Method and apparatus for demodulating a multicarrier signal, taking a channel response estimate and an estimate of white frequency distortion into account

0001The field of the invention is that of the reception of multicarrier signals. More specifically, the invention relates to the optimization of the demodulation of the symbols modulating such signals.

0002The invention applies to all types of signals using a plurality of carrier frequencies, that is to say to systems using signals transmitted using the frequency division multiplexing technique (in English: Frequency Division Multiplex (FDM)), and for example the COFDM system (Coded Orthogonal Frequency Division Multiplex (multiplexing of coded orthogonal frequencies)), implemented in particular within the framework of the European project Eureka 147 "DAB" (Digital Audio Broadcasting digital audio)), and also anticipated for the transmission of television signals.

0003In such transmission systems, the source data to be transmitted are organized into symbols (consisting of one or more source data) each modulating, for a predetermined time interval, a carrier frequency chosen from among a plurality of carriers. The signal formed by all of the modulated carriers is transmitted to one or more receivers, which receive an emitted signal disturbed by the transmission channel.

0004Demodulation generally consists; in principle, to estimate the response of the transmission channel for each symbol, then to divide the signal received by this estimate to obtain an estimate of the symbol transmitted.

0005Many demodulation techniques are known, which can be differential or consistent. A technique facilitating coherent demodulation using reference symbols known to the receivers and regularly inserted among the useful symbols is for example described in patent FR-94 07984 in the name of the same applicants.

0006The major problem with these known techniques is that the estimation of the response of the channel obtained is not always exact or precise, since it can be disturbed by a white frequency distortion often - but not only - induced by the receiver.

0007In other words, by agreeing to note, in a multicarrier system, n the time index and k the frequency index (n and k belonging to <b>Z</b>), on transmission, each carrier k of a symbol n is therefore modulated by a symbol C_{n, k} complex.

0008If we note H_{n, k} the complex response of the transmission channel, then we receive:<maths id="math0001" num="(1)"><math display="block"><mrow><msub><mrow><mtext>Y</mtext></mrow><mrow><mtext>n, k</mtext></mrow></msub><msub><mrow><mtext> = H</mtext></mrow><mrow><mtext>n, k</mtext></mrow></msub><msub><mrow><mtext> . VS</mtext></mrow><mrow><mtext>n, k</mtext></mrow></msub><msub><mrow><mtext> . ⌀</mtext></mrow><mrow><mtext>not</mtext></mrow></msub><mtext> + white noise</mtext></mrow></math><img file="EP0762702A1_D0001.tif" /></maths>

0009White noise is a term that is neglected later, for the sake of simplicity of presentation.

0010⌀_not is a complex term, a priori variable in phase and amplitude which depends only on n, and therefore describes any "white" frequency distortion which affects the received signal. The ⌀_not are assumed to be poorly correlated from symbol to symbol.Typically but not exclusively, ⌀_not is the phase noise of the tuner.

0011Recovery by the receiver of information C_{n, k} transmitted implies knowing how to isolate the term C_{n, k} from equation (1), by division of Y_{n, k} received by an estimated value of H_{n, k}.⌀_not.

0012A way often used to facilitate the coherent demodulation of the received signal consists in inserting on transmission in the frame "pilots" (or reference symbols), that is to say to transmit for certain values ​​of k and n - predetermined in advance and known to the receiver - C values_{n, k} particular a priori known to the receiver.

0013They are noted thereafter P_{n, k}, the notation C_{n, k} being reserved for vectors a priori unknown to the receiver, that is to say carriers of information.

0014Of course, for reasons of maximization of the useful bit rate transmitted, the number of vectors C_{n, k} sacrificed in P_{n, k} should be as low as possible. We can agree to note<b>P</b>² the subset of <b>Z</b> x <b>Z</b> couples (n, k) such that the carrier indexed k of the symbol n carries a pilot P_{n, k}·

0015Since P_{n, k} is assumed by the receiver, it can calculate the division Y_{n, k}/ P_{n, k} and thus obtain an estimate of the product H_{n, k}.⌀_not - marked D_{n, k} (D as distortion) in the following - by all the couples (n, k) of <b>P</b>².

0016D̂ values_{not<sub2>0</sub2>, k<sub2>0</sub2>} for all values ​​n₀ and k₀ possible in <b>Z</b> are then calculated by the receiver by interpolation and / or extrapolation of the D values_{n, k}, with (n, k) belonging to <b>P</b>².

