Method for calculating a correspondence table between a variance of input samples of a flexible demodulator and a variance associated with LLR bits a priori in a turbo receiver

Abstract

Method for calculating a correspondence table between a variance of input samples of a soft demodulator and a variance associated with a priori LLR bits in a turbo receiver The invention relates to a method, implemented by computer simulation, for determining a correspondence between variance of input samples of a soft demodulator and average a priori variance of a priori LLR bits provided by a decoder in a turbo receiver, comprising: the generation (601, 602) of noisy input samples of variance, the demodulation (603) of the extrinsic LLR bits, and the decoding (604) of the a priori LLR bits, AP, , the calculation (606) of LLR symbols AP (606) from the , the calculation (607) of mass probabilities, of soft symbols AP (608) and their instantaneous variance (609) from the , and an intermediate measurement (610) from the , the reiteration of the steps, to determine a final value of .The invention also relates to corresponding computer programs and media. Figure for abstract: Figure 6.

Description

Title of the invention: Method for calculating a correspondence table between a variance of input samples of a flexible demodulator and a variance associated with LLR bits a priori in a turbo receiver 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 calculating a correspondence table that can be used to efficiently implement a flexible modulation function in a turbo receiver. 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, 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 only. The iterations 210 are called autoiterations. A turbo receiver carries out at least one turbo equalization, and can carry out none, one or more autoiterations. Note that a detector, for example a MIMO detector (acronym for Multiple Input Multiple Output), can be used instead of the equalizer 201.

[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 allowing reorganization the data transmitted by the decoder. The rest of the description ignores the interleaver and the deinterleaver, since these processes do not affect the content of the transported data, but only their organization.

[0010] The flexible modulation blocks of the turbo receivers of the prior art seek to estimate the symbols of a modulated digital signal (or return signal) and their reliability starting from an observation (received signal), a measurement of the noise disturbing this received signal, and a priori information (AP) 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] The main use of the return signal is the suppression of intersymbol interference within a signal received on a receiver, in particular in the context of a receiver comprising an adaptive decision feedback equalizer (Digital Feedback Equalizer, or DFE) allowing equalization of the received symbols.

[0012] Turbo receivers can be used, for example, for single-carrier communication systems with frequency domain equalization (Single Carrier-Frequency Domain Equalization, SC-FDE) or time domain equalization, or for systems with single-carrier frequency division multiple access (Single Carrier-Frequency Division Multiple Access, SC-FDMA). They can also be used for orthogonal frequency division multiplexing (OFDM) systems, possibly with OFDMA, such as the 3GPP cellular standards for 4G and 5G, or the WiMAX (IEEE 802.16) or WiFi (IEEE 802.11) standard, for systems using filtered modulations (Filter Bank Multi-Carrier, FBMC), or for systems using similar techniques.

[0013] 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 demapping block, as in [Fig.2], - turbo-iterated DFE equalizer (here also called turbo DFE or turbo DFE): 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].

[0014] The invention is presented in the context of a turbo 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.

[0015] 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) injected into the decoder are separate from the operations 302 for calculating the flexible feedback EP and v*, although in reality some operations may be common.

[0016] The flexible demodulation / modulation block EP can be called several times within a receiver, in particular following an equalization / detection (in this case it is a self-iteration indexed by the index 5 going from 0 to Xr), or following a decoding test (in this case it is a turbo-iteration indexed by the index r going from 0 to T). For each turbo-iteration ' there are self-iterations. For a turbo iteration given, indexed by the index ', the soft demodulation / modulation block generates times a soft return to the equalizer / detector, without activating the decoder. When the index s reaches the value the soft demodulation / modulation block generates the extrinsic LLR bits and provides them to the decoder. If t = T, the decoder, from the extrinsic LLR bits at input, provides an estimate of the message sent by the transmitter and the reception process stops for this received signal. If t < T, the decoder, from the extrinsic LLR bits at input, provides the soft demodulation / modulation block with probabilistic information on the coded bits sent by the transmitter and increments the turbo index which goes to the value t + 1. The soft demodulator / modulator uses at least this probabilistic information on the coded bits to calculate a new return signal for the equalizer / detector, and resets s - 0, index which will vary up to Sr+i.

[0017] The operations of the soft modulator 302 are performed on an input data vector Xe comprising Ai input samples xk indexed on k = 1, ..., K. The value 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 âk corresponding to the sent symbol x*, and therefore to the equalized signal (sometimes called observation). Note that the a priori LLRs do not change during the self-iterations performed at the turbo-iteration of index T, 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 x* which is taken from a constellation S as follows: v -JJloùj _Lz j 1 xk- <P\aiJ ak-[ak& ..., est le Lié me groupe de Q éléments du vecteur d qui est le vecteur des bits codés (et entrelacés) de taille QK correspondant au bloc de données, et est une fonction dite « d’étiquetage » associant les bits ou suites de bits à un point d’une constellation pour déterminer un symbole complexe. Le vecteur de bits dk peut être interprété comme l’étiquette binaire du symbole XK On note aussi j j 'c ^‘ième . bit of the label of the symbol XL with q = 0, ..., Q - 1. To finish, we also set = èj, i.e. the set of all the symbols of the constellation which have a bit of value Z? (0 or 1) in the g-th position of their binary label. The size of the constellation E is । M — 2^' c"c is therefore formed of M distinct symbols.

