Precompensation of interference induced by an OFDM/OQAM modulation that is faster than Nyquist

Abstract

The invention relates to precoding (or rather pre-equalization) for a faster-than-Nyquist OFDM or OFDM/OQAM type transmitter. Compression of faster-than-Nyquist OFDM pulses over time introduces an inter-symbol interference (ISI) and a sub-carrier interference (ICI). Assuming a Gaussian-type channel (AWGN), the ISI and ICI can be estimated at the transmitter and, in this way, some of the symbols (at most half) can be precoded (according to the value of the adjacent symbols), such as to cancel the ISI and ICI introduced during transmission and reception.

Claims

1. A method of generating a multicarrier signal, from a set of symbols, characterized in that it includes: a step of precoding (31) a first subset of symbols of said set of symbols, delivering a first subset of precoded symbols, said step of precoding (31) modifying the value of a symbol of said first subset for taking account of interference generated on this symbol by at least one other symbol of said set of symbols intended to be transmitted at the same instant or at the same frequency according to a predetermined time/frequency transmission pattern, and a step of modulating (32) a set of carriers from said first subset of precoded symbols and a second subset of non-precoded symbols of said set of symbols, delivering said multicarrier signal, said step of modulating (32) modulating each carrier of said set of carriers by a precoded symbol of said first subset or by a non-precoded symbol of said second subset according to said predetermined transmission pattern.

2. The method as claimed in claim 1, characterized in that said multicarrier signal is formed of a temporal succession of multicarrier symbols intended to be transmitted at a faster-than-Nyquist rate.

3. The method as claimed in claim 1, characterized in that the number of precoded symbols of said first subset is less than or equal to the number of non-precoded symbols of said second subset.

4. The method as claimed in claim 1, characterized in that said step of modulating (32) implements a faster than nyquist/orthogonal frequency division multiplex/offset quadrature amplitude modulation (FTN-OQAM) type modulation, and in that said step of precoding (31) delivers, from a symbol a.sub.m.sub.0.sub.,n.sub.0 of the set of symbols, a precoded symbol c.sub.m.sub.0.sub.,n.sub.0 intended to modulate a carrier at the location (m.sub.0,n.sub.0) in said predetermined transmission pattern, such that: $c_{m_0,n_0}=\{\begin{array}{c}(a_{m_0,n_0}-\mathrm{ISI}\left(\mathrm{if}=0\mathrm{and}{n}_0=k\mathrm{mod}\left(l+2\right)\mathrm{and}{n}_0=\left(k+1\right)\mathrm{mod}\left(l+2\right),\left(k\mathrm{and}kl+1\right)\right)\\ \left(a_{m_0,n_0}-\mathrm{ICI},\mathrm{if}\left(=0\mathrm{and}{m}_0=k\mathrm{mod}\left(l^{}+1\right),\left(k\mathrm{and}k{l}^{}\right)\right)\right)\\ (a_{m_0,n_0}-\mathrm{ISI}-\mathrm{ICI}\mathrm{if}\left(m_0=k\mathrm{mod}\left(l^{}+1\right),\left(k\mathrm{and}k{l}^{}\right)\right)\mathrm{and}\\ n_0=k^{}\mathrm{mod}\left(l+2\right)\mathrm{and}{n}_0=\left(k^{}+1\right)\mathrm{mod}\left(l+2\right),\left(k^{}\mathrm{and}{k}^{}l+1\right))\end{array}$ with: mod the modulo operator, and selection factors of a type of interference to be processed, 0, 1 ICI an intercarrier interference term determined on said carrier at the location (m.sub.0,n.sub.0) and coming from symbols a.sub.m.sub.0.sub.+q,n and a.sub.m.sub.0.sub.q,n, ISI an intersymbol interference term determined on said carrier at the location (m.sub.0,n.sub.0) and coming from symbols a.sub.m.sub.0.sub.,n.sub.0.sub.+p and a.sub.m.sub.0.sub.,n.sub.0.sub.p p, q.sup.+, p[l,l] and q[l,l], l,lN.

5. The method as claimed in claim 1, characterized in that said step of modulating (32) implements an FTN-OFDM type modulation, and in that said step of precoding (31) delivers, from a symbol a.sub.m.sub.0.sub.,n.sub.0 of the set of symbols, a precoded symbol c.sub.m.sub.0.sub.,n.sub.0 intended to modulate a carrier at the location (m.sub.0,n.sub.0) in said predetermined transmission pattern, such that: $c_{m_0,n_0}=\{\begin{array}{c}\left(a_{m_0,n_0}-\mathrm{ISI}\mathrm{if}\left(=0\mathrm{and}{n}_0=k\mathrm{mod}\left(l^{}+1\right),\left(k\mathrm{and}k{l}^{}\right)\right)\right)\\ \left(a_{m_0,n_0}-\mathrm{ICI}\mathrm{if}\left(=0\mathrm{and}{m}_0=k\mathrm{mod}\left(l+1\right),\left(k\mathrm{and}kl\right)\right)\right)\\ \left(a_{m_0,n_0}-\mathrm{ISI}-\mathrm{ICI}\mathrm{if}\left(m_0=k\mathrm{mod}\left(l+1\right),\mathrm{and}{n}_0=k^{}\mathrm{mod}\left(l^{}+1\right),\left(k,k^{},kl\mathrm{and}{k}^{}{l}^{}\right)\right)\right)\end{array}$ with: mod the modulo operator, and selection factors of a type of interference to be processed, 0,1, ICI an intercarrier interference term determined on said carrier at the location (m.sub.0,n.sub.0) and coming from symbols a.sub.m.sub.0.sub.+q,n and a.sub.m.sub.0.sub.q,n, ISI an intersymbol interference term determined on said carrier at the location (m.sub.0,n.sub.0) and coming from symbols a.sub.m.sub.0.sub.,n.sub.0.sub.+p and a.sub.m.sub.0.sub.,n.sub.0.sub.p p, q.sup.+, p[l,l] and q[l,l], l,lN.

6. The method as claimed in claim 1, characterized in that said predetermined transmission pattern is selected by taking into account at least one element belonging to the group including: a type of modulation implemented in said step of modulating; a type of prototype filter used in said step of modulating; a type of channel used for the transmission of said multicarrier signal.

