FR3024806A1 - METHOD AND DEVICE FOR RECEIVING SIGNALS - Google Patents

Abstract

The method of receiving signals resulting from the transmission on a MIMO channel of T symbol streams from a STBICM comprises: - the determination for each coded bit (dt, l, q) used to label a symbol, of several groups of symbols (S1, S2, S3) each comprising symbols selected from T symbols of the T streams and including the symbol labeled with the coded bit; for each group determined for a coded bit: estimating the symbols of this group from the received signals, comprising eliminating the interferences affecting the group of symbols by applying an MMSE criterion; ○ the detection of the coded bit from the estimates of the symbols of the group, comprising an elimination by application of a MAP criterion of a residual interference affecting the coded bit generated by the symbols of the group, and an estimate of a likelihood (λ (m) Φs, t → dt, l, q) of the coded bit; and obtaining a combined likelihood (λ (f) Φ → dt, l, q) for each coded bit by combining the estimated likelihoods on this coded bit for the groups determined for this bit.

Description

BACKGROUND OF THE INVENTION The invention relates to the general field of digital communications. It relates more particularly to a method and a signal receiving device resulting from the transmission of a plurality of coded, interleaved and modulated data streams over a multiple input and multiple output (or MIMO channel for "Multiple Input") transmission channel. Multiple Output "). The data are, for example, symbols resulting from the application of coded modulation with binary spatio-temporal interleaving over a plurality of information bits, also known as STBICM modulation for "Space Time Bit Interleaved Coded Modulation", and sent via a plurality of transmitting antennas on a propagation channel to a receiving device equipped with a plurality of receiving antennas. The use of advanced receivers is necessary to maximize the spectral efficiency and power of radio access techniques used today in wireless communications systems. Indeed, each multiple access technique, although initially designed to limit the complexity of the receivers, inevitably reintroduces, in the race towards ever greater spectrum and power efficiencies, new sources of interference that must be eliminated. . For example, LTE (Long Term Evolution) communication systems use an Orthogonal Frequency Division Multiple Access (OFDMA) technique which in theory cancels the intra-frequency interference. Cell type Interference Between Symbols or IES (or ISI for "Inter Symbol Interference"). However, the use by these multiple antenna systems in transmission and reception reintroduces spatial intracellular interference or MAI (for "Multiple Antenna Interference").

The use of multiple transmit and receive antennas makes it possible, according to information theory, to increase the degree of freedom (DOF) of the radio propagation channel. More specifically, with a moderate signal-to-noise ratio, the use of multiple antennas makes it possible to increase the capacity of the channel by simultaneously transmitting coded data streams on the same radio resource (ie during the same use of the channel). independent modulated. We also speak of spatial layers. Techniques based on this principle are called MIMO single-user or SU-MIMO (for "Single User MIMO") if all spatial layers are dedicated to the same user, or MIMO multi-users or MU-MIMO (for " Multi User MIMO ") if the spatial layers are dedicated to different users or come from different users.

The interference appearing between the different spatial layers can be eliminated by means of effective treatments implemented in transmission (eg via precoding) and / or in reception. The processing implemented in transmission is generally based on the existence of a limited return path between the receiver and the transmitter. This return channel 3024806 2 allows the receiver to transmit to the transmitter information representative of the state of the propagation channel between the transmitter and the receiver. This information is then used by the transmitter to reduce the interference between the different spatial layers, for example by adapting a precoding matrix applied in transmission. Thus, the information sent back by the sender may include an index of a precoding matrix to be applied by the sender. Due to the limited nature of the return path between transmitter and receiver, residual interference is still present at the receiver despite the application of the transmit precoding matrix. The cancellation of this residual interference can substantially increase the spectral efficiency of the system as well as its efficiency in terms of power, especially when large numbers of transmitting and receiving antennas are used. As an illustration, in LTE type communication systems, schemes based on 8 transmit antennas and 8 receive antennas are envisaged today. For these large MIMO systems, the efficiency of advanced receivers is essentially limited by their complexity. Thus, in particular, the Maximum Likelihood (ML) criterion recommended by the detection theory for optimally detecting the information bits associated with the symbols belonging to the different spatial layers is of such complexity. that its direct implementation is impossible to achieve in practice (its complexity varies indeed exponentially depending on the number of bits of information to be transmitted).

In order to reduce the complexity of the receivers of the MIMO systems, one solution consists in detecting and decoding the spatial layers separately, but in an iterative manner according to a so-called "turbo" principle. More specifically, according to this principle, the decoding provides, at the end of an iteration, extrinsic or a posteriori information on the symbols of the spatial layers to be detected, which are then used as information a priori on these symbols when they are detected at a distance. next iteration. This principle relies on the use of bit interleaving in the transmission scheme between so-called channel coding and modulation. Such interleaving is found in the case of linear coded and interleaved bitwise modulations with linear precoding (STBICM-LP) or without (STBICM), commonly used in industry. The most efficient algorithm for performing the actual detection of the spatial layers relies, in known manner, on the criterion of Maximum A Posteriori or MAP. The complexity of implementation of this criterion, however, quickly becomes inextricable: it is indeed exponential as a function of the number of spatial layers and the number of bits encoded per symbol considered. This is why there is today abundant literature on iterative receivers of reduced complexity, sub-optimally implementing the MAP criterion or adopting instead of the MAP criterion an LMMSE criterion (for "Linear Minimum Mean Square Error"). ") Of minimum mean squared error. This LMMSE criterion, combined with the use of prior information (or considered as such), is also known as LMMSE with Interference Cancellation or LMMSE IC (for "LMMSE Interference Cancellation").

The document by R. Visoz et al. entitled "A New Class of Iterative Equalizers for SpaceTime BICM Over MIMO Fading Block Multipath AWGN Channel," IEEE Transactions on Communications, vol. 53, No. 12, Dec. 2005 (hereinafter D1), presents an iterative equalization method for space-time communications on MIMO channels (N transmit antennas and R on receive), block fading and intersymbol interference. This method relies on a separation of the temporal equalization, intended to eliminate the inter-symbol interference (IES), of the spatial equalization, intended to eliminate the interference between antennas (MAI). More precisely according to this method, the equalization is performed on multivariate modulated symbols by application of the LMMSE criterion. These multidimensional modulated symbols result from a predetermined partition of all the N modulated symbols intended to be transmitted simultaneously on the N transmit antennas of the system (in other words N spatial layers), this partition designated by [Ai, i = 0,, N, - 1) where N, denotes an integer such that N1 N, distributing the N modulated symbols in several groups of symbols whose indices are given by sets Ai. The equalization performed then consists in canceling the interference between symbols (IES), and the interference between antennas (MAI) between the different groups of multidimensional symbols defined by the partition. At the output of this equalization, a Gaussian approximation can be made on the distribution of residual interference and thermal noise affecting the coded symbols of the group in question.

This Gaussian approximation can be reduced to a conventional MIMO detection scenario for which very effective detection techniques are known. Spatial equalization is thus performed in a second step to eliminate the residual spatial interference (MAI) within each group of symbols defined by the partition, preferably based on the MAP criterion or on a suboptimal implementation of this criterion. criterion.

This two-step equalization is combined with so-called channel decoding and implemented iteratively. When the MAP criterion is used in combination with the LMMSE criterion, this equalization technique achieves substantial performance gains over conventional iterative EQ techniques based solely on the MMSE criterion.