[0018] The following details the operations necessary to calculate the outputs of the soft demodulator / modulator: the K extrinsic LLR bit vectors LeÇdk}, the soft symbols EP xk and their variance vx. These calculations correspond for example to those described in patent EP 3,528,443 Bl.

[0019] For each set of inputs Vx, L"- the soft demodulator 301 calculates a set of K vectors Le(dk), i.e. K vectors of Q LLR extrinsic bits, which is supplied to the decoder. Note that when Q = 1, the vectors ^(d^ 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.

[0020] From the K vectors of Q LLR bits AP L" provided by the decoder, also =[£„(4.o) .£„(4,) ...£„(4.0-0]if|,we wish to show 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: Lk ( a ) = log [ ( a ) / ¾ ( a GE (1) 100211 Oî,lognt(a) = -^,^(0)^(4,)+(^ VaeE. V*=l. ...,X Choosing aref equal to the symbol with the binary label |-q 0] F 0^ we have ra , , v~ i / xria \ ■ a ) with « e E are called the probabilities of mass (or equivalently the probability distribution) of the soft symbols a priori. The same vector of LLR symbols AP corresponding to the emitted symbol xk is denoted La(xk) and it has a size of M, its entries Lk(a) being indexed on the M symbols of the constellation "e E.

[0022] The log-likelihoods corresponding to the input signal are calculated by block 304, for example using the formula [4*a|2, where ^pam = 2 for constellations linear type PAM (English acronym for Pulse Amplitude Modulation, or modulations in amplitude of pulse), BPSK (English acronym for Binary Phase Shift Keying, or modulation by binary phase change) or tt / 2-BPSK, and Mam ~ 1 for the other constellations.

[0023] Block 305 can then calculate K vectors of LLR symbols a posteriori (APP) Lk, the inputs of which are written: ^k ( ® — ^PAM^r ^PAM”* ® ) ' ^ref' ® (2)

[0024] These are called LLR a posteriori (APP) symbols because they include knowledge of the observation in addition to the prior. These vectors of LLR APP symbols are then provided as input to block 306 which uses them to obtain the mass probabilities of the a posteriori symbols (which are a linear scale probability distribution): A , , _ ___ (3)

[0025] where dk( a ) = eLk^ are defined as the LLR APP symbols in linear scale. The K APP soft symbols and their instantaneous variances (APP) are calculated by block 306 from the APP mass probabilities: ^ = ^2^-^1^0) = LJ «l%-( «) - l^l2 (4)

[0026] 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 v 1. This function is formally denoted by Pd'

[0027] Similarly, the instantaneous variance of the APP soft symbol depends on the symbol and the a priori information through the function yd • ( vj) >-> For some applications, such as equalization in the frequency domain, it is more advantageous to calculate the empirical average APP variance over the block of data ri = (5)

[0028]

[0029] 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 Identical formulas can be applied using the a priori soft symbol distribution (if 3¾ ( ") 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 ^ = EaeSanfe(a) (6) v^ = EÆJa-x£|2n^a) =Ef^ - |xf|2.

[0030] It is also possible to calculate their average a priori variance: Lr xJv (7)

[0031] where Kc is the overall size (sum) of all data blocks whose symbols come from the same code word.

[0032] Then block 306 calculates the soft symbol variance EP Kl through an operation called "Gaussian division". is a non-linear function of the inputs, and is calculated as follows: vl: (O = otherwise (8)

[0033] where E is a fixed parameter typically taking values ​​between 1()-3 and 10"4- The variance can also be seen more simply as a function ,,*1^ rx)

[0034] Note that it is possible to use the same formulas by substituting for yd the instantaneous APP variances and à the instantaneous variances of the disturbance to obtain instantaneous EP variances useful in certain applications, as well as the corresponding EP soft symbols.

[0035] Block 306 also calculates through this “Gaussian division” procedure the soft symbols EP according to the following function which is parameterized by vJ,: (9) otherwise

[0036] The calculation of the flexible return signal EP requires a large number of computational passes, with the frequent use of the exponential non-linear function, when calculating the mass probabilities of the symbols a posteriori (equation (3)), and numerous divisions, which may prove too complex to implement, in particular for equipment constrained in cost and consumption.

