HK1058868B - Method for estimating the transfer function of a multicarrier signal transmission channel and corresponding receiver - Google Patents

Description

The field of the invention is that of transmission or dissemination of sampled digital and/or analogue data from and/or to mobile terminals in particular.

Multiport modulations, combined with error-correcting coding and interlacing, have shown their interest in particular for broadband broadcasting in a radio-mobile environment as illustrated in FR 2 601 210 and FR 2 733 869 patents dealing respectively with OFDM (Orthogonal Frequency Division Multiplexing) and IOTA (Isotropic Orthogonal Transform Algorithm) modulation.

In the case of consistent data demodulation, it is necessary to be able to estimate the channel at any point in a time-frequency plane in order to correctly demodulate the information received by the receiver.

The invention relates in particular to the optimization of channel estimation techniques in the case of a multi-carrier transmission.

Generally, when data is transmitted at high bandwidth over a radio channel, the signal is subject to Doppler effects (related to the movement of the transmitter, receiver or any reflectors) and multiple path problems (related to, for example, the reflection of the signal on different objects) resulting in a spread of the impulse response of the channel (in English "Delay Spread") or variations in the amplitude of the signal. These effects depend in particular on the moment and frequency considered.

According to the state of the art (see EP 0 838 928), in the case of multi-port modulation, the channel estimate from which the degradation caused by a mobile radio channel can best be corrected is: In the case of the transmission of the signal, the signal is transmitted by the receiver to the receiver at a distance of approximately 1 km from the receiver.There are two methods: In broadcasting, pilot symbols are distributed regularly in the time-frequency plane. From these pilots, a sub-sampled version of the channel is obtained. In reception, a two-dimensional interpolation is performed, in time and frequency, to determine the value of the channel at any point in the time-frequency network. This method is used in particular by the DVB-T standard (for <<Digital Video Broadcasting - Terrestrial >>).The channel can be considered as quasi-static on a given frame (choice of system parameters such as the channel varies slowly with respect to the time of the symbol), the channel estimate on the reference symbol is valid for all OFDM symbols in the frame (this method is particularly applied to the European Telecommunication Standard Institute (ETSI) HIPERLAN/2 standard).

In the case of a split-pilot estimation, in order to limit the complexity of the channel estimator, two one-dimensional interpolation filters are usually used instead of a two-dimensional filter, since the implementation complexity is then significantly lower for an acceptable degradation of estimation quality.

For DVB-T, for example, a Wiener filter is used for frequency interpolation, while time interpolation is a simple linear interpolation.

Interpolation is therefore done in time and then in frequency.

In addition, it is difficult to make a Wiener filter adaptive, i.e. to recalculate the coefficients of the receiving filter according to the channel parameters, so that a Doppler worst case filter dimensioning and channel impulse response spread is systematically necessary.

The invention is intended in particular to overcome these disadvantages of the earlier technology.

Specifically, one purpose of the invention is to optimize the decoding of a data frame emitted over a high-spread Doppler channel when multi-port modulation is used.

One objective is also to optimise the estimation of the transfer function of a transmission channel in multi-carrier transmission.

Another objective of the invention is to allow a simple interpolation of the channel transfer function over a time/frequency network from the estimated values of this function to the locations of the pilot symbols inserted in the data frame being emitted.

Another objective of the invention is to offer a good compromise between useful flow rate and quality of channel estimation.

These and other objectives will be achieved by means of a method for estimating the transfer function of a multi-carrier signal transmission channel consisting of a time sequence of symbols consisting of a set of data elements, each of which modulates a carrier frequency of the signal, data elements comprising reference elements, called pilots, the value of which at the time of transmission is known to at least one receiver intended to receive the signal, and so-called informational data elements, representative of at least one source of the signal to be transmitted.

According to the invention, such a process includes: a step for determining a set of two-dimensional discrete flattened spheroidal sequences (SSAD); a step for writing the transfer function as a combination of at least some of the two-dimensional discrete flattened spheroidal sequences in the set; a step for two-dimensional interpolation in time and frequency of at least some coefficients of the combination, in order to obtain an estimate of the transfer function at any point in a time-frequency network.

It is noted that a time-frequency space is a bounded space of model type that allows a multi-carrier signal to be represented.

Thus, the invention allows the implementation of an estimation of a transfer function of a multi-carrier signal transmission channel of reasonable complexity and enabling the decoding of information data elements reliably and efficiently even in the presence of a large Doppler effect and/or spread of the impulse response of the channel.