0017The state of the art consists in defining the function f (n₀, k₀) for calculating D̂_{not<sub2>0</sub2>, k<sub2>0</sub2>}, from D_{n, k}, (n, k) belonging to <b>P</b>².

0018A major problem, detected by the inventors but not expressly known to those skilled in the art, comes from the fact that the D̂_{not<sub2>0</sub2>, k<sub2>0</sub2>} thus estimated does not allow to distinguish each of the two terms of the product: D̂_{not<sub2>0</sub2>, k<sub2>0</sub2>} = Ĥ_{not<sub2>0</sub2>, k<sub2>0</sub2>}.φ̂_{not<sub2>0</sub2>, k<sub2>0</sub2>}, where Ĥ_{not<sub2>0</sub2>, k<sub2>0</sub2>} denotes what would have been the result of f (n₀, k₀) if all D_{n, k} (= H_{n, k}.⌀_not) used as a basis for the calculation verified ⌀_not = 1, that is to say in the absence of any white frequency distortion.

0019A method to get rid of the term φ̂_{not<sub2>0</sub2>, k<sub2>0</sub2>} could consist in strongly filtering temporally (i.e. according to the index n), D_{n, k} where (n, k) belongs to <b>P</b>² when calculating f (n₀, k₀). Under these conditions, we have φ̂_{not<sub2>0</sub2>, k<sub2>0</sub2>} ≈ 1.

0020Unfortunately, and inevitably, this temporal filtering also affects the term Ĥ_{not<sub2>0</sub2>, k<sub2>0</sub2>} which therefore ceases to be an acceptable estimate of the complex frequency response of the channel (at time n₀ and for the carrier k₀), if it is not sufficiently stationary.

0021The invention particularly aims to overcome these drawbacks.

0022Thus, an objective of the present invention is to provide a method for demodulating a multicarrier signal, and a corresponding device, making it possible to optimize the demodulation of the symbols forming the received signal.

0023More specifically, the invention aims to provide such a method, taking into account the distortions induced by the receivers.

0024Another objective of the invention is to provide such a demodulation method, in which the estimation of the response of the transmission channel is optimized, whatever the distortions induced by the receivers.

0025These objectives, as well as others which will appear subsequently, are achieved according to the invention by a method of demodulating a multicarrier signal formed by a temporal succession of symbols modulating a plurality of carrier frequencies, during a time interval given, process comprising the following steps:<ul id="ul0001" list-style="dash" compact="compact"><li>determination, for each of said symbols and each of said carriers, of first information Ĥ_{not<sub2>0</sub2>, k<sub2>0</sub2>} representative of an estimate of the response of the transmission channel, n₀ representing the index of the time of emission and k₀ representing the carrier frequency index;</li><li>determination, for each of said time intervals, of second information <img file="EP0762702A1_D0002.tif" /> representative of an estimate of the white frequency distortion; and</li><li>division of each symbol to demodulate Y_{not<sub2>0</sub2>, k<sub2>0</sub2>} by said first information <img file="EP0762702A1_D0003.tif" />and by said second information <img file="EP0762702A1_D0004.tif" />, to deliver an estimated symbol Ĉ_{not<sub2>0</sub2>, k<sub2>0</sub2>},</li></ul> said steps of determining the first and second information taking account of at least one reference symbol carried by at least one of said carrier frequencies during at least one of said time intervals.

0026Thus, according to the invention, two values ​​are determined, in absolute terms, representing precisely respectively the response of the transmission channel and the white frequency distortions, then an estimate of the received symbol is determined by division. This technique is completely new to a person skilled in the art, the objective of which, according to the state of the art, is to limit, in relative terms, the effect of the distortions.

