Method for estimating a soft return signal in a turbo receiver based on expectation propagation

Abstract

Method for estimating a soft return signal in a turbo receiver based on expectation propagation The invention relates to a method for estimating a return signal comprising soft symbols EP and their variance in a turbo receiver with expectation propagation from input symbols, their variance and vectors of LLR bits a priori, comprising: - calculating (502) extrinsic LLR bits from the and - calculating (503) LLR bits a posteriori from the and - calculating (504) soft symbols a posteriori from the - recovering an average a priori variance in a table (506) taking as input - recovering a coefficient in a table (507) taking as inputs and - calculating (505) and from the , the and of . The invention also relates to a turbo receiver implementing the method. Figure for abstract: Figure 5

Description

Title of the invention: Method for estimating a soft return signal in a turbo receiver based on expectation propagation Technical field

[0001] The invention lies in the field of telecommunications, and more particularly in the field of receivers for radio communication systems.

[0002] More specifically, the invention aims to define a method for efficiently implementing a flexible modulation function in a turbo receiver based on expectation propagation. Prior art

[0003] The transfer of information from a source to a destination involves its propagation through a transmission channel which may be, for example, a radio channel, a wired channel (for example, a coaxial cable), an acoustic channel, etc. Some propagation means generate so-called "inter-symbol interference" (or ISI) on the received signal. In other words, the received signal sampled at a given time, after compensation for propagation and processing delays and having correct synchronization, does not only contain the symbol sent (possibly amplified and with a phase disturbance) plus noise, but a mixture (linear combination) of symbols sent.

[0004] It is common to use equalizers to reduce the harmful effect of inter-symbol interference. Many equalization methods have been studied in the past years. They try to approach the theoretical optimal performances (given by the bound of the matched filter) while trying to be achievable in practice. In other words, these algorithms must have a computational complexity, a memory occupation and a processing latency compatible both with the applications that use the receivers in question and the constraints of the hardware platforms on which they are implemented. The general problem of equalization is therefore to find the algorithm offering the right compromise between performance and implementation complexity in relation to the targeted applications.

[0005] There are different classes of equalizers: linear equalizers, Decision Feedback Equalizers (DFE), Interference Cancellation Equalizers, etc. Each type of equalizer has its strengths and weaknesses.

[0006] [Fig.l] very roughly represents the key elements of a transmission chain for digital radio communications equipment. The bits to be transmitted are first coded by a channel coder 101, which aims to allow the receiver to detect and correct possible transmission errors. The coded bits are then processed by an interleaver 102, which reorders them so as to improve their robustness against transmission errors and disturbances in the propagation channel. Note that the interleaver is not mandatory. The interleaved bits are then shaped by a modulator 103, which transforms them into complex symbols in order to transmit them efficiently on the propagation channel. The receivers sequentially implement the successive inverse processes of demodulation, deinterleaving and decoding.

[0007] Higher-performance receivers are known as turbo-receivers, in which the reception algorithm blocks are declined in iterative form, as shown in [Fig.2]. There is therefore a reiterated exchange of probabilistic information between the processing blocks which makes it possible to improve the performance of the receiver. These iterations require the presence of a soft modulator 205 to process the signals transmitted by the decoder, in addition to the soft demodulator 204 which generates the information transmitted to the decoder from the samples it receives, which is why we speak of a soft demodulation / modulation block 202. We speak of turbo equalization when successive iterations 211 are carried out between the decoder 203 and the equalizer 201, passing through the soft demodulation / modulation block 202. The iterations 211 are called turbo iterations.We speak of simple DFE equalization (or possibly self-iterated equalization) when successive iterations 210 are carried out between the equalizer 201 and the flexible demodulation / modulation block 202. The iterations 210 are called self-iterations. A turbo receiver carries out at least one turbo equalization, and can carry out none, one or more self-iterations. Note that a detector, for example a MIMO detector (acronym for Multiple Input Multiple Output), can be used instead of the equalizer.

[0008] The soft demodulator / modulator 202 therefore comprises two blocks: a soft demodulation block 204, configured to supply the decoder 204 from equalized symbols supplied to the equalizer 201, and a soft modulation block 205 (in English soft mapper), configured to reform sequences of samples transmitted to the equalizer from information including that supplied by the decoder.

[0009] When the transmission includes interleaving of the bits, the turbo receiver also includes a deinterleaver 206, and an interleaver 207 for reorganizing the data transmitted by the decoder. The remainder of the description ignores the interleaver and the deinterleaver, since these processes do not influence the content of the data transported, but only their organization.

[0010] The invention is placed within the framework of a turbo receiver, and relates in particular to a method making it possible to efficiently calculate an estimate of the symbols of a modulated digital signal and their reliability starting from an observation (received signal), a measurement of the noise disturbing this received signal, and a priori information relating to the signals sent. These estimates can be used for: - derive an estimate of the propagation channel (or some of its parameters) between the transmitter and the receiver; - derive an estimate of the signal or receiver parameters such as, for example, the clock offset, or the time of signal reception; - derive link quality metrics, such as mutual information between transmitted and received symbols, reliability of the estimate of the sent signal, signal-to-noise ratio or signal-to-noise plus interference.

[0011] However, the main use of the return signal is the suppression of inter-symbol interference within a signal received on a receiver. The invention therefore applies in particular in the context of a receiver comprising an adaptive decision feedback equalizer (in English Digital Feedback Equalizer, or DFE) allowing equalization of the symbols received.

[0012] The invention also applies 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 carried by a signal transmitted by a user due to disturbances inherent in the propagation channel.

[0013] It is particularly interesting when the receiver operates in environments where the propagation channel is very selective, such as for example systems operating in the UHF (Ultra High Frequency), HF (High Frequency) band, etc., or when the propagation channel is artificially selective, such as for example for cooperative transmission systems where several transmitters transmit the same signal simultaneously. Indeed, in a frequency-selective channel, several replicas of the sent signal are received with delays of the order of the symbol time (the inverse of the symbol time, the symbol frequency, being proportional to the spectral band occupied by the signal) or greater, and these delayed replicas interact with each other by generating inter-symbol interference. Such selective channels also exist in wired communications, in acoustic communications, in magnetic recording applications, etc.The invention can also be used in the case of non-selective propagation channels.

[0014] The invention applies in particular to single carrier communication systems with equalization in the frequency domain (in English Single Carrier- Frequency Domain Equalization (SC-FDE) or for systems with Single Carrier-Frequency Division Multiple Access (SC-FDMA) modulation. For example, the 3GPP 4G and 5G cellular standards use such technologies. The method proposed in the invention can be extended to Orthogonal Frequency Division Multiplexing (OFDM) systems, possibly to Multiple Access (OFDMA), such as the 3GPP 4G and 5G cellular standards, or the WiMAX (IEEE 802.16) or WiFi (IEEE 802.11) standard that use such technologies, or to systems using Filter Bank Multi-Carrier (FBMC) modulation, or to systems using similar techniques.

[0015] The main application of the invention relates to receivers implementing linear or DFE type equalizers, turbo-iterated or not, preferably implemented in the frequency domain. The estimation made by the flexible demodulator / modulator of the symbols of the sent signal (also called return signal, or feedback signal) and their reliability can in fact be used by the equalizer to reduce the ISI and extract the information contained in the received signal with fewer errors. Attention is focused here on equalizers working in the frequency domain (FD) for two reasons: - they are generally less complex than their time-domain equivalents to implement, particularly for wideband signals; - thanks to the equalization processing in the frequency domain, the equalized symbols obtained are affected by noise plus residual interference (not eliminated by the processing) whose variance is constant for all the symbols in the processing block. This property can be exploited to reduce the calculations required to estimate the return signal.

[0016] Hereinafter, the following definitions are used: - DFE equalizer: any type of equalizer using a return signal estimated by the receiver. This return signal is called "hard" if the estimated signal is composed of symbols belonging to the transmission constellation. The return signal is called "soft" if the estimated symbols it contains do not belong to the transmission constellation but can assume values ​​on the complex plane, - self-iterated DFE equalizer (also called simple DFE here): this is a DFE equalizer where the return signal comes from the soft demodulation block (in English soft demapping), as in [Fig.2], - turbo-iterated DFE equalizer (also called turbo DFE or turbo DFE here): this is a DFE equalizer where, in addition to having a return signal from the soft demodulation block, there is also a return signal from the decoder, as in [Fig.2].