7. A method of receiving a multicarrier signal, delivering a set of estimated symbols, characterized in that it includes: step of demodulating (41) a set of carriers forming said multicarrier signal, delivering a first subset of demodulated precoded symbols and a second subset of demodulated non-precoded symbols, a step of time and/or frequency equalization (42) of the demodulated precoded symbols, delivering equalized demodulated precoded symbols, a step of time and/or frequency equalization (43) of the demodulated non-precoded symbols, taking into account an estimate of interference affecting said demodulated non-precoded symbols obtained from said equalized demodulated precoded symbols, delivering equalized demodulated non-precoded symbols.

8. The method as claimed in claim 7, characterized in that it also includes a step of decoding said equalized demodulated precoded symbols, delivering a first subset of estimated symbols, and delivering said estimate of interference affecting said demodulated non-precoded symbols, and a step of decoding said equalized demodulated non-precoded symbols, delivering a second subset of estimated symbols.

9. The method as claimed in claim 8, characterized in that said step of decoding said equalized demodulated non-precoded symbols also delivers an estimate of interference affecting said demodulated precoded symbols, and in that said step of time and/or frequency equalization (43) of the demodulated precoded symbols takes account of the estimate of said interference affecting said demodulated precoded symbols.

10. The method as claimed in claim 8, characterized in that said steps of decoding implement an algorithm of the Maximum A Posteriori (MAP), logarithmic MAP (Log-MAP) or maximum logarithmic MAP (Max-Log-MAP) type.

11. A generating device for generating a multicarrier signal, from a set of symbols, characterized in that it includes: a precoding module of a first subset of symbols of said set of symbols, delivering a first subset of precoded symbols, said precoding module modifying the value of a symbol of said first subset for taking account of interference generated on this symbol by at least one other symbol of said set of symbols intended to be transmitted at the same instant or at the same frequency according to a predetermined time/frequency transmission pattern, and a modulating module of a set of carriers from said first subset of precoded symbols and a second subset of non-precoded symbols of said set of symbols, delivering said multicarrier signal, said modulating module modulating each carrier of said set of carriers by a precoded symbol of said first subset or by a non-precoded symbol of said second subset according to said predetermined transmission pattern.

12. A receiving device for receiving a multicarrier signal, delivering a set of estimated symbols, characterized in that it includes: a demodulation module of a set of carriers forming said multicarrier signal, delivering a first subset of demodulated precoded symbols and a second subset of demodulated non-precoded symbols, a time and/or frequency equalization module of the demodulated precoded symbols, delivering equalized demodulated precoded symbols, a time and/or frequency equalization module of the demodulated non-precoded symbols, taking into account an estimate of the interference affecting said demodulated non-precoded symbols obtained from said equalized demodulated precoded symbols, delivering equalized demodulated non-precoded symbols.

13. A non-transitory computer-readable medium storing a computer program comprising instructions for implementation of a method when this program is executed by a processor, the method of generating a multicarrier signal, from a set of symbols, wherein the method includes: a step of precoding (31) a first subset of symbols of said set of symbols, delivering a first subset of precoded symbols, said step of precoding (31) modifying the value of a symbol of said first subset for taking account of interference generated on this symbol by at least one other symbol of said set of symbols intended to be transmitted at the same instant or at the same frequency according to a predetermined time/frequency transmission pattern, and a step of modulating (32) a set of carriers from said first subset of precoded symbols and a second subset of non-precoded symbols of said set of symbols, delivering said multicarrier signal, said step of modulating (32) modulating each carrier of said set of carriers by a precoded symbol of said first subset or by a non-precoded symbol of said second subset according to said predetermined transmission pattern.

14. A non-transitory computer-readable medium storing a computer program comprising instructions for implementation of a method when this program is executed by a processor, the method of receiving a multicarrier signal, delivering a set of estimated symbols, wherein the method includes: step of demodulating (41) a set of carriers forming said multicarrier signal, delivering a first subset of demodulated precoded symbols and a second subset of demodulated non-precoded symbols, a step of time and/or frequency equalization (42) of the demodulated precoded symbols, delivering equalized demodulated precoded symbols, a step of time and/or frequency equalization (43) of the demodulated non-precoded symbols, taking into account an estimate of interference affecting said demodulated non-precoded symbols obtained from said equalized demodulated precoded symbols, delivering equalized demodulated non-precoded symbols.

Description

4. LIST OF FIGURES

(1) Other features and advantages of the invention will appear more clearly on reading the following description of a particular embodiment, given by way of a simple, illustrative and non-restrictive example, and the appended drawings, in which:

(2) FIGS. 1 and 2 depict an example of an FTN transmission system according to the prior art;

(3) FIG. 3 illustrates the main steps implemented by a method of generating a multicarrier signal according to a particular embodiment of the invention;

(4) FIG. 4 illustrates the main steps implemented by a method of receiving a multicarrier signal according to a particular embodiment of the invention;

(5) FIG. 5 depicts an example of an FTN transmission system according to a particular embodiment of the invention;

(6) FIGS. 6, 8, and 10 provide examples of transmission patterns making it possible to reduce the intersymbol, intercarrier, or intersymbol and intercarrier interference respectively, in an FTN/OQAM transmission system;

(7) FIGS. 7, 9 and 11 depict examples of receivers making it possible to receive a multicarrier signal using the transmission pattern of FIGS. 6, 8 and 10 respectively;

(8) FIGS. 12 and 13 provide examples of transmission patterns making it possible to reduce the intersymbol, or intersymbol and intercarrier interference, respectively, in an FTN/OFDM transmission system;

(9) FIGS. 14 and 15 respectively illustrate the simplified structure of a transmitter implementing a technique of generating a multicarrier signal, and a receiver implementing a technique of receiving according to a particular embodiment of the invention.

5. DESCRIPTION OF AN EMBODIMENT OF THE INVENTION

5.1 General Principle

(10) The general principle of the invention is based on the precoding of at least one symbol modulating a carrier of a multicarrier signal, by modifying its value for taking into account, on transmission, intersymbol ISI and/or intercarrier ICI, interference normally affecting this symbol. The invention thus provides for at least partially precanceling intersymbol and/or intercarrier interference for at least one symbol.

(11) Such a technique may in particular be implemented for data transmission at a faster-than-Nyquist rate.

(12) It is therefore provided according to the invention for at least partially precanceling, on transmission, ISI and ICI.sub.n interference since they are known to the transmitter. Thus, instead of transmitting symbols a.sub.m,n, precoded symbols c.sub.m,n may be transmitted such that:
c.sub.m,n=a.sub.m,nISIICI.sub.n

(13) It is to be noted first of all that for a symbol a.sub.m,n, the symbols a.sub.m,n+p and a.sub.m,np participate in ISI, and the symbols a.sub.m+q,n and a.sub.mq,n participate in ICI, with p, q.sup.+, p[l, l] and q[l,l]. It is therefore not possible to precode the whole set of symbols, i.e. to precancel the interference of all the symbols.