The method is remarkable in that the writing step involves a projection of the pilots onto flattened discrete two-dimensional spheroidal sequences.

Thus, the invention advantageously allows the use of a base composed of two-dimensional SSADs.

According to a particular characteristic, during the determination step, the process shall implement at least one selection step of at least some of the discrete flattened spheroidal sequences, according to at least one characteristic of the transmission channel.

Thus, the invention preferably allows the selection of two-dimensional SSADs particularly well suited to the channel, which allows for an overall improvement in its reliability.

In this way, a Doppler worst-case filter sizing and channel impulse response spread is no longer systematic since the estimate is channel-adapted.

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Thus, the invention makes it advantageous to take into account important channel characteristics present in particular in the case of communication from and/or to mobile terminals.

The process is remarkable in that the selection step involves a sub-step of sorting two-dimensional discrete flattened spheroidal sequences according to a predetermined energy criterion.

Thus, the invention considers only useful and/or necessary SSADs as advantageous, thus limiting implementation complexity while maintaining a good reliability of the estimation of the transfer function.

The method is remarkable in that the number of flattened discrete two-dimensional spheroidal sequences selected during the selection step takes into account at least one quality criterion for estimating the transfer function.

In this advantageous way, the invention allows the transfer function to be estimated in a manner appropriate to the desired quality.

The process is remarkable in that the number of discrete two-dimensional flattened spheroidal sequences selected during the selection step is less than or equal to the number of signal drivers.

The method is remarkable in that during the determination step a two-dimensional SSAD of the set is obtained by the tensor product of at least two one-dimensional SSADs.

Thus, the invention makes it advantageous to use two-dimensional SSADs by limiting complexity, by performing a sensible operation on at least two one-dimensional SSADs.

The method is remarkable in that it uses an estimation-maximization algorithm.

Thus, if the quality of the estimated channel is not sufficient, the estimation-maximisation algorithm can be improved.

The method is remarkable in that it includes at least one step in the writing stage in which at least some of the coefficients of the combination are estimated using the least squares method.

The invention also implements a method of receiving a digital signal, remarkable in that it implements a step of estimating a transfer function of a signal transmission channel according to the method of estimating the transfer function of a multi-carrier signal transmission channel.

In addition, the invention concerns a multi-port signal receiver consisting of a time sequence of symbols consisting of a set of data elements, each of which modulates a carrier frequency of the signal, the data elements comprising reference elements, called pilots, the value of which is known at the time of emission to at least one receiver intended to receive the signal, and the information data elements, representative of at least one source signal to be transmitted.

The receptor is remarkable in that it includes: means of memorizing a set of two-dimensional discrete flattened spheroidal sequences (SSAD); means of writing a transfer function of a signal transmission channel in the form of a combination of at least some of the two-dimensional flattened discrete spheroidal sequences in the set; means of two-dimensional interpolation in time and at the frequency of at least some coefficients of the combination, so as to obtain an estimate of the transfer function at any point in the time-frequency network.

The invention also relates to an application of the method of estimating the transfer function of a multi-carrier signal transmission channel to at least one of the following areas: The Commission has already adopted a proposal for a directive on the approximation of the laws of the Member States relating to the labelling of foodstuffs.

The advantages of the receiver, receiver and application of the estimation method are the same as those of the channel transfer function estimation method, they are not further detailed.

Other features and advantages of the invention will be more clearly seen by reading the following description of a preferred embodiment, given as a mere illustrative and non-limiting example, and the attached drawings, among which: Figure 1 illustrates the two-dimensional SSADs of the invention; Figure 2 illustrates the one-dimensional SSADs used to construct the two-dimensional SSADs as illustrated in Figure 1; Figure 3 illustrates the rapid decay of the eigenvalues of a one-dimensional SSAD in Figure 2; Figure 4 represents a simplified synoptic diagram of a transmitting station and a receiving station implementing two-dimensional SSADs as illustrated in Figure 1; Figure 5 presents an organization chart implemented in a channel estimation module as illustrated in Figure 4; Figure 6 illustrates a model of radio communication in itself; Figure 7 illustrates the result of the channel estimation model implemented in Figure 5 and applied in Figure 6.

The general principle of the invention is based on a two-dimensional interpolation technique for the estimation by distributed pilots and more specifically on the use of two-dimensional SSAD constraints, the number of which is adapted to the characteristics of the channel considered worst and preferably not permanently frozen depending on the propagation case.

