The techniques of multicarrier transmission have many advantages, especially in the context of wired or non-wired multipath channels.
Thus, OFDM type modulations are particularly well suited to countering the effects of fading in multipath channels. However, these OFDM modulations have the drawback of generating a signal with poor frequency localization.
Alternative solutions have then been proposed, leading to multicarrier modulation techniques in which the signal is shaped by filters (for a discretized signal) or functions (for a continuous signal) known as prototype filters, enabling better frequency localization through properties of orthogonality. These are for example OFDM/OQAM or BFDM/OQAM type modulations, conventionally used for radiofrequency communications as described especially in the patent application WO 2008/007019 published 17 Jan. 2008 on behalf of the present Applicant. It may be recalled that the OFDM/OQAM signal can be represented in discrete form, as follows:
            s      ⁡              [        k        ]              =                  ∑                  m          =          0                          M          -          1                    ⁢                        ∑                      n            ∈            ℤ                          ⁢                              a                          m              ,              n                                ⁢                                                    g                ⁡                                  [                                      k                    -                    nN                                    ]                                            ⁢                              ⅇ                                  j                  ⁢                                                                          ⁢                                                            2                      ⁢                      π                                        M                                    ⁢                                      m                    ⁡                                          (                                              k                        -                                                                                                  ⁢                                                  D                          2                                                                    )                                                                                  ⁢                              ⅇ                                  j                  ⁢                                                                          ⁢                                      ϕ                                          m                      ,                      n                                                                                                          ︸                                                g                                      m                    ,                    n                                                  ⁡                                  [                  k                  ]                                                                          ,
with:                am,n being a real value data element to be transmitted on a carrier m at the instant n;        M the number of carrier frequencies;        g the prototype filter used by the modulator;        D=Lg−1, with Lg being the length of the prototype filter g:        N=M/2 being a discrete temporal shift;        φm,n being a phase term chosen so as to achieve a real part/imaginary part alternation enabling orthogonality or more generally bi-orthogonality, for example equal to        
                    π        2            ⁢              (                  n          +          m                )              +          ϕ      0        ,                 with φ0 chosen arbitrarily; and        j2=−1.        
However, one drawback of these OFDM/OQAM or BFDM/OQAM modulation techniques is that the condition of orthogonality or of bi-orthogonality is achieved only for real values of the data elements to be transmitted. Now, the fact of having available only an orthogonality of translated values in the real sense makes the process of channel estimation more difficult.
Indeed, to estimate the complex gain of the channel on a given carrier, it is appropriate to obtain the complex projection of the signal received on said carrier. Now, the fact that there is no guard interval and that the orthogonality is only real according to this type of modulation implies the presence of intrinsic intra-carrier or inter-carrier interference even on an ideal channel. Indeed, the imaginary part of the projection of the signal received on the basis of the translated values of the prototype filter is not zero. This is expressed by a disturbing term which gets added to the demodulated signal and which must be taken into account for the estimation of the channel.
In concrete terms, if the data element am,n is sent at the frequency/time location (m,n), it can be shown that the following signal is obtained at reception without taking account of the noise:ym,n(c)≈Hm,n(c)(am,n+jam,n(i)),where Hm,n(c) designates the channel coefficient and et am,n(i) designates the residual interference that persists around the symbol of index n and each carrier of the index m.
The approaches of estimation by preamble considered hitherto seek to optimize the structure of the preamble by producing either a preamble that can be used to cancel interference at reception as described in the patent application WO 02/25883 published on 28 Mar. 2002 or, on the contrary, a preamble that increases the power of this interference in reception as described in the patent application WO 2008/007019 mentioned here above.
This second approach, also called the IAM or Interference Approximation Method gives better results for the channel estimation. Indeed, for a given transmission power, the gain anticipated by this IAM approach increases in proportion to the imaginary interference generated for each data element transmitted. The increase in interference is therefore beneficial up to a certain point.
According to this second approach and as described in the patent application WO 2008/007019 mentioned here above, the receiver uses an approximation of the residual interference am,n(i). For example, if we consider a neighborhood sized 3×3, denoted as Ω*1,1, around a frequency-time position (m0, n0), in excluding the position (m0, n0), the imaginary component am,n(i) can be approximated by:
      a                  m        0            ,              n        0                    (      i      )        ≈            ∑                        (                      p            ,            q                    )                ∈                  Ω                      1            ,            1                    *                      ⁢                  a                                            m              0                        +            p                    ,                                    n              0                        +            q                              ⁢                        〈          g          〉                                                    m              0                        +            p                    ,                                    n              0                        +            q                                                m            0                    ,                      n            0                              where gm0+p,n0+qm0,n0) is equal to the scalar product of gm0,n0 by gm0,n0 by gm0+p,n0+q.
In the presence of noise η, this leads to a channel estimation given by:
            H      ^                      m        0            ,              n        0                    (      c      )        =            H                        m          0                ,                  n          0                            (        c        )              +                            η                                    m              0                        ,                          n              0                                                (                                    a                                                m                  0                                ,                                  n                  0                                                      +                          j              ⁢                                                          ⁢                              a                                                      m                    0                                    ,                                      n                    0                                                                    (                  i                  )                                                              )                    .      