(14) The values of l and l may be determined from at least one element belonging to the group including: the length of the prototype filter used, the compression factor and the type of modulation.

(15) In order to limit the reduction in the power of the useful symbol a.sub.m,n, two factors and are introduced making it possible to select the type of interference that it is desired to at least partially cancel thanks to the precoding, and a first subset of precoded symbols c.sub.m,n=a.sub.m,nISIICI.sub.n is transmitted in a first part of the frame. In the rest of the frame, a second subset of non-precoded symbols a.sub.m,n is transmitted.

(16) This technique of at least partially precanceling interference may be designated as an SIPC precoding technique, or Sparse Interference Pre-Cancellation, in English.

(17) This technique has many advantages.

(18) In particular, comparing the bit error rate (BER) curves as a function of the signal-to-noise ratio (SNR) for an FTN/OQAM system with and without precoding shows a faster convergence of the system with precoding. For example, in the case of a 64-QAM modulation, the system begins to converge from iteration 3.

(19) The precoding technique according to the invention also makes it possible to reduce the value of to 0.7 for a 16-QAM modulation, or to 0.8 for a 64-QAM modulation, which allows transmission of a greater volume of information over a given period.

(20) FIG. 3 illustrates the main steps implemented by a method of generating a multicarrier signal according to an embodiment of the invention.

(21) Such a method receives a set of symbols a.sub.m,n as input which may be real values or complex values.

(22) In the course of a first step 31, a first subset of symbols of the set of symbols is precoded. Thus a first subset of K precoded symbols, denoted by c.sub.m,n, is thus obtained. As already mentioned, the step of precoding modifies the value of a symbol of the first subset for taking account of interference generated by at least one other symbol of the set of symbols intended to be transmitted at the same instant or at the same frequency according to a predetermined time/frequency transmission pattern.

(23) In the course of a second step 32, the set of carriers is modulated, e.g. in the form of a frame of MN carriers, from the first subset of precoded symbols and a second subset of non-precoded symbols, of the set of symbols, delivering said multicarrier signal s. The step of modulating modulates each carrier of the set of carriers by a precoded symbol of the first subset or by a non-precoded symbol of the second subset, according to the predetermined transmission pattern.

(24) The frame of MN carriers is therefore composed of precoded symbols and non-precoded symbols respecting a particular transmission pattern.

(25) FIG. 4 illustrates the main steps implemented by a method of receiving according to an embodiment of the invention.

(26) Such a method receives the multicarrier signal as input, after passage in a transmission channel.

(27) In the course of a first step 41, the received multicarrier signal r is demodulated, delivering a first subset of demodulated symbols corresponding to the precoded symbols, referred to as demodulated precoded symbols y.sub.m,n.sup.c, and a second subset of demodulated symbols corresponding to the non-precoded symbols, referred to as demodulated non-precoded symbols y.sub.m,n.sup.a.

(28) In the course of a second step 42, the demodulated precoded symbols y.sub.m,n.sup.c are time and/or frequency equalized.

(29) Then in the course of a next step 43, the demodulated non-precoded symbols y.sub.m,n.sup.a are equalized in time and/or in frequency, taking into account an estimate of interference affecting the demodulated non-precoded symbols, obtained from the demodulated non-precoded symbols, delivering equalized demodulated non-precoded symbols.

(30) Examples of implementation of the invention are described below in relation to FIG. 5, for an FTN/OQAM or FTN/OFDM type modulation.

5.2 First Embodiment: FTN/OQAM Type Modulation

(31) FIG. 5 illustrates an example of a transmission system for an FTN/OQAM transmission according to an embodiment of the invention.

(32) On transmission, the bits of a source signal are first coded by a channel coder CC 51, which represents e.g. a convolutional code, and interleaved by an interleaver 52. The interleaved coded bits are then mapped to OQAM symbols, in a mapping module 53, using, for example, the Gray mapping technique. A set of symbols is thus obtained.

(33) According to an embodiment of the invention, one part of these symbols, again referred to as the first subset, is precoded in a precoding module 54, the other part, again referred to as the second subset, is not precoded.

(34) For example, the precoding module 54 delivers, for each symbol a.sub.m.sub.0.sub.,n.sub.0 of the first subset, a precoded symbol c.sub.m.sub.0.sub.,n.sub.0 intended to modulate a carrier at the location (m.sub.0,n.sub.0) in the predetermined transmission pattern, such that:

(35) $c_{m_0,n_0}=\{\begin{array}{c}(a_{m_0,n_0}-\mathrm{ISI}\left(\mathrm{if}=0\mathrm{and}{n}_0=k\mathrm{mod}\left(l+2\right)\mathrm{and}{n}_0=\left(k+1\right)\mathrm{mod}\left(l+2\right),\left(kN\mathrm{and}kl+1\right)\right)\\ \left(a_{m_0,n_0}-\mathrm{ICI},\mathrm{if}\left(=0\mathrm{and}{m}_0=k\mathrm{mod}\left(l^{}+1\right),\left(kN\mathrm{and}k{l}^{}\right)\right)\right)\\ (a_{m_0,n_0}-\mathrm{ISI}-\mathrm{ICI}\mathrm{if}\left(m_0=k\mathrm{mod}\left(l^{}+1\right),\left(kN\mathrm{and}k{l}^{}\right)\right)\mathrm{and}\\ n_0=k^{}\mathrm{mod}\left(l+2\right)\mathrm{and}{n}_0=\left(k^{}+1\right)\mathrm{mod}\left(l+2\right),\left(k^{}N\mathrm{and}{k}^{}l+1\right))\end{array}$

(36) Each of these lines corresponds to a different case of precoding, making it possible to partially cancel the ISI (SIPC in time, first line), the ICI (SIPC in frequency, second line), or the ISI and the ICI (SIPC in time-frequency, third line).

(37) The other symbols a.sub.m,n, belonging to the second subset, are not precoded.

(38) The carriers of the multicarrier signal are then modulated with the precoded OQAM symbols of the first subset and the non-precoded OQAM symbols of the second subset in an FTN-OQAM modulator 55.

(39) After passage in an AWGN channel 56, the received signal is first demodulated by an FTN-OQAM demodulator 57.

(40) The symbols coming from the FTN-OQAM demodulator 57 are then filtered by a specific SISO MMSE filter 58, deinterleaved by a deinterleaver .sup.159, then decoded by a decoder 60.

