LINEAR TURBO-EQUALIZATION METHOD IN A WIDE SENSE IN A MULTI-USER CONTEXT AND FOR A MULTI-CHANNEL REC

专利摘要:
A method of equalizing a signal received by a plurality of antenna elements, said received signal being derived from the transmission of signals transmitted by a plurality of transmitters, said method comprising: A step of converting the received signal into the domain frequency, • a step of subtracting (203k, m), to said signal, an estimate of the interference between symbols and the interference between users, so as to obtain a complex corrective signal, • A step of linear filtering at the broad direction (204k, m, 201) of said complex corrective signal and the complex conjugate corrective signal to obtain an equalized signal, • A step of conversion of the equalized time domain corrected signal, • A step of calculating (101) the coefficients the equalizer filter from the covariance matrix and the pseudo-covariance matrix of the received signal.
公开号:FR3021471A1
申请号:FR1401178
申请日:2014-05-23
公开日:2015-11-27
发明作者:Antonio Cipriano；Olivier Goubet
申请人:Thales SA；
IPC主号:

专利说明:

[0001] FIELD OF THE INVENTION The field of the invention is that of digital radio communication systems and more particularly multichannel communications receivers, i.e. comprising a plurality of receiving antennas. The invention also relates to multi-user systems in which the communication resources are shared between several users who can simultaneously communicate by sharing frequency bands or time slots. More generally, the invention relates to all multi-user communication systems in which high levels of interference are generated both between transmitters associated with different users but also between the symbols conveyed by a signal transmitted by a user of the device. makes disturbances inherent to the propagation channel. In order to eliminate or at least limit the interference generated on the received signal, it is known to implement an equalization method within the receiver. This feature is intended to clean the signal received from the various sources of interference before it is decoded. In this context, the invention specifically concerns the field of signal equalization in a multi-user context and also the field of turbo-equalization which consists in the iteration of the equalization and decoding functions in the final goal to improve the bit error rate or packet error rate on decoded symbols. The invention finds particular application in cellular communication systems such as the 3GPP LTE system. The invention particularly aims to design a turbo-equalizer based on a linear equalization filter in the broad sense. Such a filter has the property of separately processing the real part and the imaginary part of the signal so as to make the best use of all the information contained in the signal in order to improve the equalization performance. A linear equalizer in the broad sense has improved performance more particularly for signals modulated from a real constellation or a complex constellation having the non-circularity property. The invention also aims at a method of equalization in the frequency domain and which is adapted to a multi-user context. The field of signal equalization subjected to intersymbol interference or inter-user interference has been the subject of numerous publications. Among these, mention may be made of references [1] to [6] (see references at the end of the description). However, the known equalization methods do not make it possible to take into account jointly the following three aspects: The use of a linear filtering technique in the broad sense which consists in applying an equalizing filter at the same time to the complex signal received, but also to its conjugate, the implementation of equalization in the frequency domain, the management of multi-user constraints, in other words the management of the equalization of the multi-user interference and not only the inter-symbol interference for a single user. When this technique is employed, it is most often used for single user applications and for time domain processing. The invention proposes, in order to improve the known equalization methods, a linear equalization method in the broad sense which aims to eliminate the interference between several users and which applies in the frequency domain. The invention is particularly advantageous when the signal is modulated using a real constellation which implies that the pseudo-correlation matrix of the signal is non-zero and can be exploited to improve the equalization filter. To this end, the subject of the invention is a method of equalizing a signal received by a plurality of antenna elements, said received signal being derived from the transmission of signals transmitted by a plurality of transmitters, said method comprising A step of converting the signal received in the frequency domain; a step of subtracting, to said signal, an estimate of the interference between symbols and of the interference between users, so as to obtain a complex corrective signal; A step of linear filtering in the broad sense of said complex corrective signal and of the complex corrective signal conjugated together to obtain an equalized signal; a step of conversion of the corrected signal in the time domain; a step of calculating the coefficients of the equalizer filter from the covariance matrix and the pseudo-covariance matrix of the received signal. According to a particular variant embodiment, the method of equalizing a received signal according to the invention further comprises: a step of subtracting said received signal from an estimate of the transmitted signal and a step of combining the equalized signal with an estimate of the transmitted signal, - The wide linear filtering step being configured to produce, from a number NR, equal to the number of antennal elements, of complex corrective signals, a number K, equal to number of transmitted signals, complex corrected signals equalized. According to a particular aspect of the invention, the wide linear filtering step comprises filtering said complex correction signal by a first equalizing filter and the complex correction signal conjugated by a second equalizing filter.
[0002] According to one particular aspect of the invention, the wide linear filtering step comprises filtering said complex correction signal by an equalizing filter and said equalization method further comprises a step of extracting the real part of each value. of the equalized signal converted into the time domain.
[0003] According to a particular aspect of the invention, the wide linear filtering step comprises filtering said complex correction signal by an equalizing filter and said equalizing method further comprises a step of extracting, alternatively, the real part or the imaginary part of each successive value of the equalized signal converted into the time domain. According to one particular aspect of the invention, the step of calculating the coefficients of the equalizing filter comprises at least: a substep of calculating the equalizer filter in the frequency domain and calculating an estimate of the amplitude of the symbols of the transmitted signal, - A substep of calculation of the covariances and pseudo-covariances of the signal after equalization. The subject of the invention is also a method for turbo-equalizing a received signal comprising the iterative execution of the following steps: a step of executing the method of equalizing a signal received according to the invention; step of transforming the equalized signals into demodulated bits, - a step of decoding the demodulated bits, - a step of transforming the decoded bits into an estimate of the transmitted signal. The invention also relates to the use of the method of equalizing a received signal or the turbo-equalization method according to the invention applied to a signal modulated according to a real constellation, for example a constellation 10 of the BPSK or M-type. WFP. The invention also relates to the use of the method for equalizing a received signal or the turbo-equalization method according to the invention applied to a signal modulated according to an alternately real or imaginary constellation, for example a constellation of the type n / 2-BPSK or u / 2-M-PAM. The invention also relates to a computer program comprising instructions for executing the method of equalizing a received signal or the turbo-equalization method according to the invention, when the program is executed by a processor. and a receiver having a plurality of antenna elements for receiving a signal transmitted by a plurality of transmitters and a processor configured to perform the received signal equalization method or the turbo-equalization method of the invention. Other features and advantages of the present invention will become more apparent upon reading the following description in relation to the accompanying drawings which show: FIG. 1, a diagram of a multi-user communication system comprising an antenna receiver FIG. 2 is a block diagram of a transmitter intended to operate in cooperation with a receiver comprising a turbo-equalizer according to the invention. FIG. 3 is a block diagram of a receiver according to the invention. FIG. 4, a block diagram of a turbo-equalizer according to the invention according to a first implementation variant; FIG. 5, a diagram detailing the equalization function of a symbol within the turbo-generator; equalizer according to FIG. 4; FIG. 6, a diagram detailing the interference suppression function within the equalization function of FIG. 5; FIG. 7, a diagram detailing the broad linear filtering function at sei n of the equalization function of FIG. 5, - FIG. 8, a block diagram of a turbo-equalizer according to the invention according to a second variant of implementation, FIG. 9, a diagram detailing the generation function of a corrective signal within the turbo equalizer according to FIG. 8, - FIG. 10, a diagram detailing the linear filtering function in the broad sense within the turbo-equalizer according to FIG. 8 and according to a first variant of implementation FIG. 11 is a diagram detailing the linear filtering function in the broad sense within the turbo-equalizer according to FIG. 8 and according to a second variant of implementation, FIG. 12, a diagram detailing the function of combination with estimated a useful signal within the turbo-equalizer according to FIG. 8 for the general case of a signal modulated according to a complex constellation; FIG. 13, a diagram detailing the function of combination with estimated useful signal within the turbo-equalizer; r according to FIG. 8 for the particular case of a signal modulated according to a real constellation, FIG. 14, a block diagram of the function for calculating the coefficients of the equalizer in the general case of a signal modulated according to a constellation FIG. 15 is a block diagram of the function for calculating the coefficients of the equalizer in the particular case of a signal modulated according to an actual constellation; FIG. 16 is a diagram again detailing the generation function of a corrective signal within the turbo-equalizer according to FIG. 8 in the case of particular constellations, FIG. 17, a diagram detailing the linear filtering function in the broad sense within the turbo-equalizer according to FIG. 8 and in the case of 18, a diagram of the packet error rate as a function of the signal-to-noise ratio expressed in decibels in a SC-FDMA 1 receiving antenna system with a propagation channel of ETU type for a linear turbo-equalizer according to the prior art coupled with a QPSK modulation and a rate convolutional code equal to 1/3 and a linear broadband turbo-equalizer according to the invention coupled with a 4-PAM modulation and a convolutional rate code equal to 1/3, FIG. 19, a diagram of the packet error rate as a function of the signal-to-noise ratio expressed in decibels in a SC-FDMA type system with 2 reception antennas with a channel of propagation of the ETU type for a linear turbo-equalizer according to the prior art coupled with a QPSK modulation and a rate convolutional code equal to 1/3 and a linear turbo-equalizer in the broad sense according to the invention coupled with a modulation 4- PAM and a convolutional rate code equal to 1/3. Throughout the description of the invention, the following notations will be used. Variables designated by a lowercase letter, such as x, denote a scalar; Variables designated by a lowercase letter in bold, such as x, denote a vector; Variables designated by a capital letter in bold, such as X, denote a matrix; [Xi] ;. 1..N is a vector containing the coefficients xi; NR is a block matrix that contains the matrices Xi; diag (x) is a diagonal matrix with the coefficients x on its diagonal; circ (x) is a circulating matrix with its first column equal to x; E [X] denotes the expectation of the random variable X; ® means the product of Kroenecker between two matrices; xT is the transposed vector of x; XT is the transposed matrix of X; x "is the Hermitian vector of x, that is, the transposed and conjugated vector of x; X" is the Hermitian matrix of X, that is, the transposed and conjugate matrix of X; tr (X) is the trace of the matrix X; IN is the identity matrix of size NxN Fm is the Fourier transform matrix of size MxM, the input k, I of this matrix is equal to [Fm] k, / = 7 exp (-2 ÷ `I), k = O ... M-1 and I = 0 ... M-1. The inverse of the Fourier transform matrix coincides with its conjugate transpose: Fei.