These performances however depend on the choice of the partition of the symbols {Ai, i = 0,..., N, -1} considered for the LMMSE equalization. Thus in D1, the partition defined by N, = 1 and Ao = {0,1, N - leads to obtaining significant gains in terms of performance, but at the cost of a significant computational complexity. The document by R. Visoz et al. entitled "Frequency-Domain Block Turbo-Equalization 35 for Single-Carrier Transmission over MIMO Broadband Wireless Channel", IEEE Transactions on Communications, vol. 54 No. 12, December 2006, hereinafter D2, is based on a similar principle and proposes a method for choosing a partition from the observation of the Gram matrix of the propagation channel. According to this method, a partition is chosen according to which the most correlated components of the Gram matrix are grouped together within the same group. However, although very effective due to the combined exploitation of the LMMSE and MAP criteria, the equalization method proposed by R. Visoz et al. remains distant in terms of the performance of the theoretical capacity fixed by criterion ML. OBJECT AND SUMMARY OF THE INVENTION The invention makes it possible in particular to come closer to this terminal by proposing to add an additional degree of freedom to the receiver. More specifically, the invention is directed to a method for receiving signals resulting from the transmission, on a multi-input and multiple-output propagation channel, of T symbol streams resulting from the application of a coded inter-space coding modulation. temporally binary over a plurality of information bits, T designating an integer greater than (strictly) 1, this method comprising: a step of determining, for each coded bit used to label a symbol of a stream, of a plurality of groups of symbols, each group comprising a plurality of symbols selected from T symbols respectively belonging to the T streams, this plurality of symbols including the symbol labeled with the encoded bit; for each group of symbols determined for a coded bit: a step of estimating the symbols of this group from the received signals, this estimation step comprising an elimination of the interferences affecting the group of symbols by applying a criterion of minimum mean squared error; a step of detecting the coded bit from the estimates of the symbols of the group, this detection step comprising an elimination by application of a criterion of Maximum a Posteriori of a residual interference affecting the coded bit generated by the symbols of the group , and an estimate of a likelihood value of the encoded bit; and a step of obtaining a combined likelihood value for each encoded bit by combining the estimated likelihood values on that encoded bit for the plurality of groups of symbols determined for that encoded bit.

Correspondingly, the invention also relates to a device for receiving signals resulting from the transmission, on a multi-input and multiple-output propagation channel, of signal flows resulting from the application of a coded modulation with spatial interleaving. binary time over a plurality of information bits, where T denotes an integer greater than 1, this device comprising: a determination module able to determine, for each coded bit used to label a symbol of a flow, a plurality of groups of symbols, each group comprising a plurality of symbols selected from T symbols respectively belonging to the T streams, this plurality of symbols including the symbol labeled with the encoded bit; Estimation and detection modules, activated for each group of symbols determined for a coded bit, and such that: said estimation module is able to estimate symbols of this group from the received signals, eliminating interference affecting the group of symbols by applying a minimum mean squared error criterion; said detection module is able to detect the coded bit from the estimates of the symbols of the group by eliminating, by applying a criterion of Maximum a Posteriori, a residual interference affecting the coded bit generated by the symbols of the group, and estimating a likelihood value of the coded bit; and a combined likelihood value obtaining module for each encoded bit adapted to combine the estimated likelihood values on that encoded bit for the plurality of groups of symbols determined for that encoded bit. It should be noted that for the purposes of the invention, the term "maximum a posteriori" or "MAP" is understood to mean the application of this criterion in the strict sense of the term or a suboptimal implementation of that criterion. -this. The additional degree of freedom provided by the invention therefore comes from the combination of a plurality of estimated likelihood values for the same coded bit and from the application of a MAP type detector to several groups of "intersecting" symbols. (that is, which include common symbols). The MAP criterion is used to eliminate residual interference on the encoded bit generated by the symbols of the group to which it is applied. Each of the groups determined for a coded bit comprises at least two symbols from two distinct spatial layers. Each group can be of fixed cardinality. The number of groups considered for each coded bit depends on a compromise complexity versus performance. Thus, for a cardinality and a number T of given flows, all the groups constructed on the T streams having this cardinality can be considered exhaustively or only by selecting a subset from criteria similar to those recalled previously and described in D2 (eg groups built from the most correlated columns of the Gram matrix). The invention thus proposes to adopt a "divide and conquer" strategy. On the one hand, the interference generated by the modulated symbols within a group can be handled effectively using the MAP criterion (implemented in optimal or suboptimal form). And on the other hand, the interference generated by the symbols of the other spatial layers not included in this group is eliminated using a linear receiver of low complexity implementing the LMMSE criterion.

The combination of the estimated likelihoods for a given coded bit from different overlapping groups of symbols, i.e. sharing at least one and the same symbol labeled with the encoded bit, allows diversity to be introduced, and by this bias, to get closer to the performance of a receiver (ie global detector) optimal type ML or MAP. It should be noted that the optimal receiver has much better performance than an LMMSE receiver when the number of spatial layers is greater than the number of receiving antennas, the MIMO propagation channel is spatially correlated, and / or when the spectral efficiency envisaged is very high (for example because of a high coding efficiency, that is to say close to 1, of a high modulation order, and / or of a large number of spatial layers ). Such hypotheses correspond to scenarios for which the invention has a privileged application.

Thus, the invention is not limited to the selection of a single partition as in D1 or D2 according to a criterion which may be difficult to determine. On the contrary, the invention proposes to define a plurality of partitions in the sense of D1 for each coded bit, each of these partitions defining two distinct and disjoint groups of symbols, namely a first group of symbols belonging to distinct spatial layers and comprising the symbol labeled by the coded bit considered, and a second group formed by the symbols belonging to the spatial layers not selected to belong to the first group. For each of the partitions chosen for a coded bit, the first group advantageously comprises the symbol labeled by this coded bit. In other words, there is overlap between the first groups defined by the different partitions, and each of them can provide substantial and complementary information on the coded bit considered. The invention therefore makes it possible to exploit, through this cross-check and the combination of estimated likelihoods from each first group of each partition, a new degree of freedom with respect to the equalization schemes proposed in D1 and D2. According to one embodiment, the likelihood values can be combined with each other according to a maximum ratio combining principle or MRC (for "Maximal Ratio Combining"). According to a first variant of this embodiment, the combined likelihood value for a coded bit results from a sum of the likelihood values (if the likelihoods are homogeneous with logarithmic ratios of probabilities) estimated on this bit coded for plurality. groups. In other words, the likelihood values are combined as if they were statistically independent. This first variant is particularly easy to implement and applies to any type of channel, both ergodic and non-ergodic. According to a second variant, the obtaining step comprises a prior step of bleaching the likelihood values before combining them to obtain the combined likelihood value. This second variant makes it possible to take into account the correlation of the likelihood values used to obtain the combined likelihood value. It is particularly suitable for a non-ergodic propagation channel, which represents most of the propagation channels encountered in practice. Indeed, since the likelihood values corresponding to the different groups associated with the same coded bit are evaluated from the same observations (i.e. signals received by the receiving device), they are statistically dependent. However, the maximum ratio combining principle or MRC is based on the assumption that the statistical distribution of the likelihood values that are combined follows a Gaussian Additive White Gaussian Noise (AWGN) binary channel model. ). In other words, the vector whose components respectively correspond to the values of the likelihoods before being combined is considered to be a binary AWGN channel with a single input and multiple outputs. Since these values are in practice correlated with each other, the application of a whitening filter to this channel makes it possible to more effectively combine the likelihood values according to an MRC principle. The invention is not limited to a combination principle of MRC type. Thus, for example, the combination of likelihood values can also be done according to a Bayesian combination principle. In a particular embodiment, the reception method further comprises a step of decoding the coded bits using the combined likelihood values obtained on these coded bits. Correlatively, the receiving device further comprises a decoder adapted to decode the coded bits by using the combined likelihood values obtained by the obtaining module. In this embodiment, the estimation and detection steps carried out for each group of symbols determined for a coded bit use a priori information on this coded bit estimated during the decoding step. Correlatively, the estimation, detection, and obtaining modules and the decoder are arranged to be used during a plurality of iterations of an iterative process. This gives a particularly efficient reception scheme, and easy to use in an iterative or turbo receiving scheme. Thus, in a particular embodiment, the estimation, detection, obtaining and decoding steps are implemented iteratively. In another embodiment, during the detection step, a suboptimal implementation of the MAP criterion is applied. This reduces the complexity of the receiving device. This implementation can for example be based on a list sphere decoder (or "list sphere decoder" in English), well known to those skilled in the art. In a particular embodiment, the various steps of the reception method are determined by computer program instructions.

Accordingly, the invention also relates to a computer program on an information carrier, this program being capable of being implemented in a receiving device or more generally in a computer, this program including adapted instructions. implementing the steps of a reception method as described above.

This program can use any programming language, and be in the form of source code, object code, or intermediate code between source code and object code, such as in a partially compiled form, or in any other form. another desirable form. The invention also relates to a computer-readable information medium, comprising instructions of a computer program as mentioned above.