0027Advantageously, the step of determining said first information <img file="EP0762702A1_D0005.tif" /> includes the following steps:<ul id="ul0002" list-style="dash" compact="compact"><li>calculation of a first demodulation datum Ĥ_{not<sub2>0</sub2>, k}.φ_{not<sub2>0</sub2>, k} , corresponding to the product of a term corresponding to the estimation of the response of the transmission channel and of a term corresponding to the estimation of the white frequency distortion;</li><li>deletion of said term corresponding to the estimation of the white frequency distortion, so as to produce said first information <img file="EP0762702A1_D0006.tif" />.</li></ul>

0028The first step is known per se. The following deletion processing is however specific to the invention. It can advantageously include the following steps:<ul id="ul0003" list-style="dash" compact="compact"><li>insertion among the carriers transmitted of P pilots_{n, k} known to receivers, staggered at times and on predetermined carrier frequencies, so that at least some of said carrier frequencies regularly carry reference elements, at different times for neighboring carrier frequencies;</li><li>the division <maths id="math0002" num=""><math display="inline"><mrow><mfrac><mrow><msub><mrow><mtext>Y</mtext></mrow><mrow><mtext>n, k</mtext></mrow></msub></mrow><mrow><msub><mrow><mtext>P</mtext></mrow><mrow><mtext>n, k</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP0762702A1_D0007.tif" /></maths> gives D_{n, k} ;</li><li>optionally, temporal interpolation filtering, for each of said carrier frequencies carrying reference elements, so as to associate with each carrier placed between two reference elements on said carrier frequency an intermediate datum D̂_{not<sub2>0</sub2>, k} ;</li><li>frequency interpolation filtering, for each of said time intervals, of said intermediate data D̂_{not<sub2>0</sub2>, k} , so as to produce said first information <img file="EP0762702A1_D0008.tif" />.</li></ul>

0029It should be noted that it is the particular distribution of the reference symbols, in staggered rows, and not orthogonal, which makes it possible to effectively remove the term due to the distortion, ensuring good decorrelation, as will be seen below. .

0030Advantageously, said frequency interpolation filtering step uses a finite impulse response filter of length N substantially equal to the repetition period of the reference elements on a given carrier frequency.

0031According to a preferred characteristic of the invention, said second information <img file="EP0762702A1_D0009.tif" /> is obtained from the division δ_{not<sub2>0</sub2>+ i, k} of data D_{not<sub2>0</sub2>+ i, k} by said first information <img file="EP0762702A1_D0010.tif" /> (i small integer possibly zero).

0032In other words, after having deleted the term φ, we recalculate it, by comparison with the basic information.

0033Advantageously, in order to maintain the stationary hypothesis of the channel, i is equal to -1, 0 or 1.

0034Preferably, said second information <img file="EP0762702A1_D0011.tif" /> is a weighted average of at least two of said divisions δ_{not<sub2>0</sub2>+ i, k} .

0035So the second piece of information <img file="EP0762702A1_D0012.tif" /> is worth:<maths id="math0003" num=""><img file="EP0762702A1_D0013.tif" /></maths> with:<maths id="math0004" num=""><img file="EP0762702A1_D0014.tif" /></maths>

0036The invention also relates to a device for demodulating a multicarrier signal formed by symbols modulating a plurality of carrier frequencies, during a given time interval, comprising:<ul id="ul0004" list-style="dash" compact="compact"><li>first means of calculating, for each of said symbols and each of said carriers, first information <img file="EP0762702A1_D0015.tif" /> representative of an estimate of the response of the transmission channel, n₀ representing the emission time and k₀ representing said carrier frequency;</li><li>second means for calculating, for each of said time intervals, second information <img file="EP0762702A1_D0016.tif" /> representative of an estimate of the white frequency distortion; and</li><li>means for dividing each symbol to be demodulated Y_{not<sub2>0</sub2>, k<sub2>0</sub2>} by said first information <img file="EP0762702A1_D0017.tif" /> and by said second information <img file="EP0762702A1_D0016.tif" /> , to deliver an estimated symbol Ĉ_{not<sub2>0</sub2>, k<sub2>0</sub2>} ,</li></ul> said means for calculating the first and second information taking account of at least one reference symbol carried by at least one of said carrier frequencies during at least one of said time intervals.

0037Other characteristics and advantages of the invention will appear on reading the following description of a preferred embodiment of the invention, given by way of simple illustrative and nonlimiting example, and of the appended drawings, in which:<ul id="ul0005" list-style="dash" compact="compact"><li>FIG. 1 illustrates in general the demodulation method of the invention;</li><li>FIGS. 2 and 3 illustrate two advantageous structures for distributing the reference symbols in time-frequency space;</li><li>Figure 4 is a simplified block diagram of a demodulation device according to the invention.</li></ul>

0038As already indicated, and as illustrated in FIG. 1, the general principle of the invention consists in determining (11) an absolute estimate <img file="EP0762702A1_D0018.tif" /> of the response of the transmission channel, then (12) an absolute estimate <img file="EP0762702A1_D0019.tif" /> of the distortion induced by the receiver, and finally to divide (13) the symbol received by these two estimates.