[0004] Subsequently, the term mapping will be used to designate the transformation of one or more bits to a symbol of the constellation of the modulation used to format the signal. The term demapping will be used to designate the inverse transformation to the mapping operation, namely the transformation of a modulated symbol into one or more bits according to the constellation used.
[0005] The expression "soft mapping" designates the mapping operation when it is executed for so-called soft bits, otherwise called bits represented by a non-binary value, typically between 0 and 1 which is characteristic of their probability of likelihood.
[0006] The expression soft demapping designates the operation inverse to the soft mapping operation. Figure 1 shows schematically the communications system considered by the invention. It is a multi-user wireless transmission system comprising a plurality of transmitters 101, ... 10K each transmitting a radio signal to the same receiver 20 which is provided with a plurality of antennas receiving Ai, ... ANr, with Nr the number of antennas at least equal to 1. The transmitters 101, ... 10K each transmit a signal operating the same time and frequency resources which causes interference between users of the viewpoint of the receiver 20. K is equal to the number of transmitters or users. The system described in FIG. 1 is usually designated by distributed Multiple Input Multiple Output (MIMO) system.
[0007] FIG. 2 describes an example of a compatible transmitter 10k of the system targeted by the invention. It should be noted that the invention specifically relates to an equalization method implemented by a receiver 20 and does not include steps performed by a transmitter. However, the type of transmitter envisaged is described solely by way of example and this to facilitate the general understanding of the invention. The functionalities presented in FIG. 2 can be rendered optional and more generally the described transmitter can be replaced by other types of transmitters. The transmitter 10k receives as input bits of information which are coded with an error correction coder 11 which may be a convolutional code, a turbo code, an LDPC code or any other code for which there is a decoding algorithm. which produces soft information, i.e. non-binary information. The bits encoded at the output of the encoder 11 are interleaved with an interleaver 12k which may be different for each transmitter 101, ... 10K.
[0008] The interleaved bits are then modulated by a 13k modulator which may be different from one user to another. The modulator 13k outputs symbols belonging to a given constellation defined according to the type of modulation chosen. As will be described in more detail below, the invention has improved performance, particularly for real constellations, ie for which the modulated symbols have a zero imaginary part. More generally, the invention makes it possible to obtain improved results with respect to known linear equalization techniques when the constellation used for the modulation of the transmitted signal has a so-called non-circularity property. The non-circularity property is expressed formally by the fact that if s (n) is a random symbol of the constellation emitted at time n, then the expectation of this squared symbol is different from zero E [s2 ( n)] # O. The quantity E [s2 (n)] is also called pseudo-covariance in the literature. This property also extends to sampled or continuous signals.
[0009] For the vectors representing a portion of a signal, the pseudo-correlation is written E [s s I. The invention is advantageously applied when this pseudocorrelation has a non-zero value. Real constellations, also called rectilinear (real-valued) constellations such as Binary Phase Shift Keying (BPSK) modulation, or Pulse Amplitude Modulation (PAM) amplitude modulations, are non-circular. The invention can be applied also to real constellations periodically rotated like the u / 2-BPSK, which alternates on each modulated symbol a classical BPSK constellation {÷ 1, -1} and a BPSK constellation rotated by Tr / 2 radians {+ not a word}.
[0010] The invention can also be applied to constellations called quasi-rectilinear, that is to say constellations whose symbols can be obtained by complex filtering of a signal described by the symbols of a real constellation. Examples of such modulations are Minimum 5 Shift Keying (MSK), Gaussian Minimum Shift Keying (GMSK), Continuous Phase Modulation (CPM) continuous phase modulations with Binary Alphabet or Offset Quadrature Amplitude Modulation (OQAM). The invention can also be applied to non-circular complex symbols, such as, for example, rectangular QAM constellations which have no circular symmetry (eg 8-QAM). More generally, the invention is advantageously applied to modulations which have the property of non-circularity. The invention can also be applied to modulations that do not have this property but in this case the improvement of the equalization performance will be negligible. The modulated symbols are then forwarded to a framing block 14 which organizes the block data in a frame and may also insert pilot sequences which will be used, for example, at the receiver for channel estimation. The pilot sequences are generated by a module 15. In addition, the block 14 implements a method of partial periodization of the data blocks, which allows the receiver to implement an equalizer in the frequency domain. For example, block 14 may implement Orthogonal Frequency Division Multiplexing (OFDM) modulation with a total of N subcarriers including M subcarriers used with a prefix CP and possibly a cyclic suffix CS. Block 14 can implement a Single Carrier-Frequency Division Multiple Access (SCFDMA) modulation, with M the number of subcarriers used for precoding with a Discrete Fourier Transform (DFT). Here again the prefix CP and possibly the suffix CS are used.
[0011] In this context, if N = M, the transmitter implements a single carrier signal (Single Carrier - SC). The transmitter also has an RF analog channel 16 for shaping the signal for transmission by radio. This chain 16 introduces imbalances between the channel in phase I and the quadrature channel Q which leads to the output of block 16 a signal which is non-circular. If the imbalances I, Q are known on reception, then the invention can also be applied to this type of signal even if the modulation used does not have the property of non-circularity.
[0012] Subsequently, the method of equalization according to the different variants of the invention is described in detail. The appended figures describe the functional structure of a receiver device configured to implement the equalization method according to the invention. These figures diagrammatically represent the modules that comprise a receiver device according to the invention and the implementation steps of the method according to the invention, it being understood that each module is configured to execute a corresponding step of the method according to the invention.