[0017] The method according to the invention described here is applicable to any receiver comprising a turbo-iterated DFE equalizer, with or without self-iterations. It is also applicable to the case of a receiver implementing a turbo-iterated linear equalizer with interference cancellation (known as turbo LMMSE-IC) in the frequency domain. In this field it is known that equalizers, turbo or not, based on a soft return signal calculated according to the so-called "Expectation Propagation" (EP) method exhibit good performance. Expectation propagation is a Bayesian approximate inference method that seeks to infer (in other words, estimate) a statistical description of the symbols sent. Expectation propagation models each symbol sent as a Gaussian, and not as a point in the original constellation. A Gaussian is completely defined by its mean and its variance.The symbols of the soft feedback signal correspond to the averages of the Gaussian random variables estimated by expectation propagation. Their reliability coincides with the variance of these Gaussian random variables. Other equalizers, turbo or not, based on soft feedback have good performances, such as equalizers with a posteriori (APP) or extrinsic (EXT) feedback. However, the calculations to obtain the soft feedbacks (performed by the soft modulator 205 of [Fig.2]) are very expensive from a computational point of view.

[0018] Figure 3 schematically represents the structure of a state-of-the-art flexible expectation propagation demodulator / modulator. In this example, the operations 301 for calculating the extrinsic bit Log-Likelihood Ratios (LLRs) Le(dk) used to feed the decoder are separate from the operations 302 for calculating the soft return EP and v*, although in reality some operations may be common. The soft demodulation / modulation block EP may be called several times within a receiver, in particular following equalization / detection. In this case it is a self-iteration indexed by the index s going from 0 to ^T, or following a decoding attempt, it is in this case a turbo-iteration indexed by the index T = 0, ..., T. For each turbo-iteration T there are self-iterations.The index E,- = 0 indicates that there is no self-iteration during the turbo-iteration T; if all are 0, the turbo receiver never performs self-iterations. The index T = 0 indicates that there are no turbo-iterations (the equalizer is a simple DFE). In the following, since the description focuses on the soft modulator 302 itself, the self- and turbo-iteration indices . are not displayed when it is not confusing to do so, in order to improve the readability of the text.

[0019] The operations of the soft modulator 302 are performed on an input data vector Xe comprising K input samples indexed on k = 1, ..., K. The value yx corresponds to the variance of the additive noise plus residual interference present on the data block Xe. In the following, we will speak more briefly of variance of the residual noise, including all possible disturbances. We consider this variance as constant for all inputs of the data block Xe, which is the case in frequency equalization applications. In other applications, for example temporal equalization or detection in multi-antenna systems (MIMO), this variance may differ depending on the input of the data block. In this case the following formulas are identical, using an index k for the corresponding variance. The vector is the vector of LLR bits a priori (AP) provided by the decoder.These LLRs are a priori information on the bits dk corresponding to the sent symbol x\ and therefore to the equalized signal (sometimes called observation) x%. Note that the a priori LLRs do not change during the self-iterations performed at turbo-iteration ', and change at each new turbo-iteration since they are generated by the decoder. In the absence of disturbance, xk coincides with the sent symbol xk which is taken from a constellation E as follows: r Y where j _ [jj ] is the fc-th Xk-^kP ak-[akQ, • ■ ■ > a(k+i}Q-\\ . group of Q elements of the vector d which is the vector of coded (and interleaved) bits of size QK corresponding to the data block, and is a so-called "labeling" function associating the bits or sequences of bits with a point of a constellation to determine a complex symbol. The bit vector dk can be interpreted as the binary label of the symbol xk. We also note » / Ve q-th bit of the label of the symbol ^kQ+q — P^k) xk, with q = 0, ..., Q - 1. Finally, we also set 1 a E ( a ) = b J ■> ie-the set of all symbols in the constellation that have a bit of value b (0 or 1) in the g-th position of their binary label. The size of the constellation E is |2| — M = it is therefore formed of M distinct symbols.

[0020] The following details the operations necessary to calculate the outputs of the soft demodulator / modulator: the K extrinsic LLR bit vectors L^Çd^), the soft symbols EP xk and their variance vx. These calculations correspond for example to those described in patent EP 3,528,443 Bl.

[0021] For each set of inputs x^ the soft demodulator 301 calculates a set of Æ vectors L^d^), i.e. vectors of Q LLR extrinsic bits, which is supplied to the decoder. Note that when Q—\ the vectors are one-dimensional vectors. Several methods are well known to those skilled in the art for calculating these outputs. These methods are more or less complex and are not detailed here.

[0022] From the Æ vectors of Q LLR bits AP £“ provided by the decoder, also noted j- ta X( A xt (A \ t tA \] if we wish to show . La(a^Q.] )] that the LLR bits are a function of the bits sent dk, it is possible to calculate, by block 303, the K vectors of LLR symbols AP: Lak(a} =log[nfc(«) / n*((Zref)],^ aeS (1) 100231 ^10^(0) = -2^(8)^(^)+016 VaE V*=l. ...,K En choosing equal to the symbol having the binary label jq()] g we have Ta zxi / \ r / j \ a) with "e E are called the probabilities of LkM = -Lq^ <Pql(a)La(dk^) * FF F mass (or equivalently the probability distribution) of the soft symbols a priori. The ^-th vector of LLR symbols AP corresponding to the emitted symbol is denoted La( xk) and it has a size of AI, its entries Lk(a) being indexed on the M symbols of the constellation ae E.

[0024] The log-likelihoods corresponding to the input signal are calculated by block 304, for example using the formula [4-4, where &PAM = 2 for constellations linear type PAM, BPSK or pi / 2-BPSK, and ^pam- 1 for other constellations.

[0025] Block 305 can then calculate K vectors of LLR symbols a posteriori (APP) whose inputs are written: T f \ _ , T«(

[0026] These vectors of LLR symbols APP are then provided as input to block 306 which uses them to obtain the mass probabilities of the symbols a posteriori (which are a probability distribution in linear scale): azx _ ___ (3)

[0027] where ( a ) — are defined as the LLR APP symbols in linear scale. The APP soft symbols and their instantaneous variances (APP) are calculated by block 306 from the APP mass probabilities: ^-üAk(a) =L fi, pAx-Ca) = £ ^JaPA^ / a) - \u, P. ' x,k *—*ae£.i rk 1 KA 7 F £ 1 (4)

[0028] We note that is finally a function of the symbol at the input of the flexible demodulator and of the a priori information (if present), and that it is parameterized on the variance of the residual input noise. This function is formally denoted by

[0029] Similarly, the instantaneous variance of the soft symbol APP pdk depends on the symbol and the a priori information through the function yd :(¾ L^, ~ For For some applications, such as frequency domain equalization, it is more advantageous to calculate the empirical average APP variance over the data block rx k xk (5)

[0030] which is an estimate of the statistical expectation of the APP variance viewed as a random variable or, in other words, of the mean square error between the APP soft symbols and the sent symbols. The empirical mean APP variance is therefore a function of all the entries corresponding to a data block, and it is denoted by '1

[0031] Identical formulas can be applied using the a priori soft symbol distribution (if 1¾( a) is available, after a decoder pass through a turbo-iteration). It is therefore possible to calculate the a priori soft symbols and their instantaneous variance 4=EaeS«nfc(a) = E,ÆJal2nA(a) - |x{|2. (6)

[0032] It is also possible to calculate their average a priori variance: (7)

[0033] where Kc is the overall size (sum) of all data blocks whose symbols come from the same code word.

[0034] Then block 306 calculates the variance of soft symbols EP Er through an operation called "Gaussian division". is a non-linear function of the inputs, and is calculated as follows: : ({x A [Lj}, / X TTTj. smon lx 7x (8)

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041] where is a fixed parameter typically taking values ​​between 1Q'3 and 104. Variance can also be seen more simply as a function Note that it is possible to use the same formulas by substituting for yd the instantaneous APP variances y^ and for U the instantaneous variances of the disturbance to obtain instantaneous EP variances useful in certain applications, along with the corresponding EP soft symbols. Block 306 also calculates through this “Gaussian division” procedure the EP soft symbols according to the following function which is parameterized by vJ,: v^ yd + s . KA smon (9) The calculation of the EP soft return signal requires a large number of computational passes, with the frequent use of the exponential nonlinear function, when calculating the a posteriori symbol mass probabilities (equation (3)), and many divisions, which may prove too complex to implement, especially for cost and consumption constrained equipment. In some implementations, the soft demodulator / modulator can provide the equalizer / detector with the outputs xf and vJ, i.e. the soft AP symbols and their variance Average AP, instead of EP soft symbols and their average EP variance, for example when observations are considered not good or not representative, and only a priori information from the decoder is present (for example, this may be the case after a decoding attempt made by the decoder). Smoothing treatments 307 can advantageously be implemented on the signals x*k and For example, the block 307 can perform linear filtering operations on the available values ​​of xk and those of the current and previous auto-iterations and / or those of the current and previous turbo-iterations, the filters being able to change at each auto or turbo-iteration. An object of the invention is therefore to define a method making it possible to reduce the number of calculations and to simplify the type of operations required to implement flexible return within the framework of a turbo receiver, without significantly degrading the performance in terms of packet error rate (in English Pocket Error Rate, PER), or bit error rate (in English Bit Error Rate, BER), while reducing or controlling the memory footprint. Summary of the invention