0039It should be noted that this approach is new, and not trivial. Indeed, the two estimates are generally known in the form of a single inseparable product, and the prior art aims at best to limit the effect of the distortion on this product. According to the invention, on the other hand, it is proposed to determine the two values ​​independently, in order to optimize the result of the demodulation.

0040The preferred method for obtaining these two values ​​is also not obvious to a person skilled in the art. It consists first of all in eliminating the effect of the distortion ⌀ on the estimate D of the product, by implementing a particular distribution of reference symbols (structure called subsequently staggered structure, as opposed to the classical orthogonal structure) and an adequate filtering, then to recalculate an absolute estimate of the distortion.

0041Thus, with reference to FIG. 1, we receive (14) the transmitted signal, in the form of complexes Y_{not<sub2>0</sub2>, k<sub2>0</sub2>} . The carriers received corresponding to the reference carriers are analyzed (111) in order to determine the estimates D_{n, k} corresponding. An optional temporal filtering 112 is then performed, making it possible to obtain the estimates D̂_{not<sub2>0</sub2>,<sub2>k</sub2>} between two D_{n, k} consecutive, on a given carrier k.

0042Finally, a frequency filtering 113 is performed on these estimates D̂_{not<sub2>0</sub2>, k}. As will be seen more precisely below, owing to the staggered distribution of the reference symbols, the estimates D̂_{not<sub2>0</sub2>, k} are based on reference symbols transmitted at different times of transmission, and therefore highly decorated in terms of white frequency distortions. Consequently, the filtering 113 makes it possible to eliminate, or at least to greatly attenuate, the effect of this distortion, and therefore delivers precise estimates of the response of the transmission channel.<img file="EP0762702A1_D0020.tif" /> .

0043From this estimate <img file="EP0762702A1_D0021.tif" /> , a recalculation (12) according to the invention is estimated of the distortion<img file="EP0762702A1_D0022.tif" />. For this, we divide (121) the value D_{not<sub2>0</sub2>+ i, k} by <img file="EP0762702A1_D0023.tif" /> Advantageously, the result of this division is averaged and weighted (122), in order to reduce the noise.

0044Finally, we can estimate (13) precisely the complex received, by dividing Y_{not<sub2>0</sub2>, k<sub2>0</sub2>} by product <img file="EP0762702A1_D0024.tif" /> . <img file="EP0762702A1_D0025.tif" />

0045The operations to be performed are now described more precisely.

0046We choose the law f (n₀, k₀) already mentioned so that two estimated values ​​D̂_{not<sub2>0</sub2>, k<sub2>0</sub2>} = Ĥ_{not<sub2>0</sub2>, k<sub2>0</sub2>}.φ̂_{not<sub2>0</sub2>, k<sub2>0</sub2>} and D_{not<sub2>0</sub2>, k<sub2>1</sub2>} = Ĥ_{not<sub2>0</sub2>, k<sub2>1</sub2>}.φ̂_{not<sub2>0</sub2>, k<sub2>1</sub2>} corresponding to the same time index n₀ and to two frequency indices k₀ and k₁ close (typically 1 ≤lk₀-k₁l≤ 16) are calculated (by f) respectively from the D_{n, k<sub2>0</sub2>} (n, k₀) belonging to <b>P</b>² and D_{m, k<sub2>1</sub2>} (m, k₁) belonging to <b>P</b>² chosen such that the subsets of n and m are as disjoint as possible. In other words, the D_{n, k<sub2>0</sub2>} and D_{m, k<sub2>1</sub2>} must come from (by division of Y_{n, k<sub2>0</sub2>}/ P_{n, k<sub2>0</sub2>} and Y_{m, k<sub2>1</sub2>}/ P_{m, k<sub2>1</sub2>} of different symbols, so that the quasi-decorrelation hypothesis of ⌀_not from symbol to symbol remains valid between φ̂_{not<sub2>0</sub2>, k<sub2>0</sub2>} and φ̂_{not<sub2>0</sub2>, k<sub2>1</sub2>}.