The invention consists in using two-dimensional SSADs which can be used in particular in the case where the channel has Doppler spread and Interference between Symbols (or IES) (Doppler delay channel), such as satellite or mobile communications systems and thus allow an optimal channel estimation in the case of a multi-port system.

For a channel with impulse response spread and Doppler effect, the transfer function of the channel, locally stationary, is modeled by a two-dimensional (time and frequency) narrow-band white noise.

The estimation window has a limited size and the number of two-dimensional SSADs used is adapted to the size of the estimation window.

In these conditions, the use of two-dimensional SSADs allows a quality channel estimate to be obtained, while optimizing the number of pilots for reasonable implementation complexity.

In particular, in the two-dimensional case of the present invention, the variable channel transfer function is modeled by two-dimensional narrowband noise. The receiver generally having incomplete knowledge of the characteristics of its local oscillator and those of the two-dimensional delay-Doppler spectrum of the channel, the latter is assumed to be flat, with a bounded support, of width equal to the Doppler spread BD on the frequency axis and maximum delayed Tmax on the time axis. It is therefore modeled by a parallelepiped, corresponding to the smallest parallelepiped encompassing the actual support. This model therefore includes all possible cases of delay and Doppler.

The autocorrelation function of T(f, t), for the Doppler power spectrum defined above, is separable in time and frequency in the form: where Tmax is the maximum spread, 2fD is the Doppler spread, f is a frequency, Δf is a frequency change, t is a time, Δt is a time change and sinc is the cardinal sine function.

A block of dimension N1xN2, N1 (number of time symbols, e.g. equal to 25) corresponding to the time dimension and N2 (number of subcarriers, e.g. equal to 35) to the frequency dimension is considered. The parameters N1 and N2 are predetermined according to a given complexity and/or according to a compromise between the complexity and the desired reliability of the estimation.

Due to the time and frequency separability of the channel, these two-dimensional SSADs are defined as the tensor product of one-dimensional SSADs.

In fact, 2D (i.e. two-dimensional) SSADs, defined in this way, allow decorrellated channel decomposition coefficients to be obtained:

Let Rc be the covariance tensor of the channel, defined by: with: i and k being taken from 1 to N1 and j and l being taken from 1 to N2;ckl* representing the conjugate of the complex value ckl;the function E[x] representing the expectation or the mean of the variable x; andthe complex vector c to be estimated representing here an implementation of the two-dimensional discrete channel at the level of the data stream emitted, and being composed of N1.N2 complex coefficients cij.

The channel is separable, which is equivalent to writing that the tensor Rc is the tensor product of the covariance matrices corresponding to each of the time and frequency dimensions: Where is it? R (t) = {sin c (t) ∈ J (t) ∈ Tmax}jl; and where R (t) = {sinc (t) ∈ 2π (t) ∈ K (t) ∈ FD (t) ∈ I).

The discrete channel decomposition coefficients on the basis of SSAD-2D are therefore decorrelative.

It can be shown that the SSAD-2Ds thus constructed are indeed the eigenvectors of the order 4 covariance tensor of the two-dimensional channel.

It is possible to find an orthonorm base of the complex space at N1.N2 dimensions CN1.N2, whose normalized vectors i = 1..N1 and j = 1..N2 (the notation x = a..b meaning that the values of x are taken from a to b) are the eigenvectors of the covariance tensor.

The family of two-dimensional SSADs is therefore the family Where: the ortho-normed two-dimensional SSADs are the matrices and the associated eigenvalues are: λ(1,i), λ(2,j) with: two families of one-dimensional SSADs on the temporal and frequency dimensions respectively, and their associated eigenvalues.

The sequences are time sequences of standard bandwidth-limited size N1 [-WpWt] and the sequences are standardised bandwidth-limited frequency sequences of size N2 [0 ; 2Wf], with ${\text{W}}_{\text{t}}{\text{= f}}_{\text{D}}{\text{×τ}}_{\text{0}}\text{et}{\text{W}}_{\text{f}}\text{=}\frac{{\text{T}}_{\text{max}}{\text{×ν}}_{\text{0}}}{\text{2}}$

The vectors corresponding to the time dimension are equal to the restriction of the N1 SSADs, real time discrete sequences of N1 dimension and with a standardised limited band [-Wt;Wt] most concentrated on the discrete interval The most concentrated SSADs are by definition the SSADs with the largest energies over the range considered.