The information carrier may be any entity or device capable of storing the program. For example, the medium may comprise storage means, such as a ROM, for example a CD ROM or a microelectronic circuit ROM, or a magnetic recording medium, for example a diskette (floppy disc) or a disk hard. On the other hand, the information medium may be a transmissible medium such as an electrical or optical signal, which may be conveyed via an electrical or optical cable, by radio or by other means. The program according to the invention can be downloaded in particular on an Internet type network. Alternatively, the information carrier may be an integrated circuit into which the program is embedded, the circuit being adapted to execute or to be used in performing the method in question. According to another aspect, the invention also relates to a communication system comprising: a transmission device able to apply to a plurality of information bits coded modulation with spatio-temporal binary interleaving so as to generate T symbol flow; transmitted as signals on a multi-input and multiple-output propagation channel, T denoting an integer greater than 1; and a reception device according to the invention adapted to receive these signals and to obtain a combined likelihood value on each coded bit used when applying the coded modulation to label a symbol.

It can also be envisaged, in other embodiments, that the receiving method, the receiving device and the communication system present in combination all or some of the aforementioned features. BRIEF DESCRIPTION OF THE DRAWINGS Other features and advantages of the present invention will become apparent from the description given below, with reference to the drawings and the appendices which illustrate an embodiment thereof which is not limiting in any way. In the figures: FIG. 1 represents, in its environment, a communication system according to the invention, in a particular embodiment; FIG. 2 represents a transmission device belonging to the communication system of FIG. 1; Figure 3 shows a receiving device according to the invention, in a particular embodiment; Figure 4 shows various functional modules of the receiving device of Figure 3; FIG. 5 illustrates the hardware architecture of the receiving device of FIG. 3, in a particular embodiment; Figure 6 illustrates a factor graph modeling the communication system of Figure 1; Figures 7A-7C represent different factorizations allowed by the factor graph to evaluate marginal probabilities; and Figs. 8A-8C show various local factorizations used by the receiving device of Fig. 3 to detect bits encoded in accordance with the invention.

15 On the Appendices: Appendix A links the GaBP approach to the LMMSE criterion; and Appendix B specifies a way to empirically evaluate the variance of LLR when an MRC combination is adopted.

DETAILED DESCRIPTION OF THE INVENTION As a preliminary to the detailed description of the invention, we introduce the following notations used in this document: the letters in bold denote matrices or vectors, the vectors being represented by lowercase letters and matrices by capital letters; If A is a matrix, the k-th column of A is denoted ak. The entry j) of A is denoted or [A] ,,,; O denotes a zero vector of size n; In is the identity matrix of dimensions n x n (i.e. to n rows and n columns); NK with K integer denotes the set of integers {1,2, ..., K}; 30 g (S2) = Es1 f (S1, S2) represents the marginalization on Si of the function f depending on the sets of variables S1 and S2. For example, let Si = X2}, S2 = {x3} with x1, x2, x3 taking their values in sets Ai, A2, A3 then g (x3) = Y '-x, EAlEx, EA2 f x2, X3) VX3 E A3. A vector of variables is considered in this context as all its components; Similarly, let S1 = x2, ..., S2 = y2, ..., yis21} and z = 0 (S1) be a variable dependent on the variables of Si then: 3024806 10 9 (52) = f, SS) 1, 2 z = 0 (Si): xi = ai => f (Z (Xi,, xi_i, ai, xi + i, ---, x2,, Xi_i, ai, 52) If \ xi where ISI is the cardinality of the set S, let S be a set (or a vector representing all of its components) and Si c S, then S \ S1 is the set remaining after subtracting the elements of S1 to S, the exponents * , T and I respectively denote the complex conjugation operator, the transposition operator and the Hermitian operator; P (x) = .Nic (x; m, y) denotes a symmetric circular symmetric Gaussian probability density of mean m and variance v; P (x) = .7v-c (x, m, V) denotes a symmetric circular symmetric multi-dimensional Gaussian probability density of mean vector m and of covariance matrix V. By abuse 10 of notation, xP (x) means that the random vector x follows a probability density ility (or pdf for "probability density function") or a mass function or pmf (for "probability mass function") P (x); if S denotes a set and Si c S, S1 = S \ Si is the residual set after removal of the elements of S1 from S; in other words, {S1, forms a partition of S; For any matrix M of dimension L x N, it is possible to define a vector rn = vec (M) = [mo, ---, mL_1] T of dimension LN (i.e. having LxN components); we denote Ep [x] = EX xP (x) and Vp [x] = Ex lx - lEp [x] l2P (x) where P (x) denotes the pmf of the random variable x, in other words, Ep [x] and VI,. [x] denote the mean and variance of the random variable x; 20 denotes the Kronecker matrix product; and we denote by [PROP] the hook of Iverson in which PROP is a proposition, and which returns a number equal to 1 if the proposition PROP is true and to 0 otherwise. FIG. 1 represents, in its environment, a communication system 1 according to the invention, operating for example in a wireless telecommunications network, in a particular embodiment. No limitation is attached to the nature of the telecommunications network or to the transmission techniques implemented on this network (eg single-carrier or multi-carrier transmission, etc.). It can be an LTE network, Universal Mobile Telecommunication System (UMTS), etc. The communication system 1 comprises a transmission device 2 and a reception device 3 according to the invention, both equipped with multiple antennas and separated by a propagation channel 4. In the example envisaged here, the transmission device 2 is a mobile terminal having NTx transmit antennas, and receiver 3 is a base station of the telecommunications network having R receiving antennas. The transmission device 2 implements coded coding with binary space-time interleaving or STBICM, known per se and illustrated schematically in FIG. 2. More precisely, it comprises for this purpose: a binary linear coder 5, implementing by example a turbo-code, a convolutional code or a LDPC code (for "Low Density Parity Check"), and able to generate from a vector u E n of K bits of information transmitted by a source, a word c code E 10 IFF comprising NC coded bits; a spatio-temporal binary interleaver 6, able to interleave the bits of the codeword c and reorganize them here in T spaceflows or spatial layers represented by a matrix D of dimensions (TxL) xQ, where L designates the number of uses of the channel, assumed fixed for each transmission. Each entry of the matrix D is a sequence of Q bits, where Q is a predetermined integer dependent on the constellation X used by the modulation. In other words, D E / .(2TxL) xQ Furthermore, in the example considered here, T = NTx; and for each transmitting antenna, a modulator 7 adapted to transform each encoded and interleaved bit stream into a coded modulated symbol stream of a predetermined complex X-constellation. Each symbol of the constellation results here from the labeling of Gray of Q 20 bits. The application of these modulators 7 to the matrix D results in an X matrix of modulated symbols encoded with X E xTxL. It should be noted that in the example envisaged here, for the sake of simplification, the same constellation and the same labeling are considered on each antenna. However, this hypothesis is not limiting in itself.

With reference to FIG. 1, the modulated and coded symbols of the matrix X are transmitted in the form of signals via the NTx transmitting antennas of the transmitting device 2 on the propagation channel 4 intended for the transmission device. 3. In the example considered here, it is assumed that there is a non-ergodic propagation channel. The propagation channel 4 is more precisely a Rayleigh fading MIMO channel, non-frequency selective (ie flat) and Gaussian additive white noise (AWGN for "Additive White Gaussian Noise"), modeled by a complex matrix H1 E exT , I designating the use of the channel considered, each coefficient of this matrix following a complex normal law of zero mean and variance 1. For the sake of simplicity, it is assumed that for the non-ergodic regime, the matrix of the channel is random, constant over the duration of a code word 35 and changes independently from one code word to another. The signals received by the reception device 3 are modeled by a matrix YE CRxL whose columns are given by: YI = 141 + w1 where w1 - 71lic (W1; OR, Ew) and w1et w1 'VI # l are independent. The matrix designates the noise covariance matrix (possibly including interference sources). The white character of the noise refers to its orthogonality for different channel uses. In the remainder of the description, the following notations are used to schematize the previously described operations implemented by the transmission device 2 and the propagation channel 4: uen ±> D c IFT2xLxQ .._> 1) xe xTXL ±, y E ext, dt, / = Idt, /, q) E IF. '11)> xt, 1 EX, Vt NT = [0,1, ..., T - 1), V1 E NL = [0,1, ..., L - 1) where ip designates the operation coding and interleaving, 0 denotes the operation of mapping (or "mapping" in English) coded bits interleaved with a symbol of the constellation X and E denotes the transmission on the propagation channel. On the other hand, it is assumed, without loss of generality, that the power of the symbols of the constellation is normalized to 1, r ', that is, Ep [IXt, li21 = I - No information or only one partial information on the state of the channel (or CSI for "Channel State Information") is assumed to be available at the transmitter device 2. It is also assumed for the sake of simplification that the knowledge of the channel by the reception device 3 ( including the knowledge of the matrix of covariance of the noise AWGN introduced by the channel) is perfect so that in the continuation of the description one does not distinguish by different notations the response of the channel of propagation of its estimate. However, of course, the invention also applies when the estimate of the channel available at the reception device 3 is made from estimation means known per se capable of providing an estimate likely to be affected by an estimation error. The person skilled in the art would easily adapt the developments presented below in the case of a non-perfect channel estimate. The receiving device 3 is, in the embodiment described here, an iterative receiver comprising an equalization module 8 adapted to process the signals received from the transmission device 2 on its R receiving antennas followed by a decoder 9, the equalization module 8 and the decoder 9 being configured to operate iteratively and perform several iterations of equalization and decoding. The decoder 9 is a soft-input decoder with flexible outputs capable of performing the inverse decoding operation of the coding operation performed by the binary linear coder 5.

