediate frequency covariance matrix M2f representing the frequency variations of the channel due to the temporal profile of the channel centred on the timing synchronisation position, and
        intermediate temporal covariance matrix M2t representing the temporal variations of the channel due to the frequency profile of the channel centred on the frequency synchronisation position.
    
    


Intermediate frequency covariance matrix M2f may be determined, for example, by applying a Fourier transform to the spread window of the signal's temporal profile centred on the signal's timing synchronisation position.
Similarly, intermediate temporal covariance matrix M2t may be determined, for example, by applying an inverse Fourier transform to the spread window of the signal's frequency profile centred on the signal's frequency synchronisation position.
In addition, determination means 16 are configured to calculate an intermediate global covariance matrix M2 according to the Kronecker product: M2=M2tM2f.
b) Calculation Means 18
Channel estimation module 14 also includes means 18 for calculating a matrix E′ according to the relationship E′=E·TH, where T=TfTf, in which E is a diagonal matrix including the pilot symbols transmitted in a frame at the positions of the pilot symbols, where the other symbols are zero, Tf is a diagonal centring matrix (Nf, Nf) defined by



  
    
      T
      f
    
    =
    
      [
      
        
          
            1
          
          
            0
          
          
            ...
          
          
            ...
          
          
            0
          
        
        
          
            0
          
          
            
              e
              
                i
                ⁢
                
                  
                
                ⁢
                φ
              
            
          
          
            ...
          
          
            
              
            
          
          
            
              
            
          
        
        
          
            ...
          
          
            ...
          
          
            
              e
              
                i
                ⁢
                
                  
                
                ⁢
                2
                ⁢
                φ
              
            
          
          
            ...
          
          
            
              
            
          
        
        
          
            ...
          
          
            
              
            
          
          
            ...
          
          
            ...
          
          
            0
          
        
        
          
            0
          
          
            ...
          
          
            ...
          
          
            0
          
          
            
              e
              
                
                  i
                  ⁡
                  
                    (
                    
                      Nf
                      -
                      1
                    
                    )
                  
                
                ⁢
                φ
              
            
          
        
      
      ]
    
  




  
    
      where
      ⁢
      
        
      
      ⁢
      φ
    
    =
    
      2
      ⁢
      
        π
        ·
        
          
            τ
            moyen
          
          
            N
            f
          
        
      
      (
    
  



and Tf is a diagonal centring matrix (Nt, Nt) defined by




  
    
      T
      l
    
    =
    
      [
      
        
          
            1
          
          
            0
          
          
            ...
          
          
            ...
          
          
            0
          
        
        
          
            0
          
          
            
              e
              
                i
                ⁢
                
                  
                
                ⁢
                ψ
              
            
          
          
            ...
          
          
            
              
            
          
          
            
              
            
          
        
        
          
            ...
          
          
            ...
          
          
            
              e
              
                i
                ⁢
                
                  
                
                ⁢
                2
                ⁢
                ψ
              
            
          
          
            ...
          
          
            
              
            
          
        
        
          
            ...
          
          
            
              
            
          
          
            ...
          
          
            ...
          
          
            0
          
        
        
          
            0
          
          
            ...
          
          
            ...
          
          
            0
          
          
            
              e
              
                
                  i
                  ⁡
                  
                    (
                    
                      Nt
                      -
                      1
                    
                    )
                  
                
                ⁢
                ψ
              
            
          
        
      
      ]
    
  




  
    
      where
      ⁢
      
        
      
      ⁢
      ψ
    
    =
    
      
        -
        2
      
      ⁢
      
        π
        ·
        
          
            f
            moyen
          
          
            N
            t
          
        
      
    
  



c) Estimation Means 20
Channel estimation module 14 also includes means 20 for estimating propagation channel 8 configured to calculate a column vector C′ which minimises the relationship




  
    
      
        
        
          R
          -
          
            
              E
              ′
            
            ·
            
              C
              ′
            
          
        
        
      
      2
    
    
      σ
      2
    
  
  +
  
    
      
        C
        ′
      
      H
    
    ·
    
      M
      2
      
        -
        1
      
    
    ·
    
      C
      ′
    
  




where R is a column vector of dimension (Nt×Nf) consisting of the received symbols, and to estimate the channel according to the relationship C=TH·C′, from calculated vector C′.