Similarly, the vectors corresponding to the frequency dimension are equal to the restriction of the N2 SSADs, real discrete frequency sequences of N2 dimension and with a standardized limited band [0 ; 2Wf] most concentrated on the discrete interval. corresponding to the frequency support restriction of the transmitted block.

The decomposition coefficients of the two-dimensional discrete channel are then given by:

For the sake of clarity, a simple indexing is now used:

The choice of good one-dimensional functions therefore allows for the construction of good two-dimensional interpolation functions.

Only the most concentrated SSADs are needed to describe the channel.

According to the preferred embodiment, the most concentrated N' SSAD-2D is obtained by calculating the N1 (respectively N2) eigenvalues λ(1,i) (respectively λ(2,i)) in the time dimension (respectively frequency) and then selecting the highest N' values of the products λij = λ(1,i).λ(2,j.

According to a less complex but less good estimating variant (for a given number of selected 2D SSADs) than the preferred mode of implementation, the selection is simplified by first selecting the highest N1 values for λ(1,i) and the highest N2 values for λ(2,j) to obtain N' (equal here to N'1.N'2) values giving the most concentrated SSAD-2Ds.

The estimate of the channel is therefore: $\underline{\underline{\hat{\text{c}}}}{\text{}}^{\text{(N')}}\text{=}\underline{\underline{\text{c}}}\text{+}\underline{\underline{\text{n}}}{\text{}}_{\text{c}}$ where nc is the estimation noise.

By analogy with the signal-to-noise ratio, the following quality criterion for the estimation is defined: where . defines the norm of a matrix.

So we could write:

In the first step of the estimation algorithm, the coefficients are obtained by projecting the reference symbols onto the preserved SSADs.

In a preferred mode of implementation, reference symbols are projected onto the stored SSADs without the EM (Estimation - Maximisation) algorithm described below.

However, in order to optimise the channel estimation for arbitrary reasons of synchronisation and taking into account all or part of the coded structure of the data emitted, a variant estimation-maximization algorithm is implemented similar to that described in FR 2 747 870 (on behalf of the same applicants and entitled Multiple reference block digital signal for channel estimation, channel estimation processes and corresponding receivers ).

For example, the case of a model of type Vehicular B at 250 km/h , where fD is close to 930 Hz, Tmax is 20 μs, τ0 is equal to 133.33 μs and υ0 to 3.75 kHz, is shown in Figure 1. It is inferred that time is limited to an interval [-Wt+,Wt] where Wt is equal to 0.0622 and that frequencies are limited to an interval [0,+2Wf] where Wf is equal to 0.0375.

The obtaining of one-dimensional SSAD families will now be detailed.

Consider the case of the time dimension (the case of the frequency dimension being quite similar).

The complex vector c corresponding to the time dimension to be estimated here, representing a discrete channel realization at the output data stream, is composed of N (equal to N1) complex coefficients cn.

It is possible to find an orthonorm base of the complex space of N dimensions CN, whose normalized vectors {p(i)}, i = 1..N are the eigenvectors of the covariance matrix of c associated with the eigenvalues {λi}, i = 1..N.

The Doppler spectrum of the latter channel is assumed to be flat, with a finite support, of width equal to the Doppler spread BD = 2fD, fD representing the maximum Doppler frequency.

These vectors are in this case equal to the restriction of N SSADs, discrete real sequences of dimension N and with a standardized limited band [-W';W'] where W'= Wt = fD×τ0 the most concentrated on the discrete interval {n} $\frac{\text{N-1}}{\text{n=0}}$ The most concentrated SSADs are by definition the SSADs with the highest energies over the given interval, so only the N SSADs with the highest energy are retained and the others are excluded.

In other words, yes. where the bi-factors are independent complex Gaussian random variables verifying the following relations: The variance of the bi variables is λ2:E[|bi|2] = λiThe covariance between bi and bj, i and j being different, is zero:E[bi.bj*] = 0 si i≠jwhere the variable bj* is the conjugate of the complex variable bj

The basic vectors (i.e. the SSADs that have been preserved) are given by the relation: $\text{E}\text{[}\underline{\text{c}}\text{.}\underline{\text{c}}{\text{}}^{\text{H}}\text{]}\text{.}\underline{\text{p}}{\text{}}^{\text{(i)}}\text{=}{\text{λ}}_{\text{i}}{\text{p}}^{\text{(i)}}$ where (.) H is the vector's transposition-conjugation operator (.).

The vectors {p(i)}, i = 1..N verify the following system of equations: This corresponds to the definition of standardised N-size and standardised band SSADs [-W'; W'].