Such a decoder is for example a BCJR decoder (Baht Cocke Jelinek and Raviv) implementing the MAP criterion, known per se. It uses here as input logarithmic likelihood ratios on the coded bits (likelihoods in the sense of the invention), evaluated by the equalization module 8 according to the invention, as well as, if appropriate, logarithmic ratios of probabilities a priori. on the information bits or on the coded bits. The decoder 9 outputs logarithmic ratios of posterior probabilities on the information bits (which can be used to make a decision on these bits) as well as logarithmic ratios of extrinsic probabilities on the coded bits that are used after interlacing to reconstruct information a priori on the symbols to be detected. As a variant, the equalization module 8 uses the logarithmic reports of posterior probabilities delivered at the output of the decoder 9 after interleaving in order to reconstitute a priori information on the symbols to be detected. This prior information is then provided to the equalization module 8 which uses it at the next iteration to detect the modulated symbols, etc. The operation of such a decoder is known per se and is not described further here.

In accordance with the invention, the equalization module 8 relies on the MAP criterion (or a suboptimal implementation of it) and on the LMMSE criterion to approach the performance of an optimal detector ML. It also exploits a new degree of freedom by offering the possibility of combining several MAP detections carried out on several (i.e. M, with M greater than or equal to 2) distinct but overlapping groups of symbols, for the same coded bit.

The functional structure of the equalization module 8 is illustrated schematically in FIG. 4 in a context where T = 4, for a particular coded bit (d2, 41) and M = 3 groups of symbols (S1, S2, S3) selected. for this coded bit. This structure is reproduced by the equalization module 8 for all the coded bits. This example is of course given for illustrative purposes only.

The selection of the groups for a given coded bit is performed by a selection module 10. These groups are here fixed cardinality ISI. The module 10 selects, for example, for each use of the channel indexed by I, all groups of ISI symbols among the T symbols of the T streams that contain at least one symbol labeled by a modulator 7 using the coded bit considered.

Alternatively, the module 10 may take an approach other than an exhaustive approach to select the groups associated with a given coded bit. In particular, it can use the Gram matrix of the propagation channel and select groups corresponding to the most correlated columns of the matrix, etc. Similarly, for the sake of simplification, it is assumed here that the selected groups are all similarly ISI cardinality for a given coded bit, and that this cardinality does not vary from one coded bit to another. Likewise, the same number M of groups is considered for each coded bit. However, these hypotheses are not limiting in themselves, and one can envisage more complex models where the number of groups varies according to the bits as well as their cardinalities. In the example illustrated in FIG. 4, it is assumed that the module 10 has selected M = 3 groups (Si, S2, S3) for the coded bit d2, 1, 1. M more generally denotes an integer greater than or equal to 2. Each group consists of a plurality of symbols chosen from among the T symbols of the T streams transmitted simultaneously on the propagation channel 4 (that is to say during a same use of the channel indexed by I), and shares at least one symbol with the other selected groups that has been tagged from bit d2,1,1. Thus, in the particular example illustrated in FIG. 4, for T = 4, and M = 3, it is assumed that the symbol 2 (that is to say belonging to the second stream or the second spatial layer transmitted (e ) by the 2nd antenna) has been tagged with the coded bit d2, 1, 1 and the selection by the selection module 10 of a first group S1 = {1,2,3}, of a second group S2 = {2,3,4} and a third group S3 = {1,2,4}. These three groups have one symbol in common, namely the symbol 2. For the sake of simplification and to lighten the notations, each group is represented by the indices of the flows to which the symbols belong rather than by the symbols themselves.