[0042] For this purpose, the present invention describes a method for estimating a return signal in a turbo receiver with expectation propagation. The return signal includes K soft symbols EP x£, with k — 1, ..., K, and an associated variance C. It is estimated from A input symbols x|, with k = 1, ..., Æ, and the associated variance Vx, provided by an equalizer / detector (201), and K a priori bit LLR vectors L^d^} -, with k — 1, , A. provided by a decoder (203). The method according to the invention comprises:

[0043] - a step of calculating K vectors of extrinsic LLR bits Le[dk) from the input symbols x| and the associated variance v*'

[0044] - a step of calculating K vectors of LLR bits a posteriori L(dk) from the K a priori bit LLR vectors La{dk) and K extrinsic bit LLR vectors

[0045] - a step of calculating K soft symbols a posteriori fi^ from the K vectors of LLR bits a posteriori L(dk),

[0046] - a step of recovering an average a priori variance in a table of one-dimensional correspondence taking variance as input

[0047] - a step of recovering a cep coefficient in a correspondence table at two dimensions taking as inputs the variance and the variance v£,

[0048] - a step of calculating the K soft symbols EP xk and the associated variance >4, at from the K soft symbols EP x^ of the K soft symbols a posteriori and the coefficient cep.

[0049] According to an embodiment of the method for estimating the return signal in a turbo receiver with expectation propagation according to the invention, the K soft symbols EP xk are obtained by the formula: xk = (pd-+

[0050] and the variance vk is obtained by the formula:

[0051] =

[0052] According to one embodiment, the method for estimating the return signal in a turbo receiver with expectation propagation according to the invention comprises a preliminary step of calculating the correspondence table used during the step of recovering a cep coefficient. This step is carried out using a digital simulation implementing a decoder configured to calculate vectors of LLR bits a priori La( dk ) and digital processing making it possible to determine an average a priori variance on said vectors of LLR bits a priori h^d^)-

[0053] According to one embodiment, the method for estimating the return signal in a turbo receiver with expectation propagation according to the invention comprises a preliminary step of calculating the correspondence table used during the step of recovering an average a priori variance vJ by a digital simulation implementing a decoder configured to calculate vectors of LLR bits a priori The ( dk ) and numerical treatments allowing to determine an average a priori variance Vy on said vectors of LLR bits a priori

[0054] According to an embodiment of the method for estimating the return signal in a turbo receiver with expectation propagation according to the invention, the cep coefficient recovered during the step of recovering a cep coefficient in a correspondence table, is set to a value close to or equal to 0 when the average a priori variance H- is less than a threshold.

[0055] According to an embodiment of the method for estimating the return signal in a turbo receiver with expectation propagation according to the invention where the turbo receiver performs turbo-iterations, i.e. iterations between decoder and demodulator / soft modulator, and auto-iterations, i.e. iterations between equalizer / detector and demodulator / soft modulator, the step of calculating K extrinsic LLR bit vectors Le(dk) from the K input symbols and the associated variance is performed for each auto-iteration and each turbo-iteration.

[0056] According to an embodiment of the method for estimating the return signal in a turbo receiver with expectation propagation according to the invention where the turbo receiver performs turbo-iterations, i.e. iterations between decoder and demodulator / soft modulator, and auto-iterations, i.e. iterations between equalizer / detector and demodulator / soft modulator, the step of recovering an a priori average variance Vy is performed only after a call to the decoder in a turbo-iteration.

[0057] Advantageously, the step of calculating A" a posteriori soft symbols pdk from the K a posteriori LLR bit vectors L(d^ comprises the calculation of a hyperbolic tangent approximated by one or other of the following functions:

[0058] X. Ixi <0.5 tanhx« 0.5x + 0.25sigrix), 0.5 <lxi<1.5 sigr^x), sinon

[0059] x, Ix 1 < 0.5 0.5x + 0.25 sigr^x), 0.5 < ix 1 <1.0 tanhx- 0.25x + 0.5 sigt^x), 1.0< Ixl < 2.0 sigr^x\ otherwise

[0060] According to an embodiment of the method for estimating the return signal in a turbo receiver with expectation propagation according to the invention, the input symbols xff are modulated according to a 16-APSK constellation from a DVB standard, Digital Video Broadcasting. The step of calculating K soft symbols a posteriori to

[0061]

[0062]

[0063] from the K vectors of LLR bits a posteriori L^dk) includes, for each of the £ soft a posteriori symbols p^, the following calculations: POx) (^6 + ^16^+ (Di6P}-C^)P2)P3' l(Px) = (^16^ + ^16)^)^4- with (l+ÆVl,» -vzLk,r Ul-M-, A^ = Rï-lf- B'6-R^ C>0-^ p tinh ( > 0 being the radius of the points on the inner circle of the constellation, y > 1 being the ratio between the radius of the outer circle and the radius of the inner circle of the constellation, P ( p^ ) and I ( p^ ) being respectively the real part and the imaginary part of the symbol p[.

[0064] The invention also relates to a computer program product comprising program code instructions recorded on a computer-readable medium, for implementing the steps of the method for estimating the return signal according to the invention when the computer program is executed on a computer, as well as to a computer-readable recording medium on which such a computer program is recorded.

[0065] Finally, the invention relates to a turbo-receiver with expectation propagation including: - means of equalizing or detecting a signal, - means for flexible demodulation of an input signal provided by the equalizing means, the input signal comprising input symbols xek, with k = 1, .... K, and an associated variance, - means for flexible modulation of a return signal, the return signal comprising K flexible symbols EP x^ with k = 1, ..., K, and an associated variance vx, - decoding means configured to calculate K a priori LLR bit vectors L^d^ from K extrinsic LLR bit vectors Le( dk ) provided by the demodulation means of an input signal.

[0066] The turbo receiver is then configured to calculate the return signal by implementing a method for estimating a return signal according to the invention. Brief description of the drawings

[0067] The invention will be better understood and other characteristics, details and advantages will appear more clearly on reading the following description, given without limitation, and thanks to the appended figures, given by way of example.

[0068] [Fig.l] [Fig.l] represents very roughly the key elements of a transmission chain for digital radio communications equipment.

[0069] [Fig.2] [Fig.2] represents very roughly the key elements of a chain of reception for a turbo receiver.

[0070] [Fig.3] [Fig.3] schematically represents the structure of a flexible demodulator / modulator with expectation propagation according to the state of the art.

[0071] [Fig.4] [Fig.4] is a block diagram of a method for estimating a return signal in a turbo receiver with expectation propagation according to the invention.

[0072] [Fig.5] [Fig.5] represents in the form of a block diagram an embodiment of the method for estimating a return signal according to the invention.

[0073] [Fig.6a] [Fig.6a] represents a 4-QAM constellation according to the 3GPP 5G standard.

[0074] [Fig.6b] [Fig.6b] represents a 16-QAM constellation according to the 3GPP 5G standard.

[0075] [Fig.6c] [Fig.6c] represents a 64-QAM constellation according to the 3GPP 5G standard.

[0076] [Fig.6d] [Fig.6d] represents an 8-PSK constellation with Gray labeling.

[0077] [Fig.6e] [Fig.6e] represents a 16-APSK constellation according to the DVB standard.

[0078] [Fig.6f] [Fig.6f] represents a 16-APSK constellation according to the HF MIL- STD-110C.

[0079] [Fig.6g] [Fig.6g] represents a 64-APSK constellation according to the HF standard MIL-STD-110C.

[0080] [Fig.7] [Fig.7] represents in the form of a block diagram another mode of implementation of the method for estimating a return signal according to the invention.

[0081] Identical references may be used in different figures when they designate identical or comparable elements. Description of the embodiments

[0082] The method for estimating a return signal in a turbo receiver with expectation propagation according to the invention differs from the prior art in that it proposes to calculate, within the functional block of the soft modulator, the estimation of the symbols of the return signal and their variance by calculating LLR bits APP (unlike the prior art described in equation (2), which calculates the return signal from the LLR symbols APP). These LLR bits APP are obtained at a lower cost from the extrinsic LLR bits L^d^} calculated by the soft demodulation block and the a priori LLR bits L* (also noted L^d^l provided by the decoder. They are then transformed into soft symbols pak (i.e. symbols taking values ​​in the complex plane) by an approximation technique subsequently called "bitwise soft mapping" (English term equivalent to generation of soft symbols from the LLR bits).