For illustration, Figure 2 gives an example of one-dimensional SSADs. According to this example, the 25 (N is 25) SSADs with the highest energy have been selected. On Figure 20, the three SSADs 21, 22 and 23 with the highest energy have been chosen to be represented, whose amplitude (axis of orders) is given in terms of time (axis of abscisses whose scale is in standardized units, i.e. in number of time symbols). The concentration or energy of SSADs depends on the eigenvalues: the greater the module of a eigenvalue corresponding to an SSAD, the greater the energy of the corresponding SSAD is also.

Since the concentration of an SSAD is equal to the nth eigenvalue λn of the covariance matrix of c, relation (1) shows that only the most concentrated SSADs are needed to describe the channel.

The paper Prolate Spheroidal Wave Function, Fourier Analysis and Uncertainty-I by D. SLEPIAN and H. O. POLLAK published in the journal The Bell System Technical Journal in January 1961 shows that these eigenvalues decrease very sharply and vanish rapidly, after a number of 2W'N values. It is noted that according to the example illustrated in Figure 3, the product of 2W'N is 3.1 for a value of W' and N equal to 0.062 respectively and that in fact the eigenvalues expressed in dB (i.e. a decog value scale of type 10L λ2/02) represent a λ and λ0 where λ are the highest value after this threshold equal to 3.0.1.

The SSAD family is orthogonal, however, nothing ensures the orthogonality of the sub-sampled SSADs, so the projection of the reference symbols on these SSADs gives an approximation of the channel decomposition.

The three steps in the channel estimation are: the receiver calculates, from N' reference symbols of the modulated block, the di coefficients corresponding to the channel decomposition on the reduced family of N' SSAD.wi =λiλi + N0NcEsNc (N0) being the channel variance (additive noise) and Es the energy of the transmitted reference symbols, the decomposition coefficients are estimated as follows:bˆi = wi di i = 1...N'To improve the estimates obtained, the EM algorithm detailed in the aforementioned FR 27 47870 patent uses not only the reference sub-carriers but also the useful carriers, in order to improve the quality of the estimator in the sense of the maximum probability criterion a posteriori (MAP).The receiver then determines an estimate of the channel by preserving an interpolation by the stored SSADs.

The reader may refer to the aforementioned patent FR 27 47870 for more details on the implementation of single dimensional SSADs.

A method of carrying out the channel estimation according to the invention is shown in relation to Figure 4.

Figure 4 shows in simplified form:a transmitting station 41 of a signal formed of modulated data streams according to the invention; a transmission channel 42 of the emitted signal; and a receiving station 43 of the emitted signal implementing, inter alia, a channel estimation according to the invention.

The transmitting station 41 includes in particular an information source 411 of arbitrary rate generating binary data or not corresponding to source signals of any type (sounds, images, data, etc.).

The coded data generated from these codes (useful symbols) are then organized into data trains, and modulated (413). They are therefore appropriately distributed and interlaced over several data trains in order to bring about the necessary diversity and decorate the fading affecting the transmitted symbols. Reference elements are also introduced into each data train, according to the distribution principles specified by the specification. Finally the data are modulated according to a modulation of the type OFDM/QAM (from English Quadrature Amplitude Modulation ) (for example, OFDM with block interval) or OFDM/OQ (from English Offset Quadrature Amplitude ) (for example, modulation).

The signal is then translated into frequency, amplified and emitted by the 414 transmitter through channel 42.

Channel 42 is any radio transmission channel, for example, when passing through channel 42, the signal is noisy and subjected to multiple paths, interference, or Doppler effect.

The wireless transceiver generally models the channel to optimize coding/decoding and modulation/demodulation.

Here, according to a model of this channel, the channel is considered to be subject: a white Gaussian noise characterised by a signal/noise ratio or SNR (Signal/Noise Ratio) supposedly known; the Doppler effect, whose power spectrum is normalised by a parallelepiped of standardised half-bands Wt and Wf, and an expansion of the impulse response (related in particular to multiple paths resulting from signal reflections on environmental elements (e.g. buildings)).

Err1:Expecting ',' delimiter: line 1 column 166 (char 165)

In receiving station 43, the input floors are conventional. Receiver station 43 receives the signal emitted by transmitting station 41 and transmits through channel 42. The signal corresponding to a received data stream is preamplified 431, then converted to intermediate frequency to achieve appropriate channel 432 filtering. The intermediate frequency signal is then converted to base band on two square tracks, then sampled (437).