Sl = {4), SZ = {1), and S3 = {3) denote the complementary groups of groups S1, S2 and S3 on the set consisting of the symbols belonging to the T = 4 flows. Of course, this example is given for illustrative purposes only. Following this selection, the equalization module 8 processes in two stages the signals received by the reception device 3 on its reception antennas, for each group 15 individually. More specifically, for each use of the channel 4 indexed by I, and for each group determined by the selection module 10 for the coded bit considered: the equalization module 8 estimates first from the signals received on its antennas. reception, the symbols of the group considered. This estimation is performed by an estimation module 11 which relies for this purpose on the LMMSE criterion, and eliminates the interference affecting the group of symbols considered that is created by the symbols of the streams not selected in the group. In other words, in the example of FIG. 4, for the group Si, the estimation module 11 eliminates the interference created by the symbols of the set Si (modeled by the subtraction of the term h4,04,1 on the Figure 4); the equalization module 8 then detects the coded bit considered, eliminating the residual interference within each group (ie generated by the symbols of the group on the coded bit) and by applying the MAP criterion (or a suboptimal implementation thereof), with the aid of a detection module 12. This detection module 12 is able to deliver a likelihood (logarithmic likelihood ratio here) on the coded bit. The operations performed more precisely by the estimation modules 11 and 12 are described in more detail later. The equalization module 8 activates estimation and detection modules 11 and 12 for each group determined for a given coded bit (ie for each of the groups S1, S2 and S3 in the example of FIG. 4), and for each bit coded. It should be noted that FIG. 4 represents the functional architecture of the equalizing module 8. It does not necessarily reflect its hardware architecture, namely that the same LMMSE 11 and / or MAP 12 estimation module can be used and configured for multiple groups of symbols and / or multiple coded bits. Likewise, the estimation module 11 can rely on a hardware architecture distinct from that envisaged in FIG. 4 and be implemented for example by means of a forward filter and a backward filter ("backward") in a manner known per se. These are implementation choices that meet complexity criteria known to those skilled in the art and are not considered in more detail here. According to the invention, the equalization module 8 also comprises a combination module 13, able to obtain from the likelihoods provided by the detection modules 12 on a coded bit, a combined likelihood on this coded bit. In other words, in the example envisaged in FIG. 4, the combination module 13 combines the estimated likelihoods on the coded bit d2,1,1 from each of the groups S1, S2 and S3. Various combining principles can be applied by the combining module 13, such as a Bayesian combination principle or an MRC combination principle, as detailed later. The combined likelihood obtained is then provided by the combination module 13 to the decoder 9. This is achieved by the equalization module 8 for each coded bit. In the embodiment described here, the receiving device 3 has the hardware architecture of a computer, illustrated schematically in FIG. 5. It notably comprises a processor 3A, a read-only memory 3B, a random access memory 3C, a memory non-volatile 3D, as well as 3E communication means on the telecommunications network enabling it to communicate in particular with the transmitting device 2. The read-only memory 3B of the receiving device 3 constitutes a recording medium 20 according to the invention, readable by the processor 3A and on which is recorded a computer program according to the invention, comprising instructions for carrying out the steps of a reception method according to the invention. This computer program defines, in an equivalent manner, functional modules of the reception device 3 and their interactions, such as, in particular, the selection, estimation, detection, detection and combination modules of the equalization module. and the decoder 9 previously described. We will now describe in more detail the operating principle of the receiving device 3 and its various modules. This operating principle is based on the steps of the reception method according to the invention. These steps are schematically represented in FIG. 4 for a particular example, through the organization of the functional modules and the inputs / outputs of these modules. To better understand the invention and the operation of the receiving device 3, we first briefly recall the principle of the detection and the joint decoding that is sought to achieve with such a receiving device for signals such as those transmitted by the transmitting device 2. The Maximum A posteriori (MAP) criterion considered optimal for realizing the detection and decoding of the signals consists in the discrete case to be found: 3024806 16 'ùk = argmax P (uk = ulY ) = argmax Eu \ 12 P (uIY) (1) u uEIF2 k The exhaustive approach to solve this problem leads to an exponential complexity in K, where K denotes the size of the vector u of bits of information supplied as input 5. In other words, this complexity does not allow a practical implementation of such an approach. The marginal probability P (uk = uIY) can also be written in the form: P (uk = uIY) => u \ uk P (u, X, DIY) has Eu \ uk P (YIX) P (XID) P (D lu) (2) Taking into account the model of the system and the notations introduced previously, we obtain: m (ix) p (xiD) p (Diu) = H p (mix) np (xt. ,,, dt , /) I p (Dlu) 10 = FLN ', (P (Yt lx') MENT [xt, / = 45 (dt, t) i) [D = 4 '(u)] (3) el ot, 1 In a known manner, this factorization can be graphically represented using a model called factor graph, more commonly known by the name "factor graph" (FG) in English, which makes it possible to model the constraints imposed by the system. Communication. Such a representation makes it possible to easily calculate the marginal distributions 15 involved in equations (2) and (3) by means of a sum-product algorithm SP (for "sum-product" in English) or of propagation type of beliefs. BP more commonly known as "belief propagation" algorithm. A factor graph is a bipartite graph representing the factorization of a function. It includes nodes bound by constraints. Such a graph is illustrated for the communication system 1 in FIG. 6 for T = 4 and Q = 2 (i.e. 2 coded bits per constellation symbol). On this graph, the nodes are represented by circles and constraints to which they are linked by squares. The links are represented by edges connecting one or more nodes to one or more constraints. In FIG. 6, the constraints translate in particular the operations of coding (modeled by COD), interleaving (modeled by INTERL), modulation (modeled by MOD), etc. performed on the K bits of information. Thus, according to this example, Q = 2 interleaved coded bits make it possible to label a symbol of each constellation associated with each transmitting antenna, and T = 4 distinct spatial streams are sent on the NTx = T = 4 transmitting antennas of the device The conventional scheduling of the BP algorithm takes place in several steps, briefly recalled now: Step 1 (detection): Compute v RIT, v / E NL itfi -xt, i (xt, t ) al at the first iteration where the notation a means "is proportional to". IENL tENT o Ext, xt (Ytixt) ilt, ENT \ t tixt ,, r.ei (xt ,, I) 3024806 17 - Step 2 (demodulation): Calculate vt E NT, vl E NL, Vq E RIQ t1, 11 POt, t-.dt, i, q (dt, t, q) = Ext, / [xt, / = = ggi-xt, t (xt, t) X IIVENQ \ q ocl at the first iteration 5 Step 3 (decoding): Calculate vk E NK Iip -> uk (uk) Eu \ uk [D = IP (11)] fI (t, t, q) eNTxN1LxNQ μd1 / 4T, q-riP (dt, t , q) - Step 4 (decoding continued): Calculate vt E NT, vl E NL, vq E RIQ μ1-> dtm (dt, /, q) OC ED \ dt ,, '[D = lP (u)] lItt , 11, q1) ENTxtkILXN (2 \ (t, l, q) Pdtrj1, qt-> 11) (dt ,, P, q,) 10 - Step 5: Calculate vt E NT, VI E NL lIckt, / -> xt, i (Xt, /) Edt, i [xt, / = 0 (dt, /)] ILENQ tidt, /, q-> ot, i (dt, t, q) The first three steps consist of a transition from messages (ie information) 15 from the bottom to the top of the factor graph of FIG. 6. If the factor graph does not contain a cycle, the algorithm BP provides the exact value of the marginal probabilities P (ukIY), vk E NK at the end of step 3. In most cases, the factor graph has cycles and the algo BP provides only approximate marginal probabilities that should be refined by repeating steps 1 through 5 until the convergence of the algorithm, using the fact that μxt, ie (= itOtj -) ect, l (Xt, l) - Note that for an encoding implementing a systematic code, step 3 gives posterior probabilities on the information bits while step 4 provides extrinsic probabilities on these bits. Steps 1 and 2 make it possible to calculate a likelihood ratio or LLR (for Log Likelihood Ratio) on the interleaved coded bit dt, / ,,, coming from the detector, that is to say the logarithmic ratio. extrinsic probabilities on the coded bit (interleaved) dt ,,, q, noted ~~ t, i and defined by: 110t, t-> dt, i, q (1) = ln POt, / -> dt, /, q (0) In a similar manner, we note: In111-> dtm (1) ittp-d ,,,, q (0) the logarithmic ratio of the extrinsic probabilities on the (interlaced) coded bit dt, /, q coming from the decoding .

3024806 18 Steps 1 and 2 are the most complex point of the BP algorithm. Indeed, the message ye1 * X, 1 (xt, /) is difficult to evaluate for large MIMO systems and high-order constellations, since the discrete (sum) marginalization on x1 contains 2QT terms. Approximations must be made at this level of the BP algorithm.

Different approaches are possible for these approximations, as mentioned above, ie one can for example consider a sub-optimal implementation of the MAP criterion in which the number of terms taken into account in the marginalization is reduced, or adopt in place of the MAP criterion, a suboptimal criterion such as the LMMSE criterion. More precisely, the MAP criterion corresponds to the exhaustive marginalization of the steps 1 and 2 which together give: (Ott-> dt, t, c, = In) dt 1 jalllip, dt, iq, exp -Hixt) tE, 7, 1 (yi - Hixi) + xi = 0 (dt, /): dt, /, q = 1 (t ,, qF) ENTxNQ \ (t, q) -In (exp - 1-1 / xi) t4,7 , 1 (yi - Hixi) + x1 = 0 (dt, I): dt, l, q = 0 (tf, q0ENTx% (t, q) for observations: YI = 1-414- where H / E cRxT, w1 JvC (VI, OR, Iw), and wiet wi 'V / # 1' are independent In the case of a suboptimal implementation of the MAP criterion, the summations will be limited to lists of candidates: list Li (t , 1, q) for candidates x1 having the bit dt., /, Q = 1 and list Lo (t, 1, q) for candidates x1 having the bit dt, /, q = 0. It follows that a suboptimal implementation of the MAP criterion can be written as: () dt1,1, q1 / 11p, dt, tq, .1., /, m, dt, t, q - = In 1 exp - (3r / - read /) IE, 7.1 (y1 - Hixi) + xtek (t, /, q) (t1, q0ENTxNQ \ (t, q) (-In 1 exp - (Yi - FlixatE ,,, 1 (yi - Hixi ) +) dt1,1, q111.1p_, dt ,, i, q, xieLo (t, l, q) (tf, q1) ENTx% (t, q) The LMMSE criterion consists in replacing step 1 with interference subtraction followed by linear filtering, the previously described demodulation step 2 remaining the same. This second approach consists of replacing the MAP criterion by the LMMSE criterion by GaBP (for BP algorithm with Gaussian Approximation). It is this second approach that is retained by the invention and detailed now, first generally and then as implemented by the invention. The principle adopted by the GaBP approach is to replace certain discrete random variables in the factor graph by complex Gaussian random variables with circular symmetry. More precisely, according to this approach, the mass probabilities (pmf) are replaced by Gaussian distributions according to: Step 1A (replacement of the pmf by a Gaussian pdf distribution): Vt 'E NT \ t: Nc (xt, , t; vti, 1) mtf, / = 1Egv, 1_, 4-1 [xtr, t] 7v, 1 = ViIxtf, / -> fi [Xti'd then we replace, under hypothesis 1A, the stage 1 previously described by step 1B defined by: Step 1B: Calculate the approximate message: Pie.xt, i (xt, t) cc ixi \ xt, i P (Yl1xt) ITtrENT \ t Nic (xt, t: vt, /, and, i) Step 1B is now of polynomial complexity as a function of the number R of receiving antennas. The mean vt, 1 and the variance Ot, i are obtained by applying the LMMSE criterion. Plus __ /, precisely, if we denote and the vector such that ht, 1 = Hiet and xt, 1 = erx m \ t, i the vector containing a zero at position t and mt ,, / at positions t '# t and V \ t, / the diagonal matrix having 1 at the position t and vt, j at the positions t '* t, we can show that: gt., / = hit "/ (HIV \ t, IH + 0t, / = gt, i) - / \ t, /, vt, / = Ew) -1 (Y / - H m) Thus, v5,1 is the xti estimate by applying the unbiased LMMSE filter gijihià (HIV \ oHi + Zw) -1 to the vector yi - Him \ t / where litm \ t, / can be seen as the interference (soft) regenerated with respect to) 4.1 subtracted from the vector of observations y1. More details on the transition from the GaBP hypothesis to the LMMSE criterion are given in Appendix A for guidance. The message U e is then substituted for the message Ue in the other - ', / -> xt, i (xt, t) 20 steps of the BP algorithm. - -, 1-xt, / (xt, t) FIG. 7A illustrates on the graphical factor the approximation carried out by the GaBP approach. The bit whose marginal probability is sought is designated TARG. The nodes designated by Ga correspond to the variable nodes that are approximated by a univariate Gaussian random variable.