(41) For example, a receiver based on the principle of turbo equalization is considered. The information coming from the decoder 60 is therefore used for updating the SISO MMSE filter 58, by communicating thereto logarithmic likelihood ratio type information (LLRs) L.sub.a(x) as detailed below.

(42) A) Precoding in Time (0, =0)

(43) As already mentioned, it is found that, for a symbol a.sub.m,n, the symbols a.sub.m,n+p and a.sub.m,np participate in the ISI, and the symbols a.sub.m+q,n and a.sub.mq,n participate in the ICI, with p, q.sup.+, p[l,l] and q[l, l].

(44) According to a first example, it is sought to cancel, or at the very least reduce, only the intersymbol interference ISI, by precoding a first subset of OQAM symbols. This technique is denoted by SIPC precoding in time. It is to be noted that, for canceling or reducing the ISI, on each carrier m, the positions of the symbols to be precoded may be chosen independently of the other carriers.

(45) As illustrated in FIG. 6, according to this first example a transmission pattern is considered corresponding to an alternation in time of two precoded symbols, hatched, and two non-precoded symbols, not hatched, and an alternation in frequency of one precoded symbol, hatched, and one non-precoded symbol, not hatched, for reducing the intersymbol interference.

(46) More specifically, it is assumed that, for a symbol a.sub.m.sub.0.sub.,n.sub.0 at instant n.sub.0 and the carrier m.sub.0, the ISI is mainly generated by the two neighboring symbols a.sub.m.sub.0.sub.,n.sub.0.sub.+2 and a.sub.m.sub.0.sub.,n.sub.0.sub.2. Therefore it is chosen to place two consecutive precoded symbols for each value of m, by alternating two precoded symbols and two non-precoded symbols. It is also chosen to alternate the positions of the precoded symbols for even m and for odd m. Indeed, for a symbol a.sub.m.sub.0.sub.,n.sub.0 at instant n.sub.0 and the carrier m.sub.0, the interference generated by the carrier m.sub.0+1 and m.sub.01 diminishes as a function of n.

(47) It is to be noted that if it is assumed that the ISI is generated mainly by the four neighboring symbols a.sub.m.sub.0.sub.,n.sub.0.sub.+4, a.sub.m.sub.0.sub.,n.sub.0.sub.+2, a.sub.m.sub.0.sub.n.sub.0.sub.2, a.sub.m.sub.0.sub.,n.sub.0.sub.4, it is chosen to place two consecutive precoded symbols for each value of m, by alternating two precoded symbols and four non-precoded symbols. An alternation of the positions of the precoded symbols for even m and for odd m is retained.

(48) As mentioned above, a first subset of symbols is precoded in the course of a step of precoding 54 for canceling, or at the very least reducing, the intersymbol interference:
c.sub.m,n=a.sub.m,nISI
with, for an FTN/OQAM modulation:

(49) $\mathrm{ISI}=\left\{\underset{n{n}_0}{.Math.}{a}_{m_0,n}{e}^{\frac{j}{2}\left(n-n_0\right)}\underset{k}{.Math.}g\left[k-{\mathrm{nN}}_f\right]g\left[k-n_0{N}_f\right]e^{\frac{j2\left(k-\frac{D}{2}\right)\left(m-m_0\right)}{M}}\right\}$
using the notations given with the FTN/OQAM modulations according to the prior art.

(50) If it is assumed that, for a symbol a.sub.m.sub.0.sub.,n.sub.0, the ISI is mainly generated by the two neighboring symbols a.sub.m.sub.0.sub.,n.sub.0.sub.+2 and a.sub.m.sub.0.sub.,n.sub.0.sub.2, the equivalent channel of the ISI may be represented by h=[h.sub.1 0 1 0 h.sub.1], with h.sub.1=h.sub.1 for a symmetrical channel. If it is assumed that the ISI is generated by four neighboring symbols, the equivalent channel of the ISI may be represented by h=[h.sub.2 0 h.sub.10 1 0 h.sub.1 0 h.sub.2]. It is to be noted that the symbols in the odd n positions do not contribute to the ISI since the OQAM modulation takes the real part of the received signal.

(51) Continuing with the example in FIG. 6, the symbol a.sub.m.sub.0.sub.,n.sub.0 at the position (m.sub.0,n.sub.0) is precoded to take account of the ISI. Considering the equivalent channel model of the ISI, the precoded symbol c.sub.m.sub.0.sub.,n.sub.0 at the position (m.sub.0, n.sub.0) is such that:
c.sub.m.sub.0.sub.,n.sub.0=a.sub.m.sub.0.sub.,n.sub.0h.sub.1a.sub.m.sub.0.sub.,n.sub.0.sub.2h.sub.1a.sub.m.sub.0.sub.,n.sub.0.sub.+2

(52) The multicarrier signal therefore includes carriers modulated by precoded symbols, and carriers modulated by non-precoded symbols.

(53) It should be observed that the power of the carriers modulated by precoded symbols is less than the power of the carriers modulated by non-precoded symbols.

(54) On reception, without taking into account the ICI and the noise, the precoded symbol received at the position (m.sub.0, n.sub.0) after demodulation, denoted by y.sub.m.sub.0.sub.,n.sub.0.sup.c, is such that:
y.sub.m.sub.0.sub.,n.sub.0.sup.c=c.sub.m.sub.0.sub.,n.sub.0+h.sub.1a.sub.m.sub.0.sub.,n.sub.0.sub.2+h.sub.1a.sub.m.sub.0.sub.,n.sub.0.sub.+2=a.sub.m.sub.0.sub.,n.sub.0