III. Decoder 22
Receiver 2 also includes a decoder 22 providing an estimation of the symbols transmitted from the channel estimation made by channel estimation module 14.
Since the structure of the receiver of the invention has been described, the operation of the channel estimation method implemented in channel estimation module 14 will be described in detail.
IV. Application
In general terms the signal received by receiver 2 is written in the form R=E·C+B where R is a vector of dimension n consisting of the symbols received, C is a vector of dimension n representing propagation channel 8, E is a diagonal matrix of dimension (n,n) consisting of the symbols transmitted in a frame and B is a vector of dimension n representing the noise of channel 8.
It is considered conventionally that the channel noise is a Gaussian noise of variance, or power, σ2. The probability of receiving vector R if channel vector C is known is then equal to




  e
  
    -
    
      
        
          
            
            
              R
              -
              EC
            
            
          
          2
        
        
          2
          ⁢
          
            σ
            2
          
        
      
      .
    
  




In addition, in the case of a land mobile radio channel varying according to a Rayleigh law, the channel's probability is equal to




  e
  
    
      -
      
        
          
            C
            H
          
          ·
          
            M
            
              -
              1
            
          
          ·
          C
        
        2
      
    
    ,
  




where M1 is the global covariance matrix representing the real physical time and frequency constraints of channel 8, and where notation X′′ indicates that this is a conjugate transpose matrix X.

As regards the choice of σ2 and of M1, it should be noted that M1 can be taken to be covariance matrix of the normalised channel, i.e. the channel of average unit power. In this case σ2 then represents the inverse of the signal-to-noise ratio. A target signal-to-noise ratio value can be set, where this value does not change whatever the effective value of the noise power value and of the useful signal power value. Other solutions are possible, such as, for example, estimating the signal-to-noise ratio as the received information is received and demodulated, for example for the pilot symbols which are known to the transmitter and the receiver. In this case the signal-to-noise ratio can be modified dynamically in the channel estimation process.
The method according to the invention implements the maximum a posteriori or MAP criterion. The resolution of the channel estimation problem in the sense of the MAP amounts to maximising the probability that a virtual intermediate channel is equal to an intermediate channel vector C′, if vector R is known, whilst responding to its physical constraints expressed in a global intermediate covariance matrix noted M2, which is symmetrical and centred on a timing synchronisation position and on a frequency synchronisation position.
This amounts to maximising probability




  
    e
    
      
        
          
          
            R
            -
            
              
                E
                ′
              
              ⁢
              
                C
                ′
              
            
          
          
        
        2
      
      
        2
        ⁢
        
          σ
          2
        
      
    
  
  ,
  
    e
    
      -
      
        
          
            
              C
              ′
            
            H
          
          ·
          
            M
            2
            
              -
              1
            
          
          ·
          
            C
            ′
          
        
        2
      
    
  
  ,




which amounts to minimising the opposite of the logarithm of this expression, equal to





  
    
      
        
        
          R
          -
          
            
              E
              ′
            
            ⁢
            
              C
              ′
            
          
        
        
      
      2
    
    
      σ
      2
    
  
  +
  
    
      
        C
        ′
      
      H
    
    ·
    
      M
      2
      
        -
        1
      
    
    ·
    
      
        C
        ′
      
      .
    
  




Solution C′ is therefore the one for which the following expression, noted [1], obtained by cancelling the gradient relative to C′ of the previous expression, is verified:

(E′H·E′+σ2·M2−1)C′=E′H·R  [1].

