Receiver, transceiver system and associated receiving method

[0001] This application is a National Stage of International patent application PCT/EP2022/085484, filed on Dec. 13, 2022, which claims priority to foreign French patent application No. FR 2113831, filed on Dec. 17, 2021, the disclosures of which are incorporated by reference in their entireties.

[0002] The present invention relates to the field of digital data transmissions, and more particularly to equalization for digital communications.

[0003] It relates more particularly to a receiver, to a transmission/reception system comprising said receiver, and to an associated reception method.

[0004] Conventionally, a digital receiver on a transmission chain comprises an equalizer for reducing errors in the detection of symbols transmitted by a transmitter, in the presence of noise and inter-symbol interference (ISI).

[0005] Inter-symbol interference may be caused by:

• • [0006] a limited bandwidth of certain components of the transmission chain, for example photodetector of the receiver, attenuating or phase-shifting some frequencies of the modulated signal more greatly than others;
  • [0007] superposition, at the receiver, of multiple echoes of the modulated signal that are received with their own distinct attenuations, delays and phase shifts, typically in the case of a multipath transmission channel.

[0008] As is known, the receiver comprises:

• • [0009] a sampler designed to sample a received signal that has propagated in a propagation channel, successive symbols being encoded in this received signal, in order to provide one or more samples per received symbol, the symbols belonging to a predefined alphabet;
  • [0010] an equalizer designed to compute, for each received symbol, an estimate of this symbol based on a linear combination of the samples for this symbol; and
  • [0011] a decision module designed to determine the symbol of the alphabet closest to the estimate as detected symbol.

[0012] The article entitled “MMSE Decision-Feedback Equalizers and Coding—Part I: Equalization Results” by John M. Cioffi and M. Vedat Eyuboglu, published in IEEE Transactions on Communications, Vol. 43, No. 10, in October 1995, describes one example of a minimum mean-squared-error decision-feedback equalizer. This type of filter is commonly referred to as an MMSE-DFE.

[0013] The inventors have observed that a receiver using this type of equalizer may exhibit reduced reception performance (for example high bit error rate).

[0014] It may thus be desirable to provide a receiver that improves reception performance.

[0015] What is therefore proposed is a digital data receiver comprising:

• • [0016] a sampler designed to sample a received signal that has propagated in a propagation channel, successive symbols being encoded in this received signal, in order to provide one or more samples per received symbol, the symbols belonging to a predefined alphabet;
  • [0017] an equalizer designed to compute, for each received symbol, an estimate of this symbol based on a linear combination of the samples for this symbol; and
  • [0018] a decision module designed to determine the symbol of the alphabet closest to the estimate as detected symbol;
  • [0019] characterized in that the alphabet exhibits a decentering such that the transmitted symbols have a non-zero predefined expectation, and in that the equalizer is designed to add a non-zero scalar component to the linear combination in order to compensate at least partially for the decentering.

[0020] Indeed, the non-centering of the modulation alphabet induces a bias in the estimate. In particular, with a non-centered alphabet, the MMSE-DFE equalizer from the prior art recalled above is not optimum in that it does not make it possible to minimize the mean-squared-error criterion.

[0021] Adding the non-zero scalar component before making the decision makes it possible to compensate at least partially for the induced bias, and thus to obtain more efficient symbol detection, in particular by achieving a reduced bit error rate.

[0022] This means that the decision module following the equalizer may consist of decision thresholds or regions the value or form of which are independent of the equalizer, and dependent solely on the modulation alphabet. The practical implementation thereof is therefore simplified as a result, for example compared to the decision module of the receiver from the prior art described above, where the decision thresholds have to be adapted to the value of the coefficients of the equalizer.

[0023] The invention may furthermore comprise one or more of the following optional features, in any technically feasible combination.

[0024] Optionally, the equalizer is designed to compute the scalar component based on coefficients of the linear combination of the samples and the predefined expectation.

[0025] Also optionally, the equalizer is designed to compute the scalar component based on a channel matrix representative of the propagation channel.

[0026] Also optionally, said channel matrix is a block Toeplitz matrix.

[0027] Also optionally, the equalizer is designed to compute said scalar component so as to minimize a mean squared error between the transmitted symbols and the estimates.

[0028] Also optionally, the equalizer comprises a feedforward filter, preferably a finite impulse response filter, and the equalizer is designed to apply this feedforward filter to the samples in order to provide said linear combination.

[0029] Also optionally, the equalizer is designed to compute, for each received symbol, the estimate of this symbol independently of previously detected symbols.

[0030] Also optionally, the equalizer is designed to compute, for each received symbol, the estimate of this symbol based on a difference between the linear combination of the samples for this symbol and a linear combination of previously detected symbols, the scalar component being added to this difference.