[0083] This way of proceeding makes it possible to avoid the implementation of the steps described above in equations (1) to (4), in particular the calculation of exponential functions, and is therefore much less complex and costly in terms of calculation resources.

[0084] Figure 4 is a block diagram of a method for estimating a return signal in an expectation propagation turbo receiver according to the invention. It applies in the classic case of determining a return signal comprising soft symbols EP xk and an associated variance vx from input symbols of the associated variance U and vectors of LLR bits a priori (AP) The input symbols and variance are provided by an equalization block such as block 201 of [Fig.2]. The LLR AP bits are provided by a decoder such as decoder 203 of [Fig.2],

[0085] The method for estimating the return signal according to the invention comprises a first step 401 of calculating K extrinsic LLR bit vectors Lg^d^) from the input symbols xk and the associated variance.

[0086] It also comprises a second step 402 of calculating LLR bit vectors a posteriori (APP) L(dk) from the LLR bit a priori La(dk) and the LLR bit extrinsic L^d^}, then a third step 403 of calculating soft symbols APP from the K LLR bit vectors a posteriori Hd^)- A fourth step 404 aims to recover an AP variance vZ in a table taking as input the variance 'x, and a fifth step 405 aims to recover a coefficient cep associated with the variance Ve* and the variance v*.

[0087] Finally, the method according to the invention comprises a sixth step 406 of calculating the soft symbols EP xk and the associated variance Kl-, where: • the calculation of the soft symbols EP xk includes the calculation of a difference between the soft symbols a posteriori weighted by a factor depending on the coefficient cep, and the input symbols xk multiplied by the coefficient cep, • the calculation of the variance '1 includes the multiplication of the variance by the cep coefficient.

[0088] These steps are described in more detail in the remainder of the description.

[0089] The method according to the invention carries out the demodulation and modulation steps flexible, in a turbo receiver. It is intended to be executed several times. The method according to the invention is used to generate flexible symbols and their variance, associated with the use of an equalizer (for example block 201 in Figure 2) or another type of detector accepting such inputs. It is executed either when the flexible demodulator / modulator receives a new block of LLR bit vectors a prioriLÀA), k=l, .... Kc from the decoder (which corresponds to the triggering of a new turbo-iteration), or when it receives a new block of inputs x^ k - 1, ..., K and their variance (which corresponds to the triggering of a new self-iteration). In addition, the turbo receiver in which it is implemented work can also perform turbo detection, if the equalizer is substituted by a detector, for example a MIMO detector.

[0090] When a new block of inputs k = 1, K and their variance are presented, the turbo receiver performs self-iterations, indexed by an index ranging from 0 to where ' corresponds to an index of the turbo-iterations. Subsequently, when it is necessary to specify to which self-iteration the inputs refer, the index of the self-iteration will be noted in superscript and in parentheses, for example and pd-9. To simplify the description, the index of the self-iteration is not mentioned when it is not necessary.

[0091] [Fig.5] represents in the form of a block diagram an embodiment of the method for estimating a return signal according to the invention, the blocks representing the different stages of the method.

[0092] The invention relates to the steps implemented by a flexible demodulator / modulator 501 interfacing on the one hand with an equalizer / detector, and on the other hand with a decoder, in a manner comparable to the flexible demodulator / modulator 202 of [Fig.2],

[0093] Block 502 performs the first step of the return signal estimation method, namely step 401 of calculating K extrinsic LLR bit vectors Le(d^) from the input symbols and the associated variance. This step corresponds to a conventional soft demodulation step. Each vector is of size Q. with Q the number of bits per symbol of the constellation used to modulate the input samples, C?- 1- The extrinsic LLR bits} correspond to a reliability index on the fact that the transmitted bits have the value 0 or the value 1. These extrinsic LLR bits are used by the decoder, in the usual manner. Unlike the methods of the prior art, they are also used by the soft modulator for calculating the return signal.

[0094] Different methods for calculating the extrinsic LLR bits are well known to those skilled in the art, and are not detailed here. The invention works regardless of the method used. The exact calculation of these metrics is possible and gives the best performance, but is very complex to implement. Conversely, approximate methods with low computational complexity exist, such as for example the max-log-MAP method. In a preferred embodiment of the method according to the invention, we assume that the constellations are labeled according to the Gray labeling method or according to a method giving a result close to a Gray labeling method (in which the binary labels of the symbols closest to a certain symbol of the constellation and the binary label of the latter have at most one different bit). In this case it is possible to ignore the a priori information in the calculation of extrinsic LLR bits, with limited performance degradation. The method according to the invention also applies to constellations with a labeling method different from that of Gray, in which case block 502 can also take as inputs the vectors of LLR bits AP £,^(^), to take into account the a priori information provided by the decoder.

[0095] The adder 503 performs the second step of the method for estimating a return signal according to the invention, of calculating a posteriori soft LLR bit vectors from the K a priori (AP) LLR bit vectors La(dk) and the K extrinsic LLR bit vectors Le(dk) - These are called a posteriori (APP) LLR bits because they include knowledge of the observation in addition to Va priori. This is a simple sum between the AP LLR bits coming from the decoder L(( ( ), and the LLR bits extrinsics calculated by the soft demodulator For all 'cs symbols k of the block, such that:

[0096] L(dk) -Lu(dk) +Le(dk).

[0097] For a given k these are vectors of size Q. When T = 0, that is to say before the first passage of information to the decoder, the LLR bits AP La(dk) are initialized to 0, and the LLR bits a posteriori L(dk) are equal to the extrinsic LLR bits

[0098] Block 504 performs the third step of the return signal estimation method, namely step 403 of calculating K soft symbols from the K vectors of LLR bits a posteriori L(dk)- For this, it associates the vector k comprising Q LLR bits APP among the LLR bits APP to generate a soft APP symbol p^ (i.e. a symbol taking values ​​in the complex plane), this symbol not necessarily belonging to the constellation from which the transmitted symbols are taken, with Q = log (m) and M the size of the constellation (i.e. the number of symbols ü &2\ / distinct from the constellation). This conversion is carried out in such a way as to go through all the LLR bits APP L(dk), by a “bitwise soft mapping” technique, used in the prior art in MIMO detectors.

[0099] To detail this method, we recall here the definition of the LLR bit, which is L(dq) log[LI(dç = 0) / II(d9 = 1) ], the symbol meaning "is equal by definition". The person skilled in the art knows how to adapt the formulas starting from the definition with the ratio between bit at 1 and bit at 0. We also define p* and^ ( 1-2^( am) ) e {-1,1} •

[0100] The APP symbol can then be written: since the formulas are identical for all symbols and am ..., Mr.

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107] Examples of constellations from different systems and their labeling are given in Figures 6a, 6b and 6c (which represents the 3GPP 5G (New Radio) labeling for 4-QAM, 16-QAM and 64-QAM constellations), in [Fig. 6d] (which represents a Gray labeling for an 8-PSK constellation), in [Fig. 6e] (which represents a DVB (Digital Video Broadcasting) compliant quasi-Gray labeling for a 16-APSK constellation), and in Figures 6f and 6g (which represent the MIL-STD-110C HF standard quasi-Gray labeling for 16-APSK and 64-APSK constellations). These bit-to-symbol conversion formulas can easily be extended to other types of labeling and constellations. In the rectangular QAM constellation of Figures 6a, 6b and 6c, the real and imaginary parts consist of -PAM constellations where the symbols are separated by a distance of 2d^ between + ct [ j fl, independently for the real and imaginary components. There are therefore two identical expressions for the real and imaginary parts of flexible symbols, which depend on two sets disjoint of Q!2 bits. For the 4-QAM constellation of [Fig.6a], in posant J4 = ^ / 2 We have P() = d^p, 1(^)= d4p,The computational complexity of this soft modulator is 2Mr, where Mr indicates real multiplication. For a QPSK constellation, the 4-QAM constellation formulas can be used, but the received signal must first be rotated 45 degrees. For the 16-QAM constellation of [Fig.6b], by posing P(^) = di6(2-p2)p4,€ € € € I(pd)^d16(2-p^p3. The computational complexity of this soft modulator is 2 ( 2Mr + Ar ), where Ar denotes real addition. 16 = JÏÔ / 10' nousavons For the 64-QAM constellation of [Fig.6c], in P° sant d a = ^42 / 42 et en considering the symmetry of the sign of the sixth bit, we have: (P^P^Pf^ € € € The computational complexity of this soft modulator is 2 ( 3Mr + 2Ar ). Similar formulas can be easily derived for square QAM constellations larger than 64. For M-PSK constellations, given the symmetries of the constellations, it is sufficient to consider a single quadrant of the complex plane and calculate the soft symbol on Af / 4 symbols with Q-2 bits. For example, for the 8-PSK constellation of [Fig.6d], the second bit controls the sign symmetry on the real axis and the third bit controls the sign symmetry on the imaginary axis. So we have: P(X) = (A8 +B,Pi)pr I(^) = (A^J^with = and _ 1 sin ( ^ ) ) • The computational complexity of this flexible modulator is of 3Mr + 2Ar.