Since only the pilot symbols are known to receiver 2, zeros are placed in matrix E′ at the positions of the other symbols unknown to the receiver.
The constraints of channel 8 in the time domain are independent of its constraints in the frequency domain. The channel's covariance matrix M2 is therefore separable in terms of time and frequency by expressing it as the Kronecker product of two covariance matrices M2f and M2t, where matrix M2f expresses the channel's constraints in the frequency domain and matrix M2t expresses the channel's constraints in the time domain.
Thus, in a step 24a/24b, covariance matrices M2f and M2t of channel 8, respectively in the frequency domain and in the time domain, are determined by determination means 16 by using respectively the spread window of the temporal profile and the spread window of the frequency profile of channel 8 stored in memory 10. These matrices M2f and M2t are stored in memory 10.
According to the invention, intermediate covariance matrix M2 is determined by determination means 16 in a step 26 according to the Kronecker product: M2=M2tM2f.
A matrix E is then calculated by calculation means 18 in a step 28 according to the relationship E′=E·TH, where T=TtTf and in which E is a diagonal matrix including the pilot symbols transmitted in a frame at the positions of the pilot symbols, where the other symbols are zero.
Column vector C′ which minimises the relationship




  
    
      
        
          
          
            R
            -
            
              
                E
                ′
              
              ·
              
                C
                ′
              
            
          
          
        
        2
      
      
        σ
        2
      
    
    +
    
      
        
          C
          ′
        
        H
      
      ·
      
        M
        2
        
          -
          1
        
      
      ·
      
        C
        ′
      
    
  
  ,
  ,




is then calculated by estimation means 20 in a step 30a/30b by implementing the maximum a posteriori or MAP criterion in order to estimate propagation channel 8 according to relationship C=TH·C′.

Step 30a/30b of calculation of vector C′ is described below in a first implementation 30a (steps 32 to 38) and in a second implementation 30b (steps 32 to 34 and 40 to 44) of the method according to the invention.
a) First Implementation
The flowchart of FIG. 2 illustrates a first implementation of the channel estimation method of the invention implementing the MAP criterion.
In a step 32, covariance matrices M2f v and M2t are decomposed into eigenvectors and eigenvalues by decomposition means 18 according to the relationships MF=WFHNFWF and MT=WTHNTWT, in which:

    
    
        WF is a matrix of eigenvectors of matrix M2f;
        NF is a diagonal matrix including eigenvalues associated with the eigenvectors of matrix M2f;
        WT is a matrix of eigenvectors of matrix M2t; and
        NT is a diagonal matrix including eigenvalues associated with the eigenvectors of matrix M2t.
    
    


In step 34, decomposition means 18 calculate the Kronecker product of the eigenvector matrices WF and WT to obtain a global matrix of eigenvectors W of dimension (n, n). They also calculate a global diagonal matrix of eigenvectors N of dimension (n, n) containing the products of the eigenvalues of matrices NF, and NT. Matrices WF, NF, WT and NT are also stored in memory 10.
Global intermediate covariance matrix M2 of channel 8 is then equal to M2=WHNW. Expression [1] can thus be written (E′HE′+σ2·WH·N−1·W)·C′=E′H·R:
By supposing C′=WH·√{square root over (N)}·b where b is a dimensional vector n, and where √{square root over (N)} is a diagonal matrix, each term of the diagonal of which is the square root of the corresponding term of the diagonal of diagonal matrix N, expression [1] is written: (√{square root over (N)}·W·E′H·E′·WH·√{square root over (N)}+σ2·I)b=√{square root over (N)}·W·E′H·R [2] where I is the identity matrix.
In step 36, channel estimation means 20 calculate matrix P=√{square root over (N)}·W·E′H·E′·WH·√{square root over (N)} and decompose this matrix P into eigenvectors and eigenvalues according to relationship P=XHQX in which X is a matrix of eigenvectors of matrix P and Q is a diagonal matrix including eigenvalues associated with the eigenvectors of matrix P.
In step 38, channel estimation means 20 estimate channel 8 from relationship 2 according to the following expression [3]:

C′=WH·√{square root over (N)}·XH·(Q+σ2·I)−1·X·√{square root over (N)}·W·E′H·R  [3].