[0031] Also optionally, the equalizer furthermore comprises what is referred to as a backward filter, preferably a finite impulse response filter, and the equalizer is designed to apply this backward filter to the previously detected symbols so as to provide said linear combination of previously detected symbols.

[0032] Also optionally, the equalizer is designed to compute the scalar component based on the feedforward filter.

[0033] Also optionally, the equalizer is designed to compute the scalar component based on the backward filter as well.

[0034] Also optionally, the equalizer is designed to iteratively update the scalar component on the basis of symbols previously determined by the decision module.

[0035] What is also proposed is a digital communication system, characterized in that it comprises a transmitter designed to transmit symbols selected from an alphabet with a non-zero expectation, and a receiver according to the invention.

[0036] What is also proposed is a method for receiving digital data, comprising:

• • [0037] for each of multiple successive symbols encoded in a received signal that has propagated in a propagation channel, the symbols belonging to a predefined alphabet, receiving multiple samples;
  • [0038] carrying out a linear equalization by computing, for each received symbol, an estimate of this symbol based on a linear combination of the samples for this symbol; and
  • [0039] determining the symbol of the alphabet closest to the estimate as detected symbol;
  • [0040] characterized in that the alphabet exhibits a decentering such that the transmitted symbols have a non-zero predefined expectation, and in that the linear equalization comprises adding a non-zero scalar component to the linear combination in order to compensate at least partially for the decentering.

[0041] What is also proposed is a computer program able to be downloaded from a communication network and/or recorded on a computer-readable medium, characterized in that it comprises instructions for executing the steps of a method according to the invention when said program is executed on a computer.

[0053] Hereinafter, vectors will be indicated in bold so as to distinguish them from scalars. The exponent^H associated with a matrix will hereinafter denote the conjugate transpose of this matrix.

[0054] One example of a digital communication system 100 in which the invention is implemented will now be described with reference to FIG. 1.

[0055] The digital communication system 100 comprises a transmitter 102, a receiver 104 and a propagation channel 106 connecting the transmitter 102 to the receiver 104.

[0056] More specifically, the transmitter 102 is designed to transmit a signal e(t) carrying a digital message. By definition, a digital message is a sequence of binary elements, commonly referred to as bits.

[0057] The transmitter 102 is designed to successively encode, in the signal e(t), symbols s_n respectively representing blocks or words of p successive bits. Each symbol s_n corresponds to one or more modulations of a carrier signal at a carrier frequency, such that the modulated carrier signal forms the signal e(t). Each symbol s_n belongs to an alphabet Ω with K elements {S₀, S₁, . . . , S_K−1} respectively associated with the various possible combinations of bits in a word. The transmitter 102 is designed to transmit the symbols regularly with a symbol period Ts.

[0058] In the context of the present invention, this alphabet Ω is non-centered, that is to say that the transmitted symbols s_n have a non-zero expectation, that is to say [s_n]≠0, in particular when the transmitted data lead to a substantially equiprobable selection of the elements of the alphabet Ω.

[0059] Modulations having a non-centered alphabet include intensity modulations, such as on-off keying (OOK) or else the K-ary generalizations thereof (K being the number of possible intensity levels). Any other modulation may also be used, provided that the alphabet that is used is non-centered.

[0060] In general, it will be assumed that the transmitted symbols are decorrelated from one another, that is to say that the value of a transmitted symbol does not depend on the value of the previously transmitted symbols, and that the transmitted symbols s_n have a non-zero variance:

[0061] ${\sigma }_s^2$
=[|s_n|²]−²[s_n].

[0062] For example, in the case of an optical communication system implementing optical on-off keying (OOK), the transmitter 102 may be an amplitude-modulated laser source configured to transmit a laser pulse of amplitude A upon each symbol associated with the bit “1”, but no pulse (that is to say substantially zero amplitude) upon each symbol associated with the bit “0”. The reverse association could also be used. In this case, the transmitted symbols s_n take their values equiprobably from the binary alphabet {0, A}, and so their expectation [s_n] is equal to A/2 and their variance

[0063] ${\sigma }_s^2$
is equal to A²/4.

[0064] In general, the propagation channel 106 is a physical medium designed to transmit the signal e(t) transmitted by the transmitter 102, for example in the form of electromagnetic (that is to say optical or radiofrequency) waves, such that it is able to be received by the receiver 104. For example, the propagation channel 106 is an optical fiber, a coaxial electrical line, air or water or any other natural medium able to transmit for example an optical or radiofrequency signal.

[0065] The propagation channel 106 is linear in the sense that the effects or deformations that it induces on the signal are linear. To this end, the transmitter 102 is for example configured to transmit at a power lower than a non-linear distortion threshold of the propagation channel 106, for example a non-linear dispersion threshold.

[0066] For example, in the case of an optical communication in which the propagation channel 106 is an optical fiber, the transmitted optical power is adapted according to the optical fiber that is used in order to avoid the non-linear effects of the fiber.