[0013] FIG. 3 describes the overall functional structure of a linear receiver in the broad sense according to the invention. Such a receiver 300 implements an iterative Interference Cancellation (IC) algorithm whose purpose is to suppress as much as possible the Inter-Symbol Interference also designated by ISI interference and the multi-user interference (Multi- User Interference - MUI) also referred to as MUI interference. When the transmitting antennas are located in the same equipment the multi-user interference MUI is called rather inter-antenna interference. Moreover, the algorithm implements in the iterations a linear filtering in the broad sense, which makes it possible to discriminate the signals received from two transmitters even with a single antenna. In the system considered here, the inter-symbol interference is generated when the signal symbols of the user of interest pass through a multi-path (frequency-selective) channel. The MUI interference is generated by the signals of other users that are transmitted in the same time-frequency resources and are superimposed on the signal of the user of interest in a non-orthogonal manner. This is because, although user signals are transmitted by different antennas, in general there is no perfect spatial separation, except in very special cases. FIG. 3 shows a block diagram with the functional view of the receiver 300 in the case where the transmitted signals are obtained with a so-called SC-FDMA technique with CP prefix insertion. It is assumed here that the signals of the transmitters are synchronized to the receiver with a precision less than the duration of the CP prefix and that a synchronization algorithm has provided the synchronization instant to the receiver. The signals are received by the different antennas A1, ... ANR of the receiver and are formatted into data blocks. On each reception channel, data blocks are extracted and then a step S1, ... SNR deletion of the prefix CP is executed. The data blocks from the receiver's antennas then go through a F-size FFT1, ... FFTNR, (Fast Fourier Transform - FFT) transform step of size N to convert the time domain signals to the frequency domain . Then the sample blocks at the output of the FFTs go into blocks D1,... DNR which operate a selection of the inputs corresponding to the subcarriers actually occupied by the wanted signal. The users use the same M subcarriers, that is, only the useful signals allocated to the M subcarriers used are recovered at this stage and the unused subcarriers are deleted. At the output 302 14 71 14 blocks or steps of sub-carrier de-allocation, the data are grouped into vectors r ,,, n = 1, ..., NR of size M. In parallel, the pilot sequences are extracted signals from the receiving antennas and sent to the block 110 which makes an estimate of the response of the channels and the variance of the noise. This step 110 is used to obtain an estimate of the frequency response of the channels between each transmitter and each receiving antenna, on the M subcarriers of interest (those used by the users to send the information). These frequency responses are organized by simplicity of exposure in a matrix H = [Hill 1 = 1 ... NR k = 1 ... K diagonal by size block (NR M) x (KM), where each matrix is diagonal and contains on its diagonal the estimate of the frequency response of the channel between the user k and the receiving antenna i. The step executed by the block 110 also provides an estimate of the variance of the thermal noise on each receiving antenna or the average of all these variances. In the following we use the second hypothesis. The estimate of the MIMO channel H and the variance of the noise is then passed to the block 101 which carries out a step of calculating the equalizer and parameters related to soft demapping. This block also takes as input the quantities EAp [sk], k = 1, ... K, which are vectors containing the flexible estimates of the symbols sent by the transmitters, and the quantities i5k2, k = 1, K, which are measures of variance of the symbols sent by the transmitters, averaged over the block length M for each transmitter. EApH denotes the average conditioned on all prior information from the decoders and calculated during the previous iteration. The quantities EAp [sk] and uk2 are provided at block 101 by the modules 1021, ... 102K of soft mapping which will be described later. The receiver 300 performs iterative processing.
[0014] At the first iteration, when there is no soft information coming from the decoder, the quantity / 5-k2 = Es, where Es is the average energy of the symbols of the original constellations of the users, supposed constant for all users, and EAp [sk] = 0, for all k = 1, ... K.
[0015] The block 101 outputs at each iteration the coefficients of the equalizer q, and QQ, the parameters rik for k = 1, K, which give a measure of the average amplitude of the useful signals after equalization and the quantities (7 " , q, kk = 1, K, which are estimates of noise after equalization for each user.
[0016] The vectors rn, n = 1,..., NR of size M are transmitted to the module 100 which carries out the turbo-equalization step according to the invention and which takes as input the coefficients of the equalizer Q and EQ, the parameters rik for k = 1, K, and the vectors with the soft estimates of the emitted symbols EAP [sk], k = 1, ... K. Block 100 carries out the interference suppression (IC) for the 15 ISI interferences and MUI. It outputs K vectors of equalized symbols zk, k = 1, K of size M. We note that for the general case of complex constellations (not shown in FIG. 3) we will have two sets of parameters thk and rio, k for k = 1, K, which correspond to the estimated amplitudes of the wanted signal and its conjugate. Each vector zk corresponding to a transmitter is then sent to a module 1031, ... 103K of soft demapping, which produces flexible metrics for each bit which are related to the probability that the bit is 0 or 1. This flexible demapping module takes different forms according to the signal statistic after equalization: if the starting constellation is real one can use a demapper for symmetric complex Gaussian statistics, otherwise a demapper for Gaussian statistics with non-zero pseudo-covariance is more suitable. The soft metrics are then deinterleaved by a de-interleaver 1041, ... 104K which is the inverse block of the 12k interleaver employed by a transmitter. Then, when all the bits of a data packet are retrieved, the soft metrics are sent to a decoder 1051,... 105K which produces estimates of the bits sent and extrinsic information EXT which measures the probability that the bits are 5 0 and 1 but after decoding the error correction code by removing the influence of the equalizer. The extrinsic EXT information is then sent to the interleaver 12k of the user k to be interleaved. The extrinsic EXT interleaved information enters a flexible mapping module 102k which calculates for each block the soft estimates of the emitted symbols E Ap [S k] and the estimate of the average variance of the emitted symbols uk2. The outputs of blocks 12k are sent to blocks 100 and 101 to start a new iteration. Equalization 100 and decoding steps 1051, ... 105K are iterated a predetermined number of times.
[0017] The method of equalization according to the invention executed by the turbo-equalization module 100 of the receiver 300 in a first implementation variant is now described in greater detail. FIG. 4 illustrates this first variant of implementation of the turbo equalization module 100. The turbo-equalization module 100 implements, according to the invention, the method of turbo linear equalization broadly in frequency on the signals coming from the NR antennas of the receiver. Functionally, the turbo equalization block 100 aims to erase the MUI interference and the ISI interference and to equalize the signals in the spatio-frequency domain. A first implementation of the block 100 consists in applying an equalizer 1001.1 ... 100K, m to each received signal symbol on each of the 30 M useful frequency subcarriers and K transmitters transmitting a signal to the receiver simultaneously as represented in FIG. Figure 4.
[0018] Each equalizer 100k, m is composed of two main functions, a first function 203k, m suppression of the interference and a second function 204k, m of linear filtering in the broad sense of the frequency signal. This decomposition is shown in FIG.
[0019] To explain in more detail the structure of the turbo equalizer according to the invention, we must introduce definitions that allow us to process the soft information output decoders. Let E '[] be the average conditioned on all the prior information and Ek, m [.] The average conditioned on all the prior information except for the information relating to the mth symbol of the kth user. This corresponds to the fundamental intuition of the turbo processing according to which, in the treatment of a given symbol, it is not necessary to use the soft information coming from the previous iteration which concerns this same symbol. As a consequence, Ek, m [sk, m 1- = o and Ek ,,,, [5k, m = EÇ. It follows that EE Ap [s] E Ap [S m + (k_mw - E April where the vector - â = s sk, in eM + (k-1) M is equal to the vector s with the (m + (k- - VM ) -e entry zeroed, and where the vector em + (k-1) M is a column vector of size KM x 1 consisting of zeros with the exception of the coefficient of index (m + (k-1) M) which is equal to 1.