a) Second Implementation
The flowchart of FIG. 3 illustrates a second implementation of the channel estimation method of the invention also implementing the MAP criterion. In this figure steps 24, 26, 28 and 30 to 34 are identical to those of FIG. 2. The description of these steps is not therefore repeated.
In step 40, channel estimation means 20 extract a diagonal matrix N′ from matrix N, where matrix N′ includes a determined number n′ of the largest eigenvalues of N and determine a matrix W including the eigenvectors associated with these n′ largest eigenvalues. Matrices N′ and W′ are stored in memory 10.
The eigenvalues of matrix N generally decrease rapidly. The sum of the eigenvalues retained in matrix N′ thus account for most of the energy of channel 8. Matrix W′ thus includes the most representative eigenvectors to express the channel's constraints.
Expression [1] can thus be written: (E′HE′+σ2·W′H·N′−1·W′)·C′=E′H·R.
By supposing C′=W′H·√{square root over (N)}·b where b is a vector of dimension n′, expression [1] is written (√{square root over (N′)}·W′·E′H·E′·W′H·√{square root over (N′)}+σ2·I)b=√{square root over (N′)}·W′·E′H·R [4] where I is the identity matrix.
In step 42, channel estimation means 20 calculate a matrix P′ according to the relationship P′=√{square root over (N′)}·W′·E′H·E′·W′H·√{square root over (N′)} and decompose this matrix P′ into eigenvectors and eigenvalues according to relationship P′=X′HQ′X′ in which X′ is a matrix of eigenvectors of matrix P′ and Q′ is a diagonal matrix including eigenvalues associated with the eigenvectors of matrix P′.
In step 44, channel estimation means 20 estimate channel 8 from relationship [4] according to the following expression [5]

C′=W′H·√{square root over (N′)}·X′H·(Q′+σ2·I)−1·X′·√{square root over (N′)}·W′·E′H·R  [5].

Since matrix W′ is of dimension (n′,n′) and matrix N′ is of dimension (n′,n′), this implementation allows less complex calculations than the first implementation.
In a preferred implementation, the n′ eigenvectors of matrix W′ are the Kronecker products of a limited number n′f of eigenvectors of matrix WF and of a limited number n′t of eigenvectors of matrix WE and the n′ eigenvalues of matrix N′ are the products of the eigenvalues of matrix NT corresponding to the n′t eigenvectors of matrix WT and eigenvalues of matrix NT corresponding to the n′t eigenvectors of matrix WT. In this case matrix W′ is separable in terms of time and frequency. It can then be recorded in the form of the Kronecker product of two matrices, and it is then equal to a total dimension of [(n′f, n)+(n′t, n)], which enables the complexity of the method to be reduced.
In both implementations described above, the matrix of real channel C is then estimated according to the invention in a step 50 according to the relationship C=TH·C′ to from calculated vector C′.
Other implementations can of course also be envisaged.
More specifically, the calculation of the covariance matrices can be accomplished dynamically in order to take into account the variations of the channel's constraints.

## Claims

1. A method for estimating a radio propagation channel between a transmitter and a receiver, where the transmitter transmits a signal including frames each of which uses Nf frequency subcarriers over each of which Nt symbols are transmitted, where among all the symbols, certain pilot symbols, are known to the receiver, where the signal is synchronised by the receiver from a timing synchronisation position and a frequency synchronisation position, wherein a temporal profile of the channel is symmetrical and centred around an effective central timing position τmean different from the timing synchronisation position, wherein a frequency profile of the channel is symmetrical and centred around an effective central frequency position fmean different from the frequency synchronisation position, and wherein the method, implemented by the receiver, comprises:
determining an intermediate frequency covariance matrix M2f representing frequency variations of the channel, due to a theoretical temporal profile of the channel, which is symmetrical and centred on the timing synchronisation position, wherein the theoretical temporal profile of the channel is obtained from the channel's temporal profile translated to a time of τmean so as to be symmetrical around the timing synchronisation position;
determining an intermediate temporal covariance matrix M2t representing temporal variations of the channel, due to a theoretical frequency profile of the channel, which is symmetrical and centred on the frequency synchronisation position, wherein the theoretical frequency profile of the channel is obtained from the channel's frequency profile translated to a frequency of fmean so as to be symmetrical around the frequency synchronisation position;
calculating an intermediate global covariance matrix M2 according to the Kronecker product: M2=M2tM2f;
calculating a matrix E′ according to the relationship E′=E·TH, where T=TtTf and in which E′ is a diagonal matrix including the pilot symbols transmitted in a frame at the positions of the pilot symbols, wherein the other symbols are zero, Tf is a diagonal centring matrix (Nf, Nf) defined by




  
    
      T
      f
    
    =
    
      [
      
        
          
            1
          
          
            0
          
          
            ...
          