[0108]

[0109]

[0110] [YES]

[0112]

[0113]

[0114] For APSK constellations, deriving the soft symbol equations is more tedious than for PSK or QAM constellations, because the symmetry of the APSK geometry is much less important. Consider here the DVB-like 16-APSK constellation of [Fig.6e], which has many more symmetries than the MIL-STD-110C HF APSK constellations of Figs. 6f and 6g, but whose minimum distance property is slightly worse. This 16-APSK constellation is optimized for a rate 13 / 18 channel code, with an inner radius R2 = 0.39709 and an outer radius R = y13 ^2, with yi3 18 = 2.85. Since the third bit controls the sign symmetry on the real axis, and the fourth bit controls the sign symmetry on the imaginary axis, we have: P(^) = (A16 + Bl6pi-Cl6p2+Dibp]p^p3 CA^+BibPl+ (Dlhp3-Clf>)p2)p? KjO = (At6-Cl(P] + B]6p2 + Di6p^ (Ae-CiePA (Di6P} + Bi6')P2)P4- with (1+M, DW,r _Æ, The computational complexity of this flexible modulator is 7Mr+6Ar. It is possible to generalize the previous calculation to all code rates for 16-APSK constellations from the DVB standard, using (1+^3),.44, A16 = R2 d Uî-M'' „ tanb f Y being the radius Ci6-^ D]6 = r„^ pq tanlH 2 J points on the inner circle 601 of the constellation, and y > 1 being the ratio between the radius of the outer circle 602 and the radius of the inner circle 601 of the constellation. Note that it is also possible to generalize the previous formulas to the case of the constellations in Figures 6f and 6g, which are a "mixture" between rectangular QAM and APSK constellations. The preceding formulas contain the calculation of hyperbolic tangents (tanh). This calculation can be tabulated, or performed using an approximation of the hyperbolic tangent function. The table below shows different possible approximations of this function, the operator sigrY) denoting the sign of a value and Cr indicating a actual comparison operation: Approximation Complexity tanhx « x, Ixl < 1 sign(x), otherwise cr tanhx « x, Ixl <0.5 0.5x+0.25 sigr^x), 0.5 < Ixl < 1.5 sigrix), otherwise At.+ 2Cr tanhx ~ x, Ixl < 0.5 0.5x + 0.25 sign^x), 0.5 < Ixl <1.0 0.25x + 0.5 sigr^x), 1.0 < Ixl < 2.0 sigr^x), otherwise Ar + 3Cr tanhx» ( 1 - 0.5 x 0.54324x ) x + 0.016 sig^x), 1 x I < 1.52 (0.4519-0.5x0.16957)x+0.4519sigr(x\ 1.52< Ixl <: sign(x), otherwise 2Ar + 2Mr + .57

[0115] Note that the second and third of the approximations proposed in the table above have the advantage, compared to other linear approximations in the literature, of having multiplier coefficients which are powers of / 2, which facilitates the hardware implementation of the operation since the division can be carried out by a simple register shift.

[0116] Block 505 of Figure 5 performs the so-called “Gaussian division” step making it possible to obtain the symbols x*k of the output signal and their variance vx. This step corresponds to the implementation of equations (9) and (8).

[0117] However, in order to simplify the calculations, the invention proposes to set the following cep coefficient: CEP ~ CEP ( Vx> • (10)

[0118] This coefficient EP is a function of yj, y^, but also of the LLR bits AP of the decoder via y^. The calculation of the soft symbols xk of the output signal can then be written: 7: = ' 4 + K (^Cei^-Cep^ otherwise (1)

[0119] Similarly, the variance L of the soft symbols EP of the output signal can be written: ^y^ + s v&ep otherwise (2)

[0120] The use of the EP cep coefficient makes it possible to reduce the operational complexity of the Gaussian division, since equations (11) and (12) do not contain divisions, unlike equations (9) and (8).

[0121] However, the calculation of the cep coefficient can be complex, since it requires the calculation of the average APP variance.

[0122] Many state-of-the-art articles formulate proposals to simplify the calculations of formula (5), the average APP variance yd, of formula (8), the average EP variance K, and of formula (7), the average AP variance v%.

[0123] Some suggest evaluating the average APP variance p4 by approximating it by its Minimum Square Error (MSE): MSE^ e[ |nd(xT, La', ) -x|”], (3)

[0124] to approximate the average EP variance L by its MSE: MSEX. E[ -x|2] (4)

[0125] and / or, in the presence of only a priori coming from the decoder, to approximate the variance of the soft symbols a priori v* by its EQM: MSEX, Eflx^Z / Txl2]. (5)

[0126] In all these formulas, the expectations are calculated on the statistics of the symbols sent, the residual noise and possibly the a priori LLRs (these random variables can be dependent or correlated with each other). However, these formulas are theoretical, and the different known solutions are distinguished only on the way in which these quantities are calculated. Moreover, in the previous formulas the index & is not indicated because the symbols and are considered independent and identically distributed.

[0127] One way to do this is to pre-calculate these quantities, and store them in a LookUp Table (LUT) in the receiver's memory. Rather than calculating the quantity of interest, the receiver retrieves it quickly and without calculations from the lookup table, which reduces the number of calculations to be performed and the time required for the calculation.

[0128] When the a priori information from the decoder is available, we distinguish two receiver configurations requiring different processing concerning the calculation of the variance of the soft EP return: - either the turbo receiver does not use self-iterations between the equalizer / detector 201 and the demodulator / modulator 202, which is the case for example for a turbo equalizer / detector of the LMMSE IC type. This turbo receiver is available in several variants depending on the type of soft feedback used: either the LLR bits AP of the decoder are used to calculate the soft symbols, or the soft feedback is calculated according to the expectation propagation method. In the first case, it is necessary to use a look-up table to estimate the average a priori variance. This look-up table is subsequently called the "AP variance LUT" (this case is not illustrated in [Fig.5]). In the second case, it is necessary to additionally use a second look-up table to estimate the EP soft symbols and their average variance (case shown in [Fig.5]), - either the turbo receiver uses self-iterations between the equalizer / detector 201 and the demodulator / modulator 202, for example in the case of a turbo DFE receiver based on expectation propagation, equivalently called Self Iterated Linear Equalizer based on EP (SILE-EP). In this case it is necessary to use at least one look-up table to estimate the soft symbols EP and their average variance. This look-up table is generally a function of both the observations and the LLR bits AP coming from the decoder (through the value of the a priori average variance v£).

[0129] First case: turbo receiver without self-iterations

[0130] This case was studied in the article by J. Ma, L. Liu, X. Yuan, L. Ping, “On orthogonal AMP in coded linear vector Systems”, IEEE Transactions on Wireless Communications, September 2019, in the context of MIMO transmissions. A LMMSE turbo-detector IC is presented there, which uses a soft feedback EP calculated from the observations of the previous turbo iteration. The article also presents the case of a soft feedback calculated only from the LLR bits AP provided by the decoder.

[0131] The authors of this article noticed that the Mean Square Error of the EP returns of formula (14) can be used to have good predictions of the receiver performance in the case of large code words. The predictions are poorer for small or medium code words (of the order of a few hundred bits). Indeed, in the article, the MSEX. is evaluated at the input of the soft demodulator / modulator by generating -Ve symbols obtained by a model with a white complex additive Gaussian noise of zero mean and variance Vx: x^x + n6 where «e~XN(0, vJ)- (6)

[0132] The AP LLR bits from the decoder are considered a simple function of Xe and Ve, because the extrinsic LLRs calculated by the soft demodulator / modulator do not take into account the a priori information from the previous turbo iteration, and are calculated only from Xe. Thus, with this assumption, the MSE of the EP symbols becomes a function of the single parameter and is denoted here MSEx*(i4). This function can be evaluated by a Monte Carlo method, and tabulated in a lookup table as a function of ^x. This same technique is used to tabulate the MSE of the AP symbols from equation (15), the formula using the soft symbols xp obtained by the AP LLR bits from the decoder instead of the EP symbols. In this case too, the AP LLR bits can be considered as depending only on the observations, so the MSE of the AP symbols becomes a function of the single parameter U and is denoted here MSEX?( ).While this approach does indeed reduce the implementation complexity of the calculations, its drawback is that it only works well for long codewords.