The invention repeats the principles of the GaBP approach presented above, but relies on another factorization of the marginal probability that is described in equation (3) and which is conventionally considered in the BP algorithm. More precisely, suppose that we are interested in the marginal probability of the coded bit dt, t, q, and that we define two complementary groups on the set NT, namely S g NT and S. {S, g } is a partition of NT. One can write: P (Y, X, D lu) oc nieNL (P (yilxi) P (xs, ilds, i) 'Las, P (xt ,, ildt ,, i)) P (Diu) 3024806 20 = ritENLP (Y / i xi) [xs, 1 = Os (ds, 1)] M'Es, [xt ,, / (el os, 1 = Oti (dt ,, I)] [D = 0 (u)] ( 4) 1 ---- F-- ..-- (Pt /, 1 with xs, 1 = fxt, i: t ES), (i) s, 1 = [0t, 1: t ES) and dsi = {dt, e, q: t ES, q E NQ) and where, because of the coding structure considered: [xs, 1 = cPs (ds, z)] = ilts [xt, 1 = 4) (dt, i)] Figure 7B illustrates on the factor graph this alternative factorization, for a particular example in which we consider the groups S = {1,2) and: 5 "= {3,4) With regard to this other factorization , steps 1 and 2 of the BP algorithm become: Step 1 '(detection): Calculate: Pei-xs, / (xs, t) to Exi \ xs ,, P (yilxi) Hues Pxt ,, i- > ei (xt ,, t) - Step 2 '(demodulation): Calculate: Pos, / - dt, /, q (dt, i, q) Eds, Adt, i, q EX5,1 [XS, I OS ( dS, I) 1 X 11 (tr, q0ESxNe (t, q) The accuracy of the message remains unchanged with respect to the BP algorithm applied to the classical factorization represented by shown in FIG. 7A. If one applies the GaBP principle to this new factorization, one obtains: - Step 1A ': replacement of the pmf by a Gaussian pdf: 20 E iixt ,, r.fi (xt ,, t) (xtm; n4 /' I = E12,1,1 d Vt ,, I = V r [XV'I] fxt \ xs, / - Step 1B ': Calculate the approximated message under the assumption of step lA: 25 P (37 / I xi) M'Es.Nic (xt ,, i; vt ,, i) dxi \ xs, / ifei-> xs, i (xs, t) (xs, t; vs, /, Os, i) The message ifei , xs, i (xs, t) is then substituted for the messagexsi (xs, 1) in steps 2 ', and 3 to 5 described above.

FIG. 7C illustrates the GaBP principle on the graph factor resulting from the alternative factorization based on the groups S = {1,2) and g = {3,4} and illustrated in FIG. 7B. The nodes designated by Ga are approximated by a complex Gaussian random variable with circular symmetry.

The mean vs, / and the variance Us, t are obtained by applying the LMMSE criterion. More precisely, if we denote by Es the matrix such that Hst = H / Es and Xs, 1 = Esxt, M \ s, i the vector containing 0 at positions t ES and mt, / at positions t 'ES, and V Since the diagonal matrix has 1 at positions t ES and vt ,, / at positions t 'E -S., It can be shown that (see Appendix A for further details): rs, 1 = Ht ( H / v \ s, / Hil. + Ew) -11-15,1 os, 1 = 1711 (4 -1'5,1) Vs., 1 = + Ew) -1 (Yi -111111 \ s, t So, vs, / is the estimate of x5,1 by applying the LMMSE unbiased s rs7 / 111 ;, / (111V \ s, illi + Ew) -1 to the vector yi - Hom t where H mt can be seen as the interference (soft) regenerated with respect to X5,1 subtracted from the vector of observations y /. This interference, in the case of an iterative scheme, is regenerated in a manner known per se from the output of the decoder 9. More details on the transition from the GaBP hypothesis to the LMMSE criterion are set out in Appendix A as an example. code. In other words, and with reference to FIG. 4, vs, / is the estimate of the symbols of the group S (S = S1, S2 or S3 in FIG. 4) provided by the estimation module 11. In accordance with the hypotheses previously formulated , the estimate vs, / is written as: vs, / = xs, 1 + ns, / 15 where ns, / denotes a factor comprising the residual interference within the group S after interference elimination performed by the detection module 11 and a Gaussian additive white noise. This factor has the covariance matrix 0 s This estimate is provided at the input of the MAP detection module 12 which implements the steps 1B 'and 2' of the GaBP algorithm described above for detecting the coded bits and providing a value of likelihood on these coded bits. This likelihood value corresponds to the value At.ot / -> dt available at the end of step 2 and calculated by each detection module / // MAP 12 for the coded bit considered (in the example of FIG. 4, for the coded bit dzo), from the output of the LMMSE filter vs, 1 and the logarithmic ratios of extrinsic probabilities A'l, _, dtuq, duly intertwined provided by the decoder 9 and used as logarithmic ratios of prior probabilities by the detection module MAP 12. More precisely, the detection module MAP 12 evaluates: At (m) = ln (Nt _if (tr, q1) ESxNe (t, q) dt, 4-1C1t r)) 4, s , / -> dt, /, q exp - (vs, / - Xsj) 0 s, i 0 1 st - X5,1) + xs, I = es (ds, t): dt, /, q = 1 - In () of, l, cilill, b-> dtrwr exp - (v5,1 xs, I = Os (ds, i): dt, /, q = o ^ xs, /) t 05,1 - X5,1 ) + (tl, q ') ESxNQ \ (t, q) As mentioned previously, these estimation steps according to the criterion LMMSE by the module 11 and of detection according to the criterion MAP by the module 12 are implemented. for each group selected by the selection module 10 for the coded bit in question (i.e. for S = Si, S2 or S3 in the example of Figure 4). In other words, according to the invention, for the execution of the GaBP algorithm, we do not consider a local approximate factorization model but a plurality of factorization models, each leading to the estimation of a likelihood value for the coded bit considered. The likelihood values obtained from each detection module 12 are provided to the combining module 13 to combine them into a combined likelihood value according to a predetermined combination principle. The combined likelihood value is then supplied to the decoder 9 for performing steps 3, 4 and 5 of the BP algorithm described above. It should be noted that if the linear encoder 5 implements an LDPC code, steps 3, 4 and 5 can be implemented as is by the decoder 9. If the code implemented by the encoder 5 is a turbo-code, an algorithm BCJR type can be used to implement these 15 steps. It should be noted that the calculation of es, i and vs, 1 can be facilitated by parallelizing certain operations, as mentioned previously: it is thus possible to limit itself to a matrix inversion using the channel. In addition, the existence of rs7 / 1 requires that rs, / is not singular, which is verified since ISI 5_ R.

On the other hand, it is noted that the accuracy of the messages is improved by considering this alternative factorization with the GaBP principle compared to the classical factorization illustrated in FIG. 7A. The interference on the coded bit dt, i, q coming from the modulated symbols belonging to the group S is indeed treated according to a MAP criterion in step 2 while the GaBP applied to the classical factorization uses an MMSE criterion to eliminate the interference from the modulated symbols xt ,, i, t 'e S \ t. We will now detail various combination principles that can be applied by the combination module 13 to generate a combined likelihood value for the coded bit considered from the likelihood values provided by the detection modules 12 for the different groups selected by the selection module 10 for this coded bit. In the remainder of the description, for the sake of simplification and readability, index (m) each local factorization model considered for a given coded bit duc, and corresponding to a group S selected by the selection module 10 for this bit code. M (dt, f, q) denotes all the models defined for the coded bit dt, i, q. M (cit, /, q) depends only on t and the cardinality of each group S.