[0067] In addition, the propagation channel 106 is of a dispersive nature, that is to say liable to generate inter-symbol interference. For example, this is the case for a chromatic-dispersion optical fiber that induces widening of optical pulses during propagation or for a multipath radio or optical transmission channel in which multiple copies of one and the same symbol are detected by the receiver 104 with different delays.

[0068] Moreover, the propagation channel 106 may be marred by a noise w(t), for example with zero mathematical expectation and independent of the transmitted symbols s_n. For example, the noise w(t) is a centered Gaussian additive noise with a variance σ_w².

[0069] The receiver 104 is designed to receive an analog signal r(t) corresponding to the transmitted signal e(t) after propagation through the propagation channel 106.

[0070] Conventionally, the receiver 104 is for example configured to receive the received signal r(t) on the carrier frequency of the signal from the transmitter 102 and to transpose this signal into baseband (that is to say around a zero frequency) and to filter it, for example, by applying a low-pass filter. The signal after transposition and filtering is still denoted r(t).

[0071] Knowing the alphabet Ω, the receiver 104 is also designed to detect, in this received signal r(t), the symbols s_n that were initially transmitted, in particular in the presence of noise and inter-symbol interference in the received signal r(t). The receiver 104 is thus designed to provide a detected symbol ŝ_n for each transmitted symbol s_n.

[0072] A first embodiment of the receiver 104 will now be described with reference to FIG. 2.

[0073] The receiver 104 comprises a sampler 208 designed to sample the received signal r(t) and thus provide successive samples y_n,m of this signal r(t).

[0074] In particular, for each symbol period T_s corresponding to the transmission of a symbol s_n, the sampler 208 provides a set y_n of M samples y_n,m (M being greater than or equal to one) such that:

[0075] $\begin{array}{cc}{y}_n=\left(\begin{array}{c}{y}_{n,M-1}\\ \dots \\ y_{n,0}\end{array}\right)& \left[\mathrm{Math}1\right]\end{array}$
where m is an integer index varying from 0 to M−1, M denoting the total number of samples per symbol received during the symbol period T_S.

[0076] FIG. 3 schematically illustrates one example of a received signal r(t) and the corresponding digitized signal y_n as provided at output of the sampler 208.

[0077] In general, the sampler 208 is configured to take M samples per symbol with a sampling period T_e between each sample, such that T_e=T_S/M.

[0078] In the example of FIG. 3, the sampler 208 is configured to take two samples (M=2) per symbol period T_S. The sampling period T_e is equal to half the symbol period T_S, such that T_e=T_S/2. The sampler 208 thus provides the following three sample vectors for the three consecutive symbols s_n, S_n+1, S_n+2, respectively:

[0079] $\begin{array}{cc}{y}_n=\left(\begin{array}{c}{y}_{n,1}\\ y_{n,0}\end{array}\right);y_{n+1}=\left(\begin{array}{c}{y}_{n+1,1}\\ y_{n+1,0}\end{array}\right);y_{n+2}=\left(\begin{array}{c}{y}_{n+2,1}\\ y_{n+2,0}\end{array}\right)& \left[\mathrm{Math}2\right]\end{array}$

[0080] Returning to FIG. 2, the receiver 104 furthermore comprises an equalizer 210 connected to the output of the sampler 208. The equalizer 210 is configured to provide, at each symbol period T_S, an estimate z_n of the received symbol based on the M samples y_n,m provided by the sampler 208.

[0081] The receiver 104 furthermore comprises a noise estimator 212 connected to the output of the sampler 208, on the one hand, and to the equalizer 210, on the other hand. Conventionally, the noise estimator 212 is configured to compute the variance σ_w² of the noise based on the samples y_n provided by the sampler 208 and to provide this variance to the equalizer 210.

[0082] In the present example, the noise is a Gaussian additive noise that is centered (that is to say with zero expectation), with a variance σ_w² and independent of the transmitted symbols. More generally, the noise characteristics are specific to the communication system in question and depend notably on the nature of the transmission channel 106. These characteristics will thus be able to be adjusted depending on the transmission system under consideration.

[0083] The receiver 104 furthermore comprises a channel estimator 214 connected to the output of the sampler 208, on the one hand, and to the equalizer 210, on the other hand. The channel estimator 214 is configured firstly to compute, based on the samples y_n, a channel matrix H representative of the deformations that the propagation channel 106 imposes on the symbols, and secondly to provide this channel matrix H to the equalizer 210. This matrix describes the inter-symbol interference model specific to the propagation channel in question.

[0084] Preferably, the channel matrix H is a block Toeplitz matrix, comprising for example at least one non-zero block in the first position of the first row and the first column.

[0085] The equalizer 210 is configured to receive data relating to the modulation format used by the transmitter 102 to transmit the symbols. For example, these data include the expectation [s_n] and/or the variance

[0086] ${\sigma }_s^2$
of the transmitted symbols s_n.