The samples corresponding to a data stream are used by the receiver to determine a detailed estimate 438 later.

This estimate allows a reliable demodulation of 439 samples.

The demodulated data is then decoded, possibly un-interlaced to be delivered to the recipient 434.

In addition, the channel estimation allows automatic gain correction (GAC) 435, which controls preamplification 431.

The assumption here is that the data trains are short, no synchronization is required, and for long data trains, a sample-based synchronization allows for proper synchronization on the transmitted symbols and/or the data train itself to properly sample the received signal.

The estimate of channel 438 according to the invention will now be detailed according to the organisational diagram described in Figure 5.

During an initialization step 51, two-dimensional SSADs appropriate to the channel type used are determined using the following method.

It is assumed that the system parameters (i.e. time symbol τ0 and spacing between subcarriers v0) have been chosen so that channel 42 can be considered as nearly constant at the scale of an OFDM mesh (τ0, v0) (an OFDM mesh corresponds to the surface dimension τ0 in time and ν0 in frequency of the time-frequency network), namely: Where is it? Bc is the coherence band of the channel; and Tc is the coherence time of the channel. (the symbol << meaning is much less than )

The channel then behaves as a multiplicative channel, characterized by an amplitude and a phase, corresponding to the value of T (f,t), the variable transfer function of the channel, for the moment and the frequency considered.

For the mesh corresponding to a symbol transmitted am,n, we have: Tf,t = Tf,n,n,t0 andτf,n,n,t0 = ρm,neiθm,n where ρ is an amplitude and θ is a phase.

Either the following matrix notation: - What? matrix of binary symbols issued sample matrix received at the demodulator output discrete channel coefficient matrix The discrete channel is modeled by the relation: $\underline{\underline{\text{r}}}\text{=}\underline{\underline{\text{c}}}\text{•}\underline{\underline{\text{a}}}\text{+}\underline{\underline{\text{n}}}$ where the operator • represents the forward forward term product.

Or in an equivalent way, the channel being locally assimilated to a multiplicative channel: ${\text{r}}_{\text{m,n}}\text{=}{\text{c}}_{\text{m,n}}{\text{a}}_{\text{m,n}}\text{+}{\text{n}}_{\text{m,n}}$

The aim is to determine the values cm,n.

It is recalled that reference symbols are inserted in the block to be transmitted before the OFDM modulator and that these symbols are regularly distributed in the time-frequency plane.

The characteristics of the propagation channel, i.e. maximum (bilateral) Doppler diffusion and maximum (unilateral) delay, are assumed to be known (e.g. these values can be estimated from a channel model and/or measured).

It is assumed that the Doppler Power Spectrum of the channel is modelled by a standardised half-band parallelopeped Wt and Wf (as specified in the description of the general principle of the invention): ${\text{W}}_{\text{t}}{\text{=f}}_{\text{D}}{\text{× τ}}_{\text{0}}$ and ${\text{W}}_{\text{f}}\text{=}\frac{{\text{T}}_{\text{max}}{\text{×ν}}_{\text{0}}}{\text{2}}$

One-dimensional SSADs corresponding to these standard bands are pre-calculated: According to the time dimension: R (N, Wt) is the covariance matrix of dimension N (corresponding to the time dimension of the treated block) of a 2Wt standardised band complex white noise,Rm,n = 2Wt sin(2πWt (m-n))The 1D (i.e. one-dimensional) SSADs corresponding to the time dimension are defined as standardized eigenvectors of the matrix R(N, Wt), ordered in ascending order of their eigenvalues. We do the same thing: R (N, Wf) is the covariance matrix of dimension N (corresponding to the frequency dimension of the treated block) of a white noise complex of standardized bands 2Wf,Rm,n = 2Wf sin(2πWf(m-n))The 1D SSADs corresponding to the frequency dimension are defined as standardized eigenvectors of the matrix R(N,Wf), ordered in ascending order of their eigenvalues.

The 2D (i.e. two-dimensional) SSADs are then constructed by term-to-term multiplication of a 1D SSAD corresponding to a time dimension and a 1D SSAD corresponding to a frequency dimension: Pi,j = PiPjT; andλi,j = λi.λj. where: Pi,j defines a two-dimensional SSAD of eigenvalues λi,j,Pi and Pj corresponding to one-dimensional SSADs of respective eigenvalues λi and λj (simplified notations for greater legibility).

The SSADs obtained are selected from the SSADs with the highest energies.

In a first embodiment, the number of selected 2D SSADs is predetermined and is, for example, in the order of 25.