[0037] In some implementations, the soft demodulator / modulator may provide the equalizer / detector with the outputs xf and ie the soft symbols AP and their mean variance AP, instead of the soft symbols EP and their mean variance EP, for example when the observations are considered not good or not representative, and only the a priori information from the decoder is present (for example, this may be the case after a decoding test made by the decoder).

[0038] Smoothing treatments 307 can advantageously be implemented on the signals x*k and For example, the block 307 can carry out linear filtering operations on the available values ​​of xk and C: those of the current auto-iteration and the previous ones and / or those of the current turbo-iteration and the previous ones, the filters being able to change at each auto or turbo-iteration.

[0039] In order to reduce the number of calculations and simplify the type of operations required to implement flexible return in the context of a turbo receiver, without significantly degrading performance in terms of packet error rate (PER) or bit error rate (BER), while reducing or controlling the memory footprint, the inventors filed patent application FR2315402. [Fig.4] represents in the form of a block diagram an embodiment of the method for estimating a return signal described in this patent application.

[0040] This turbo receiver differs from the state of the art on several points allowing its implementation to be simplified and its memory footprint to be limited.

[0041] First, soft APP LLR bits are obtained (at 403) from the extrinsic LLR bits (obtained at 402) and the AP LLR bits supplied by the decoder. These APP LLR bits are then converted (at 404) into APP soft symbols using a technique called "bitwise soft mapping" (English term k equivalent to generating soft symbols from LLR bits), unlike the prior art which directly calculates LLR APP symbols by implementing functions that are difficult to implement (see equation (2)). This way of proceeding makes it possible to avoid implementing 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 computing resources.

[0042] Then, the Gaussian division 405 is carried out using the following cep coefficient: CEP^CEp{^^) = (10) to simplify the calculations.

[0043] The calculation of the soft symbols xk of the output signal can then be written: iT. (x^L^^ i K . ( 1 + ~ CeA Otherwise (H)

[0044] Similarly, the variance of the soft symbols EP of the output signal can be written:

[0045] 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).

[0046] Patent application FR2315402 uses a two-dimensional table 407 for obtain directly and without calculations the value of the cep coefficient as a function of the values ​​of 14 and v%.

[0047] Patent application FR2315402 also uses a one-dimensional table 406 to obtain directly and without calculations the value of the average AP variance v* from the variance of the input samples only.

[0048] This table establishes a "relationship" between the residual noise variance at the input and an estimate of the average AP variance y? at the output. We speak of a "relationship" because there is no 1 to 1 correspondence or a function properly speaking between these two quantities. The correspondence table must therefore represent in a suitable manner (i.e. the performance of the receiver must not be significantly degraded compared to the exact reference receiver) the behavior of the soft demodulator (with regard to the calculation of the extrinsic bit LLRs), of the decoder (with the possible steps of deinterleaving and interleaving and puncturing / repetition) and of the soft modulator which generates AP soft symbols.

[0049] Each table is therefore specific to a combination of corrector code (type, size, efficiency), decoder parameterization (for example, number of internal turbo iterations for a turbo code or an LDPC code (English acronym for Low Density Parity Check code, or code with low density parity verification equations), method of calculating the internal metrics of the decoder, etc.) and the constellation used in the system. However, the same table can be used for several different configurations (for example for close code word sizes).

[0050] It is necessary to define a method for establishing these single-dimensional lookup tables (LUTs) for establishing the relationship between the average AP variance v? of the AP soft symbols, calculated from the LLR bits a priori provided by the decoder, and the variance of the input samples.

[0051] Many state-of-the-art articles formulate proposals to simplify the calculations of formula (7), the average AP variance v£- Some suggest evaluating the variance of the soft symbols a priori 14 by its EQM (Mean Square Error, or MSE in English for Mean Square Errof): MSExP e[|a / (L“)-x|2]. (13)

[0052] In this formula, the expectation is calculated on the statistics of the symbols sent and the LLR bits a priori (these random variables can be dependent or correlated with each other). Note that the index & is not indicated because the symbols Xk and are considered independent and identically distributed as a function of k. However, this formula is theoretical and it does not reveal as a function of how many and which parameters the MSExP metric must be described, nor how to calculate it in detail. The most suitable choice of its parameterization is linked to its use and to technical considerations, such as for example the fact that its calculation, carried out with good precision, can prove to be too complex or require too much time. In the literature it is therefore possible to find different parametric descriptions of equation (13), as well as different ways of approximating and calculating it.

[0053] This problem has been studied in the paper 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 turbo-detector based on a linear equalizer with turbo-iterated interference cancellation (known as turbo LMMSE-IC) is presented, which uses a soft feedback EP calculated from the observations of the previous turbo iteration. The paper also presents the case of a soft feedback calculated only from the LLR bits AP provided by the decoder.