[0087] The equalizer 210 will be described in more detail below with reference to FIG. 4.

[0088] The receiver 100 furthermore comprises a decision module 216 designed to select the symbol of the alphabet Ω closest to the estimate z_n. The selected symbol is thus taken as detected symbol ŝ_n-α, where Δ is the restitution delay, which is a parameter of the equalizer 210.

[0089] For example, the decision module 216 is designed to compare the estimate z_n with regions defined by predefined thresholds, each region being respectively associated with one of the symbols of the alphabet Ω. The thresholds are independent of the equalizer 210 and in particular of its coefficients p^H and of its scalar component Θ, which will be described later.

[0090] The equalizer 210 of the receiver 104 from FIG. 2 will now be described in more detail with reference to FIG. 4.

[0091] The equalizer 210 comprises a sample combiner, referred to as feedforward combiner 400, designed, for each symbol period T_S, to receive the samples y_n and to provide a linear combination y′_n of said samples.

[0092] For example, the feedforward combiner 400 is defined by forward coefficients p^H, such that the linear combination y′_n is obtained by weighting the samples y_n with the forward coefficients p^H, such that y′_n=p^H×y_n, where × is the scalar product.

[0093] For example, this feedforward combiner 400 is a feedforward filter, preferably a finite impulse response (FIR) digital filter.

[0094] The equalizer 210 furthermore comprises a configuration module 400a for configuring the feedforward combiner 400, for configuring said combiner on the basis of configuration parameters.

[0095] For example, these configuration parameters include channel parameters specific to the propagation channel 106, such as the channel matrix H and/or the noise variance σ_w². These configuration parameters may also include parameters specific to the modulation alphabet Ω, such as the variance σ_s² of the transmitted symbols s_n.

[0096] If the feedforward combiner 400 is an FIR filter, the configuration module 400a determines the coefficients p^H defining the filter. For example, this vector p^H comprises N×M coefficients, such that the feedforward combiner 400 provides a linear combination of samples every T_S seconds.

[0097] The equalizer 210 furthermore comprises a feedback loop between the decision module 216 and the feedforward combiner 400, in order to improve symbol detection based on the previously detected symbols. This loop comprises a detected-symbol combiner, referred to as feedback combiner 420, at the output of the decision module 216, on the one hand, and a subtractor 440 between the feedforward combiner 400 and the feedback combiner 420, on the other hand.

[0098] The feedback combiner 420 is configured to provide, for each symbol period T_S, a linear combination of the symbols ŝ_n−Δ−1, ŝ_n−Δ−2, . . . previously detected by the decision module 216 Δ symbol periods earlier. This linear combination of symbols is denoted ŝ′_n.

[0099] For example, the feedback combiner 420 is a backward filter, preferably a finite impulse response (FIR) digital filter. As an alternative, the backward filter could be an infinite impulse response (IIR) filter.

[0100] The equalizer 210 furthermore comprises a configuration module 420a for configuring the feedback combiner 420, designed to configure said combiner on the basis of parameters specific to the propagation channel 106, such as the channel matrix H, and configuration parameters of the feedforward combiner 400, such as the coefficients p^H.

[0101] If the backward filter is an FIR filter, the configuration module 420a for configuring the symbol feedback combiner 420 determines a vector of coefficients q^H defining the filter, this vector comprising N_b coefficients, such that the backward filter 420 provides a linear combination of samples every T_S seconds.

[0102] The subtractor 440 is configured to compute a difference d between the linear combination y′_n of the samples y_n and the linear combination of the previously detected symbols ŝ′_n, that is to say the difference

[0103] $d=y_n^{\prime }-{\hat{s}}_n^{\prime }.$

[0104] The equalizer 210 furthermore comprises an addition module 460 between the subtractor 440 and the decision module 216. Advantageously, the addition module 460 is configured to add a non-zero scalar component Θ to the difference d, such that the estimate z_n is given by

[0105] $z_n=y_n^{\prime }-{\hat{s}}_n^{\prime }+\Theta .$

[0106] Adding this non-zero scalar component Θ makes it possible to compensate at least partially for the bias resulting from the impact of the expectation [s_n] of the transmitted symbols s_n through the combined action of the channel matrix H and the coefficients p^H.

[0107] The equalizer 210 furthermore comprises a configuration module 460a designed to compute the non-zero scalar component Θ and to provide this component to the addition module 460 so as to add it to the difference d.

[0108] For example, the configuration module 460a is configured to compute the non-zero scalar component Θ on the basis of parameters related to the alphabet Ω, such as the expectation [s_n] of the transmitted symbols s_n, of configuration parameters of the pre-combiner 300, such as the coefficients p^H, and/or of parameters specific to the propagation channel 106, such as the channel matrix H.