(55) Without taking into account the ICI and the noise, a non-precoded symbol received at the position (m.sub.i, n.sub.i) after demodulation, denoted by y.sub.m.sub.i.sub.,n.sub.i.sup.a, is such that:
y.sub.m.sub.i.sub.,n.sub.i.sup.a=a.sub.m.sub.i.sub.,n.sub.i+h.sub.1a.sub.m.sub.i.sub.,n.sub.i.sub.2+h.sub.1c.sub.m.sub.i.sub.,n.sub.i.sub.+2
y.sub.m.sub.i.sub.,n.sub.i.sup.a=a.sub.m.sub.i.sub.,n.sub.i+h.sub.1a.sub.m.sub.i.sub.,n.sub.i.sub.2h.sub.1.sup.2a.sub.m.sub.i.sub.,n.sub.i.sub.4h.sub.1.sup.2a.sub.m.sub.i,.sub.n.sub.i+h.sub.1a.sub.m.sub.i.sub.,n.sub.i.sub.+2h.sub.1.sup.2a.sub.m.sub.i,.sub.n.sub.ih.sub.1.sup.2a.sub.m.sub.i.sub.,n.sub.i.sub.+4
y.sub.m.sub.i.sub.,n.sub.i.sup.a=(12*h.sub.1.sup.2)a.sub.m.sub.i.sub.,n.sub.i+h.sub.1a.sub.m.sub.i.sub.,n.sub.i.sub.2h.sub.1.sup.2a.sub.m.sub.i.sub.,n.sub.i.sub.4+h.sub.1a.sub.m.sub.i.sub.,n.sub.i.sub.+2h.sub.1.sup.2a.sub.m.sub.i.sub.,n.sub.i.sub.+4

(56) A reduction is found here in the power of the useful symbol a.sub.m.sub.i.sub.,n.sub.i represented by the factor (12*h.sub.1.sup.2), partially offset by the introduction of the selection factors et .

(57) Therefore first of all the demodulated precoded symbols, then the demodulated non-precoded symbols, are equalized, by taking into account interference affecting the non-precoded symbols determined from the equalization of the precoded symbols.

(58) FIG. 7 illustrates an example of a receiver according to an embodiment of the invention, implementing at least one decoding iteration.

(59) In the course of a first decoding iteration, the demodulated precoded symbols y.sub.m,n.sup.c are equalized with an MMSE-t equalizer 581 in time. The equalized demodulated precoded symbols are interleaved by the interleaver 59, and decoded by the decoder 60. For example, such a decoder is of the Max-Log-MAP type providing soft information in terms of maximum likelihood ratio (LLR), that is used for constructing soft symbols. A first estimate is therefore obtained of the precoded symbols .sub.m,n.sup.c at the output of the first decoding iteration (=.sub.m,n at the positions corresponding to the precoded symbols).

(60) This information in terms of LLR allows a first interference cancellation module SIC 1 (Soft Interference Cancellation) 71 of the receiver to determine the intersymbol interference generated by the precoded symbols on the non-precoded symbols on the same carrier of index m. This SIC 1 module 71 also determines the intercarrier interference generated by the symbols of the other carriers on the carrier of index m. The receiver therefore also makes it possible to cancel, or reduce, a part of the interference.

(61) In the course of the first decoding iteration, the demodulated non-precoded symbols y.sub.m,n.sup.a are equalized with an MMSE-t equalizer 581 in time, by taking into account the interference determined by the first SIC 1 module 71. The equalized demodulated non-precoded symbols are interleaved by the interleaver 59, and decoded by the decoder 60. For example, such a decoder is of the Max-Log-MAP type. A first estimate is therefore obtained of the non-precoded symbols .sub.m,n.sup.a at the output of the first decoding iteration (=.sub.m,n at the positions corresponding to the non-precoded symbols).

(62) This information in terms of LLR allows a second interference cancellation module SIC 2 72 of the receiver to determine the intersymbol interference generated by the non-precoded symbols on the precoded symbols.

(63) In the course of a second decoding iteration, the equalization of the estimated precoded symbols .sub.m,n.sup.c is refined with the MMSE-t equalizer 581 in time, which takes account of the interference determined by the second SIC 2 module 72. The steps of interleaving and decoding are iterated, for obtaining a refined estimate of the precoded symbols at the output of the second decoding iteration and a refined estimate of the interference generated by the precoded symbols on the non-precoded symbols.

(64) The equalization of the estimated non-precoded symbols .sub.m,n.sup.a is also refined in the course of a second decoding iteration, with the MMSE-t equalizer 581 in time, by taking into account the refined estimate of the interference generated by the precoded symbols on the non-precoded symbols. The steps of interleaving and decoding are iterated, for obtaining a refined estimate of the non-precoded symbols at the output of the second decoding iteration and a refined estimate of the interference generated by the non-precoded symbols on the precoded symbols.

(65) A plurality of iterations may be implemented until a convergence is obtained in the estimate of the precoded .sub.m,n.sup.c and non-precoded symbols .sub.m,n.sup.a, again denoted by .sub.m,n.

(66) It is to be noted that for an MMSE-t equalization in time, the SIC module (first or second SIC module) removes, or at the very least reduces, the interference ICI by using the estimated OQAM symbols .sub.m,n:

(67) ${\hat{y}}_{m_0,n_0}=y_{m_0,n_0}-\left\{\underset{m{m}_0}{.Math.}\underset{n}{.Math.}{\hat{a}}_{m,n}{e}^{\frac{j}{2}\left(m-m_0+n-n_0\right)}\underset{k}{.Math.}g\left[k-{\mathrm{nN}}_f\right]g\left[k-n_0{N}_f\right]e^{\frac{j2\left(k-\frac{D}{2}\right)\left(m-m_0\right)}{M}}\right\}$

(68) It is also to be noted that the MMSE equalization filter used by the MMSE-t equalizer 581 differs from that used for a conventional FTN/OQAM modulation. The equalization filters of the demodulated precoded symbols and demodulated non-precoded symbols must therefore be recalculated.

(69) B) Precoding in Frequency (=0, 0)

(70) According to a second example, it is sought to cancel, or at the very least reduce, only the intercarrier interference ICI.sub.n, by precoding a first subset of OQAM symbols. This technique is denoted by SIPC precoding in frequency.

(71) As illustrated in FIG. 8, according to this second example a transmission pattern is considered corresponding, in time, either to a series of precoded symbols, hatched, or to a series of non-precoded symbols, not hatched, and, in frequency, to an alternation of one precoded symbol, hatched, and one non-precoded symbol, not hatched, for reducing the intercarrier interference.

(72) More specifically, it is assumed that, for a symbol a.sub.m.sub.0.sub.,n.sub.0 at instant n.sub.0 and the carrier m.sub.0, the ICI.sub.n is mainly generated by the two neighboring symbols a.sub.m.sub.0.sub.+1,n.sub.0 and a.sub.m.sub.0.sub.1,n.sub.0. It is chosen to alternate the positions of the precoded symbols for even m and for odd m, for reducing the intercarrier interference.