[0054] In this article, the LLR bits AP La coming from the decoder are considered as 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 coming from any previous turbo iterations, and are calculated only from Xe. Thus, with this assumption, the MSE of the AP symbols becomes a function of the single parameter and is denoted MSExP(vJ ). This function can be evaluated by a Monte Carlo method, and tabulated in a lookup table as a function of 'A While this approach does indeed reduce the implementation complexity of the calculations, its drawback is that it only works well for long codewords. The predictions are poorer for small or medium-sized codewords (of the order of a few hundred bits).

[0055] Other works, such as those in the article 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. In this paper, the values ​​of the average AP variances v? are generated according to formula (7) from LLR AP bits generated as realizations of 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). Indeed, there is a one-to-one correspondence between the CGA used to generate the LLR AP bits and the average AP variance v^. However, the CGA becomes increasingly poorer as the number of turbo iterations of the turbo receiver increases, even in the case of a BPSK constellation. For higher-order constellations, the CGA of 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.

[0056] Thus, patent application FR2315402 proposes to determine the correspondence tables between the variance of the input samples and the value of the average AP variance by implementing a computer simulation. This implementation makes it possible to use real LLRs generated by a decoder rather than by a consistent Gaussian approximation, thus avoiding the problems linked to the parametric modeling of the probability density of the LLRs at the output of the decoder.

[0057] There is therefore a need for the definition of a method for determining correspondence tables implemented from a simulation. Summary of the invention

[0058] To this end, the present invention describes a method for determining a correspondence table between a variance of input samples of a soft demodulator (204) and an average a priori variance Vx of a priori soft symbols associated with a priori LLR bits provided by a decoder (203) in a turbo-receiver.

[0059] In the method according to the invention, the correspondence table is determined by implementing a computer simulation comprising: - a step of generating a vector of K symbols xk with k = 1, .... K, generated in accordance with a particular modulation and coding scheme, - a step of adding a variance noise to the symbols xk, to form a vector of input samples x^ with k = 1, ..., K, - a step of soft demodulation of the input samples x^, in order to obtain extrinsic LLR bits L^d^}, - a step of decoding the extrinsic LLR bits (d^), in order to obtain a priori LLR bits, AP, - a step of calculating LLR symbols AP logll^ a) from the LLR bits AP^jJ, for each “ belonging to the constellation of the modulation and coding scheme, - a step of calculating mass probabilities nA(a) of the H symbols of the constellation of the modulation and coding scheme, from the LLR symbols AP lognk(a), - a step of calculating soft symbols AP X? and calculating their instantaneous variance from the mass probabilities nfe(a), - a step of calculating an intermediate measure of average AP variance from the variances - a step of repeating the previous steps, and determining a final value of the average AP variance v# from the intermediate measurements of average AP variance v? obtained for the different iterations.

[0060] According to a particular embodiment of the invention, the step of determining a final value of the average AP variance v% is done by averaging the Nh largest intermediate values ​​of said average AP variance

[0061] According to another particular embodiment of the invention, the step of determining a final value of the average AP variance v% is done by averaging the Nh smallest intermediate values ​​of said average AP variance

[0062] According to an embodiment compatible with the previous ones, the step (509) of determining a final value of the average AP variance is done by saturating the minimum value of the final value of average AP variance

[0063] Advantageously, the steps of the method according to the invention are implemented a plurality of times, so as to establish a correspondence for a plurality of input variance values ​​v*. In this case, the plurality of input variance values ​​can advantageously be established according to a logarithmic scale.

[0064] Advantageously, the steps of the method according to the invention are iterated for a plurality of different modulation and coding schemes.

[0065] 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 according to the invention for determining a correspondence table between a variance *1 of input samples of a soft demodulator and an average a priori variance of a priori soft symbols associated with a priori LLR bits provided by a decoder in a turbo receiver when said computer program is executed on a computer.

[0066] Finally, it also relates to a computer-readable recording medium, on which is recorded a computer program comprising program code instructions for executing the steps of the method according to the invention for determining a correspondence table between a variance of input samples of a flexible demodulator and an average a priori variance of a priori flexible symbols associated with a priori LLR bits supplied by a decoder in a turbo receiver. 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 reception chain 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] schematically represents the structure of a flexible demodulator / modulator with expectation propagation according to patent application FR2315402.

[0072] [Fig.5] [Fig.5] represents, in the form of a block diagram, an embodiment of a method for determining a correspondence table according to the invention.

[0073] [Fig.6] [Fig.6] represents an embodiment of a method for determining a correspondence table according to the invention in the form of block diagrams.

[0074] [Fig.7] [Fig.7] represents the performance of turbo receivers using correspondence tables established according to different embodiments of the invention.

[0075] Identical references may be used in different figures when they designate identical or comparable elements. Description of the embodiments

[0076] The invention relates to the definition of a method for determining a correspondence table between a variance of input samples transmitted to a flexible demodulator, and an average a posteriori variance of samples provided by a decoder for a turbo-receiver, hereinafter called "AP variance correspondence table".