[0109] Thus, if the equalizer 210 implements an FIR pre-filter 300 defined by the coefficients p^H and a backward FIR filter 320 defined by the coefficients q^H, the estimate z_n provided at input of the decision module 216 is such that:

[0110] $\begin{array}{cc}{z}_n=p^H\times y_n-q^H\times {\hat{s}}_n+\Theta & \left[\mathrm{Math}4\right]\end{array}$

• • [0111] where

[0112] ${\hat{s}}_n=\left(\begin{array}{c}{\hat{s}}_{n-\Delta -1}\\ \dots \\ {\hat{s}}_{n-\Delta -\mathrm{Nb}}\end{array}\right)$

• • [0113]  denotes the vector grouping together the N_b past decisions relating to the symbols transmitted Δ+1 symbol periods earlier.

[0114] The configuration modules 400a, 420a, 460a are designed to configure the feedforward combiner 400, the feedback combiner 420 and the scalar component addition module 460, respectively. These modules may be implemented in the form of software executed by one and the same information processing module, such as that described below with reference to FIG. 9.

[0115] A method 500 for configuring the equalizer 210 will now be described with reference to FIG. 5, in the case where the pre-combiner 400 and the feedback combiner 420 are FIR filters as described with reference to FIG. 4.

[0116] In an initialization step E50, the receiver 104 receives a known reference message from the transmitter 102. The noise estimator 212 and the channel estimator 214 described above with reference to FIG. 2 determine, based on analysis of this known message, the noise variance σ_w² and the channel matrix H, respectively, and provide this information to the equalizer 210.

[0117] In a sampling step E51, the sampler 208 samples the received signal r(t) corresponding to an unknown message e(t) transmitted by the transmitter 102, so as to provide a set of blocks of M successive samples for N received symbols. A block of M samples is thus provided every T_S seconds (symbol period) by the sampler 208.

[0118] By collecting the last N×M received samples (that is to say N blocks of M samples), up to the time NT_S+(M−1) T_S/M, in the form of vectors, the samples may be written in the framework of the model presented as follows:

[0119] $\begin{array}{cc}\left(\begin{array}{c}{y}_n\\ ⋮\\ y_{n-N+1}\end{array}\right)=\left(\begin{array}{cccccc}{h}_0& \dots & h_{L-1}& 0& & 0\\ 0& \ddots & & \ddots & & ⋮\\ ⋮& 0& \ddots & \ddots & & 0\\ 0& \dots & 0& h_0& \dots & h_{L-1}\end{array}\right)\left(\begin{array}{c}{s}_n\\ ⋮\\ s_{n-N-L+2}\end{array}\right)+\left(\begin{array}{c}{w}_n\\ ⋮\\ w_{n-N+1}\end{array}\right)& \left[\mathrm{Math}5\right]\end{array}$

• • [0120] H denoting the channel matrix, preferably equal to a block Toeplitz matrix describing the inter-symbol interference model specific to the propagation channel, s_n being the vector of the transmitted symbols contributing to the inter-symbol interference present in the last N×M received samples, and w_n is a centered Gaussian noise vector with a variance σ_w² on each coordinate and independent of the transmitted signal.

[0121] For example, the channel matrix comprises two null blocks, more specifically a lower null triangular block and an upper null triangular block.

[0122] In a computing step E53, the configuration module 400a for configuring the feedforward combiner 400 computes the coefficients p^H, the configuration module 420a for configuring the feedback combiner 420 computes the coefficients q^H and the configuration module 460a for configuring the addition module 460 computes the non-zero scalar component Θ.

[0123] For example, the parameters p^H, q^H, Θ of the equalizer 210 are computed so as to minimize the mean squared error (MSE) cost function between the estimate z_n and the symbol s_n-Δ, where Δ denotes the delay in the restitution of the symbols by the receiver, denoted:

[0124] $\begin{array}{cc}J\left(p^H,q^H,\Theta \right)=𝔼{❘z_n-s_{n-\Delta }❘}^2& \left[\mathrm{Math}6\right]\end{array}$

• • [0125] As an alternative, the parameters p^H, q^H, Θ of the equalizer 210 are computed so as to minimize a bit error rate (BER).

[0126] Advantageously, the delay Δ may be optimized. For example, it is possible to trial multiple values of the delay Δ (for example by scanning) to find the best one, that is to say the one that minimizes the cost function J.