The three models considered in FIG. 4 are illustrated respectively in FIGS. 8A, 8B and 8C. In these figures, TARG designates the coded bit d2,1,1 considered and the groups SI = {1,2,3}, S2 = {2,3,4} and S3 = {1,2,4} respectively considered in each model m = 1, m = 2 and m = 3 are represented. The notation Ga denotes the set of symbols on which the Gaussian approximation is carried out, namely, for the first model m = 1 on the symbol of S1 = {4), for m = 2 on the symbol of S-2 = {1), and for m = 3 on the symbol of S3 = {3). The combination module 13 combines the likelihood values Je) in the logarithmic domain, or u (on121 -dt, /, q (dt, /, q) provided by the detection modules MAP 12 associated respectively with each model m. For this purpose, it uses a fusion function f generically defined by: ti4pms, dt, /, q (dt, i, q): EM (dt, t, q)} 4 (or in the logarithmic domain (for likelihood ratios): ff (f) EM (dt, t, q) i -> with: 15 (m), (hf) λ (m) = In i0s, / - dt, /, q ( 1) A. (f) = In t4- d '' "(1) os, / - dt, /, q 4 (n) (0) 1 (f) 0) 4S, 1-dt, l, qd (As mentioned above, different principles can be envisaged to combine the likelihoods provided by the detection modules 12 for a given coded bit, and thus to define the function f implemented by the combination module 13.

Thus, it can be envisaged that the combination module 13 implements a Bayesian combination principle. According to this principle, if we denote P (M = m) the prior probability of selecting the model m EM (dt, /, q) for the coded bit dt, /, q, we have:) = LnEM (dt, i, q) `M = -Jr-cks, t-> dt, t, q be equivalent to:. (f) = ln 1 + EmEm (dt, i, q) (Â (m) P (M = m) tanh of s'i -> cit'l'q 2 1 - Lnem (dt, I, q) 2. (m) P (M = m) tanh 2 If one does not have one knowledge of the prior probabilities P (M = m), these can be chosen uniformly In a variant, the combination module 13 can implement a combination principle of the MRC type (Maximal Ratio Combining) .A first possible implementation of this principle Based on the assumption that the log likelihood ratios to be combined are statistically independent, the combined likelihood ratio 2. (1, f, _,), /, iq is then obtained by summing the ratios likelihoods S) ~ dtiq delivered by each detection module 12 is:] (f) = 2, (m) Os, / -> cit, /, q mem (at, /, q) Such a pproche is particularly simple to implement by the combination module 13.

It should be noted that the likelihood ratios are however statistically correlated because they are derived from the same observations Y. To take account of this correlation, the inventors propose a combination scheme which relies on a bleaching of the logarithmic ratios. likelihoods. Such a scheme is particularly well suited for a non-ergodic propagation channel model.

10 This scheme is based on the assumption that the likelihood ratio 2. (7s) ~ dtlq has been calculated from an AWGN noise virtual binary channel, according to: ° on) (m) - P tq (nt ) Z - = + n (m) t, l, q 2 y, A t, l, q with cit, i, q = 2dtja - 1 and where the variance of Tir / g) is K: 71). As shown in Appendix B, the noise variance δ (e) can be empirically estimated as: (m) t, q (m) = 2 t, q at, q where a (m) = 1 I, (m) 2 t, q L cks, 1-> dt, t, q 1 = 1 On the basis of this hypothesis, the MRC combination principle proposed by the invention is broken down into 4 steps: Step MRC 1: a virtual Gaussian model is recreated at single input and multiple outputs (SIMO) 20 for detecting the du / following coded bit: Z (m) = [1.1 t + @ n, i, q nt, i, q = Zt, l, q = nt, l, q From this model, the covariance matrix of the noise nt, i4 is estimated empirically according to: Cov [Ama] = Cov [zt, /, q] - 11T Step MRC 2: the preceding Gaussian SIMO model is bleached for obtain a new SIMO Gaussian virtual model in order to detect the coded bit dug: 1 + I1 + a (m) 3024806 25 Zt (intq) = [ft (i 1 dt, i, q + nt (tmci) This transformation results from the multiplication of the previous model by the matrix Cor [nt, i, cil-1/2.

Step MRC 3: the likelihood ratios are reevaluated according to: (m) P (dt, i, q = lizt (C 1) 1) P (dt, i, q = i-liztrat P (dt, l, q = -11Zt, i, q) P (dt, l, q = cqz: I, ', 1) = = In In 0 S, 1-4 dt, l, q 1 (m) 1 (771) In other words, we obtains likelihood ratios that have been "laundered" and are now statistically independent of each other.

Step MRC 4: The likelihood ratios obtained in step MRC 3 are combined according to: -0 1 (f) -v 2./(m) -> dt / ,, z, mEm (d ,, /, q As mentioned above, by taking into account different local factorization models and combining the resulting likelihoods, the invention offers a new degree of freedom allowing to approach the ML theoretical performance. . We will now briefly present some considerations as to the complexity of implementing the method of reception proposed by the invention. The complexity of implementation of the invention is dictated mainly by the itosr likelihood evaluation complexity, duq (dtja) which is in (2Q1sI) where ISI denotes the cardinality of each group S considered for detecting the coded duq bit. . This complexity can be reduced by limiting the number of terms considered to calculate the marginal probabilities. Thus, a compromise must be envisaged between the cardinality ISI and the accuracy of the messages exchanged during the GaBP. In the same way, the cardinality of M (dt, 14) intervenes in complexity. The maximum cardinality of M (dt, / ,, i) is: (TIsi 1) _ Ci'si_11) 1111 (dt, /, q) 1 - 25 As an indication, some numerical results are given below: ISI \ T 4 8 16 32 64 2 3 7 15 31 63 3 3 21 105 465 1953 4 - 35 455 4495 39711 It is therefore understood that for large values of T (eg for large values of the number of antennas of emission), it may be relevant to reduce the complexity of selecting a reduced number of groups for a coded bit. . . . . . - `......-..., --- ^, ..........., = z 1 t, 1, q = ni t, 1, q 3024806 26 Others Considerations can be taken into account to reduce the complexity of implementation of the invention. Thus, according to one alternative, an approximation of replacing the instantaneous variances by their averages in the LMMSE filter (unconditional conversion rule) can be done, ie: 1 seen, / 7.2.1 = 1 ue This can be done prove useful for non-ergodic channel models since the same inverse matrix (HV \ sH + / w) -1 is considered for all uses of the channel. According to another variant, the expectations with respect to the messages μ ',,, i-fi can be replaced by expectations with respect to the beliefs 13xtm (Xtr, 1) = iixt ,, ie [(xt ,, t) - Pei -) xt ,, i (xt ,, i), = lEfixtm vti, / = VRxt, [xt ,, d According to another variant, we have access to: n1 / 41 [xt, d, Vt EV / = Etixt , i-ei [xt, 11 = Let m1 be the vector with mt, / at positions t E DIT and V1 the diagonal matrix with vt, / at positions 15 t E NT. We can write: m \ s, i = (I - EsEDmt V \ S, 1 = Vt + Es (lisi - Vs, t) Els.ms, / = E7Sm / Vs, / = E7s: V / Es Using the matrix inversion lemma we can show that: 20 rs, / = [They '+ rs, / (Iisi Vs, a] 1rs, / with rs, / = His./(H/v/Ht + and "vs , / = ms, / + rs7 / 111;, / (11 / V / 111 /. + Ew) -1 (3, / - Himt) It follows that the quantities vs, / and Os, / for a group given S (and a model m associated with this group) can be computed from the inversion of a single matrix (1-1! V / H + Ew) -1 which does not depend on S (if we neglect the In principle, the complexity of the main operations required for the implementation of the invention is recalled below for an ergodic channel model and for a channel model. non-ergodic: Ergodic channel - using channel: matrix inversion in 0 (R3) - using channel and m (or group S) model: matrix inversion in 0 (1S13) - using channel and model m (o group S): marginalization in 0 (2 (21s1) 3024806 27 Non-ergodic channel (with application of the unconditional conversion rule mentioned above) - once for all uses of the channel: matrix inversion in 0 (R3 ) - once per model m (or group S): matrix inversion in 0 (1S13) 5 - by use of channel and by model m (or group S): marginalization in 0 (2Q1s1) It should be noted that in In practice, the channel is never ergodic and can always be assumed constant over a number B of consecutive uses of the channel. On the other hand, it is noted that if the LMMSE filtering does not implement an Interference Rejection Combining (IRC), ie E, = 024, the complexity of the matrix inversion can be reduced for R> T on the basis of the matrix inversion lemma which leads to: 11; 1. (11 / V / W + / w) -1 = (IT + F1-47,11.00-iiiitEiv In other words, Matrix inversion at 0 (R3) can be replaced by a matrix inversion at 0 (T3).