[0020] Assuming that we seek to equalize the same symbol of the k-th user, we first subtract an estimate of the total interference reconstructed from the soft information of all the symbols except the same symbol of the k -e user (which is formally expressed by the operator Ek ,, '[s]) and thus form the signal rk, m. rkm = r Fm) Ek, ', [s] = rk, m [s] (1) The interference suppression block 203k m produces the vector rk, m from the input signal vector r, the estimation matrix of the H channel and the EAp symbol estimates [s] provided by the soft mapping modules 102k. FIG. 6 shows in more detail the functions implemented by the block 203k, n, of suppression of the interference. This block executes neither more nor less the treatments represented by equation (1). In other words, the estimate EAp [s] is multiplied by the vector e ',, km and the multiplication result is subtracted from the estimate EAp [s] to produce the vector Ek, m [S] and then a transform of Fourier inverse DFT1, ... DFTK is applied to each portion 10 of the vector Ek, m [s] corresponding to a user. Finally, a step GSI of generating the interfering signals executes the multiplication of the outputs of the DFTs by the estimation matrix of channel H. The interfering signal obtained is finally subtracted from the received signal r. The signal represented by the vector rk, m corresponds to the received signal from which the interference generated by all the symbols except the m-th symbol of the k-th user has been removed. It is then filtered via a step 204k, m of linear filtering in the broad sense. This filtering step is described in FIG. 7. The vector rk, m and its conjugate r * k, m are separately filtered by a multi-antenna filter 403k, m broadly linear from two equalizing filters gi, k ,, and gQ, k ,,,, Let: rk, m1 (2) rk, m, the global vector containing the concatenation of the signal received after suppression of the estimate of the interference with its conjugate: The output of the The filtering step 403k, n, is given by the following expression: ## EQU2 ## is given by the following expression: ## EQU1 ## where: ## EQU1 ## 3) gWL, k, m is a vector of size 2NRM which represents the linear filter in the broad sense and which can also be described in an equivalent way by the two filters g, k, n and gQ, k, ', of size NRM each. The wide-linear filter gWL, k, m therefore jointly processes the signal and its conjugate. Note also that this filter contains an inverse Fourier transform operation. The equalized symbols obtained at the output of this filter are therefore delivered in the time domain. There are two equivalent ways of expressing the signal after suppressing the interference rk, m, which gives two practical interpretations. The first formulation is rk, m = 11 (1K®FM) (i EAPg + HOK® FM 'm + (k-1) MSke + W = 13 (at EAp [4+ SkelYke, Since Ek, m [S] = EAP [s] - EAp [Ske] em '(k_mm = EAP [g] as described above, ii (IK ®FM) EAP [i] is the reconstructed interference (ISI and MUI) that is removed from the signal, and H (IK OFA4) em + (k-1) MSk, m is the useful signal (the useful symbol) highlighted in the expression This expression gives the structure of the block 100 shown in Figure 8. In particular, for each symbol to be decoded from each user, from the soft information from the decoders, the turbo equalizer according to the invention reconstructs the interfering signal which is given by the sum of the signals of the other users (interference MUI) and the ISI interference reconstructed from the symbols of the user of interest minus the symbol that is to be decoded.This reconstructed global interfering signal is then subtracted from the total signal.Then the purified signal d The interference is passed through a frequency equalizer which further improves the separation between users and equalizes the residual ISI interference. The implementation of linear filtering in the broad sense, that is to say a filtering which processes the signal and its conjugate separately via two equalizer filters (4) significantly improves the equalization performance with respect to a standard equalizer filter. Figures 4 to 7 illustrate the general principle of the equalizer according to the invention according to a first implementation for which an equalizing filter is applied to each symbol from each user. The block diagram of Figure 4, however, has the disadvantage of a significant implementation complexity. A second implementation of the equalization method according to the invention is now described in which the processes, although functionally equivalent to those presented for the first implementation above, have a decreased implementation complexity. The relation (4) can be rewritten according to the second equivalent equivalent formulation. rke = r - H (IK O FM) EAP [s] + H (IK 0 FM) e '(k-1) ME APtS kei = r - IBEAp [s] + b-keEAp [ske 13 = H (IK 0 The relation (5) shows that the signal rk, m can be obtained from an estimate of the useful symbol transmitted through the propagation channel H (IK O Fm M + (k-1) ME AP [S ke] and corrected by the corrective term q = r -11 (IK Fm) EAp [s] where the quantity H (IK ®Fm) EAp [s] is a signal estimate 25, after the filtering, it is possible to express the output of the equalizing filter as the sum of the estimate of the useful signal weighted by the coefficient g7k ,, n1-1-k. , in and (5) With its conjugate weighted by the coefficient gak. ', bk *, m and the correction signal filtered by the equalizer: (r-BEAp [Sb [b..k mEAPFSk: m Z k, m = gHWL, k, mrk, m = SWL km (r - / 3 sp EAp [givilL, k, n, 7_ty, * E sk, m AP k, m gWL, k5 m * Ap [Sk, m1 + This interpretation leads to the implementation of the turbo equalizer 5 proposed in FIG. 8 which is composed of three steps 200, 201, 202. According to this second implementation, instead of subtracting the MUI interference and the ISI interference from each useful symbol of each user, the block 200 is intended to subtract an estimate of the overall signal (more useful interference) in order to obtain a corrective signal. This corrective signal is then filtered by the wide linear filter block 201 to increase separation between users and further reduce ISI interference. The filtered corrective signal is then combined with the estimation of the useful signal obtained from the soft information at the output of the decoders at the previous iteration, so as to progressively improve (iteration after iteration) the estimation of the useful signal final. The diagram of FIG. 8 is functionally equivalent to the method described in FIG. 4 but allows a reduction of complexity thanks to the fact that the reconstruction of the signal received in the block 200 can be made by working in block mode with a fast Fourier transform. This is possible when the aim is to reconstruct the received signal in its entirety, ie the wanted signal and the interfering signal, but is no longer possible when the aim is to reconstruct the interfering signal alone as is the case in the first one. implementation variant described in FIGS. 4 to 7. According to the second implementation, the equalizer 100 according to the invention comprises a first block 200 for generating NR corrective signals q1, .. qNR, a second block 201 for linear filtering at broad sense 201 of the corrective signals to produce a set of K corrected filtered signals YK and a third block 202 of combining the filtered corrective signals with an estimated useful signal to produce a set of K equalized signals z1, .. zK. The first block 200 subtracts from the received signal the reconstructed signal from the output information of the soft mapping module. This first block 200 is described in FIG. 9. It converts into the frequency domain each vector of size M containing the soft estimates of the emitted symbols EAp [sk], k = 1, ... K, through a transform of Fourier direct DFT-1, ... DFTK, of size M. A module 300 then performs the following operations. The output vectors of the direct Fourier transforms are concatenated together, the concatenated vector is then multiplied by the channel estimation matrix H and the output vector of size NRM is segmented into NR vectors of size M. The output signals of the Module 300 represents an estimate of the signals received from the reconstructed symbols using the outputs of the decoders. They therefore include MUI interference and ISI interference, ie all sources of interference, as well as the useful signal that is to be decoded. The operations 3011,... 301NR perform an input-input subtraction between the received signals ri_rNR and the estimated output signals of the module 300. At the first iteration of the equalization method, the soft information from the decoder is initialized to zero, and therefore the block 200 does not modify the incoming signal: q '= r'. At the last iteration, assuming that the iterative receiver has converged to correct estimates of the transmitted symbols, the reconstructed signal at the output of the module 300 corresponds to the signals transmitted through the filters of the propagation channels. So the vectors q 'will only represent noise. During the intermediate iterations, when the total signals reconstructed at the output of the module 300 are only a more or less good approximation of the signals actually received without noise, the block 200 produces corrective signals q which, once filtered by the block filtering 201 and summed to the flexible estimates of the useful signals by the block 202 allow the signals zk to gradually approach the useful signals actually emitted (naturally within the limit of the noise present).
[0021] The second wide linear filter block 201 is described in FIG. 10. The NR corrective signals produced at the output of the first block 200 and represented by vectors of size M are concatenated 401 in a single vector q which can be written in the form: q = r -11 (IK FFm) EAp [s] and which is of size equal to NRM Fm is the Fourier transform matrix defined in the preamble of the present description. The vector q is then conjugated 403 input by input to obtain the vector q *. The vectors q and q * are transmitted to the multi-antenna filtering unit 402, which performs the following operation: y qHp + G0 * [gr qiii] cilqw H qW [GQ qg The filtering performed is a linear filtering in the broad sense, c ' that is, the vector q and its conjugate q * are separately filtered. The vector Y, of size equal to MK, is then segmented into K vectors Y k of sizes equal to M. The matrix operation can be done efficiently because the matrices each have only NRMK inputs other than zero. The number K of users is assumed to be known or a hypothesis is taken on this number. Finally, the filtered vectors are converted in the time domain by means of K inverse Fourier transform modules IDFT1, ... IDFTK. The structure of Figure 10 is a generic structure that can be applied to any type of constellation (real, quasi-rectilinear, complex).
[0022] FIG. 11 describes a variant of implementation of the linear filtering module in the broad sense 201 in the case where the emitted signal is modulated with a real constellation. In this case only, the structure of Figure 10 can be optimized to achieve the same function but with a limited number of operations. Indeed, for real constellations it is possible to show that the filter Q1 which is intended to filter the corrective signal q and the filter QQ, which is intended to filter the corrective signal q * are linked by the following relation: ijQ = q (4,1 J) The matrix J is defined as follows: J = FA ,, FA7; - = We notice that the following identities are true: J = Jr = Jr "= J * = J-1. represents the inversion of the frequency axis of a discrete and periodic signal, it can be appreciated by applying an input vector and looking at the output.The multiplication by this matrix can be implemented by permutations. vector obtained by concatenation of all the vectors qn, n = 1,..., NR, and y the vector obtained by concatenation of the vectors yk, k = 1, K, using the preceding property the vector of equalized symbols may be write Y = eq + (lm 0 44H) * (lm ®J) (IM ®J) q * The expression above can be interp Retained as a filter followed by an extraction operation of the real part. Indeed, the filter represented by the frequency-domain Q1 block diagonal matrix has a time-domain impulse response that can be expressed by a block-circulating matrix = (IK®Filf) gi (IK® Fm). The frequency response of the conjugate filter qi * ,, is (im e) .1) (q7 Pim 0J). Moreover, if qt (Ii <oFkl) q is the real signal in the time domain, then in frequency the following identity is verified ('K Fm) q; `= (' M 4q *. This completes the proof.