[0077] The method is defined in the form of a block diagram in [Fig.5], and in the form of a block diagram in [Fig.6].

[0078] The method is intended to be implemented by a computer simulation operated by any digital calculation means, typically a microprocessor, but also 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 any combination of these means or hardware components.

[0079] The correspondence tables are adapted to a precise configuration of modulation and coding / decoding scheme of the turbo receiver.

[0080] The method for determining a correspondence table of the variance AP according to an embodiment of the invention comprises a first step 501 of generating a vector, or block, of K symbols x, generated in accordance with a particular modulation and coding scheme (MCS, acronym for Modulation and Coding Scheme). The symbols are designated by with k = 1, ., K. This step is implemented by a modulation and coding block such as block 601, which generates sequences of bits coded by an error correction coder whose configuration is compatible with that of the decoder of the turbo receiver (i.e. same type of code, for example turbo code or LDPC code, same configuration of code word size and rate, etc.), and modulated according to a constellation corresponding to the constellation implemented by the turbo receiver.Optionally, the coded bits may be interleaved, punctured and / or repeated (this is the case in particular for rate matching in the 3GPP standard). It is possible for a code word to occupy several blocks of symbols.

[0081] The method for determining a correspondence table of the variance AP according to an embodiment of the invention comprises a second step 502 of adding 602 a noise ne to the symbols x, for example a white noise following a Gaussian model where all the elements of the vector are independent and identically distributed (iid), and have a zero mean and a variance 'A. The resulting noisy samples are called input samples, and are denoted Xe. The variance Vx can also be seen as the variance of the samples Xe conditioned on the fact that the symbols emitted are equal to x, and therefore models the variance of the residual noise which affects the symbols emitted x at the input of the soft demodulator. In the following we will use a more concise name by also calling the variance of the input samples (of the soft demodulator) or, equivalently, we will say that the samples Xe have a variance *A.

[0082] The variance of the input samples of the soft demodulator is the only input parameter of the desired correspondence tables. The simulation therefore operates successively for precise variance values. To determine a value of the variance ^x, it is possible to measure it on the symbols Xe. that is to say that the program generates or reads from a database noisy samples (or symbols) and, from the knowledge of the corresponding emitted symbols x, calculates an estimate of as JT* । „ i2 possibly also averaging K^k=VXk~Xk\ on several blocks of K symbols. An alternative method consists of predetermining the values ​​of the variance Vx, and for each value, using a noise generator (e.g. software accepting as input the parameters of the statistical description of the noise including its variance) suitably configured, for example a Gaussian white noise generator with zero mean and variance the desired value of ^x, and adding the noise samples created by the noise generator to the emitted symbols x to obtain the noisy symbols or samples Xe at the input of the flexible demodulator.

[0083] For a given value, a large number Nr of input vectors Xe can be generated. By large, we mean several hundred or even several thousand vectors, for example Nr = 5000 or more.

[0084] The method for determining a correspondence table of the variance AP according to an embodiment of the invention then comprises a step 503 of soft demodulation 603 of the input samples Xe. in order to determine extrinsic LLR bits ^(dk), with k — 1, ..., K. This block is identical to block 402 of FIG. 4, and must implement the same calculation algorithm as that implemented in the turbo receiver. It takes as input a vector of input samples Xe and the corresponding variance. It can also take as input the LLR bits AP calculated during the previous iteration (which are harmed during the first iteration). However, not taking into account these LLR bits AP does not significantly impact the performances when the constellation considered is a Gray or quasi-Gray type constellation. This omission also makes it possible to simplify the procedure for generating the correspondence tables.In practice, it is common for these AP LLR bits to be ignored in determining the extrinsic LLRs. Furthermore, there is no dependency when the turbo receiver does not perform turbo iterations, i.e. when T = T = 0, with T the index of the current turbo iteration and T the number of turbo iterations to be performed, which is a sensible configuration in practice. Indeed, at iteration T = 0, there is no a priori information. If the AP LLR bits have a significant effect in calculating the extrinsic LLR bits Le(dk), in the Nr realizations it will be necessary to take care to vary them so as to sufficiently cover the space of possible realizations for the current value, which can lead to significantly increasing the value of Nr.

[0085] The method for determining a correspondence table of the variance AP according to an embodiment of the invention then comprises a step 504 of decoding 604, by a decoder accepting soft inputs and providing soft outputs (in English SISO for Soft Input Soft Output), of the extrinsic LLR bits he ( d^ ) 1 after implementation of deinterlacing, depunching, and / or summation processing when the inverse operations have been carried out in block 601. The sequence and the exact content of these processings depend on the communications system targeted, and on the way in which the transmitter is implemented.

[0086] Since the decoder operates by code words, when a code word covers several input sample vectors, which can happen for long code words, it is necessary to save the extrinsic LLR bits calculated from several input sample vectors Xe to implement the decoding. Conversely, for short code words, several code words can be covered by a single input sample vector.