0047The φ̂ now require the addition of the two time and frequency indices, while the ⌀_not were white in frequency. It then remains to filter the D̂s frequently_{not<sub2>0</sub2>, k<sub2>0</sub2>} = Ĥ_{not<sub2>0</sub2>, k<sub2>0</sub2>}.φ̂_{not<sub2>0</sub2>, k<sub2>0</sub2>} by a function noted g_{not<sub2>0</sub2>, l<sub2>0</sub2>} , to eliminate the term φ̂_{not<sub2>0</sub2>, k<sub2>0</sub2>} without any hypothesis being necessary on the temporal variations of the channel.

0048The annoying hypothesis of stationarity of the channel, necessary in the absence of the invention, and which supposes a strong temporal correlation between H_{n, k} and H_{n + 1, k} for all n and all k of <b>Z</b> is replaced by a frequency correlation hypothesis between H_{n, k} and H_{n, k + 1}, which is all the better verified when the time spread of the impulse response of the channel is low (short echoes in front of the symbol duration).

0049Since we get an estimate of <img file="EP0762702A1_D0026.tif" /> for all n₀ and l₀ of <b>Z</b>, the estimate<img file="EP0762702A1_D0027.tif" /> can be compared to D_{not<sub2>0</sub2>+ i, k} = H_{not<sub2>0</sub2>+ i, k}.φ_{not<sub2>0</sub2>+ i} (i will advantageously be chosen small, typically i = 0 or ± 1, so that the stationarity hypothesis of the channel during | i | + 1 symbols is true, that is to say that <img file="EP0762702A1_D0028.tif" /> ≈ H_{not<sub2>0</sub2>+ i, k} for all values ​​of k such that the couple (n_{0 + i,} k) corresponds to the pilot broadcast.

0050The quotient:<maths id="math0005" num=""><img file="EP0762702A1_D0029.tif" /></maths> provides a 1st estimate of φ_{not<sub2>0</sub2>+ i}, noted φ_{not<sub2>0</sub2>+ i}.

0051Optionally, a weighted average of these δ_{not<sub2>0</sub2>+ i, k} according to the index k then gives a second less noisy estimate of φ_{not<sub2>0</sub2>+ i}, noted <img file="EP0762702A1_D0030.tif" />. This average is written for example:<maths id="math0006" num=""><img file="EP0762702A1_D0031.tif" /></maths> with for example:<maths id="math0007" num=""><img file="EP0762702A1_D0032.tif" /></maths> the couple (n₀+ i, k) corresponding to the emission of a pilot.

0052On receipt of the symbol n₀+ i, the values ​​received:<maths id="math0008" num=""><math display="block"><mrow><mtext>Y</mtext><msub><mrow><mtext>​</mtext></mrow><mrow><msub><mrow><mtext>not</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext>+ i, k</mtext></mrow><mrow><mtext>0</mtext></mrow></msub></mrow></msub><mtext> = H</mtext><msub><mrow><mtext>​</mtext></mrow><mrow><msub><mrow><mtext>not</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext>+ i, k</mtext></mrow><mrow><mtext>0</mtext></mrow></msub></mrow></msub><mtext>.φ</mtext><msub><mrow><mtext>​</mtext></mrow><mrow><msub><mrow><mtext>not</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><mtext>+ i</mtext></mrow></msub><mtext>.VS</mtext><msub><mrow><mtext>​</mtext></mrow><mrow><msub><mrow><mtext>not</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext>+ i, k</mtext></mrow><mrow><mtext>0</mtext></mrow></msub></mrow></msub><mtext> + noise</mtext></mrow></math><img file="EP0762702A1_D0033.tif" /></maths> finally allow to correctly estimate C_{not<sub2>0</sub2>+ i, k<sub2>0</sub2>}, as following :<maths id="math0009" num=""><img file="EP0762702A1_D0034.tif" /></maths>

0053In the choice of the pilot insertion structure (that is to say the choice of the carriers k and of the symbols n on which pilots are inserted), the orthogonal structures defined by:<maths id="math0010" num=""><math display="block"><mrow><msup><mrow><mtext>(n, k) ∈ P</mtext></mrow><mrow><mtext>2</mtext></mrow></msup><mtext> <=> n = constant (modulo N)</mtext><mspace linebreak="newline" /><mtext>and k = constant (modulo K)</mtext></mrow></math><img file="EP0762702A1_D0035.tif" /></maths>