[0023] The filtering module 201 therefore comprises, according to the second implementation applicable to real constellations and described in FIG. 11, a first module 401 for concatenating the input vectors to obtain the unique vector q, a filtering module 410 of the corrective signal q from the equalizer filter q, a module 411 for segmentation of the K-filtered corrective signal vectors yk, k = 1, K which are each then converted into the time domain via an inverse Fourier transform IDFTk. Finally a last module 411k performs an extraction of the real part of each input of each vector and a multiplication by 2 to provide the equalized corrective signals. Figure 12 depicts the third block 202 of combining the filtered corrective signals with an estimate of the wanted signal. Block 202 adds to each output of filter block 201 an estimate of useful signals, weighted by factors tp, k and riQ, k for k = 1, K, which represent the amplitude of the useful component of the signal and of the conjugate signal of each user after equalization. Block 202 therefore has the function of adding to the corrected signals filtered at the output of the filter block 201 the estimates of the useful signals obtained from the soft information of the decoders calculated at the previous iteration and weighted by the estimates of the amplitudes. rio (and rhk- At the first iteration, the soft information from the decoders is zero, so block 202 has no effect at the first iteration of the process just like block 200 and the output of the filter block 201 is the estimate of the useful signals used.
[0024] At the last iteration, assuming that the iterative receiver has converged to correct estimates of the transmitted symbols, the block 202 adds a noise term from the filtering 201. In the intermediate iterations the function of the block 202 is to improve the estimation of the useful signal by means of the corrective signal at the filter output 201. In the case where the emitted signal is modulated with a real constellation, the block 202 of combination with the estimates of the useful signals takes a simplified form as described in FIG. .
[0025] Since the reconstructed signal is real, the amplitudes tp, k and r1Q, k can be summarized in a single factor rik for k = 1, K, which represents the amplitude of the useful component of the signal of each user after equalization. A single coefficient is therefore sufficient. The logical and functional description of block 202 is the same as for the general case of complex constellations. We now detail the steps necessary to calculate the equalizer filter or filters that are used by the multi-antenna filtering step 402,410 of the linear broadband filter block 201 of the equalizer according to the invention. Firstly, the calculation of the equalizer filters in the general case of a modulated signal with a complex constellation is described. Then one distinguishes successively the case of real constellations of the M-PAM or BPSK type on the one hand and real constellations of the M-PAM or BPSK rotated type also called n / 2-M-PAM or n / 2-BPSK. FIG. 14 describes the module 101 for calculating the coefficients of the equalizer according to a first variant of embodiment applicable to complex constellations. This module 101 comprises a first block 501 for calculating the equalizer 30 in the frequency domain and for calculating an estimate of the amplitude of the useful symbols.
[0026] The module 101 also comprises a second block 502 for calculating the noise variance after equalization. More precisely, block 502 determines the covariances and pseudo-covariances of the signal after equalization. Its implementation is not developed here because it concerns calculation principles known to those skilled in the art. The first block 501 calculates an equalizer according to the criterion of minimization of the mean square error called MMSE criterion. Unlike a zero-forcing equalizer, which aims to perfectly cancel out interference, the goal of this MMSE equalizer is to reduce MUI and ISI interference, if possible up to noise. To achieve this, this equalizer uses the degrees of freedom it has at its frequency response to limit the ISI interference of each user. It also uses the spatial degrees of freedom, given by the number of antennas in reception, to limit the MUI interference and the degrees of freedom related to the statistical properties of the non-circular signals, to further limit the interference MUI. In the following we describe the technique to highlight the location where a multi-user, multi-antenna wide linear approach is used which is one of the novel features of the present invention. Let us define the global vector is.k, ', which contains the concatenation of the received signal rk ,,, after suppressing the estimate of the interference with its conjugate. The MMSE filter, which receives all the samples of the global received signal at the input after removing the estimate of the interference Ik n, and outputs the mth symbol of the k-th user after equalization is written in our case. according to the general formula of an MMSE equalizer. gWI'k, m = gi'k'1 m = C; .- 1 Cr 8 gQ, k, m -km -k, mk, in (7) where ci. is the covariance matrix of Ck, m and c ', ,, k is the cross-covariance or cross-covariance vector of rk, m and the m-th symbol of the kth user sk, m. We note that Cr- = - EAPfr'k'11 "k, m - Crk ', Crk', (8) [C * C * rk, ', and Cj.k, inSk, in 1 k, n1Sk.m C rk msk m, (9) The preceding expressions show that, naturally, the covariance and the cross covariance calculated on the global signal Ik, ', reveal the covariance and the pseudo-covariance of the signal received after suppression of interference rk, m as well as the cross-covariance and pseudo-cross covariance of the signal rk, m with the symbol sk, m which one seeks to equalize. Starting from the expression (5) of rk ,,, it is possible to show that the covariance matrix of rk, ma the following form Crk, = = H k ', trkm -1-13 (diag (17) 02 , ..., F) K2 _1) 01 m) 1311 to 114m = + E1,1 And that the pseudo-covariance matrix of rk, ma the following form Ek ,, n [rk, ', r17,:', +13 (cliaW02 t) 1_1) 01 m) BT (1 1) - mb-) & k, k, m (Es _ ûk2 »k, m er -FE 1,2 15 where the estimates of covariance and pseudo-covariance at From the soft information provided by the decoders are calculated as follows: 2 M 2 k = 1, ..., K k = 1, ..., K Uk = - m M m = 1 M -2 1-) k = .441-) kmm = 1 (10) Where v 12, = E Ap [1S E Ap [Sk ,, n1 2,., --- vk, m = EApk, Sk, m-EAp [sk, ', ]) 2] and Es =] for all k and m, and Ès = Ek ,, n [S km, 2] for all indices k and m. Note that E, and /) ,, n are real numbers and that -Es and 1-51 ', are generally complex numbers. For real constellations Es = Es, 5 "'k, m = The k, m - crk, and Cr, are matrices of size NRM x NRM The presence of multiple users is indicated by the matrix (diag (t7 , 2, ..., ui._3®im) which is of size KM x KM, and its corresponding for the pseudocovariance matrix, and by the matrix B = H (IK © FM) which is of size NRM x KM. We also note that the terms uk2 and ùk2 describe the influence of the soft information from the decoders on the expression of the equalizer, in particular these values give the estimate of the variances and pseudovariances of the transmitted symbols at the first iteration. , uk2 = Es and ûk2 = Ès and we obtain the non-iterative wide-linear linear MMSE spatio-frequency filter (ie without the presence of information from the decoder) Cross-covariance and pseudo-covariance matrices crossed between rk, m and the symbol sk, m are equal to Crkms = Eke [rk ,,, sk ,, '' Es bk, n Crk, ', s = E kmbk, mS k sb-k, m (12) They are vectors of size NRM. Using formulas (10), (11), (12), the equalizing filter can be written as C, o bk, m 0 oo bk *, mg WL, k, tn = Es:: 1 (13) ± [bi, m. 0 - o bk, m (Es t7k2 s ûk2 - (È S) * Es - t.7 The preceding expression is valid for any constellation, complex or real The terms (Es -uk2) and (Ès - & 2 ) measure the progress of the convergence At the first iteration they are zero, at the last iteration = = 612NR ',, and the matrix in the middle is ES 5. We note that the filter E E ss equalizer is a vector of size 2NRM and can also be written as grn mg I, k'm-gl, k, m and gQ, k, m are vectors of size NRM which filter g Q, k, m respectively the signals and their conjugates and constitute one of the outputs of the block 501 for all k and all M. The matrix Ê is defined by: = = E k 'i - E Ap [11) ". - E Ap [dH1 = .E k,. [HH] = [l. Cr e = C ,. Cr / 1,1 / 1: 2 I12 / 1,1 (14) The matrix Eia represents the covariance matrix of the received signal r formed by the concatenation of the vectors rn at the input of the block 100. The vector r is written in the following form: r = 11 (IK OFAjs + w OÙ s is formed by the concatenation of the sk data blocks of the K users and w is a complex zero Gaussian white noise vector with a variance estimated at 6 We can therefore write the covariance matrix as Et, = E Ap - EAp [r]) (r - E Ap 'j Where EAF [] is the calculated expectation using the prior information from the decoders and computed during the previous iteration At the first iteration, this prior information is set to zero and the covariance matrix takes the following form E1,1 - ESHHH + δ-INRA4 where Es = E [Isk (m) 12] for all k = 1, K, and m = 1, ..., M. The covariance is a measure of the correlation between the variation of the signal with respect to its mean e The assumption here is that the symbols emitted by the K users are independent between users and the symbols of each user are independent. This is expressed by the fact that E [sk skH] = ES lm, for each user, and E [ssfri] = Es In ", for the global signal. After passing through the channel, the H terms in the correlation illustrate that the multi-age channel (between the users and the receiver's antennas) introduces a correlation, a link between the received signals. This expresses the fact that the 10 channels between the users and the receiver are not independent "tubes", but there is interference between antennas. Indeed Eti is diagonal block, but it has many non-zero terms outside the main diagonal. At successive iterations, the covariance matrix of the received signal takes the following form Ela =) (Dim) 8 "+ cr 'IN Rm = H (diag (U2, ..., t7i) 01 m) 1111 + (5-1A , Rm This expression holds for any constellation The multi-user aspect is more clearly described when calculating the NR x NR blocks of size M x M of the matrix Ela: K-1 [block (p, q) of, NR kHgrik + 8p-gM (16) 1.0 Ag-4, N, where sp = 1 if p = 0 and sp = 0 otherwise The blocks can be computed quickly because the matrices Hp, k are matrices In addition, Hermitian = z (1 ,,) The matrix Y., 1,2 represents the pseudo-covariance matrix of the received signal r E1 z = EAp [(r- EAp [r]) (r - EAp [r] f Pseudo-covariance is a measure of the correlation between the signal (without its mean, therefore the variation of the signal) with the same variation (15) Since a complex signal is formed of a real part and of an imaginary part, therefore of two random variables, we need two relations for define the statistical behavior of a complex signal. Complex signals whose distribution has a central symmetry around the origin (so-called circularity), have a pseudo-covariance zero. By introducing the received signal model into the definition of the pseudo-covariance matrix one can write (one supposes a complex Gaussian noise with circular symmetry, which gives a zero pseudo-covariance for this noise) E1,2 10K Fm kAp - EAp [sYs - E Ap [S] fliK OFMfir E Ap [WW1 = H (IK Fm) -Es K FI; We have explained the dependence of the pseudo-covariance on the transmitted signal to highlight the impact of the form and the statistics of the transmitted symbols. This pseudo-covariance changes according to the constellation and therefore gives different implementations and also possibilities of different simplifications in the calculation of the equalizer according to the shape of the covariance. Since all the symbols have the same pseudo-covariance (fundamental but not limiting hypothesis that we did) at the first iteration, the pseudo-covariance matrix of the received signal then becomes E1,2 = È, 11 (Iic ® Fm XII (Fl;) 11T E AP [WW1 = = K ® =; 11 (1 K ® j) HT (17) We have defined J = FmFIA; = 1 0 - - 0 0: - ..- ..- o (18) 0 1 0 0 Which in fact represents the pseudo-covariance of the symbols in the frequency domain normalized by the value Ê.