(73) As mentioned above, a first subset of symbols is precoded in the course of a step of precoding 54 for canceling, or at the very least reducing, the intercarrier interference:
c.sub.m,n=a.sub.m,nICI.sub.n
with, for an FTN/OQAM modulation:

(74) ${\mathrm{ICI}}_n=\{\underset{m{m}_0}{.Math.}\underset{n}{.Math.}{a}_{m,n}{e}^{\frac{j}{2}\left(m-m_0+n-n_0\right)}\underset{k}{.Math.}g\left[k-{\mathrm{nN}}_f\right]g\left[k-n_0{N}_f\right]e^{\frac{j2\left(k-\frac{D}{2}\right)\left(m-m_0\right)}{M}}$
using the notations given with the FTN/OQAM modulations according to the prior art.

(75) The multicarrier signal therefore includes carriers modulated by precoded symbols, and carriers modulated by non-precoded symbols.

(76) On reception, once the multicarrier signal is demodulated, the demodulated precoded symbols, then the demodulated non-precoded symbols, are equalized, by taking into account interference affecting the non-precoded symbols determined from the equalization of the precoded symbols.

(77) FIG. 9 illustrates an example of a receiver according to an embodiment of the invention, implementing at least one decoding iteration.

(78) The modules implemented for estimating the precoded symbols and the non-precoded symbols are similar to those illustrated in FIG. 7, replacing the MMSE-t equalizer in time used for equalizing the demodulated non-precoded symbols by an MMSE-f equalizer 582 in frequency. Indeed, as the intercarrier interference term ICI.sub.n, depends on time, the equivalent channel in time of the non-precoded symbols also depends on time. Therefore it is chosen to equalize the demodulated non-precoded symbols in frequency (on the m axis). The operation of the receiver is therefore not detailed again here.

(79) It is to be noted that for an MMSE-f equalization in frequency, the SIC 1 module 91 eliminates, or at the very least reduces, the interference by using the estimated OQAM symbols .sub.m,n:

(80) ${\hat{y}}_{m_0,n_0}=y_{m_0,n_0}-\left\{\underset{n{n}_0}{.Math.}\underset{m}{.Math.}{\hat{a}}_{m,n}{e}^{\frac{j}{2}\left(m-m_0+n-n_0\right)}\underset{k}{.Math.}g\left[k-{\mathrm{nN}}_f\right]g\left[k-n_0{N}_f\right]e^{\frac{j2\left(k-\frac{D}{2}\right)\left(m-m_0\right)}{M}}\right\}$

(81) The SIC 2 module 92, like the SIC 2 module 72, eliminates, or at the very least reduces, the intercarrier interference generated by the carriers modulated by non-precoded symbols on the carriers modulated by precoded symbols.

(82) C) Precoding in Time and in Frequency (0, 0)

(83) According to a third example, it is sought to cancel, or at the very least reduce, the intersymbol interference ISI and the intercarrier interference ICI.sub.n, by precoding a first subset of OQAM symbols. This technique is denoted by SIPC precoding in time-frequency.

(84) As illustrated in FIG. 10, according to this third example a transmission pattern is considered corresponding, in time, to an alternation of two precoded symbols of two non-precoded symbols, and, in frequency either to an alternation of one precoded symbol and one non-precoded symbol, or to a series of non-precoded symbols, for reducing the intersymbol and intercarrier interference.

(85) More specifically, it is assumed that, for a symbol a.sub.m.sub.0.sub.,n.sub.0 at instant n.sub.0 and the carrier m.sub.0, the ISI is mainly generated by the two neighboring symbols a.sub.m.sub.0.sub.,n.sub.0.sub.+2 and a.sub.m.sub.0,.sub.n.sub.0.sub.2. Therefore it is chosen to place two consecutive precoded symbols for each value of m, by alternating two precoded symbols and two non-precoded symbols. It is also assumed that the ICI.sub.n is generated mainly by the two neighboring symbols a.sub.m.sub.0.sub.+1,n.sub.0 and a.sub.m.sub.0.sub.1,n.sub.0. It is therefore chosen to alternate the positions of the precoded symbols for even m and for odd m.

(86) As mentioned above, a first subset of symbols is precoded in the course of a step of precoding 54 for canceling, or at the very least reducing, the intersymbol interference:
c.sub.m,n=a.sub.m,nISIICI.sub.n
using the values previously defined for the ISI and the ICI for the FTN/OQAM transmissions.

(87) The multicarrier signal therefore includes carriers modulated by precoded symbols, and carriers modulated by non-precoded symbols.

(88) On reception, once the multicarrier signal is demodulated, the demodulated precoded symbols, then the demodulated non-precoded symbols, are equalized, by taking into account interference affecting the non-precoded symbols determined from the equalization of the precoded symbols.

(89) FIG. 11 illustrates an example of a receiver according to an embodiment of the invention, implementing at least one decoding iteration.

(90) In the course of a first decoding iteration, the demodulated precoded symbols y.sub.m,n.sup.c are equalized with an MMSE-t equalizer 581 in time. The equalized demodulated precoded symbols are interleaved by the interleaver 59, and decoded by the decoder 60. For example, such a decoder is of the Max-Log-MAP type providing soft information in terms of maximum likelihood ratio (LLR), that is used for constructing soft symbols. A first estimate is therefore obtained of the precoded symbols .sub.m,n.sup.c at the output of the first decoding iteration (=.sub.m,n at the positions corresponding to the precoded symbols).

(91) This information in terms of LLR allows a first interference cancellation module SIC 1 111 of the receiver to determine the intersymbol interference generated by the precoded symbols on the non-precoded symbols.

(92) In the course of the first decoding iteration, then the demodulated non-precoded symbols y.sub.m,n.sup.a carried by the same frequency as the precoded symbols are equalized, e.g. odd m with an MMSE-t equalizer 581 in time, by taking into account the interference determined by the first SIC 1 module 111. The demodulated non-precoded symbols equalized with odd m are interleaved by the interleaver 59, and decoded by the decoder 60. For example, such a decoder is of the Max-Log-MAP type, that is used for constructing soft symbols. A first estimate is therefore obtained of the non-precoded symbols .sub.m,n.sup.a with odd m at the output of the first decoding iteration (=.sub.m,n at the positions corresponding to the non-precoded symbols with odd m).

(93) This information in terms of LLR allows a second interference cancellation module SIC 2 112 of the receiver to determine the intercarrier interference generated by all the symbols of a carrier of odd index m on the non-precoded symbols of a carrier of even index k (the SIC 2 module uses the estimated precoded symbols and the estimated non-precoded symbols of the carrier of odd index m for canceling the interference that they generate on the carrier of even index k).