0054N and K are integer constants chosen consistently with Shannon's sampling theorem. The pilots are in this orthogonal structure inserted in a symbol on N, and on a carrier on K. N is chosen according to the speed of variation of the channel (typically N = 4 or 8) while K checks:<maths id="math0011" num=""><math display="block"><mrow><mtext>K ≤ (symbol useful life / duration of the guard interval)</mtext></mrow></math><img file="EP0762702A1_D0036.tif" /></maths>

0055The orthogonal diagram is to be avoided, because D̂_{not<sub2>0</sub2>, k<sub2>0</sub2>} and D_{not<sub2>0</sub2>, k<sub2>1</sub2>} (with for example k₁= k₀+4) are usually calculated by interpolation / extrapolation from the D_{n, k0}, with (n, k₀) belonging to <b>P</b>² and D_{m, k1}, (m, k₁) belonging to <b>P</b>² respectively. However, in this case, the n and the m are identical modulo N. In other words, the symbols from which the D_{n, k0} and D_{m, k1} which serve as a basis for the calculation of D̂_{not<sub2>0</sub2>, k<sub2>0</sub2>} and D_{not<sub2>0</sub2>, k<sub2>1</sub2>} are the same and are therefore affected by the same distortion ⌀_not = ⌀_m. It follows that D̂_{not<sub2>0</sub2>, k<sub2>0</sub2>} = Ĥ_{not<sub2>0</sub2>, k<sub2>0.</sub2>}φ̂_{not<sub2>0</sub2>, k<sub2>0</sub2>} and D_{not<sub2>0</sub2>, k<sub2>1</sub2>} = Ĥ_{not<sub2>0</sub2>, k<sub2>1.</sub2>}φ̂_{not<sub2>0</sub2>, k<sub2>1</sub2>} are affected in the same way φ̂_{not<sub2>0</sub2>, k<sub2>0</sub2>} = φ̂_{not<sub2>0</sub2>, k<sub2>1</sub2>}, which we can not get rid of by frequency filtering (along the k axis) later.

0056It is therefore necessary to choose a structure for inserting the pilots in staggered rows, and no longer orthogonal, as illustrated in Figures 2 and 3.

0057In these diagrams, (n, k) ∈ <b>P</b>² <=> n = cste (k) [modulo N]

0058That is, the index n of the symbol which carries the pilots depends on k.

0059Figure 2 illustrates the case where:<maths id="math0012" num=""><math display="block"><mrow><mtext>cste (k) = </mtext><mfrac><mrow><mtext>k modulo NK</mtext></mrow><mrow><mtext>K</mtext></mrow></mfrac></mrow></math><img file="EP0762702A1_D0037.tif" /></maths>

0060FIG. 3 illustrates a slightly different case, but equivalent from the point of view of the invention.

0061It should be noted that the number of pilots is not increased, compared to a conventional orthogonal structure, and that N and K remain identical compared to this structure (N = 8 and K = 4 in the example described above. and Figure 2), or even lower (N = 8 and K = 2 in the case of Figure 3).

0062Let's return to the example in Figure 2, for the sake of simplicity in the following.

0063It is necessary to calculate by interpolation and / or extrapolation D̂_{not<sub2>0</sub2>, k<sub2>0</sub2>} and D_{not<sub2>0</sub2>, k<sub2>1</sub2>}.

0064For example :<maths id="math0013" num=""><img file="EP0762702A1_D0038.tif" /></maths>

0065It is important to note that it is here the choice of the non-orthogonal structure which makes it possible to affirm that φ̂_{not<sub2>0</sub2>, k<sub2>0</sub2>} and φ̂_{not<sub2>0</sub2>, k<sub2>1</sub2>} , derived from calculations based respectively on D_{n, k0} and D_{m, k1} such that n and m are different (n = n₀-4 or n₀+4 while m = n₀-3 or n₀+5) are poorly correlated.

0066We also calculate all D̂_{not<sub2>0</sub2>, k<sub2>0</sub2>+ pK} where p belongs to <b>Z</b>.

0067Since φ̂_{not<sub2>0</sub2>, k<sub2>0</sub2>} and φ̂_{not<sub2>0</sub2>, k<sub2>0</sub2>+ pK} remain uncorrelated (at least as long as 0 ≤ p &lt;N), a frequency filter for example of the finite impulse response (FIR) type of interpolation of <img file="EP0762702A1_D0039.tif" /> (where k is arbitrary in <b>Z</b>) from D̂_{not<sub2>0</sub2>, k<sub2>0</sub2>+ pK} eliminates (at least for the most part) the distortion term ⌀.