[0087] The following steps 505 to 508 can be performed:

[0088] - either by considering each of the code words independently, in order to determine an average AP variance v? specific to each code word,

[0089] - either by considering blocks of decoded LLR bits of homogeneous size with the size of the input sample vectors, in order to determine an average AP variance v? for each input sample vector emitted.

[0090] In the remainder of the description, the first choice has been retained, but the method can easily be adapted to operate according to the second choice.

[0091] Step 504 of the method according to the invention therefore produces coded LLR bits (which can be extrinsic or APP from the point of view of the code), considered as LLR bits AP L^d^ for all the * and for all the input sample vectors occupied by the code word.

[0092] The remainder of the method for determining a correspondence table of the variance AP according to an embodiment of the invention corresponds to flexible modulation processing 605 of the LLR bits AP Lu(d^ provided by the decoder for the entire code word.

[0093] This flexible modulation first comprises a step 505 of calculating 606 LLRs symbols AP logfl^o) from the LLR bits AP £ Y using the formula:

[0094] V«eE,€ € v£=Y.,K

[0095] It then comprises a step 506 of calculating 607 the mass probabilities H / J a) of the a priori symbols, for each index k and on a linear scale, according to the formula:

[0096] n*(a) =n*(a) / LaeS^ VaeE.€ € VÆ=1,

[0097] The method for determining a correspondence table of the variance AP according to an embodiment of the invention then comprises a step 507 of calculation 608 flexible AP symbols and calculation 609 of their instantaneous variance according to the formulas of equation (6).

[0098] The method for determining a correspondence table of the variance AP according to an embodiment of the invention also comprises a step 508 of calculating the average variance AP v£ over the entire code word by the formula given in equation (7).

[0099] The preceding steps make it possible to establish the value of the average AP variance on a code word realization.

[0100] The method according to one embodiment of the invention comprises carrying out 509 a plurality of iterations of the preceding steps, which makes it possible to obtain an intermediate value of for each of the code words, and the determination of a final value of from the different intermediate values ​​calculated, so that this value, used in the turbo-receiver, makes it possible to obtain performances close to those of the exact receiver.

[0101] Assuming that a code word is contained in Nb input sample vectors, after simulation of NbNr vectors, therefore corresponding to Nr code words, there are Nr realizations of the average AP variance, noted with n ~ , Nr- These achievements are stored for example in a database.

[0102] The MSE of the AP soft symbols, which in our case is a function of can be estimated by averaging the intermediate realizations of average AP variance over a large number Nr as follows: [01031

[0104] The function MSExP(vJ) can then be used as the final estimator of the mean AP variance vf.

[0105] This method therefore makes it possible to establish, by empirical measurements obtained by means of a numerical simulation, a reliable relationship between variance values ​​of input samples of a soft demodulator and an average AP variance Vx of a priori soft symbols associated with a priori LLR bits supplied by a decoder. This table is adapted to the parameters of the receiver and the decoder (choice of constellation and coding rate, and other internal parameters of the decoder, such as for example the number of internal iterations in the case of a decoder for a turbo code or an LDPC code).

[0106] However, if the MSE AP function MSExP(vJ) thus evaluated, tabulated and used in the flexible modulator of a turbo receiver as an estimator of the average AP variance Vx, gives good performance when the size of the code words used by the system is large (a few thousand or even a few tens of thousands of bits), performance tends to degrade when codewords are shorter (a few hundred bits or less).

[0107] The problem of turbo receiver performance when short code words are used is illustrated in Figure 7 by the packet error rate performance. Here we consider a system using a turbo code of the 3GPP LTE (Long Term Evolution) 4G standard, with a rate of 1 / 2, with 128 bits of information per packet and a 4-QAM (Quadrature Amplitude Modulation) constellation. The signal passes through a very frequency-selective transmission channel, called Proakis-C, whose impulse response over the first five symbol times is [0.2294 0.4588 0.6882 0.4588 0.2294]. The solid curve 700 represents the PER of a traditional LMMSE equalizer without turbo iterations (T = 0) and without self-iterations (£ — ()), so it is not a turbo equalizer but a simple linear equalizer designed according to the criterion of minimizing the mean square error.The solid curve 701 represents the PER of a traditional IC LMMSE turbo equalizer with one turbo iteration (T = 1) and without self-iterations (£ — ())• The decoder is configured to perform 3 internal iterations at the first decoding, corresponding to the turbo-equalization index r - 0, and 5 internal iterations for the final decoding step, corresponding to the turbo-equalization index t - T = 1. The soft modulator of this receiver uses the state-of-the-art formulas (1), (6) and (7). The dotted line 702 with circles represents the PER of an IC LMMSE turbo equalizer with one turbo iteration (T = 1) and configured like that of curve 701, except that the tabulated function of the MSE AP MSErp(vJ) described previously is used to estimate v*. We observe that the performances degrade, even for a relatively low SNR.

