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

Abstract

Method for calculating a correspondence table between the variance of input samples of a flexible demodulator and the variance associated with prior LLR bits in a turbo receiver. The invention relates to a method, implemented by computer simulation, for determining a correspondence between the variance of input samples of a flexible demodulator and the average prior variance of prior 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 samples into extrinsic LLR bits, and the decoding (604) of the samples into prior LLR bits, AP, the calculation (606) of AP LLR symbols (606) from the samples, the calculation (607) of mass probabilities of AP flexible symbols (608) and their instantaneous variance (609) from the samples, and an intermediate measure (610) from the samples. the repetition of the steps, to determine a final value of .The invention also relates to the corresponding computer programs and media. Figure for the abstract: Figure 6.

Description

Title of the invention: Method for calculating a lookup table between the variance of input samples of a flexible demodulator and the variance associated with LLR bits a priori in a turbo receiver. Technical field

[0001] The invention is 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 lookup table that can be used to efficiently implement a flexible modulation function in a turbo receiver. Previous technique

[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 (e.g., a coaxial cable), an acoustic channel, etc. Some means of propagation generate so-called "inter-symbol interference" (ISI) on the received signal. In other words, the received signal, sampled at a given instant, after compensation for propagation and processing delays and having correct synchronization, contains not only the sent symbol (possibly amplified and with a phase disturbance) plus noise, but a mixture (linear combination) of sent symbols.

[0004] Equalizers are commonly used to reduce the harmful effects of inter-symbol interference. Numerous equalization methods have been studied in recent years. They attempt to approach theoretical optimal performance (given by the bound of the matched filter) while also striving for practical feasibility. In other words, these algorithms must have computational complexity, memory usage, and processing latency compatible with both the applications using 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 for the intended applications.

[0005] There are different classes of equalizers: linear equalizers, decision feedback equalizers (DFE), and other types of equalizers. interference cancellation, etc. Each type of equalizer has its strengths and weaknesses.

[0006] Figure 1 represents, very roughly, the key elements of a transmission chain for digital radio communications equipment. The bits to be transmitted are first encoded by a channel encoder 101, which allows the receiver to detect and correct any transmission errors. The encoded bits are then processed by an interleaver 102, which reorders them to improve their robustness against transmission errors and propagation channel disturbances. Note that the interleaver is not mandatory. The interleaved bits are then formatted by a modulator 103, which transforms them into complex symbols for efficient transmission over the propagation channel. Receivers sequentially perform the successive inverse operations of demodulation, deinterleaving, and decoding.

[0007] Higher-performance receivers are known as turbo receivers, in which the algorithmic reception blocks are iteratively processed, as shown in [Fig. 2]. There is therefore a repeated exchange of probabilistic information between the processing blocks, which improves the receiver's performance. These iterations require a flexible modulator 205 to process the signals transmitted by the decoder, in addition to the flexible demodulator 204, which generates the information transmitted to the decoder from the samples it receives. This is why the flexible demodulation / modulation block 202 is referred to as the block 202. Turbo equalization occurs when successive iterations 211 are performed between the decoder 203 and the equalizer 201, via the flexible demodulation / modulation block 202. These iterations 211 are called turbo iterations.Simple DFE equalization (or possibly self-iterated equalization) refers to successive iterations 210 performed only between the equalizer 201 and the flexible demodulation / modulation block 202. These iterations 210 are called self-iterations. A turbo receiver performs at least one turbo equalization and may perform none, one, or several self-iterations. Note that a detector, for example a MIMO detector (Multiple Input Multiple Output), can be used instead of the equalizer 201.

[0008] The flexible demodulator / modulator 202 therefore comprises two blocks: a flexible demodulation block 204, configured to feed the decoder 204 from equalized symbols supplied by the equalizer 201, and a flexible 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 bit interleaving, the turbo receiver also includes a deinterlacer 206, and an interlacer 207 for rearrangement the data transmitted by the decoder. The rest of the description disregards the interleaver and deinterleaver, since these processes do not affect the content of the data transported, but only its organization.

[0010] The flexible modulation blocks of prior art turbo receivers seek to estimate the symbols of a modulated digital signal (or return signal) and their reliability based on an observation (received signal), a measurement of the noise interfering with this received signal, and prior information (PA) concerning the transmitted signals. These estimates can be used to: - 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; - to derive link quality metrics, such as mutual information between transmitted and received symbols, the reliability of the transmitted signal estimate, the signal-to-noise ratio, or the signal-to-noise plus interference ratio.

[0011] The main use of the return signal is the suppression of intersymbol interference within a signal received by a receiver, particularly in the context of a receiver including a Digital Feedback Equalizer (DFE) allowing equalization of received symbols.