In a second embodiment, the number, N', of 2D SSADs selected is such that the quality factor defined as the ratio of the sum of the own values to the sum of the rejected own values is greater than a given quality factor Q0 (e.g. of the order of 30 dB).

Thus, for a time-frequency block of a given size and propagation channel characteristics, the number of two-dimensional SSADs required to interpolate the complex gain of the channel is generated from the estimate of this complex gain obtained at the locations of the pilot symbols.

Thus, during initialization step 51, the selected two-dimensional SSAD parameters are stored in the channel 438 estimation module of the receiving station.

Note that two-dimensional SSADs can be considered when designing the channel 438 estimation module and used statically during a channel estimation.

In a more complex variant (the complexity remaining reasonable, given the construction of the 2D SSADs obtained by the tensor product of two 1D SSADs), the 2D SSADs are determined dynamically by the channel 438 estimation module.

In this variant, the SSAD-2Ds to be used are chosen according to the characteristics of the propagation channel (in particular the maximum propagation time measured from the time between the reception of a first symbol and the last echo corresponding to that symbol).

Then, in a step 52, receiving station 43 waits and receives blocks of data to be demodulated, including pilots for channel estimation.

Then, in a combination writing step 53, a projection of the pilots is made onto the selected two-dimensional SSADs.

To make this projection, the coefficients (di) i=1,...,K of the channel decomposition in the space of the 2D SSADs are first calculated from the reference symbols (ai) i=1,..,K transmitted: where: N is the number of SSADs retained; K is the number of pilots; p is a 2D SSAD (N ' 2D SSADs retained) and p# is its pseudo-inverse , which is:

The number of pilot symbols used must be greater than or equal to the number of N' of SSADs retained.

Pseudo-reversals are stored in a non-volatile memory (ROM) of the receiving station, for each processed block size (an estimation window size is usually defined corresponding to the size of the smallest block that can be transmitted) and each propagation environment.

The channel being noisy and the SNR (Signal/Noise ratio) assumed to be known, an estimate of the coefficients (ai) i=1,..,K of the channel decomposition in the 2D SSAD space is obtained by the method of least squares (MMC) ${\text{â}}_{\text{i}}\text{=}\frac{{\text{λ}}_{\text{i}}}{{\text{λ}}_{\text{i}}\text{+}\frac{{\text{N}}_{\text{0}}}{{\text{E}}_{\text{s}}}}{\text{d}}_{\text{i}}$ λi is the eigenvalue of the first 2D SSAD; N0 is the noise variance; and E is the energy of the pilots at the reception.

The estimate of the channel Ĉ is then given by the equation:

Then, in step 54, the channel estimation module 438 performs an estimation of the channel transfer function by interpolating the estimation performed on the drivers, because the driver symbols, known to the receiver, allow a discrete channel decomposition to be obtained on the basis of 2D SSADs.

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The precise characteristics of the channel are as follows: The channel is rural-type. The Doppler spectrum is horned (spectrum corresponding to the power spectrum of a pure sinusoid after propagation in a moving channel with supposedly isotropic reflections). Delays (due to multiple paths) are summarized in the following table:

Retard en nsec	Atténuation en dB
0	-2.5
300	0 i
8900	-12.8
12900	-10.0
17100	-25.2
20000	-16.0

The modulation is OFDM/IOTA type modulation with the following parameters: The IOTA symbol time is 133.33 μs; and the spacing between subcarriers is 3.75 kHz.

The channel's supposed to be quiet.

Figure 7 shows the same channel as shown in Figure 6 but estimated according to the invention using 2D SSAD.

The characteristics of the 2D SSADs are as follows: the number of 2D SSADs retained is equal to 25 the step of the time-pilot symbols is equal to 5 (which gives four useful symbols for a time reference symbol) the step of the frequency-pilot symbols is equal to 8 (which gives seven useful symbols for a frequency reference symbol)

It is noted that the channel according to the model described in Figure 6 and its estimate according to the invention are very similar.

Of course, the invention is not limited to the examples of realizations mentioned above.

In particular, the professional can make any variation in the type of multiport modulation, in particular OFDM, which can be, for example, OFDM/QAM or OFDM/OQAM.

It is also noted that the invention has applications in a wide range of fields, in particular where high spectral efficiency is desired and the channel is highly non-stationary, in particular where the use of multi-port modulation techniques proves to be a sensible choice.