[0133] Second case: turbo-receiver with self-iterations

[0134] This case occurs for example in the case of a turbo DFE EP receiver. It is more complex than the previous one since the variance of the APP symbols is a function of both the current observations, the variance of the associated residual noise and the LLR AP bits provided by the decoder during the previous decoding iteration, i.e. the previous turbo-iteration.

[0135] Several approaches have been proposed in the literature to provide an alternative estimate to equation (5), calculated through equations (4).

[0136] A trivial approach would be to use the APP MSE of formula (13) by computing the expectation on the statistics of the sent symbols and the Gaussian noise, as in equation (16), but considering the AP LLR bits from the decoder as inputs to the function. In this case the APP MSE becomes a function with a multidimensional input depending on the AP LLR bits and the variance of the residual noise only, denoted MSE^Z / *, pj) ■ This approach has the problem that if, for a BPSK constellation, only one LLR bit is needed, the vector La ^Q~ log^M inputs for higher order constellations. Therefore, a direct tabulation of the APP variance as a function of the LLR values ​​is not efficient, since the dimension of the table will be Q + 1 and either a large memory or a large number of interpolation polynomials will be required to correctly represent this function.

[0137] The research community has carried out a number of works to resolve these problems. The article by S. §ahin, AM Cipriano, C. Poulliat and M.- L. Boucheret, "Evolution Analysis of Iterative B1CM Receivers with Expectation Propagation over 1S1 Charnels" 2019 IEEE International Symposium on Information Theory (ISIT), Paris, France, 2019, pp. 166-170 uses tools from state evolution (asymptotic performance prediction method) and EXtrinsic Information Transfer (EXIT) diagram analysis for performance prediction of a turbo DFE receiver implemented in the frequency domain. The average APP variance is predicted using a function l where II is obtained from the Gaussian capacity curve (i.e.with a signal having purely Gaussian statistics without any constraints) computed offline with the Monte Carlo method, and Ia is used to derive a Consistent Gaussian Approximation (CGA, where a random variable is approximated by a real Gaussian random variable that has a parametric description in terms of a single real parameter) of the LLR AP bit if injected into the receiver model. However, the CGA becomes increasingly poorer as the number of turbo iterations increases, even in the case of a BPSK constellation. For higher-order constellations, the CGA of the LLRs may not be sufficiently accurate, even with few turbo iterations. In the asymptotic regime (very long codewords of tens of thousands of bits), the prediction method proposed in this paper gives good accuracy, but this is not the case for short codewords.Additionally, for constellations other than BPSK and QPSK, if the CGA of LLR AP bits is not sufficiently accurate, the calculation of II and Ia will require multidimensional lookup tables.

[0138] To account for the finite size effects of codewords, some work on a LMMSE-IC turbo receiver for MIMO communications with LTE turbo codes uses two-dimensional lookup tables to jointly model detection and decoding. These tables are generated based on a CGA for LLRs, and use the average mutual information Ia as input. They are generated by taking into account the finite size of the codes, but this method suffers from the inaccuracies related to modeling LLRs by a CGA.

[0139] In other works, the MSE EP of equation (14) is calculated with the Monte Carlo method. The LLR bits AP if are generated according to a CGA, and therefore with a mean and a variance determined bijectively by the value I&. The random variables jf are parameterized according to the a priori mutual information Ia. Thus, by averaging the MSE EP of equation (14) over the symbols sent, the noise, and the LLR bits AP, the MSE EP becomes a function of only two variables, denoted MSEx.(pJ, IA). This method also suffers from the Gaussian hypothesis consistent for the AP LLRs on the coded bits generated by the turbo decoder. Furthermore, in order to use it, it is necessary to find a way to associate the LLRs actually generated by the turbo decoder for an entire codeword with a single Ia- value.

[0140] Other works, such as those in the paper by S. §ahm, A. M. Cipriano, C. Poulliat, and M.-L. Boucheret, "Iterative Decision Feedback Equalization Using Online Prediction" IEEE Access, vol. 8, pp. 23638-23649, 2020, investigate the use of prediction in the context of EP-based time-domain DFE turbo equalization. This paper shows that, in order to calculate the APP MSE of equation (13), using the average AP variance of soft symbols generated with AP bit LLRs is more robust than other metrics, such as maximum likelihood estimation of the average LLRs. The values ​​of the average AP variances v* are generated according to formula (7) from AP bit LLRs generated as realizations of consistent Gaussian random variables (CGA is used). There is a one-to-one correspondence between the CGA used to generate the LLR AP bits and the mean AP variance vJ.Thus, the APP MSE of equation (13) is estimated by averaging over the sent symbols, the noise, and the binary AP LLRs. The APP MSE therefore becomes a function of only two variables, and is denoted MSE^d ( ). This method . also suffers from the inaccuracies linked to the use of the CGA for LLRs.

[0141] The method according to the invention is inspired by this latter approach in that it uses a function having Vx and Vx as inputs to model the APP MSE. However, it is not the APP MSE that is tabulated, but the coefficient, which makes the tabulation simpler since the dynamics of this quantity is much more limited than that of the APP MSE. Another fundamental difference with the solutions of the prior art is that, rather than using a CGA to generate AP LLRs, the invention proposes, according to an advantageous embodiment, to calculate them using real LLRs generated by a decoder, thus avoiding the problems linked to the parametric modeling of the probability density of the LLRs at the output of the decoder. In this embodiment, the calculation of the variance p^, and of the correspondence table giving the coefficient cep calculated from the variance p^, is therefore carried out by empirical measurements obtained using a simulation.This simulation can take as input symbols x obtained from a sequence of modulated and coded (and possibly interleaved) bits, to which is added a noise iF following a Gaussian model. The resulting samples Xe, which have an input variance are then demodulated (possibly deinterleaved) and decoded, in order to obtain empirical AP bit LLRs. These LLRs are then processed by a soft modulator, which generates .

[0142]

[0143]

[0144]

[0145]

[0146]

[0147]

[0148] LLR symbols AP £“( « ) = lognfc(a) and their mass probability nt( a) according to the formulas known to those skilled in the art: WW) = -L^^a)La(dk^ V«eE,€ € Vk=L...,K, ïlk(a) =Iïk(a)fc(.^ VaeE, € € Yk=l, The soft symbols AP and their instantaneous variance vf k are then calculated using formulas (6), and the average AP variance v£ according to formula (7). When the LLR bits AP L^d^ are all 0, the symbols in the constellation are all equiprobable and therefore væ coincides with the statistical power of the constellation E, — -À YI « 12, Which is in this description by convention, and without loss of generalized, normalized to the value 1. This procedure allows us to empirically establish, by simulation, a correspondence table between the variance of the input symbols and the average AP variance v£. This table is adapted to the decoder parameters (choice of constellation and coding rate, and other internal parameters of the decoder, such as the number of internal iterations in the case of a decoder for a turbo code or a code with Low Density Parity Check (LDPC) code equations). Therefore, it is accurate even for small codewords. It also allows to establish sets of LLR bits AP associated with values ​​of mean variance AP These sets can be used to form a two-input and v% correspondence table delivering the value of the coefficient cep. This table can be obtained by simulation using the following procedure: - for a given value, generate a likelihood y O according to the A. 7 formula = VtzeS, - for a given value v%, recover LLR bits AP and transform them into LLR symbols AP Lk(a) , (as indicated previously or according to equation (1)), - calculate LLR symbols APP j according to the formula: k\ / Lk(a) =Vk(a)+Lk(a), VaeE - convert the LLR APP symbols into mass probabilities of the APP symbols AZt(a ) according to the formula (3) with dk(a) = and Lk(a) calculated at previous point, - for each k, calculate the APP soft symbols and their instantaneous variance y%k according to formulas (4), - average the instantaneous variances y^ to obtain the average APP variance y^, - calculate the coefficient

[0149] / P

[0150] This procedure makes it possible to establish a correspondence table between the variance of the input symbols, the variance of the LLR bits AP y? and the cep coefficient, determined empirically by simulation, and which is adapted to the parameters of the turbo decoder (choice of constellation and coder parameters), and which is also valid for small code words.

[0151] In Figure 5, block 506 performs step 404 of recovering an average AP variance v£ in a single-dimensional lookup table taking as input the variance of the input samples only. As materialized by switch 509, this step depends on the LLR AP bits supplied by the decoder, it is only necessary to perform it after a call to the decoder, or at the initialization of the soft demodulator / modulator. At the initialization of the soft demodulator / modulator, when T = 0, that is to say before the first passage of information to the decoder, the LLR AP bits Lu^dk) are initialized to 0 and the LUT 506 is configured to provide as average a priori variance the statistical power of the constellation £. = -XY | " |2, which is conventionally normalized to the value LL' using a table allows complex operations to be substituted by the values ​​stored in the table, and thus reduce implementation complexity and cost.This table can be defined theoretically or by simulation, as discussed previously. Determining this table by empirical measurements through simulations avoids the accuracy problem of using a consistent Gaussian approximation for the decoder's LLR AP bits, which does not provide optimal performance for small and medium codeword sizes.