[0027] At successive iterations the pseudo-covariance matrix of the received signal can be written as: (i) OIA, /) 13T =) 0 J) HT (19) The multi-user aspect is more clearly described when calculating NR x NR blocks of size M x M of the matrix, 2 which are written: K-1_ [block (p, q) of Eulp, q = 1,, N = Fk2inpkj-HqT, 4 (20) R k = 0 p , q = 1, ..., NR And can be calculated quickly because the matrices Hp, k are diagonal matrices. Moreover, 2 is a complex symmetric matrix (171,2 = E1,2) - The covariance and pseudo-covariance matrices allow to completely characterize the second-order statistics of a complex signal. For circular signals (e.g., considering a symmetric QAM constellation), the pseudo-covariance is zero. The covariance and pseudo-covariance matrices calculated here make it possible to take into account the multi-user aspect.
[0028] The estimates of the amplitudes of the wanted signal and its conjugate can be calculated as follows: ///, /, - rIQ, k = glj, k, mb-k, q7 We note that the index of the symbol m is omitted because it can be shown that this quantity is independent of the symbol index and depends only on the index of the user. So for the calculation we can choose any index m. Efficient ways to calculate these quantities exist, but they are not detailed here for the case of complex constellations. They will be for the case of real constellations.
[0029] FIG. 15 shows the functional diagram of the calculation of the equalizer in the case of signals modulated by real constellations of M-PAM or BPSK type. The constraint of real constellations makes it possible to simplify the realization of the block 101. In the case of real constellations, the expression (13) of the equalizer is simplified by the following expression: bk, mk, m_ (21) The expression previous can be simplified as follows: WL, k, m = 1, u, km = (Es1) 1 (2) 1; (22) 1+ E yl ek The filter for the symbol m of the user k depends on the soft information through the matrix,, because this matrix contains the estimates of the covariances of the transmitted symbols, and through the factor 1 + Ak , which is a filter energy normalization factor which also depends on the soft information from the decoders. These factors Ak are independent of the index m of the symbol and depend only on the user. This makes it possible to gather a filter per user by uniting the filters of all the symbols of the considered user EH (eK OFm) G WL, ks EH * (IK J) 1+ Â, k This filter, which has a size of 2NRM x M, can be suitably calculated using the property that the matrices have a diagonal block structure or the specific structure of the matrix J. We notice that the matrix (eK Fm) represents the inverse transform (when the filter is applied) from the time domain to the frequency domain, and the other terms represent the actual frequency filter. By concatenating together all the filters of the users one obtains the matrix of size 2NRM x KM, of the global filter which can thus be written GwL = qWL (IK ®Fm) Where the term (IK Fm) indicates the set of inverse DFTs to the filter output. qpn is the 2NRM x KM matrix of the frequency filter Gwc = -1 [H * (17® J) 1 (D) and 0 + .10 '1 + 4_1 is the diagonal matrix of size K x K which collects the real standardization of different users. At the first iteration, when there is no soft information from the decoder, uk2 = Es and ak = 0 and thus the matrix D is the identity of size K x K, which indicates that it There is no influence of the prior information on the calculation of the equalizer at the first iteration. It is possible to efficiently calculate this filter by noting that [I1,1 E1,2 11,2 E1,1 Then the covariance matrix of the received signal, in the case of real constellations, is written at the first iteration ESHHH 6INRA / (24) 15 And at successive iterations 1.1.1 = H (diag (.712, ..., Fik2, ..., t7 ") 04,1) 1111- At the first iteration the information a priori are not defined and the pseudo-covariance matrix takes the following form 11,2 = ESH (IK ®J) HT 20 where ss = E [(sk (421 is the pseudo-covariance of the symbol sk (m) and it is assumed here that it is equal for all k = 1, K, and m = 1, ..., M. We note that for real constellations (the derivation here is made in this case) such as BPSK and PAM, the following equality is true: Ês = Es The matrix J is defined as follows: (1 1 (23) D diag 1 0 0 J = FmF, çi - 0 1 0 0 At successive iterations, when the soft information in from the decoders is non-zero, the pseudo-covariance takes the form 11 2 = H (diag (-171, We note that the terms / 72 here are equal to those present in the covariance matrix simply because for real constellations (sk (42 = sk (m) 2; this is not true in general. Note that Eu is a diagonal matrix per block and that Et2 is a block matrix where each block has the structure of the matrix J. It will be said later that the matrix has a structure J by block. From the covariance matrix f of the received signal concatenated to its conjugate, the function calculates the blocks of the following inverse matrix, which is necessary to calculate the final equalizer derived according to the criterion of minimization of the mean squared error (Minimum Mean Square Error 15 - M MSE): s_i [If S2 S; S; which can be calculated either on the global matrix or by using the identity [A B1-1 (A - BD - 1C) - I - (A - BD - 'C) -1BD - 1 C Di [- (D - CA-'B) -ICA-1 (D-CA-'B) -1 20 And in our case the blocks are written as follows vv * v * -1 S1 = - '1,2.1 S2 = -Si EL2E; J We note that, considering the structure of the matrices in question, the inverses return to compute M times matrix inverses of size NR x (25) NR. Note also that E 1 is Hermitian. Then, if, '= s1 is also Hermitian, and s72- = s2 is symmetric and complex. These matrices are used to form the final equalization matrices. [If SI HS, H (D 0 Im) + S2H * (D (30 Im) = Es [S, g, S * 2 Si * H * (IK ® J) * 14 (D 0 Im S * 111 * (D 0 (26) WL = Es We note here that also the matrices of the equalizer can be computed quickly because they are products of diagonal matrices per block or with a block structure, the coefficients of the equalizer gQ can be calculated from those of q1 by simple conjugation and permutation.In fact, in the case of real constellations, UQ = E; (Im ® J). Only the matrix q, is therefore necessary. The term 10 Es is a design factor of the constellation of the modulation used It can be taken as equal to 1. In addition, let us define the following matrices, which can be calculated taking into account the diagonal structure or J by block: .A1 = HHS1H; A2 = HTS * 2H (27) Then the coefficients Ak, k = 1, K, which measure the influence on the equalizer of the soft information that comes from the decoders, are written: R'k = 2 (Es -Uk) M Re [tr ([A1 tr4 [A 2 lk, k - (28) Let us note that the preceding coefficients are independent of m, and can be computed only once for all the symbols in an efficient way, simply by using the diagonal coefficients of the diagonal matrices by block Ai and (i [K ®J) A2 which are of size KM x KM. The coefficients L L for k = 1, K, give a measure of the average amplitude of the useful signals after equalization / 1 * Es 2Es f 1 rik = = ReLtrei Jk, k j + trql.A2 Jk, k) .1 1 + 2k (Es -r) i) M (1 + 2k) The above expression shows that nk is independent of the index m within the data block. At the first iteration, when there is no soft information from the decoder, uk2 = E, and = 0, and therefore qk becomes exactly that of a wide linear MIMO equalizer in a non-decoder receiver. iterative. The block (502) calculates the k = 1, K estimates of the noise variance after equalization for each user 6e2q, k = Eslik (1-17k). Another embodiment of the invention applicable to modulated signals with a constellation of the type rr / 2-M-PAM or rr / 2-BPSK. According to this variant, the modulation step 13k of the transmitted signal uses real constellations, for example M-PAM or BPSK, but a phase rotation of Tr12 is applied to all the even symbols of each user. This type of modulation makes it possible to lower the ratio between the peak power and the average power of the emitted signal, thus reducing the stresses of the power amplifier relative to constellations which are not rotated. By indicating with j the imaginary unit, the following of the symbols emitted by a user will then be: ck (1) = sk (1), ck (2) = jsk (2), ck (3) = sk (3), ck (4) = jsk (4), etc. We also note that the framing function 14 divides the 25 modulated data symbols into blocks of M emitted symbols. We assume in the following that M is even. With M odd the covariance matrix will be full and the computation complexity of the equalizer will be larger, so this case will not be discussed here. The data blocks can be written as: Ck = d iag ([1 j 1 j 1A) sk = diag (9) sk It is immediate to check that the covariance matrix of such a constellation is E [ccH] = E [ss "] = Es IMK The framing function in this case uses a framing with prefix CP and possibly suffix CS.