(94) In the course of the first decoding iteration, then the demodulated non-precoded symbols y.sub.k,n.sup.a carried by another frequency than the precoded symbols e.g. even k are equalized, with an MMSE-f equalizer 582 in frequency, by taking into account the interference determined by the second SIC 2 module 112. The demodulated non-precoded symbols equalized with even k are interleaved by the interleaver 59, and decoded by the decoder 60. For example, such a decoder is of the Max-Log-MAP type. A first estimate is therefore obtained of the non-precoded symbols .sub.k,n.sup.a with even k at the output of the first decoding iteration (=.sub.m,n at the positions corresponding to the non-precoded symbols with even m).

(95) Optionally, this information in terms of LLR allows a third interference cancellation module SIC 3 103 to determine the interference caused by the non-precoded symbols of the carrier of even index k, on the precoded symbols of the carrier of odd index m.

(96) A plurality of iterations may be implemented until a convergence is obtained in the estimate of the precoded .sub.m,n.sup.c and non-precoded symbols .sub.m,n.sup.a, with even m and odd m, again denoted by .sub.m,n.

(97) As mentioned above, for an MMSE-t equalization in time or MMSE-f in frequency an SIC module eliminates, or at the very least reduces, the interference by using the previously estimated symbols .sub.m,n.

5.3 Second Embodiment: FTN/OFDM Type Modulation

(98) The transmission system illustrated in FIG. 5 may be used for an FTN/OFDM transmission according to an embodiment of the invention, by replacing the OQAM modulator 55 with an OFDM modulator.

(99) On transmission, the bits of a source signal are first coded by a channel coder CC, which represents e.g. a convolutional code, and interleaved by an interleaver it. The interleaved coded bits are then mapped to QAM symbols, in a mapping module, using, for example, the Gray mapping technique. A set of symbols is thus obtained.

(100) According to an embodiment of the invention, one part of these symbols, again referred to as the first subset, is precoded in a precoding module, the other part, again referred to as the second subset, is not precoded.

(101) For example, the precoding module delivers, for each symbol a.sub.m.sub.0.sub.,n.sub.0 of the first subset, a precoded symbol c.sub.m.sub.0,.sub.n.sub.0 intended to modulate a carrier at the location (m.sub.0,n.sub.0) in the predetermined transmission pattern, such that:

(102) 0$c_{m_0,n_0}=\{\begin{array}{c}\left(a_{m_0,n_0}-\mathrm{ISI}\mathrm{if}\left(=0\mathrm{and}{n}_0=k\mathrm{mod}\left(l^{}+1\right),\left(k\mathrm{and}k{l}^{}\right)\right)\right)\\ \left(a_{m_0,n_0}-\mathrm{ICI}\mathrm{if}\left(=0\mathrm{and}{m}_0=k\mathrm{mod}\left(l+1\right),\left(k\mathrm{and}kl\right)\right)\right)\\ \left(a_{m_0,n_0}-\mathrm{ISI}-\mathrm{ICI}\mathrm{if}\left(m_0=k\mathrm{mod}\left(l+1\right),\mathrm{and}{n}_0=k^{}\mathrm{mod}\left(l^{}+1\right),\left(k,k^{},kl\mathrm{and}{k}^{}{l}^{}\right)\right)\right)\end{array}$

(103) Each of these lines corresponds to a different case of precoding, making it possible to partially cancel the ISI (SIPC in time, first line), the ICI (SIPC in frequency, second line), or the ISI and the ICI (SIPC in time-frequency, third line).

(104) The other symbols a.sub.m,n, belonging to the second subset, are not precoded.

(105) The carriers of the multicarrier signal are then modulated with the precoded QAM symbols of the first subset and the non-precoded QAM symbols of the second subset in an FTN-OFDM modulator.

(106) After passage in an AWGN channel, the received signal is first demodulated by an FTN-OFDM demodulator.

(107) The symbols coming from the FTN-OFDM demodulator are then filtered by a specific SISO MMSE filter, deinterleaved by a deinterleaver .sup.1, then decoded by a decoder.

(108) For example, a receiver based on the principle of turbo equalization is considered. The information coming from the decoder is therefore used for updating the SISO MMSE filter, by communicating thereto logarithmic likelihood ratio type information (LLRs) L.sub.a(x) as detailed below.

(109) A) Precoding in Time (0, =0)

(110) As for OFDM/OQAM, according to a first example it is sought to cancel, or at the very least reduce, only the intersymbol interference ISI, by precoding a first subset of QAM symbols. It is to be noted that, for canceling or reducing the ISI, on each carrier m, the positions of the symbols to be precoded may be chosen independently of the other carriers.

(111) As illustrated in FIG. 12, according to this first example a transmission pattern is considered corresponding to an alternation in time of one precoded symbol, hatched, and one non-precoded symbol, not hatched, and an alternation in frequency of one precoded symbol, hatched, and one non-precoded symbol, not hatched, for reducing the intersymbol interference.

(112) As mentioned above, a first subset of symbols is precoded in the course of a step of precoding for canceling, or at the very least reducing, the intersymbol interference:
c.sub.m,n=a.sub.m,nISI
with, for an FTN/OFDM modulation:

(113) $\mathrm{ISI}=\underset{\underset{n{n}_0}{n=n_0-\left(\left[\frac{M}{N_f}\right]-1\right)}}{\overset{n_0+\left(\left[\frac{M}{N_f}\right]-1\right)}{.Math.}}{\mathrm{Me}}^{\frac{j2N_f{m}_0\left(n-n_0\right)}{M}}{a}_{m_0,n}$
using the notations given with the FTN/OFDM modulations according to the prior art.

(114) If it is assumed that, for a symbol a.sub.m.sub.0.sub.,n.sub.0, the ISI is generated mainly by the 21 neighboring symbols a.sub.m.sub.0.sub.,n.sub.0.sub.p, for p[l, l], where

(115) $l=\left[\frac{L}{N_f}\right]$
and [.] represents the entire part operator and L is the length of the prototype filter used, the equivalent channel of the ISI may be represented by h=[h.sub.l, . . . , h.sub.1, 1, h.sub.1, . . . , h.sub.l]. By considering the equivalent channel model of the ISI, the precoded symbol c.sub.m.sub.0.sub.,n.sub.0 at the position (m.sub.0, n.sub.0) is such that:

(116) $c_{m_0,n_0}=a_{m_0,n_0}-\underset{i=-l,i0}{\overset{l}{.Math.}}{h}_i{a}_{m_0,n_0-i}$

(117) It is considered, for example, as illustrated in FIG. 12, that l=1.