[0108] The inventors of the method for determining an AP variance lookup table according to the invention have discovered that the performance problem observed for short codewords is due to the fact that the MSE AP estimator often provides a very optimistic estimate of the average AP variance for packets with poor LLR values. In this case, errors are propagated while having (falsely) good reliability, which degrades performance.

[0109] Let us denote by VP(vex) = {^(k) : n - 1, ..., TVjpj} the set of realizations of for a given. Let V^(vJ) be the same set VP(Vx) but with the elements classified in decreasing order according to the increasing index n (the v^(w) are all between 0 and 1 for constellations with an energy normalized to 1), so ^(l)>t<(2)>p^(3)>.....

[0110] According to a particular embodiment of the invention, it is therefore possible to adapt step 509 of determining a final value of vÇ from a plurality of intermediate realizations of the mean AP variance vÇ, by calculating the average of the Nh largest intermediate values ​​of v£(n) in Vf (v£) for each:

[0112] The function ( p^.) can then be used as the final estimator of the mean AP variance v£.

[0113] This step produces increasingly conservative AP mean variance estimates as Nh decreases.

[0114] Alternatively, it is possible to calculate the average of the Nh smallest intermediate values ​​Vx(n ) in for each '4, thus providing a final estimate of the mean AP variance K increasingly optimistic (i.e. close to 0) as decreases. This way of estimating v? can be used, for example, to compensate for an equalizer that would provide pessimistic input samples.

[0115] Curve 703 of Figure 7 represents the PER of an IC LMMSE turbo equalizer with a turbo iteration (T= 1) which differs from that of curve 701 in that the average AP variance is estimated through the values ​​of (y£ ), obtained by keeping the Nh = 128 largest average AP variance values ​​calculated. Curve 704 represents the same for Ah = 16. It is observed that the PER performance improves as Nh decreases. However, there is a level of PER where the receiver with the AP variance LUT taken from ( V0 fails to reach the performance of the exact IC LMMSE receiver 701.

[0116] The inventors also discovered that it was possible to generate an effective AP variance correspondence table by saturating the AP variance, i.e. by limiting its minimum value, by setting: 101171 C“(»D =

[0118] where is a value to be determined by simulation as a function of the modulation scheme (i.e. the choice of constellation) and coding scheme (in all of its parameters, e.g. the type of code, the size of the code words, the type of decoding algorithm, etc.) used by the system, or MCS. The evaluation of the saturation value by simulation can be made with regard to one or more performance criteria significant for the system in the physical layer, such as the packet error rate, the bit error rate, the symbol error rate, a percentage of availability of the link, etc.

[0119] The vP®* value to be used is the one that minimizes the degradation of the chosen metric(s) in operating points that are significant for the system, for example those described in the system requirements.

[0120] The choice of the value of Nh and / or the saturation threshold v^wt can be made for example: - by imposing that the degradation of the error rate curve (packet and / or bit and / or symbol) and / or link availability rate compared to that obtained with the exact receiver is limited over a given SNR interval, or for given SNR points, - by requiring that the mean square error between the two error rate curves (packet and / or bit and / or symbol) and / or link availability rate be below a certain threshold, where the error rate / availability values ​​can be expressed on a logarithmic scale to prevent errors at high rates from being weighted more heavily.

[0121] These threshold checks can be made on a set of curves obtained by changing the type of propagation channel, and / or the type and level of any type of disturbance relevant to the system, for example clock offsets and therefore frequency offsets, synchronization instant offsets, imperfections in the RF chain, impulsive or phase noise, or interference, etc.

[0122] It may be necessary to iterate several times over different values ​​of Nh and before finding the right combination for the lookup table. For example, in the case of Figure 7, we chose = - 5 dB, and curve 705 performs very close to curve 701, which corresponds to the exact receiver, up to a PER level of 1Q'3, of interest for this example.

[0123] Thus, according to a particular embodiment of the invention, step 509 of determining a final value of v* from a plurality of realizations of the average AP variance vJ is done by saturating the minimum value of the final average AP variance calculated by retaining only the Nh largest realizations of average AP variance. This saturation is also applicable to the embodiment where the average is done on the smallest realizations of average AP variance, or to the embodiment where the value of the final average AP variance vf is obtained by the function MSExP( F( ), by setting: [°124] MSE^( tl) = max{MSExP(i4), vÿ**}

[0125] and using MSExf ( ) as the final estimator of the mean AP variance v%.

[0126] The method for determining a correspondence table of the AP variance according to the invention makes it possible to calculate the table for a particular modulation and decoding scheme (for example the type of code, the sizes of code words, the type and parameters of the decoder, such as for example the number of internal iterations for the turbo-codes or the LDPC codes at each turbo iteration, ...), and this for a set of values ​​of Intermediate values ​​can be obtained simply by performing parametric interpolations, for example linear, cubic, quadratic, polynomial, exponential or logarithmic, between the results obtained for the different values ​​of ^x.