In order to amplify or boost the power of the preamble received, particular preamble structures have been proposed, such as the one known as IAM1 in C. Lélé, P. Siohan, R. Legouable, and J.-P. Javaudin, “Preamble-based channel estimation techniques for OFDM/OQAM over the powerline” (ISPLC 2007, March 2007).
For example, the sequence illustrated in FIG. 1 comprises:                a preamble IAM1 formed by three preamble symbols referenced pm,0, pm,1 and pm,2, with m being the index for the carrier frequencies and 0, 1, 2 being the temporal index, each preamble symbol comprising M pilots for which the value and location at transmission are known to at least one receiver designed to carry out a reception of the multicarrier signal; and        data symbols.        
The structure of the preamble IAM1 is such that:pm,0=pm,2=0,p4k,1=p4k+1,1=1, andp4k+2,1=p4k+3,1=−1,with k=0, . . . , M/4−1 and M is the number of carriers per multicarrier symbol.
Consequently, the pilot received at the mth frequency and for the symbol pm,1 with a temporal index 1 interference-ridden (also called a “pseudo-pilot”) can be written as:bm,1≈pm,1+j(2pm+1,1gm+1,1m,1)where gm+1,1m,1 corresponds to the scalar product of the filters gm+1,1[k] and gm,1[k].
In denoting |gm+1,1m,1|=β0, then the power of the pseudo-pilot can be expressed in the following form:E[|bm,12|]=2σa2(1+4β02),where σa2 corresponds to the variance of the data elements am,n.
Other preamble structures of a same length (three preamble symbols i.e. 3M pilots) have also been proposed, leading to even more favorable expressions for the power of the pseudo-pilot as proposed in the document C. Lélé, P. Siohan, and R. Legouable, “2 db better than CP-OFDM with OFDM/OQAM for preamble-based channel estimation” (ICC 2008, May 2008).
It can be observed that in all these cases, the quality of the channel is directly related to parameter β0. Thus, the best results (i.e. the highest values of the parameter β0 are obtained with orthogonal filters that are well localized in time and frequency.
Thus, the classically used prototype filters use the IOTA (Isotropic Orthogonal Transform Algorithm) function, discretized and truncated to a length 4M, or the prototype filter of length M called the TFL (Time Frequency Localization) filter optimized for a defined criterion, for a signal with real values, by a time/frequency localization parameter:
      ξ    =          1              4        ⁢        π        ⁢                                            m              2                        ⁢                          M              2                                            ,where m2 and M2 are respectively the second-order moments in time and frequency defined in the document by M. I. Doroslova{hacek over (c)}ki, “Product of second moments in time and frequency for discrete time signals and the uncertainty limit” (Signal Processing, vol. 67), such that:
            m      2        ⁡          (      x      )        =                    1                                          x                                2                    ⁢                        ∑                      k            ∈            ℤ                          ⁢                                                                              (                                      k                    -                                          1                      2                                        -                                          T                      ⁡                                              (                        x                        )                                                                              )                                2                            ⁡                              [                                                                            x                      ⁡                                              [                        k                        ]                                                              +                                          x                      ⁡                                              [                                                  k                          -                          1                                                ]                                                                              2                                ]                                      2                    ⁢                                          ⁢                                    M              2                        ⁡                          (              x              )                                            =                            1                                                    (                                  2                  ⁢                  π                                )                            2                        ⁢                                                          x                                            2                                      ⁢                              ∑                          k              ∈              ℤ                                ⁢                                                    [                                                      x                    ⁡                                          [                      k                      ]                                                        -                                      x                    ⁡                                          [                                              k                        -                        1                                            ]                                                                      ]                            2                        ⁢                                                  ⁢                          with                        ⁢                          :                        ⁢                                                  ⁢                          T              ⁡                              (                x                )                                                        =                                                  ∑                              k                ∈                ℤ                                      ⁢                                                            (                                      k                    -                                          1                      2                                                        )                                ⁡                                  [                                                            x                      ⁡                                              [                        k                        ]                                                              +                                          x                      ⁡                                              [                                                  k                          -                          1                                                ]                                                                              ]                                            2                                                          ∑                              k                ∈                ℤ                                      ⁢                                          [                                                      x                    ⁡                                          [                      k                      ]                                                        +                                      x                    ⁡                                          [                                              k                        -                        1                                            ]                                                                      ]                            2                                      .            
It can be noted that the time-frequency localization ξ of a discrete signal has an upper limit ξ≦1.
All these techniques permit to obtain preamble structures that increase the power of the “pseudo-pilot” and therefore increase the level of interference produced at reception. The carriers of the preamble are then shaped by using orthogonal or bi-orthogonal prototype filters classically used in OFDM/OQAM or BFDM/OQAM modulations respectively.
Unfortunately, one drawback of this approach of estimation by preamble aimed at producing a preamble that increases the power of the interference at reception is that it does not guarantee, for a given preamble structure, that a “pseudo-pilot” of maximum energy will be obtained.
Furthermore, the fact of having available orthogonality in the real sense makes the channel estimation process more difficult.
There is therefore a need for a novel technique for transmitting and/or receiving a multicarrier signal comprising a preamble that has undergone an OFDM/OQAM or BFDM/OQAM type modulation that can be used to remedy at least some of these drawbacks and especially accurately estimate the transmission channel.