[0030] Modifications on the receiver are necessary for this variant of use, they are detailed below. The overall structure of the equalizer 100 described in FIG. 8 remains the same. However, certain sub-blocks must be modified.
[0031] The interference suppression block 200 is re-detailed in FIG. 16. It transforms each vector of size M containing the soft estimates of the emitted symbols E '[sd, k = 1,... Frequency through a transform The flexible estimates, which have real values in this embodiment, at the odd indices of the input block are left unchanged, those of even index are multiplied by the imaginary unit j. This operation is carried out by block 17. Next, the remainder of block 200 operates as before. It is therefore in this case also to generate an estimate of the signals received from the different users from an estimate of the H channel and to subtract this estimate from the received signal to obtain a corrective signal. The NR vectors of size M at the output of the block 200 thus modified concatenated together into a single vector can therefore be written in the form: q = r -11 (IK (FmdiagM)) EAp [s] of size NRM, with e = ... 1 j] vector size M.
[0032] The block 201 of linear filtering in the broad sense is also slightly modified within the framework of the real constellations turned and is described again in FIG. 17. The input is filtered by a filter q, as in the case of the real constellations (not turned) but with different coefficients. After passage in the time domain (IDFT), a new block 412 alternating extraction must be added. This block jointly accomplishes the rotation of the symbols of the constellation and the correct combination that makes it possible to exploit the fact that the constellation of origin is real. Consider a vector a = [a (1) a (M)] of size M even at the input of block 412, then the vector b = [b (1) b (M)] of size M at the output is written: b (2m - 1) = 2 Re [a (2m - 1)], m = 1, ..., M / 2 b (2m) = 2 Im [a (2m)], m = 1, ..., M / 2 where Re () and lm () are respectively the extraction of the real and imaginary part of the argument. Indeed block 412 alternately extracts the real and imaginary part of the input vector and multiplies them by 2.
[0033] Indeed, for actual rotated constellations it is possible to show that the filter Q (which filters the signal) and the filter QQ (which filters the conjugated signal) are linked by the following relation: = qi (Im 4/2) where the matrix J m / 2 is defined as follows Jm / 2 = Fmdiadi -1 1 -1]) G = Fmdiag (yoi) FM (29) Like the matrix J in the case of real constellations, J m / 2 is a permutation of the identity matrix, an anti-diagonal of values at 1 begins at the input (M12 + 1, 1) of the matrix. The values 1 are therefore localized in the entries ([(M / 2-m) mod M] +1, m), for m = 1, ..., M. A4 / 2 has the same properties as the matrix J. The multiplication by this matrix can be implemented by permutations. By calling q the vector obtained by concatenation of all the vectors qn, n = 1, ..., NR, and y the vector obtained by concatenation of the vectors yk, k = 1, K, using the preceding property the vector of symbols Equalized can be written as qiHq (1A4 4/2) 4H) * q * e ci + 0 j A 4/2) 4H q) * denoting cli ,, = (1K 0e-if) (eq) the signal in time after filtering by the filter q1 it is possible to demonstrate that, the signal passed in time and passed through the block 412 can be written y = (IK ® (diag (ço *) Fe)) Y = ( IK diag (ço *)) [cv, + (Im ® diag (yai)) cel What is the mathematical description of the operations made by block 412.
[0034] The block 202 to be used is that in the case of real constellations and is described in FIG. 13. It remains unchanged. Only the numerical values of the factors rik for k = 1, K, change.
[0035] Concerning the block 101 which calculates the equalizer and parameters for the soft demapper, the structure remains the same as in figure 15. The block 502 which calculates the variances of the noise after equalization remains unchanged compared to the case of constellations real.
[0036] Block 501 must have the following modifications. Expressions (21) and (22) remain the same but the matrix,, the vectors kk, et and the coefficients change. Indeed, in the case of real constellations turned the quantities of the preceding equations are B = H (IK O FM) (IK O diag (ço) bk.n, = FI (IK O FM) (IK O diag (dem, ( k-1) M The matrix Ê is written again in its generic form (14) Its sub-matrices take the following forms which make it possible to give an efficient way to implement the computation of the covariance matrix and its inverse It is simple to demonstrate that for the actual rotated constellations, the covariance matrix of the turned symbols is the same as that of the non-rotated real symbols.This implies that the covariance matrix of the signal received at the first iteration and iterations successive is written respectively = E, HHH + 6INRM and = H (diag (Fii2, ..., t7th 0 Im) HH + erIN Rm exactly as in the case of real constellations.
[0037] The difference appears for the matrix E ,, 2 of pseudo-covariance of the received signal. It is easy to demonstrate that at the first iteration (the prior information is not defined) the pseudo-covariance matrix takes the following form = EsH (IK ®Jm / 2) IIT where,, = E [(sk ( 421 = E, as in the case of real constellations The matrix J m / 2 is defined in equation (29) and its application can be implemented by a simple permutation The matrix Jm / 2 represents a translation of M / 2 samples in the frequency axis of a discrete and periodic signal The matrix J m / 2 is the operation corresponding to the multiplication of the signal ei = [1 -1 ... 1 -1] in time which can be seen as a modulation by a periodic signal [1 -1] At successive iterations, when the soft information coming from the decoders is non-zero, the pseudo-covariance takes the form 11,2 = H (diag (1712 JA412) FIT We note that the pseudo-covariance matrix for real constellations turned has the same structure as that of the matrix of pseudo-covariance for real constellations with the only difference that 4/2 takes the place of J. This gives in the calculations a different permutation. Note that; 1 is a diagonal matrix per block and E1,2 is a block matrix where each block has the structure of the 4/2 matrix. It will be said later that the matrix has a structure JM, 2 per block. The matrices S1 and S2 are subsequently calculated through the formula (25), which can be implemented in a less complex manner thanks to the structure of the matrices involved. The matrices S1 and S2 have the same properties as in the case of real constellations. The matrices A1 and A2 are also calculated as in (27). The coefficients / 1k, k = 1, K, which measure the influence on the equalizer of the soft information coming from the decoders, are written in a slightly modified way with respect to (28): 2 2 (Es m 17 Re [trUAI jk, k) + tqJ / 2 LA 2 ik, k As in the case of real constellations, it can be shown that these coefficients are independent of m, and can be computed once for all the symbols in an efficient way. , simply by using the diagonal coefficients of the diagonal matrixes by block Ai and (1K ®JA4 / 2) A2 which are of size KM x KM. The coefficients rite <for k = 1, K, give a measure of the mean amplitude of the useful signals after equalization and are calculated as in the case of real constellations, as a function of Ak. 2k Es 2E, ll 77k - 1 + 2k (Es - 7k2) ± Re [tr (ki) 1- tr (Jm / 2 [A2 ik, k The above expression shows that i7k is independent of the subscript m inside the data block At the first iteration, when there is no soft information from the decoder, t7k2 = Es and Ak = 0, and so qk becomes exactly that of a MIMO equalizer linear in a non-iterative receiver By concatenating all the filters (22) and using (30), by factoring the DFT Fm operation and the rotation (diag (e)), it is possible to write the matrix of the global filter of size 2NRM × KM, GwL = qv. (IK OFmdiag (ç9)) gt4lL is the 2NRM x KM matrix of the frequency filter 2k = (31) QWL qQ1 = E s H (1) 01m) H * (IK 04/2/1 The matrix Git-14 is applied to the signal, L = (IK 0 diag (ço *) F, 1141) e -IL thus showing the inverse Fourier transform IDFT Fe and the de rotation 25 diag (rp *) 302 14 71 44 qvw., has the same structure as the filter in the case of constell Real Ations with the matrix JA, y2 instead of J, the coefficients Ak calculated with (31) and D is calculated as in (23). By following the developments of the case of real constellations, qwL 5 can also be expressed in the following form gWL [g, = E [SiF10 00+ S2H * (D 4/2) qQ_s S2H (D IM IM) + S * H` (D®JMi2) We note here that also the matrices of the equalizer can be computed quickly because they are products of diagonal matrices per block or JM / 2 block structure. Indeed, as explained above, in the case of real constellations turned, GQ = q; (1A, 1®412).