[0127] The result of this computation to minimize the function J makes it possible to determine the parameters p^H, q^H, Θ of the equalizer 210 using the following expressions:

[0128] $\begin{array}{cc}{p}^H={\sigma }_s^2{h_{\Delta +1}^H\left({\sigma }_s^{2}H\left(I-J_{\Delta }{J}_{\Delta }^H\right)H^H+{\sigma }_w^{2}I\right)}^{-1}& \left[\mathrm{Math}.7\right]\end{array}$ $q^H=p^H{\mathrm{HJ}}_{\Delta }$ $\Theta =𝔼\left(s_{n-\Delta }\right)\left(1-p^H{\sum }_H+\sum _i{q}_i^{*}\right)$

• • [0129] where Σ_H=Σ_i H (:, i) denotes the sum of the values of the columns of the channel matrix H; h_Δ+1=H(:, Δ+1) denotes the column Δ+1 of the channel matrix H; (s_n) denotes the expectation of the transmitted symbols; σ_s² denotes the variance of the transmitted symbols; q_i* denotes the coefficient of rank i in q^H; I denotes the identity matrix;

[0130] $J_{\Delta }=\left(\begin{array}{c}{0}_{\left(\Delta +1\right)\times N_b}\\ I_{N_b}\\ 0_{s\times N_b}\end{array}\right)$

• • [0131]  with s=N+L−2−Δ−N_b; and 0 denotes the null matrix.

[0132] The value of the non-zero scalar component Θ is thus defined notably on the basis of the mathematical expectation of the non-centered alphabet Ω and of the channel matrix H modeling in particular inter-symbol interference.

[0133] This result is obtained making the following assumptions: the value of the transmitted symbols s_n is a stationary random variable, meaning that the mathematical expectation of the symbols is time-invariant, that is to say (s_n)=(s_n-Δ); the noise is decorrelated from the transmitted symbols s_n, meaning that the covariance of the noise and the symbols is zero; and the noise has a zero mathematical expectation, that is to say (w_n)=0.

[0134] The expressions computed above are obtained assuming a zero-mean Gaussian white noise. However, they could of course be adapted by those skilled in the art so as to take into account other noise statistics, for example a correlated noise, while still remaining within the scope of the present invention.

[0135] The equations [Math 7] are for example determined beforehand and implemented respectively in the configuration modules 400a, 420a, 460a.

[0136] In a configuration step E55, the parameters p^H, q^H, Θ are applied to the pre-filter 300, to the backward filter 320 and to the addition module 360, respectively, so as to configure the equalizer 210.

[0137] Once the equalizer 210 has been configured, the configuration parameters remain unchanged for the reception of multiple symbols.

[0138] A second embodiment of the receiver according to the invention will now be described with reference to FIG. 6.

[0139] According to the second embodiment, the equalizer, which now bears the reference 610, differs from the equalizer 210 according to the first embodiment in that it does not comprise a feedback loop.

[0140] The feedforward combiner 400 thus provides the linear combination y′_n based on the samples y_n and the addition module 460 adds the non-zero scalar component Θ to this linear combination y′_n so as to obtain the estimate z_n, such that z_n=y′_n+Θ. The estimate z_n is thereby computed independently of the previously detected symbols ŝ_n−Δ−1, ŝ_n−Δ−2, etc.

[0141] As described above, the feedforward combiner 400 may be an FIR filter configured by the configuration module 400a and designed to compute the coefficients p^H. The estimate z_n is thus determined on the basis of these coefficients, such that z_n=p^H×y_n+Θ.

[0142] The method described with reference to FIG. 5 remains valid, with the difference that only the coefficients p^H and the non-zero scalar component Θ are computed in step E53.

[0143] The parameters p^H and Θ of the equalizer 610 are computed making the same assumptions as those made previously for the first embodiment. In this case, the parameters of the equalizer 610 are determined according to the following expressions, with the same notations as previously:

[0144] $\begin{array}{cc}{p}^H={\sigma }_s^2{h_{\Delta +1}^H\left({\sigma }_s^2{\mathrm{HH}}^H+{\sigma }_w^{2}I\right)}^{-1}& \left[\mathrm{Math}.8\right]\end{array}$ $\Theta =𝔼\left(s_{n-\Delta }\right)\left(1-p^H{\sum }_H\right)$

[0145] It may be seen that the non-zero scalar component Θ depends solely on the predefined expectation of the alphabet Ω, the channel matrix H and the coefficients p^H.

[0146] Assuming that the value of the symbols s_n is a stationary random variable, then the associated expectation is time-invariant, meaning that (s_n-Δ)=(s_n). Assuming that the propagation channel 106 is stationary over a reference period, the channel matrix H is time-invariant. In this case, the non-zero scalar component Θ is a constant over this reference period.

[0147] In the two embodiments described above, the parameters of the equalizer 210 are initially computed analytically, notably on the basis of external parameters related to the propagation channel 106, to noise and to the statistical properties of the symbols s_n. In particular, the channel estimator 214 and the noise estimator 212 may be used to provide the equalizer 210 with the channel matrix H and the noise variance σ_w².

[0148] As an alternative, the parameters (Θ, p^H, q^H) or (Θ, p^H) of the equalizer 210 may be determined adaptively using a convergence and tracking technique. This technique constitutes one variant implementation that may be applied to each of the embodiments described above.