0068In other words, the filter produces an estimate:<maths id="math0014" num=""><img file="EP0762702A1_D0040.tif" /></maths>

0069So:<maths id="math0015" num=""><img file="EP0762702A1_D0041.tif" /></maths>

0070It is advantageous, but not essential, to adapt the length of the FIR filter for frequency interpolation to the value N.

0071For example, if the filter is of length N, i.e. if <img file="EP0762702A1_D0042.tif" /> is interpolated from N values <img file="EP0762702A1_D0043.tif" />, with 0 ≤ p &lt;N, the filtering of the distortion ⌀ will be maximal.

0072In the example in Figure 2, k₅ = k_{0 + 5K} = k_{0 + 20}.

0073The FIR filter produced in particular <img file="EP0762702A1_D0044.tif" />, which we can compare to D_{n0 + 1, k5} (in this preferred application, we chose i = 1). We then have:<maths id="math0016" num=""><img file="EP0762702A1_D0045.tif" /></maths> under the reasonable assumption that the H channel varied little between the symbols n₀ and N₀+1.

0074The same calculation:<maths id="math0017" num=""><math display="block"><mrow><mtext>δ</mtext><msub><mrow><mtext>​</mtext></mrow><mrow><msub><mrow><mtext>not</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext>+1, k</mtext></mrow><mrow><mtext>5</mtext></mrow></msub><mtext>+ qNP</mtext></mrow></msub><mtext> = δ</mtext><msub><mrow><mtext>​</mtext></mrow><mrow><msub><mrow><mtext>not</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext>+1, k</mtext></mrow><mrow><mtext>5</mtext></mrow></msub><mtext>+ 32q</mtext></mrow></msub></mrow></math><img file="EP0762702A1_D0046.tif" /></maths> where q belongs to <b>Z</b> can be repeated for a sufficient number of values ​​of q, so as to obtain a sufficient number of estimates φ̂_{not<sub2>0</sub2>+1} likely to feed a weighted summation type calculation as follows:<maths id="math0018" num=""><img file="EP0762702A1_D0047.tif" /></maths>

0075So the c_{not<sub2>0</sub2>+1, k<sub2>0</sub2>} , for all k₀ transmitted, can be estimated at reception without the bias provided by the distortion ⌀n₀₊₁ as following :<maths id="math0019" num=""><img file="EP0762702A1_D0048.tif" /></maths>

0076FIG. 4 illustrates in a simplified manner a receiver implementing the invention.

0077The received signal 41 is first of all transposed into low frequency, by a multiplier 42 controlled by a local oscillator 43 delivering the transposition frequency f₀. Then the transposed signal is filtered by a low-pass or band-pass filter 44, and converted into a digital signal by a sampler 45. Then, a module 46 for generating the components in phase and in quadrature delivers the channels 47_I and 47_Q.

0078In the case of COFDM, channels I and Q are subjected to a mathematical transformation FFT 48, which delivers the samples 49 Y_{n0, k0}.

0079The Sy_{not<sub2>0</sub2>, k<sub2>0</sub2>} 49 are demodulated (410) according to the method described above, by division by <img file="EP0762702A1_D0049.tif" />411 and <img file="EP0762702A1_D0050.tif" /> 412 to provide the estimated symbols Ĉ_{not<sub2>0</sub2>, k<sub2>0</sub2>} 413, which then conventionally undergo a decoding channel 414, then the continuation of the processing until the restitution of the source signal.

0080The Sy_{not<sub2>0</sub2>, k<sub2>0</sub2>} 49 supply a pilot extraction module 415 which calculates the D values_{n, k} which possibly undergo a first time filtering 416 then a second frequency filtering 417 to provide <img file="EP0762702A1_D0051.tif" /> 411 to the demodulator 410. Furthermore, a module 418 for estimating ⌀ compares D_{not<sub2>0</sub2>+ i, k} and <img file="EP0762702A1_D0052.tif" /> . A weighting module 419 calculates the estimate<img file="EP0762702A1_D0053.tif" /> 412 taking into account<maths id="math0020" num=""><img file="EP0762702A1_D0054.tif" /></maths>

0081In practice, the different modules, or at least some of them, can of course be grouped together in a single computer. Furthermore, it is clear that other embodiments can be envisaged.