[0038] Only the matrix gi is therefore necessary. FIGS. 18 and 19 illustrate the performance, in packet error rate, obtained thanks to the equalization method according to the invention. FIGS. 18 and 19 show the packet error rate in an ETU channel SC-FDMA system for a prior art linear turbo-equalizer with QPSK and convolutionary rate code 1/3 and for a linear turbo-equalizer at broad sense according to the invention with 4-PAM and convolutional code of 1/3 rate. FIG. 18 shows the performances obtained with an antenna at the reception, FIG. 19 shows the performances with two antennas at the reception. The receiver uses five iterations and the received signals all have the same average power. The curves referenced by L are those obtained with a linear turbo-equalizer according to the prior art. The curves referenced by WL are those obtained with a linear broadband turbo-equalizer according to the invention. K is the number of users, in other words the number of signals transmitted simultaneously. Linear turbo-equalization with K = 1 (single-user) and low signal-to-noise ratio has a gain on the wide-linear linear turbo-equalization which is due to the better form factor of the QPSK compared to the 4- WFP. (32) This shape factor gain disappears if we consider a 4-PAM with a linear turbo-equalizer. We note that, even in the presence of form factor gain, in the case with a receiving antenna, the linear turbo-equalizer can not support two users with an acceptable packet error rate (PER). On the other hand, the broad linear turbo-equalizer according to the invention makes it possible to decode two users with a degradation of 3 dB compared to the linear case. This gain is due to the implementation of the equalizer G,. This is due to formulas (25) where S2 is non-zero. In the case of a linear receiver S2 is zero because the pseudo-covariance matrix 4.2 is imposed zero. In the case with receiver with two antennas the conclusions are similar. For one or two simultaneously decoded users, the proposed broad linear turbo-equalization method has a loss of signal-to-noise ratio of about 2 dB over the linear turbo-equalization method. However, it manages to support more users than a standard linear receiver, including 4 users without significant performance degradation in terms of packet error rate.
[0039] The equalization method according to the invention can be implemented by software and / or hardware means. It can in particular be implemented as a computer program including instructions for its execution. The computer program can be recorded on a processor-readable recording medium.
[0040] The turbo-equalizer according to the invention may in particular be implemented in the form of a processor which may be a generic processor, a specific processor, an integrated circuit specific to an application (also known as ASIC). for "Application-Specific Integrated Circuit") or a network of programmable gates in situ (also known by the English name of FPGA for "Field-Programmable Gate Array").
[0041] 302 14 71 46 References [1] P. Chevalier, F. Pipon, "New Insights into Optimal Widely Linear Array Receivers for the Demodulation of BPSK, MSK, and GMSK Signals 5 corrupted by Noncircular Interferences - Application to SAIC", IEEE Trans. on Signal Processing, y. 54, n. 3, pp: 870-883, March 2006. [2] M. Tüchler, A. C. Singer, "Turbo Equalization: An Overview," IEEE Trans. Information Theory, vol. 57, no. 2, pp. 920-952, February 2011. [3] T. Li, Wang W., and X. Gao, "Turbo equalization for estimating LTE uplink under imperfect channel," in Proc. IEEE 20th Int. Symp. Pers., Indoor Mobile Common Radio, pp. 330-334, Sep. 2009. [4] Zhongxia Pan, Wu Gang, Shu Fang, and Dengsheng Lin, "Practical Soft-SIC Detection for MIMO SC-FDMA System with Co-channel Interference", 2010 Int. Conference on Wireless Communications and Signal Processing 15 (WCSP 2012), pp. 1-5, 21-23 Oct. 2010. [5] S.-R. Lee, F.-B. Ueng, H.-F. Wang, and Y.-K. Chang, "Iterative multiuser detection for LDPC MIMO SC-FDMA communication systems", Wiley Trans Emerging Tel Tech. doi: 10.1002 / ett.2773, 15 January 2014. [6] G. Dietl, C. Mensing, W. Utschick, "Iterative Detection Based on Widely 20 Linear Processing and Real-Valued Symbol Alphabets", 11th European Wireless Conference 2005 - Next Generation Wireless and Mobile Communications and Services (European Wireless), Nicosia, Cyprus, April 2005.

权利要求:
Claims (11)
[0001]
REVENDICATIONS1. A method of equalizing a signal received by a plurality of antenna elements, said received signal being derived from the transmission of signals transmitted by a plurality of transmitters, said method comprising: a step of converting the received signal into the domain frequency, - a step of subtracting (203k, m), to said signal, an estimate of the interference between symbols and the interference between users, so as to obtain a complex corrective signal, - A step of linear filtering at the broad direction (204k, m, 201) of said complex corrective signal and the complex conjugate corrective signal to obtain an equalized signal; - a step of converting the corrected equalized signal in the time domain; - a step of calculating (101) the coefficients the equalizer filter from the covariance matrix and the pseudocovariance matrix of the received signal.
[0002]
A method of equalizing a received signal according to claim 1 further comprising: - a step of subtracting (203k ,,, 200) said received signal from an estimate of the transmitted signal and - A step (202) of combining of the signal equalized with an estimate of the transmitted signal, - The step (204k, m, 201) of linear filtering in the broad sense being configured to produce, from a number NR, equal to the number of antenna elements, of signals complex patches, a number K, equal to the number of transmitted signals, equalized complex correction signals.
[0003]
A method of equalizing a received signal according to claim 2 wherein the wide linear filtering step (201) comprises filtering (402) said complex patch signal by a first equalizer filter (Q1) and the signal complex fix conjugated by a second equalizer filter (QQ).
[0004]
A method of equalizing a received signal according to claim 2 wherein the wide linear filtering step (201) comprises filtering (410) said complex patch signal by an equalizing filter (Q1) and said filtering method. equalization further comprises a step (411) of extracting the real part of each value of the equalized signal converted into the time domain.
[0005]
A method of equalizing a received signal according to claim 2 wherein the wide linear filtering step (201) comprises filtering (410) said complex patch signal by an equalizing filter (IQ) and said filtering process. equalization further comprises a step (412) of extracting, alternately, the real part or the imaginary part of each successive value of the equalized signal converted into the time domain.
[0006]
6. A method of equalizing a received signal according to any one of the preceding claims wherein the step of calculating (101) the coefficients of the equalizer filter comprises at least: a substep (501) for calculating the filter; equalizer in the frequency domain and calculating an estimate of the amplitude of the symbols of the transmitted signal, - a substep (502) for calculating the covariances and pseudocovariances of the signal after equalization.
[0007]
A method of turbo-equalizing a received signal comprising the iterative execution of the following steps: a step of executing the equalization method of a received signal according to any one of the preceding claims, 1031, ... 103K) of transformation of the equalized signals into demodulated bits, - A step (1051, ... 105K) of decoding the demodulated bits, - A step (1021, ... 102K) of transformation of the decoded bits into estimated signal sent. 10
[0008]
8. Use of the equalization method of a received signal according to any one of claims 1 to 6 or the turbo-equalization method according to claim 7 applied to a signal modulated according to a real constellation, for example a constellation of the type. BPSK or M-PAM.
[0009]
9. Use of the equalization method of a received signal according to any one of claims 1 to 6 or the turbo-equalization method according to claim 7 applied to a signal modulated according to an alternately real or imaginary constellation, for example a constellation of Tr / 2 BPSK or Tr / 2 M-PAM type.
[0010]
A computer program comprising instructions for performing the equalization method of a received signal according to any one of claims 1 to 6 or the turbo equalization method according to claim 7, when the program is executed by a processor.
[0011]
A receiver having a plurality of antenna elements for receiving a signal from a plurality of transmitters and a processor configured to perform the received signal equalization method according to any one of claims 1 to 6 or the method turbo-equalization apparatus according to claim 7.

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