[0152] The correspondence table 506 is different for each combination of correction code (type, size, efficiency), decoder parameterization (for example, number of internal turbo iterations for a turbo code or an LDPC, method of calculating the internal metrics of the decoder, etc.) and constellation used in the system, but the same table can be used for several different configurations (for example for close code word sizes).

[0153] Block 507 performs step 405 of retrieving a coefficient cep in a correspondence table taking as inputs the variance and to the variance v?. Here again, the use of a table makes it possible to substitute complex operations with the values ​​stored in the table, and therefore reduce the complexity of implementation and the cost. This table can be defined theoretically or by simulation, as indicated previously.

[0154] The correspondence table 507 is different for each combination of corrector code (type, size, efficiency), decoder parameterization (i.e. number of internal turbo iterations for a turbo code or an LDPC) and constellation used in the system, but the same table can be used for several configurations (for example for close code word sizes). In the absence of a priori information (vx = 1, i.e. 0 dB), this LUT depends only on the constellation.

[0155] Finally, block 505, which performs step 406 of Gaussian division, calculates the soft symbols EP x'k and the associated variance L from the coefficient cep, the soft symbols APP of the input symbols and the variance of the input symbols vx. This involves implementing formulas (11) and (12), or a simplified version of these formulas, using:

[0156]

[0157] v^=vxeEP.

[0158] Advantageously, the flexible symbol vector EP can be obtained by the formula:

[0159]

[0160] This formula, strictly equivalent to the formula given in the previous paragraph, has the advantage of requiring only one multiplication instead of two, which simplifies its implementation.

[0161] Advantageously, during step 507, the value of cep is set to 0 or to a very low value when the variances are lower than a threshold much lower than 1, which corresponds to a very high SNR (Signal to Noise Ratio). This functionality makes it possible to implement the test < y^ + s of the equations (11) and (12) in a simple way directly on the quantity cep without having to extract, calculate or save in addition the average variance APP )^. This therefore saves memory since the receiver only has to save the coefficient EP cep and not the pair consisting of the coefficient EP and the corresponding average variance APP.

[0162] Block 508 represents an optional smoothing or damping functionality for the values ​​of the samples x*k and the variances with an effect memory. This smoothing allows mixing the symbols and EP variances estimated in the current auto-iteration with the past outputs of the soft modulator. For example, it is possible to implement the following formulas which can be interpreted as filtering:

[0163] 4™-» = (

[0164] vÿwn = (1 -) vjw» +

[0165] These formulas show the turbo-iteration index ' because the smoothing coefficients fXTiS and PVTfS differ depending on the turbo-iteration index, the autoiteration index and the smoothed variable (symbol or variance). The smoothing coefficients are always between 0 (no smoothing, the final value is very close to the last calculated value) and 1 (a value close to 1 corresponds to strong smoothing, the past values ​​have a significant weight in the final value). For T = 0, S = 0, the past symbols are initialized to = 0 for all &, and the variance — f. It is also possible to use smoothing on the variance of the residual noise at the input.

[0166] The method for estimating a return signal in a turbo receiver with expectation propagation according to the invention can be implemented in a particularly efficient and effective manner thanks to: - taking into account the extrinsic LLR bits in the soft modulator, - calculating APP LLR bits from the extrinsic LLR bits and the AP LLR bits provided by the decoder, then converting the APP LLR bits into APP soft symbols using a “bitwise soft mapping” technique, unlike the prior art which directly calculates APP LLR symbols, then a probability distribution of the APP symbols and then the APP soft symbols as the average of this APP probability distribution, - to the realization of the Gaussian division using a cep coefficient, which makes it possible to significantly limit the computational complexity of this operation (absence of division), - to the tabulation of key functions in pre-calculated correspondence tables. One of the difficulties resolved by the invention consisted in fact in identifying the key functions, and in proposing an arrangement of the calculations which is not a simple tabulation of the theoretical calculations given in equations (1) to (9), in order to obtain correspondence tables of reduced dimensions.

[0167] In a particular embodiment of the invention, the correspondence tables are calculated using digital simulations integrating a decoder and digital processing making it possible to determine an associated average AP variance vx, which makes it possible to obtain correspondence tables adapted to the turbo receiver parameters and implementations using small codeword sizes.

[0168] The ordering of the steps of the method for estimating a return signal according to the invention depends on the characteristics of the turbo receiver.

[0169] In a turbo receiver without self-iterations, all steps can be implemented sequentially for each turbo-iteration.

[0170] In a turbo receiver with auto-iterations, the auto-iterations are preferably performed before the turbo-iterations. In this case, during the first set of auto-iterations (i.e. before the first decoding), the LLR bits AP L^d^ are zero' the LLR bits APP L(dk) calculated during step 402 correspond to the extrinsic LLR bits Le(dj) ct 'the average a priori variance is initialized to v* = £, = 1 or to values ​​very close to 1 (or 0 if the calculations are done on a logarithmic scale).

[0171] The AP variance is retrieved from the correspondence table 506 at each turbo iteration. Indeed, the LLR bits AP £,^ do not change between two turbo iterations. In the case of a turbo receiver performing self-iterations, it is therefore unnecessary to recalculate the AP variance at each self-iteration.

[0172] Other implementations of the method are possible.

[0173] [Fig.7] represents in the form of a block diagram another embodiment of the method for estimating a return signal according to the invention, applicable in the case where the turbo receiver performs self-iterations and turbo-iterations.

[0174] In this embodiment, the main blocks are unchanged from Figure 5. There are also switches affecting the behavior of the soft demodulator / modulator so that, after having executed the autoiterations, corresponding to the indices s ranging from 0 to Er - 1 of the turbo-iteration of index T, the soft demodulator / modulator is executed with the index S = Er. When S = Er, the demodulator 502 calculates the extrinsic LLR bits £ ûf ) and transfers them to the decoder which executes a decoding and provides new vectors of LLR bits AP L^d^ to the soft demodulator / modulator (the activation of the decoder is not shown in Figure 7). Then, the soft modulator is activated, but the switch corresponding to the L / djJ being open and the switch corresponding to the output x^ being closed, the input samples x| are ignored.Only the new LLR bits AP from the decoder are taken into account, to generate and provide at the output the a priori soft symbols x£ and the associated a priori variance Vx generated by the LUT 506 from the variance The smoothing step is not executed (see configuration of the switches in the smoothing block 701), . and the new feedback is provided to the equalizer / detector. This is a new turbo-iteration that starts, so the turbo-iteration index is incremented (7- — t+ 1) and the self-iteration index is reset to 0 (s = 0). This embodiment, which produces soft symbols depending only on the new LLR AP bits coming from the decoder at each new turbo-iteration, is advantageous when the decoder has a high correction capacity (i.e. the code efficiency is high), since in this case, following each new decoding, the LLR AP bits provided by the decoder are good enough for the calculation of the LLR APP bits. Indeed, in this case, the LLR AP bits are very reliable, and it can be detrimental to mix them with xek input samples which can be very noisy.

[0175] More precisely, when a new block of input samples arrives, the turbo-receiver first performs the self-iterations. The LLR bits AP are harmed, so that the LLR bits APP of step 402 correspond to the extrinsic LLR bits L^dj^ calculated during the first step. Step 404 of recovering a variance AP is carried out only once for all the self-iterations. At each self-iteration of the steps of the method, the index s is incremented.

[0176] When the L- self-iterations have all been performed, i.e. when S = Er, the demodulator 502 calculates the extrinsic LLR bits Le{d^ ct 'cs supplied to the decoder (which performs a decoding and produces new LLR bits AP). The switch 510 is open, so that the LLR bits APP calculated during the following step 402 correspond to the LLR bits AP La(dk) 9ue 'c decoder has just supplied. Similarly, the switch 509 is closed, so that step 404 is performed since the LLR bits apl«(4) calculated by the decoder have been updated. The LUT 506 produces an AP variance using as input the value The AP variance v% thus created will be kept as input to the LUT of the EP coefficient (block 507) for all the auto-iterations corresponding to this new turbo-iteration which begins. The following auto-iterations are done in the usual way, by calculating the LLR bits APP in step 402 by summing the LLR bits AP La(dj() ct 'cs LLR extrinsic bits L^d^-

[0177] The device 701 represents in more detail an embodiment of a device for filtering and smoothing samples. It comprises z-1 delay lines, here worth one sample, which make it possible to apply a delay to the samples of the filtered soft output signal in order to operate linear mixtures with the output of the previous autoiteration. It is also possible to use larger delays, although this affects the complexity of the filtering block and the latency of the signal). In this case of the embodiment of Figure 7, when S = Lr (i.e. at the beginning of each turbo-iteration), the soft returns of the soft modulator are initialized with the symbols and variance AP, i.e. ^.0) _ xp and ydW = yP.