(118) The multicarrier signal therefore includes carriers modulated by precoded symbols, and carriers modulated by non-precoded symbols.

(119) On reception, without taking into account the ICI and the noise, the precoded symbol received at the position (m.sub.0, n.sub.0) after demodulation, denoted by y.sub.m.sub.0.sub.,n.sub.0.sup.c, is such that:

(120) $y_{m_0,n_0}^c=c_{m_0,n_0}+\underset{i=-l,i0}{\overset{l}{.Math.}}{h}_i{a}_{m_0,n_0-i}=a_{m_0,n_0}$

(121) Therefore first of all the demodulated precoded symbols, then the demodulated non-precoded symbols, are equalized, by taking into account interference affecting the non-precoded symbols determined from the equalization of the precoded symbols.

(122) The receiver implemented for receiving and decoding the multicarrier signal is similar to that of FIG. 7. Its operation is therefore not described again.

(123) B) Precoding in Frequency (=0, 0)

(124) According to a second example, it is sought to cancel, or at the very least reduce, only the intercarrier interference ICI.sub.n, by precoding a first subset of QAM symbols.

(125) The transmission pattern in this case is similar to that illustrated in FIG. 8, corresponding to a series in time of precoded symbols or non-precoded symbols, and an alternation in frequency of one precoded symbol and one non-precoded symbol, for reducing the intercarrier interference. It is also assumed that, for a symbol a.sub.m.sub.0.sub.,n.sub.0 at instant n.sub.0 and the carrier m.sub.0, the ICI.sub.n is mainly generated by the two neighboring symbols a.sub.m.sub.0.sub.+1,n.sub.0 and a.sub.m.sub.0.sub.1,n.sub.0.

(126) As mentioned above, a first subset of symbols is precoded in the course of a step of precoding for canceling, or at the very least reducing, the intercarrier interference:
c.sub.m,n=a.sub.m,nICI.sub.n
with, for an FTN/OFDM modulation:

(127) ${\mathrm{ICI}}_n=\underset{m{m}_0}{.Math.}\underset{n_0-\left(\left[\frac{M}{N_f}\right]-1\right)}{\overset{n_0+\left(\left[\frac{M}{N_f}\right]-1\right)}{.Math.}}{a}_{m,n}\underset{k}{.Math.}{e}^{\left(\frac{j2\left(k-\frac{M-1}{2}\right)\left(m-m_0\right)}{M}\right)}{e}^{\frac{j2N_f\left(n_0{m}_0-\mathrm{nm}\right)}{M}}$
using the notations given with the FTN/OFDM modulations according to the prior art.

(128) The multicarrier signal therefore includes carriers modulated by precoded symbols, and carriers modulated by non-precoded symbols.

(129) On reception, once the multicarrier signal is demodulated, the demodulated precoded symbols, then the demodulated non-precoded symbols, are equalized, by taking into account interference affecting the non-precoded symbols determined from the equalization of the precoded symbols.

(130) The receiver implemented for receiving and decoding the multicarrier signal is similar to that of FIG. 9. Its operation is therefore not described again.

(131) C) Precoding in Time and in Frequency (0, 0)

(132) According to a third example, it is sought to cancel, or at the very least reduce, the intersymbol interference ISI and the intercarrier interference ICI.sub.n, by precoding a first subset of QAM symbols.

(133) As illustrated in FIG. 13, according to this third example a transmission pattern is considered corresponding, in time, either to an alternation of one precoded symbol and one non-precoded symbol, or to a series of non-precoded symbols, and, in frequency, either to an alternation of one precoded symbol and one non-precoded symbol, or to a series of non-precoded symbols, for reducing the intersymbol and intercarrier interference.

(134) More specifically, it is assumed that, for a symbol a.sub.m.sub.0.sub.,n.sub.0 at instant n.sub.0 and the carrier m.sub.0, the ISI is mainly generated by the two neighboring symbols a.sub.m.sub.0.sub.,n.sub.0.sub.1 and a.sub.m.sub.0.sub.,n.sub.0.sub.+1. It is also assumed that the ICI.sub.n is generated mainly by the two neighboring symbols a.sub.m.sub.0.sub.+1,n.sub.0 and a.sub.m.sub.0.sub.1,n.sub.0.

(135) As mentioned above, a first subset of symbols is precoded in the course of a step of precoding for canceling, or at the very least reducing, the intersymbol interference:
c.sub.m,n=a.sub.m,nISIICI.sub.n
using the values previously defined for the ISI and the ICI.sub.n for the FTN/OFDM transmissions.

(136) The multicarrier signal therefore includes carriers modulated by precoded symbols, and carriers modulated by non-precoded symbols.

(137) On reception, once the multicarrier signal is demodulated, the demodulated precoded symbols, then the demodulated non-precoded symbols, are equalized, by taking into account interference affecting the non-precoded symbols determined from the equalization of the precoded symbols.

(138) The receiver implemented for receiving and decoding the multicarrier signal is similar to that of FIG. 11. Its operation is therefore not described again.

5.4 Devices

(139) Finally, in relation to FIGS. 14 and 15 respectively a description is given of the simplified structure of a transmitter implementing a technique of generating a multicarrier signal according to an embodiment of the invention, and the structure of a receiver implementing a technique of receiving a multicarrier signal according to an embodiment of the invention.

(140) As illustrated in FIG. 14, such a transmitter, or device for generating a multicarrier signal, includes a memory 141 including a buffer memory, a processing unit 142, provided, for example, with a microprocessor P, and driven by an application or a computer program 143, implementing the steps of the method of generating according to an embodiment of the invention.

(141) On initialization, the code instructions of the computer program 143 are, for example, loaded into a RAM memory before being executed by the processor of the processing unit 142. The processing unit 142 receives real or complex symbols a.sub.m,n at the input. The microprocessor of the processing unit 142 implements the steps of the method of generating previously described, according to the instructions of the computer program 143, for generating a multicarrier signal s.

(142) As illustrated in FIG. 15, a receiver, or receiving device, in its turn includes a memory 151 including a buffer memory, a processing unit 152, provided, for example, with a microprocessor P, and driven by an application or a computer program 153, implementing the steps of the method of receiving according to an embodiment of the invention.

(143) On initialization, the code instructions of the computer program 153 are, for example, loaded into a RAM memory before being executed by the processor of the processing unit 152. The processing unit 152 receives a received multicarrier signal r at the input. The microprocessor of the processing unit 152 implements the steps of the method of receiving previously described, according to the instructions of the computer program 153, for estimating the transmitted symbols.