In the embodiment described here, STBICM modulation without linear precoding was considered. However, the invention also applies when the STBICM modulation is combined with a linear precoding (STBICM-LP), artificially incorporating in the above developments the linear precoding operation in the propagation channel. This manipulation presents no difficulty for those skilled in the art and is not described in more detail here.

3024806 28 APPENDIX A This appendix demonstrates the link between the previously described GaBP approach 5 and the LMMSE-IC detection. More precisely, consider the following model: y = Hx + w = Hsxs + EUES ht, xt, + w We assume that xt, -. Wc (xt,; mt'vt,) and are mutually independent, and that w, - .7q (w; 0.4 ',) and is independent of x.

We further define Es such that Hs = HEs and xs = Esx. As a reminder, we want to evaluate the message: iie-.xs (xs) "fx \ xs P (Y1x) M'Es. Nic (xti; rnt'vt,) dx \ xs OC (x_ni \ s) i-vsl (xm \ s) dx \ xs x \ xs (y_Hx) tze (y-Hx) - exs.sf Let m \ s be the vector having 0 at positions t ES and mt, at positions t 'ES, and V \ s the diagonal matrix having 1 at positions t ES and vt, at positions t'ES. By developing the exponent and keeping only the terms in x (the other terms being considered constant), we get: fx \ xs - (Y-11X), I.Z7vi (Y-1-1X) - (XM \ S) tifS1 (X-In \ S) dx \ xs cc fe- (x-ikb \ s) iA \ s (x-Aseb \ s) dx \ xs x \ xs 20 If we now define: A \ s = HtE, 7.1H + b \ s = H11,7,1y + Vslm \ s using the matrix inversion lemma we obtain: / \ s. = AIS = V \ s - V \ sHt (HV \ sHt + Ew) -1HIT \ s 25 v \ s = A- \ 2.b \ s = m \ s + li \ sHt (HV \ sHt + Ew) - 1 (y - Hin \ s) As a result: r e_ (y -14x) tE71,1 (y-Hx) - (xm s) tVsl (xm \ s) dx \ xs' x \ xs fe- (xv) This integral expresses the marginalization of a multidimensional Gaussian variable which is by definition a multidimensional Gaussian variable (of reduced size). It follows that: fx \ xs e- (xv \ s) tls (xv \ s) dx \ xs cc e- (xs-vs) tE.71 (xs-vs), where: Es = E7sS \ sEs - asi - (HV \ sHt + E, ') - 1Hs 3024806 29 vs = EIv \ s = 11; (HV \ sHt + Ew) -1 (y- Hm \ s) If we go back to the definition of the message, we a: ie-x5 (xs) oc exis "xse- (xs-vs) frs1 (xs-vs) 5 By developing the exponent and keeping only the terms in xs (the other terms being considered in the constant), we obtain: li'-xs (xs) "e- (xs-vs) tos1 (xs-vs) with Os = (EsT1 lisi) -1 10 vs = OsEsTivs These two quantities can be expressed in terms of rs (supposedly invertible and vs, according to: ## EQU1 ## 1 VS = rs VS 3024806 APPENDIX B Appendix B relates the variance of a discrete AWGN binary channel (BI-AWGN for Binary 5 AWGN) to a sequence of L observations 24 of the LLR type. The logarithmic ratio of probabilities 24 for x1 derived from a discrete BI-AWGN channel of the form: Yl = xl + where x1 = ± 1 is uniformly distributed, n1-.7 \ r (0, cr ;;), x1 and n1 are independent, is given by: = ln P (x1 = ol-11yyi) /) a 22 yi = (x1 + n1)) Kx1 on The variance a ?, is related to the variance cd of the LLRs by: VVV 0.2 = 2 Cd. Indeed, we can show that o is the only permissible solution of the polynomial equation in Cg of degree 2: cdx2 - 4x - 4 = 0. with 14 [1) (112] = 1. In In practice, we evaluate cd empirically using the estimator: L = 1 [, 6-A.2 -L 142 1 = 1 20

Claims (15)

REVENDICATIONS1. A method of receiving signals resulting from the transmission, on a multi-input, multi-output propagation channel (4), of T symbol streams from the application of a binary spatio-temporal interleaving coded modulation over a plurality of of information bits, T denoting an integer greater than 1, which method comprises: a step of determining, for each coded bit (dt ,, q) used to label a symbol of a flow, of a plurality of groups of symbols, each group (S1, S2, S3) comprising a plurality of symbols selected from T symbols respectively belonging to the T streams, this plurality of symbols including the symbol labeled with the coded bit; for each group of symbols determined for a coded bit: a step of estimating the symbols of this group from the received signals, this estimation step comprising an elimination of the interferences affecting the group of symbols by applying a criterion of minimum mean squared error; a step of detecting the bit encoded from the estimates of the symbols of the group, this detection step comprising an elimination by application of a criterion of Maximum a Posteriori of a residual interference affecting the coded bit generated by the symbols of the group, and estimating a likelihood value (e) -, ti ,,, of the encoded bit; and ^. a step of obtaining a combined likelihood value (λ1,,, /, q) for each coded bit (dt, q) by combining the estimated likelihood values on this coded bit for the a plurality of groups of symbols determined for this coded bit. 2. Method according to claim 1, wherein during the obtaining step, the likelihood values are combined according to a maximum ratio combination principle. The method of claim 2 wherein the combined likelihood value for a coded bit is a sum of the estimated likelihood values on that encoded bit for the plurality of groups. The method of claim 2 or 3 wherein the obtaining step comprises a prior step of bleaching the likelihood values before combining them to obtain the combined likelihood value. The method of claim 1 wherein during the obtaining step, the likelihood values are combined according to a Bayesian combination principle. 3024806 32 The method of any one of claims 1 to 5, further comprising a step of decoding the encoded bits using the combined likelihood values obtained on these encoded bits. 5 7. The method of claim 6 wherein the estimation and detection steps performed for each group of symbols determined for a coded bit use a priori information on this coded bit estimated during the decoding step. 10 8. The method of claim 7 wherein the steps of estimation, detection, obtaining and decoding are implemented iteratively. 9. Method according to any one of claims 1 to 8 wherein during the detection step, a sub-optimal implementation of the criterion of Maximum a Posteriori is applied. 15 A computer program comprising instructions for performing the steps of the receiving method according to any one of claims 1 to 9 when said program is executed by a computer. 20 A computer-readable recording medium on which is recorded a computer program comprising instructions for carrying out the steps of the reception method according to any one of claims 1 to 9. 12. Apparatus for receiving (3) signals resulting from the transmission, on a multi-input and multiple-output propagation channel, of T symbol streams from the application of coded modulation with binary spatio-temporal interleaving. on a plurality of information bits, T denoting an integer greater than 1, this device comprising: a determination module (10) able to determine, for each coded bit used to label a symbol of a flow, of a plurality groups of symbols, each group comprising a plurality of symbols selected from T symbols respectively belonging to the T streams, this plurality of symbols including the symbol labeled with the coded bit; estimation and detection modules, activated for each group of symbols determined for a coded bit, and such that: said estimation module (11) is able to estimate symbols of this group from the received signals, eliminating interference affecting the symbol group by applying a minimum mean squared error criterion; o said detection module (12) is able to detect the coded bit from the estimates of the symbols of the group by eliminating by applying a criterion of Maximum a Posteriori residual interference affecting the coded bit generated by the symbols of the group , and estimating a likelihood value of the encoded bit; and a module (13) for obtaining a combined likelihood value for each coded bit able to combine the estimated likelihood values on this coded bit for the plurality of groups of symbols determined for this coded bit. 13. receiving device (3) according to claim 12 further comprising a decoder (9) adapted to decode the coded bits using the combined likelihood values obtained by the obtaining module. 10 14. receiving device (3) according to claim 13 wherein the estimation modules, detection, obtaining and the decoder are arranged to be used during a plurality of iterations of an iterative process. 15 A communication system (1) comprising: a transmission device (2) adapted to apply to a plurality of information bits coded modulation with binary spatio-temporal interleaving so as to generate T transmitted symbol stream in the form of signals on a multi-input and multi-output propagation channel, where T is an integer greater than 1; and a receiving device (3) according to any one of claims 12 to 14 adapted to receive these signals and to obtain a combined likelihood value on each coded bit used when applying the coded modulation to label a symbol .