[0178] In another embodiment not shown, at each new turbo-iteration, the observations are not ignored, and the flexible modulator calculates k actually an EP return. In this case, it is as if in Figure 7, the switch 510 on the path of the LLR extrinsic bits L / d^ was closed all the time. The output switch is always open, and the switches of block 701 are always configured to receive the outputs of block 508. More precisely, when S — Er, the demodulator 502 calculates the extrinsic LLR bits and transfers them to the decoder, which performs a decoding and provides new vectors of LLR bits AP to the demodulator / soft modulator. Then, in this embodiment, the soft modulator is activated, but the extrinsic LLR bits Lj^d^) sent to the decoder are taken into account with the new LLR bits AP La(dk) from the decoder to form the LLR bits APP and, subsequently, the K soft symbols APP. The new variance AP v% is calculated as in the previous embodiment, but is directly used in the table 507 which produces an EP coefficient. Then the block 505 is activated to generate the soft feedback EP, transferred to the equalizer / detector (after an optional smoothing step).A new turbo-iteration has just started, so the iteration indices are updated: r = r+ lets = 0. .

[0179] The method for estimating a return signal in a turbo receiver with expectation propagation according to the invention is intended to be implemented on a calculation means such as a microprocessor, a DSP (English acronym for Digital Signal Processor), an FPGA (English acronym for Field Programmable Gate Array), an ASIC (English acronym for Application-Specific Integrated Circuit), or on any combination of these means or hardware components making it possible to execute the steps of the method.

[0180] The invention relates to the method itself, as well as to a computer program product comprising code instructions for executing the method, and to a recording medium, or storage device, such as for example a CD or a USB key, comprising the code instructions for executing the computer program product.

[0181] Finally, the invention also relates to a turbo-receiver with expectation propagation comprising: - means for equalizing a signal (201), - means for flexible demodulation of an input signal (204) provided by the equalization means (201), said input signal comprising K input symbols with k = 1, ,.., K, and an associated variance Vx, - means for flexible modulation of a return signal (205), said return signal comprising K flexible symbols EP with k — 1, ..., K, and an associated variance Er, - decoding means (203) configured to calculate K a priori LLR bit vectors) from extrinsic LLR bit vectors L^d^) provided by the input signal demodulation means (204).

[0182] In this turbo receiver, the means for flexible demodulation / modulation of a signal are configured to calculate the return signal by implementing a method for estimating a return signal according to the invention.

[0183] The equalization, demodulation / soft modulation and decoding means may be independent and interconnected calculation means, or functions implemented on one or more calculation means.

Claims

Claims

1. A method for estimating a return signal in an expectation propagation turbo receiver, said return signal comprising soft symbols EP with k = 1, , K, and an associated variance, from K input symbols with k = 1, ..., K, and the associated variance provided by an equalizer / detector (201), and K vectors of LLR bits a priori ha^dk), with k = 1, ,.., K, provided by a decoder (203), the method being characterized in that it comprises: - a step (401) of calculating extrinsic bit LLR vectors Le ( ) from the input symbols xk and the associated variance - a step (402) of calculating K a posteriori bit LLR vectors LÇd^) from the K a priori bit LLR vectors La(d^) and the £ extrinsic bit LLR vectors Le ( dk ), - a step (403) of calculating K a posteriori soft symbols from the K a posteriori bit LLR vectors L ( dk ), - a step (404) of recovering an average a priori variance y* in a one-dimensional correspondence table (506) taking as input the variance Vx, - a step (405) of recovering a coefficient cep in a two-dimensional correspondence table (507) taking as input the variance and the variance Vx, - a step (406) of calculating the K soft symbols EP and the associated variance >4, from the K soft symbols EP -¾.K soft a posteriori symbols and the cep coefficient.

2. A method for estimating the return signal in an expectation propagation turbo receiver according to claim 1, wherein the K soft symbols EP x*k are obtained by the formula: xk = ( ) cEP + and wherein the variance vk is obtained by the formula: vk = ^ee-

3. Method for estimating the return signal in a turbo receiver with expectation propagation according to one of the preceding claims, comprising a preliminary step of calculating the correspondence table (507) used during the recovery step (405) of a cep coefficient by a digital simulation implementing a decoder configured to calculate vectors of LLR bits a priori La(dk) and digital processing making it possible to determine an average a priori variance on said vectors of LLR bits a priori '

4. Method for estimating the return signal in a turbo receiver with expectation propagation according to one of the preceding claims, comprising a preliminary step of calculating the correspondence table (506) used during the step (404) of recovering an average a priori variance Vx by a digital simulation implementing a decoder configured to calculate vectors of LLR bits a priori La(dk) and digital processing making it possible to determine an average a priori variance on said vectors of LLR bits a priori La (dk).

5. Method for estimating the return signal in a turbo receiver with expectation propagation according to one of the preceding claims, in which the cep coefficient recovered during the step (405) of recovering a cep coefficient in a correspondence table (507), is set to a value close to or equal to 0 when the average a priori variance is less than a threshold.

6. Method for estimating the return signal in an expectation propagation turbo receiver according to one of the preceding claims, said turbo receiver performing turbo-iterations, i.e. iterations between decoder (203) and soft demodulator / modulator (202), and auto-iterations, i.e. iterations between equalizer / detector (201) and soft demodulator / modulator (202), in which the step (401) of calculating K extrinsic bit LLR vectors Le ( dk ) from the K input symbols xk and the associated variance is performed for each auto-iteration and each turbo-iteration.

7. Method for estimating the return signal in a turbo receiver with expectation propagation according to one of the preceding claims, said turbo receiver carrying out turbo-iterations, i.e. iterations between decoder (203) and soft demodulator / modulator (202), and auto-iterations, i.e. iterations between equalizer / detector (201) and soft demodulator / modulator (202), in which the step (404) of recovering an a priori variance average v£ is achieved only after a call to the decoder in a turbo-iteration.

8. Method for estimating the return signal in a turbo receiver with expectation propagation according to one of the preceding claims, in which the step (403) of calculating K soft symbols a posteriori from the K vectors of LLR bits a posteriori L(dk) comprises the calculation of a hyperbolic tangent approximated by one or other of the following functions: tanhx x, ixI < 0.5 0.5x + 0.25 sigiix\ 0.5 < Ixl < 1.5 sigrix\ otherwise x. Ixl < 0.5 0.5x + 0.25 sigidx\ 0.5 < Ixl <1.0 0.25x + 0.5 sig^x), 1.0 < I xI < 2.0 sigr^x), otherwise

9. Method for estimating the return signal in a turbo receiver with expectation propagation according to one of the preceding claims, in which the input symbols are modulated according to a 16-APSK constellation from a DVB standard, Digital Video Broadcasting, and where the step (403) of calculating K soft symbols a posteriori from the K vectors of LLR bits a posteriori L ( d^ ) comprises, for each of the K soft symbols a posteriori the following calculations:

10. P(^) (^6 + ^16^+ (D]6p}-C16)p2)p3, = (A }6 -C I6P[ + (D^ + B^p^. with (' i+Jâ'Ui, » _ » 2L1, r - A., i+( l-JiV, A *= R ^r 16 >0 being the radius of the points on the circle interior of the constellation, y > 1 being the ratio between the radius of the outer circle and the radius of the inner circle of the constellation, P(^) and I(X) being respectively the real part and the imaginary part of the symbol fd. Computer program product comprising program code instructions recorded on a computer-readable medium, for implementing the steps of the signal estimation method of

11.

12. return according to one of claims 1 to 9 when said computer program is executed on a computer. Computer-readable recording medium on which is recorded a computer program comprising program code instructions for executing the steps of the return signal estimation method according to one of claims 1 to 9. Expectation propagation turbo-receiver comprising: - means for equalizing / detecting a signal (201), - means for flexible demodulation of an input signal e (204) provided by the equalizing means (201), said input signal comprising K input symbols with k = 1, ..., K, and an associated variance, - means for flexible modulation of a return signal (20 5), said return signal comprising Æ flexible symbols EP with k — 1, ..., K, and an associated variance vx, - decoding means (203) configured to calculate K vectors of LLR bits a priori from K vectors of extrinsic LLR bits provided by the decoding means demodulation of an input signal (204), the turbo receiver being characterized in that it is configured to calculate said return signal by implementing a method for estimating a return signal according to one of claims 1 to 7.

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