          
            ...
          
          
            0
          
        
        
          
            0
          
          
            
              e
              
                i
                ⁢
                
                  
                
                ⁢
                φ
              
            
          
          
            ...
          
          
            
              
            
          
          
            
              
            
          
        
        
          
            ...
          
          
            ...
          
          
            
              e
              i2φ
            
          
          
            ...
          
          
            
              
            
          
        
        
          
            ...
          
          
            
              
            
          
          
            ...
          
          
            ...
          
          
            0
          
        
        
          
            0
          
          
            ...
          
          
            ...
          
          
            0
          
          
            
              e
              
                
                  i
                  ⁡
                  
                    (
                    
                      Nf
                      -
                      1
                    
                    )
                  
                
                ⁢
                φ
              
            
          
        
      
      ]
    
  




  
    
      where
      ⁢
      
        
      
      ⁢
      φ
    
    =
    
      2
      ⁢
      
        π
        ·
        
          
            τ
            moyen
          
          
            N
            f
          
        
      
    
  



and Tt is a diagonal centring matrix (Nt, Nt) defined by



  
    
      rT
      t
    
    =
    
      [
      
        
          
            1
          
          
            0
          
          
            ...
          
          
            ...
          
          
            0
          
        
        
          
            0
          
          
            
              e
              
                i
                ⁢
                
                  
                
                ⁢
                ψ
              
            
          
          
            ...
          
          
            
              
            
          
          
            
              
            
          
        
        
          
            ...
          
          
            ...
          
          
            
              e
              i2ψ
            
          
          
            ...
          
          
            
              
            
          
        
        
          
            ...
          
          
            
              
            
          
          
            ...
          
          
            ...
          
          
            0
          
        
        
          
            0
          
          
            ...
          
          
            ...
          
          
            0
          
          
            
              e
              
                
                  i
                  ⁡
                  
                    (
                    
                      Nt
                      -
                      1
                    
                    )
                  
                
                ⁢
                ψ
              
            
          
        
      
      ]
    
  




  
    
      
        where
        ⁢
        
          
        
        ⁢
        ψ
      
      =
      
        
          -
          2
        
        ⁢
        
          π
          ·
          
            
              f
              moyen
            
            
              N
              t
            
          
        
      
    
    ;
  


calculating a column vector representing an intermediate channel C′ which minimises the relationship





  
    
      
        
        
          R
          -
          
            
              E
              ′
            
            ·
            
              C
              ′
            
          
        
        
      
      2
    
    
      σ
      2
    
  
  +
  
    
      
        C
        ′
      
      H
    
    ·
    
      M
      2
      
        -
        1
      
    
    ·
    
      C
      ′
    
  




where R is a column vector of dimension (Nt×Nf) consisting of the received symbols, and;
estimating the propagation channel according to the relationship C=TH·C′, from calculated vector C′.

2. The method according to claim 1, wherein calculating the intermediate channel vector C′ includes:
decomposing covariance matrices M2f and M2t into eigenvectors according to the relationships M2f=WFHNFWF et M2t=NTWT, in which:
WF is a matrix of eigenvectors of matrix M2f;
NF is a diagonal matrix including eigenvalues associated with the eigenvectors of matrix M2f;
WF is a matrix of eigenvectors of matrix M2f;
NT is a diagonal matrix including eigenvalues associated with the eigenvectors of matrix M2t;
calculating a Kronecker product of the matrices of eigenvectors WF and WT, to obtain a global matrix of eigenvectors W;
calculating a global diagonal matrix of eigenvectors N equal to the Kronecker product of matrices of eigenvalues NF, and NT; and
calculating the intermediate channel vector C′ using the pilot symbols and the matrices of eigenvectors W′ and of eigenvalues N′ using the maximum a posteriori criterion.