[0127] Advantageously, for efficient implementation, the lookup table can take inputs in logarithmic scale (decibels or log base 2 which is easier to implement). Indeed, the dynamics of the input is between 0 and infinity (therefore between - infinity and + infinity in logarithmic scale). A reasonable interval consists of establishing the lookup table on a dynamics of the variance of the input signal ranging from -30dB to 10dB for example.

[0128] Advantageously and not obligatorily, the output v% is on a linear scale.

[0129] The look-up tables for obtaining the average AP variance v% of the a priori soft symbols associated with a priori LLR bits provided by the decoder as a function of the variance of input samples of the soft demodulator therefore depend on the modulation and coding scheme (MCS), as well as the type and parameters of the decoder (for example, the number of internal iterations for turbo-codes or LDPC at each turbo iteration). When the code or constellation changes, or the number of internal iterations of the decoder, a new look-up table of the average AP variance must be calculated, by implementing again the method according to the invention. The parameter validation step may involve several tests with respect to one or more metrics and one or more simulation conditions representative of the communication system of interest before converging to the best values. For example, one may plan to verify the target performance (or performances) on a plurality of different test propagation channels, for example three channels with low, medium and high frequency selectivity. This ensures that the look-up table works well on most propagation channels.

[0130] The method for determining a variance correspondence table AP according to the invention applies to the determination of correspondence tables for a turbo receiver such as that described in patent application FR2315402. It also applies to any type of turbo receiver requiring the establishment of a reliable relationship between the variance of input samples and the average a priori variance vÇ of the a priori soft symbols obtained from the LLR bits established by the decoder.

[0131] The invention relates to the method of determining the tables itself, as well as to the tables determined from the method.

[0132] It also relates 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, a USB key (English acronym for Universal Serial Bus, or universal serial bus) or an SSD memory (English acronym for Solid State Drive), comprising the code instructions for the execution of the computer program product.

Claims

1. Claims Method for determining a correspondence table (406) between a variance of input samples of a soft demodulator (204) and an average a priori variance v? of a priori soft symbols associated with a priori LLR bits provided by a decoder (203) in a turbo-receiver, the method being characterized in that the correspondence table is determined by implementing a computer simulation comprising: - a step (501) of generating (601) a vector of symbols with k = 1, ..., K, generated in accordance with a particular modulation and coding scheme, - a step (502) of adding a variance noise (602) to the symbols to form a vector of input samples e with k = 1, ..., K, - a step (503) of soft demodulation (603) of the input samples in order to obtain extrinsic LLR bits - a step (504) of decoding (604) the extrinsic LLR bits Le(dt), in order to obtain a priori LLR bits, AP, L^d^' - a step (505) of calculating (606) LLR symbols AP logüt(a) from the LLR bits AP £ Y for each aa ic J belonging to the constellation of the modulation and coding scheme, - a step (506) of calculating (607) the mass probabilities e Llfe(a) of the symbols a of the constellation of the modulation and coding scheme, from LLR symbols AP logHk(a), - a step (507) of calculating (608) soft symbols AP x% and calculating (609) their instantaneous variance from the mass probabilities 1¾ (a), - a step (508) of calculating (610) an intermediate measurement of average AP variance v? from the variances v?k, - a step (509) of repeating the previous steps, and determining a final value of the average AP variance from the intermediate measurements of average AP variance vJ obtained for the different iterations.

2. Method for determining a correspondence table according to claim 1, in which the step (509) of determining a final value of the average AP variance is done by averaging the Nh largest intermediate values ​​of said average AP variance V%.

3. Method for determining a correspondence table according to claim 1, in which the step (509) of determining a final value of the average AP variance v* is done by averaging the smallest intermediate values ​​of said average AP variance V%.

4. Method for determining a correspondence table according to one of claims 1 to 3, in which the step (509) of determining a final value of the average AP variance v* is done by saturating the minimum value of the final value of average AP variance v£.

5. A method for determining a correspondence table according to one of the preceding claims, implemented a plurality of times, so as to establish a correspondence for a plurality of input variance values ​​*1.

6. A method of determining a lookup table according to claim 5, wherein the plurality of input variance values ​​are set on a logarithmic scale.

7. Method for determining a correspondence table according to one of the preceding claims, iterated for a plurality of different modulation and coding schemes.

8. Computer program product comprising program code instructions recorded on a computer-readable medium, for implementing the steps of the method for determining a correspondence table according to one of claims 1 to 7 when said computer program is executed on a computer.

9. A computer-readable recording medium on which is recorded a computer program comprising program code instructions for executing the steps of the method for determining a correspondence table according to one of claims 1 to 7.

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