[0149] One variant of the first embodiment of the equalizer will now be described with reference to FIG. 7 for determining and adjusting the parameters of the equalizer using a convergence and tracking technique.

[0150] According to this variant, the equalizer, which now bears the reference 710, is designed to iteratively update the scalar component Θ on the basis of symbols previously determined by the decision module 216. This does not require the use of a decoder (or soft demapper) that uses multiple successive estimates to analyze them, as with error correction. On the contrary, the decision module 216 provides each symbol ŝ_n-Δ based on a single estimate z_n.

[0151] The equalizer 710 thus furthermore comprises a comparison module 780 for comparing the symbols previously detected by the decision module 216 with the estimate z_n, so as to compute an error signal e_n. For example, the error signal e_n provided at output of the comparison module 780 is such that e_n=z_n−s_n-Δ.

[0152] The comparison module 780 has an output connected to the configuration module 700a for configuring the feedforward combiner 400, to the configuration module 720a for configuring the feedback combiner 420 and to the configuration module 760a for configuring the addition module 460, such that the error signal e_n is provided, for each symbol period, simultaneously at input of these configuration modules 700a, 720a, 760a.

[0153] A method 800 for configuring the equalizer 710 will now be described in more detail with reference to FIG. 7.

[0154] In an initialization step E80, the parameters p^H, q^H, Θ of the equalizer 710 are initialized, for example with the following default values: p^H=(1, 0, 0, . . . , 0); q^H=(0, 0, 0, . . . , 0); Θ=0.

[0155] In a transmission/reception step E82, the transmitter 102 starts sending a known sequence of symbols, and the receiver 104 receives this sequence.

[0156] This known sequence of symbols is used by the equalizer 710 to update its configuration parameters p^H, q^H, Θ as it receives the symbols of the known sequence. This update is carried out iteratively, in a convergence phase B1 as described below.

[0157] Upon each new set of M samples y_n provided by the sampler 208, the configuration parameters p^H, q^H, Θ of the equalizer 710 are updated. The parameters of the equalizer 710 are thus updated once per symbol period, for each symbol of the known sequence received in the convergence phase B1.

[0158] This update is carried out by comparing the estimates z_n of the symbols with the symbols of the known sequence.

[0159] Each symbol s_n of the known sequence is received by the receiver with a delay Δ. Thus, in a comparison step E84, the comparison module 780 provides, for each symbol period, the error signal e(n) between the estimate z_n and the received symbol s_n-Δ such that e_n=z_n−s_n-Δ. This error signal e(n) is transmitted, at each symbol period, to the configuration modules 700a, 720a, 760a.

[0160] In an update step E86, the configuration modules 700a, 720a, 760a compute the configuration parameters p^H, q^H, Θ of the equalizer 710 on the basis of the initial value set in the initialization step E80 or of an earlier value of the parameters determined in the previous period (that is to say in a previous iteration).

[0161] For example, in the update step E86,

• • [0162] the configuration module 700a for configuring the pre-filter 400 is configured to compute the coefficients p^H of said filter using the following recurrence relation:

[0163] $\begin{array}{cc}{p}_{n+1}^H=p_n^H-{\mu }_1{e}_n{y}_n^H& \left[\mathrm{Math}9\right]\end{array}$

• • [0164] the configuration module 720a for configuring the backward filter 420 is configured to compute the coefficients q^H of said filter using the following recurrence relation:

[0165] $\begin{array}{cc}{q}_{n+1}^H=q_n^H+{\mu }_1{e}_n{\hat{s}}_n^H& \left[\mathrm{Math}10\right]\end{array}$

• • [0166] the configuration module 760a for configuring the addition module 460 is configured to compute the scalar component Θ using the following recurrence relation:

[0167] $\begin{array}{cc}{\Theta }_{n+1}={\Theta }_n-{\mu }_2{e}_n& \left[\mathrm{Math}11\right]\end{array}$

• • [0168] where e_n=z_n−s_n-Δ denotes the difference (or error) between the estimate z_n and the symbol s_n-Δ transmitted with a delay Δ for the symbol period T_n; μ₁ denotes an adaptation step, preferably less than 1, for adapting the coefficients p^H of the pre-filter and the coefficients q^H of the backward filter and μ₂ denotes an adaptation step, preferably less than 1, for adapting the scalar component Θ. For example, the adaptation steps p, and μ₂ are equal, such that μ₁=μ₂.

[0169] This update is carried out iteratively, that is to say period by period, so as to converge toward a target value. Thus, after each update, the equalizer 710 determines, in a test step E88, whether a convergence criterion has been reached. For example, a convergence criterion is such that the difference e_n is less than a predetermined convergence threshold e₁.