3. The method according to claim 2, wherein calculating the intermediate channel vector C′ includes:
calculating a matrix P according to a relationship P=√{square root over (N)}·W·EH·E·WH·√{square root over (N)} in which E is a diagonal matrix including the pilot symbols at the positions of the pilot symbols, where the other elements of the diagonal are zero;
decomposing matrix P into eigenvectors according to relationship P=XHQX in which X is a matrix of eigenvectors of matrix P and Q is a diagonal matrix including eigenvalues associated with the eigenvectors of matrix P; and
calculating the intermediate channel vector C′ according to the relationship C=WH·√{square root over (N)}·XH·(Q+σ2·I)−1·X·√{square root over (N)}·W·EH·R in which C is a vector representing the channel, I is the identity matrix, R is a vector including the received symbols and σ2 represents a power value of the noise in the channel.

4. The method according to claim 2, wherein calculating the intermediate channel vector C′ includes:
extracting a matrix W′ from matrix W and of a matrix N′ from matrix N, wherein matrix N′ includes a determined number n′ of eigenvalues of matrix N and matrix W′ includes the eigenvectors associated with these n′ eigenvalues; and
calculating the intermediate Channel vector C′ using the pilot symbols and the matrices of eigenvectors W′ and of eigenvalues N′ using the maximum a posteriori criterion.

5. The method according to claim 4, wherein the n′ eigenvalues are the highest eigenvalues of matrix N.

6. The method according to claim 4, wherein the n′ eigenvectors of matrix W′ are the Kronecker products of a limited number n′f of eigenvectors of matrix WF and of a limited number n′t of eigenvectors of matrix WT and the n′ eigenvalues of matrix N′ are the products of the eigenvalues of matrix NF corresponding to the n′f eigenvectors of matrix WF and eigenvalues of matrix NT corresponding to the n′t eigenvectors of matrix WT.

7. The method according to claim 4, wherein n′ is less than or equal to the number of pilot symbols in each frame.

8. The method according to claim 4, wherein calculating the intermediate channel vector C′ includes:
calculating a matrix P′ according to the relationship P′=√{square root over (N′)}·W′·E′H·E′·W′H·√{square root over (N′)} in which E is a diagonal matrix including the pilot symbols at the positions of the pilot symbols, where the other elements of the diagonal are zero;
decomposing the matrix P′ into eigenvectors according to relationship P′=X′HQ′X′ in which X′ is a matrix of eigenvectors of matrix P′ and Q′ is a diagonal matrix including eigenvalues associated with the eigenvectors of matrix P′; and
calculating the intermediate channel vector C′ according to the relationship C′=W′H·√{square root over (N′)}·X′H·(Q′+σ2·I)−1·X′·√{square root over (N′)}·W′·E′H·R in which C is a vector representing the channel, I is the identity matrix, R is a vector including the received symbols and σ2 represents the power value of the noise in the channel.