A first category of applications concerns digital terrestrial broadcasting (e.g. DAB (from English Digital Audio Broadcasting or Digital Audio Broadcasting in French) or DVB-T), whether it is image, sound and/or data.

The invention may be used in particular in high-speed digital communication systems from or to mobile phones (e.g. according to third generation mobile communication standards) and in high-speed local area networks using multi-port modulation techniques.

A third category of applications is underwater transmissions for which multi-port modulation techniques are well suited.

In general, the invention therefore has applications in all areas where multi-carrier modulation techniques themselves have applications (e.g. in systems combining CDMA ( Code Division Multiple Access or, in French, Multiple Access by Code Distribution ) and OFDM (in particular, MC-CDMA meaning Multi-Carrier CDMA or, in French CDMA with multiple carrier ).

Claims (13)

1. Method for estimating the transfer function of a channel (42) for transmission of a multicarrier signal formed by a chronological succession of symbols consisting of an ensemble of data elements, each of the said data elements modulating one carrier frequency of the said signal,    the said data elements comprising on the one hand reference elements, referred to as pilots, of which the value at transmission is known by at least one receiver (43) intended to receive the said signal, and on the other hand so-called information elements representing at least one source signal to be transmitted,    characterised in that it comprises:

   - a step of determining a set of two-dimensional discrete prolate spheroidal sequences (DPSS);

   - a step (53) of writing the said transfer function in the form of a combination of at least some of the said two-dimensional discrete prolate spheroidal sequences in the said set;

   - a step (54) of two-dimensionally interpolating at least some coefficients of the said combination in time and in frequency, so as to obtain an estimate of the said transfer function at any point of a time-frequency space.
2. Method according to Claim 1, characterised in that the said writing step (53) employs a projection of the said pilots onto the said two-dimensional discrete prolate spheroidal sequences.
3. Method according to either one of Claims 1 and 2, characterised in that during the said determination step, it employs at least one step of selecting at least some of the said discrete prolate spheroidal sequences (DPSS) as a function of at least one characteristic of the said transmission channel (42).
4. Method according to Claim 3, characterised in that the said characteristics of the transmission channel (42) comprise the maximum Doppler frequency (f _d ) and/or the maximum spread (T _max ) of the impulse response of the channel (delay spread).
5. Method according to either one of Claims 3 and 4, characterised in that the said selection step employs a substep of sorting the said two-dimensional discrete prolate spheroidal sequences (DPSS) as a function of a predetermined energy criterion (Q _o ) .
6. Method according to any one of Claims 3 to 5, characterised in that the number of two-dimensional discrete prolate spheroidal sequences selected during the said selection step takes into account at least one criterion relating to the quality of estimation of the said transfer function.
7. Method according to any one of Claims 3 to 6, characterised in that the number (N') of two-dimensional discrete prolate spheroidal sequences selected during the said selection step is less than or equal to the number of pilots (K) of the said signal.
8. Method according to any one of Claims 1 to 7, characterised in that during the said determination step, a two-dimensional DPSS in the said set is obtained by tensor multiplication of at least two one-dimensional DPSSs.
9. Method according to any one of Claims 1 to 8, characterised in that it employs an estimation maximisation (EM) algorithm.
10. Method according to any one of Claims 1 to 9, characterised in that during the said writing step, it comprises at least one step of estimating at least some coefficients of the said combination by using a least squares method.
11. Method for receiving a digital signal, characterised in that it employs a step of estimating a transfer function of a channel for transmission of the said signal according to the method of any one of Claims 1 to 10.
12. Receiver (43) for reception of a multicarrier signal (42) formed by a chronological succession of symbols consisting of an ensemble of data elements, each of the said data elements modulating one carrier frequency of the said signal,    the said data elements comprising on the one hand reference elements, referred to as pilots, of which the value at transmission is known by at least one receiver intended to receive the said signal, and on the other hand so-called information elements representing at least one source signal to be transmitted,    characterised in that it comprises:

    - means for storing a set of two-dimensional discrete prolate spheroidal sequences (DPSS);

    - means for writing a transfer function of a channel for transmission of the said signal in the form of a combination of at least some of the said two-dimensional discrete prolate spheroidal sequences in the said set;

    - means for two-dimensionally interpolating at least some coefficients of the said combination in time and in frequency, so as to obtain an estimate of the said transfer function at any point of the time-frequency space.
13. Application of the estimation method according to any one of Claims 1 to 11 to at least one of the following fields:

    - terrestrial digital radio broadcasting;

    - digital radiocommunication;

    - submarine data transmission.