[0170] Once the error e_n is less than the predetermined convergence threshold e₁ (that is to say e(n)<e₁), a tracking phase B2 is implemented, which will be described in more detail below.

[0171] In this tracking phase B2, the updating of the parameters of the equalizer 710 is governed by the previous symbol detections. Thus, the tracking step B2 differs from the convergence step B1 in that it uses the symbols ŝ_n-Δ detected in the error e_n rather than the transmitted symbols s_n-Δ to update the parameters of the equalizer 710.

[0172] Thus, in a step E89, the error signal e(n) is replaced by an error signal between the estimate z_n and the symbol ŝ_n-Δ detected with a delay Δ, such that e_n=z_n−ŝ_n-Δ.

[0173] The parameters of the equalizer 710 are determined in each iteration in the update step E86, using the same equations Math 9, Math 10 and Math 11 as described above, as long as the error e_n=z_n−ŝ_n-Δ is greater than the predetermined convergence threshold e₁.

[0174] Once this error e(n) becomes greater than the predetermined convergence threshold e₁, the method changes to the convergence phase B1 by executing steps E84, E86 as long as e_n>e₁, as described above.

[0175] One variant of the second embodiment of the equalizer will now be described with reference to FIG. 9 for determining and adjusting the parameters of the equalizer using the previously described convergence and tracking technique.

[0176] According to this variant, the equalizer, which now bears the reference 910, is designed to iteratively determine its configuration parameters Θ, p^H.

[0177] As described with reference to FIG. 7, the equalizer 910 comprises the comparison module 780 for comparing the symbols previously detected by the decision module 216 with the estimate z_n, so as to compute the error signal e_n. As described above, the configuration parameters Θ, p^H of the equalizer 910 are updated in each iteration on the basis of the error signal e(n), respectively by the configuration modules 900a and 960a, using the same method 800 as described with reference to FIG. 8, with the difference that only the parameters Θ, p^H.

[0178] For example, in the update step E86,

• • [0179] the configuration module 900a for configuring the pre-filter 400 is configured to compute the coefficients p^H of said filter using the recurrence relation [Math 9];
  • [0180] the configuration module 960a for configuring the addition module 460 is configured to compute the scalar component Θ using the recurrence relation [Math 11].

[0181] In the examples described above, the receiver 106 according to the invention may comprise a computer system 10, as illustrated in the form of a block diagram in FIG. 10, designed to implement one or more modules described above.

[0182] This computer system 10 comprises a data processing unit 10.1 (such as a microprocessor, denoted CPU for central processing unit), a main memory 10.2 (such as a random access memory, denoted RAM) accessible to the processing unit 10.1, a read-only memory 10.3, denoted ROM, accessible to the processing unit 10.1, an optional computer-readable storage medium, such as for example a local medium (such as a local hard drive 10.6, denoted HD) or else a removable medium (such as a USB (universal serial bus) key, or a CD (compact disc) or a DVD (digital versatile disc) able to be read by an appropriate reader of the computer system 10 (such as a USB port or a CD and/or DVD disc reader); an input/output module 10.7 for receiving/sending data from/to external peripherals such as a hard disk, removable storage medium or the like.

[0183] A computer program P containing instructions in the form of an executable code for the processing unit 10.1 is recorded on the medium 10.6.

[0184] This computer program P is for example intended to be loaded into the main memory in order for the processing unit 10.1 to execute its instructions. These instructions implement one or more of the modules described above, which are thus software modules.

[0185] As an alternative, all or some of these modules could be implemented in the form of hardware modules, that is to say in the form of an electronic circuit, for example a micro-wired circuit, not involving a computer program.

[0186] It is clear that a receiver such as that described above makes it possible, by adding a non-zero scalar component to the estimate z_n before detection of the symbol, to improve symbol detection performance.

[0187] It should also be noted that the invention is not limited to the embodiments described above. Indeed, it will be apparent to those skilled in the art that various modifications may be made to the embodiments described above, in the light of the teaching that has just been disclosed to them.

[0188] The above embodiments and variants have been described to improve the detection performance of a digital data receiver in the presence of inter-symbol interference, this being the most frequent use case. More generally, the invention may also be applied to any other type of distortion or interference caused by the propagation channel, since these are able to be modeled in the form of a compatible Toeplitz matrix, such that the sampled signal y_n is able to be written in the matrix form y_n=H·s_n+w_n according to the expression [Math 5].

[0189] In the examples described above, finite impulse response filters have been described for implementing the sample combiner (that is to say feedforward filter) and the previously detected symbol combiner (that is to say backward filter). Other types of filters may also be used.

[0190] In the detailed presentation of the invention given above, the terms that are used should not be interpreted as limiting the invention to the embodiments disclosed in the present description, but should be interpreted so as to include therein all equivalents that those skilled in the art have the ability to foresee by applying their general knowledge to the implementation of the teaching that has just been disclosed to them.