9. The method according to claim 1, wherein the signal is a multicarrier signal.

10. A receiver device configured to receive from a transmitter at least one signal transmitted through a radio propagation channel, wherein the signal includes frames each using Nf frequency subcarriers over each of which Nt symbols are transmitted, wherein from among all the symbols, certain pilot symbols, are known to the receiver device, wherein the signal is synchronised by the receiver device from a timing synchronisation position and from a frequency synchronisation position, wherein the temporal profile of the channel is symmetrical and centred around an effective central timing position τmean separate from the timing synchronisation position, and wherein the frequency profile of the channel is symmetrical and centred around an effective central frequency position fmean separate from the frequency synchronisation position, the receiver device comprising:
means for determining an intermediate frequency covariance matrix M2f representing the frequency variations of the channel, due to a theoretical temporal profile of the channel, which is symmetrical and centred on the timing synchronisation position, wherein the theoretical temporal profile of the channel is obtained from the channel's temporal profile translated to a time of τmean so as to be symmetrical around the timing synchronisation position;
means for determining an intermediate temporal covariance matrix M2t representing the temporal variations of the channel, due to a theoretical frequency profile of the channel, which is symmetrical and centred on the frequency synchronisation position, wherein the this theoretical frequency profile of the channel is obtained from the channel's frequency profile translated to a frequency of fmean so as to be symmetrical around the frequency synchronisation position;
means for calculating an intermediate global covariance matrix M2 according to the Kronecker product: M2=M2tM2f;
means for calculating a matrix E′ according to the relationship E′=E·TH, wherein T=TtTf and in which E is a diagonal matrix including the pilot symbols transmitted in a frame at the positions of the pilot symbols, where the other symbols are zero, Tf is a diagonal centring matrix defined by




  
    
      T
      f
    
    =
    
      [
      
        
          
            1
          
          
            0
          
          
            ...
          
          
            ...
          
          
            0
          
        
        
          
            0
          
          
            
              e
              
                i
                ⁢
                
                  
                
                ⁢
                φ
              
            
          
          
            ...
          
          
            
              
            
          
          
            
              
            
          
        
        
          
            ...
          
          
            ...
          
          
            
              e
              i2φ
            
          
          
            ...
          
          
            
              
            
          
        
        
          
            ...
          
          
            
              
            
          
          
            ...
          
          
            ...
          
          
            0
          
        
        
          
            0
          
          
            ...
          
          
            ...
          
          
            0
          
          
            
              e
              
                
                  i
                  ⁡
                  
                    (
                    
                      Nf
                      -
                      1
                    
                    )
                  
                
                ⁢
                φ
              
            
          
        
      
      ]
    
  




  
    
      where
      ⁢
      
        
      
      ⁢
      φ
    
    =
    
      2
      ⁢
      
        π
        ·
        
          
            τ
            moyen
          
          
            N
            f
          
        
      
    
  



and Tf is a diagonal centring matrix (Nt, Nt) defined by



  
    =
    
      [
      
        
          
            1
          
          
            0
          
          
            ...
          
          
            ...
          
          
            0
          
        
        
          
            0
          
          
            
              e
              
                i
                ⁢
                
                  
                
                ⁢
                ψ
              
            
          
          
            ...
          
          
            
              
            
          
          
            
              
            
          
        
        
          
            ...
          
          
            ...
          
          
            
              e
              
                i
                ⁢
                
                  
                
                ⁢
                2
                ⁢
                ψ
              
            
          
          
            ...
          
          
            
              
            
          
        
        
          
            ...
          
          
            
              
            
          
          
            ...
          
          
            ...
          
          
            0
          
        
        
          
            0
          
          
            ...
          
          
            ...
          
          
            0
          
          
            
              e
              
                
                  i
                  ⁡
                  
                    (
                    
                      Nt
                      -
                      1
                    
                    )
                  
                
                ⁢
                ψ
              
            
          
        
      
      ]
    
  




  
    
      
        where
        ⁢
        
          
        
        ⁢
        ψ
      
      =
      
        
          -
          2
        
        ⁢
        
          π
          ·
          
            
              f
              moyen
            
            
              N
              t
            
          
        
      
    
    ;
  


means for calculating a column vector representing an intermediate channel C′ which minimises the relationship





  
    
      
        
        
          R
          -
          
            
              E
              ′
            
            ·
            
              C
              ′
            
          
        
        
      
      2
    
    
      σ
      2
    
  
  +
  
    
      
        C
        ′
      
      H
    
    ·
    
      M
      2
      
        -
        1
      
    
    ·
    
      
        C
        ′
      
      .
    
  




where R is a column vector of dimension (Nt×Nf) consisting of the received symbols, and;
means for estimating the propagation channel according to the relationship C=TH·C′, from calculated vector C′.

11. A non-transitory tangible computer program product including code instructions to implement the method according to claim 1 when the program is executed by at least one processor.

12. The method according to claim 9, wherein the signal is an OFDM signal.