[0012] Turbo receivers can be used, for example, in single-carrier communication systems with frequency-domain equalization (SC-FDE) or time-domain equalization, or in single-carrier frequency-division multiple access (SC-FDMA) systems. They can also be used in 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) standards, in systems using filtered modulation (FBMC), or in systems using similar techniques.

[0013] The following definitions are used hereafter: - DFE equalizer: any type of equalizer using a feedback signal estimated by the receiver. This feedback signal is said to be "hard" if the estimated signal is composed of symbols belonging to the transmitted constellation. The feedback signal is said to be "soft" if the estimated symbols it contains do not belong to the transmitted constellation but can assume values ​​on the complex plane. - self-iterating 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 flexible 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 suppression (known as a turbo LMMSE-IC) in the frequency domain. In this domain, it is known that equalizers, turbo or otherwise, based on a soft feedback signal calculated using the 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 transmitted symbols. Expectation Propagation models each transmitted symbol as a Gaussian, and not as a point in the original constellation. A Gaussian is completely defined by its mean and variance.The symbols of the soft feedback signal correspond to the means of 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 exhibit good performance, such as equalizers with a posteriori (APP) or extrinsic (EXT) feedback. However, the calculations to obtain soft feedback (performed by the soft modulator 205 in [Fig. 2]) are very computationally expensive.

[0015] Figure 3 schematically represents the structure of a state-of-the-art expectation-propagating flexible demodulator / modulator. In this example, operations 301 for calculating the extrinsic bit log-likelihood ratios (LLRs) Le(dk) injected into the decoder are separate from operations 302 for calculating the flexible return EP and v*, although in reality some operations may be common.

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

[0017] The operations of the flexible modulator 302 are performed on an input data vector Xe comprising Ai input samples xk indexed to k = 1, ..., K. The value corresponds to the variance of the additive noise plus residual interference present on the data block Xe. Hereafter, we will refer more briefly to the variance of the residual noise, including all possible disturbances. We consider this variance to be constant for all inputs of the data block Xe, which is the case in frequency equalization applications. In other applications, for example time equalization or detection in multi-antenna (MIMO) systems, 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 Σ“ is the vector of LLR bits a priori (AP) provided by the decoder.These LLRs provide prior information about the bits âk corresponding to the sent symbol x*, and therefore to the equalized signal (sometimes called observation). Note that the prior LLRs do not change during the self-iterations performed at the turbo-iteration with index T, and change at each new turbo-iteration since they are generated by the decoder. In the absence of perturbations, xk coincides with the sent symbol x*, which is drawn 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. Finally, we also set = èj, i.e. the set of all symbols of the constellation which have a bit with value Z? (0 or 1) in the g-th position of their binary label. The size of the constellation E is 2^(M - 2^') c"c is therefore formed of M distinct symbols.

[0018] The following details the operations necessary to calculate the outputs of the flexible demodulator / modulator: the K vectors of extrinsic LLR bits LeÇdk}, the flexible 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 flexible 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 Le(dk) are one-dimensional vectors. Several methods are well known to those skilled in the art for calculating these outputs. These methods vary in complexity and are not detailed here.

[0020] From the K vectors of Q LLR bits AP L" supplied by the decoder, also If we wish to demonstrate that the LLR bits are a function of the bits sent, it is possible to calculate, using 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 By 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 flexible symbols a priori. The same vector of LLR AP symbols 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 types PAM (Pulse Amplitude Modulation), BPSK (Binary Phase Shift Keying) or tt / 2-BPSK, and Mam ~ 1 for other constellations.

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

[0024] These are called LLR symbols a posteriori (APP) because they include knowledge of the observation in addition to Va priori. 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 linear-scale probability distribution): A , , _ ___ (3)

[0025] where dk( a ) = eLk^ are defined as the LLR APP symbols on a 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] It is noted that is finally a function of the symbol at the input of the flexible demodulator and of the prior 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 soft symbol APP depends on the symbol and the prior information via the function yd • ( vj) >-> For certain applications, such as equalization in the frequency domain, it is more advantageous to calculate the empirical mean variance of APP over the data block ri = (5)

[0028]

[0029] which is an estimate of the expected statistical value of the APP variance viewed as a random variable, or, in other words, the mean squared error between the APP soft symbols and the sent symbols. The empirical mean APP variance is therefore a function of all the corresponding inputs to a block of data, and it is denoted by Identical formulas can be applied using the prior soft symbol distribution (if 3¾("") is available, after a turbo-iteration of the decoder). It is therefore possible to calculate the prior 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 prior variance: Lr xJv (7)

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

[0032] Next, block 306 calculates the variance of soft symbols EP Kl through an operation called "Gaussian division". This 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 10⁻³ 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 the instantaneous APP variances for yd and the instantaneous variances of the disturbance for yd to obtain useful instantaneous EP variances in certain applications, as well as the corresponding EP soft symbols.

[0035] Block 306 also calculates, through this "Gaussian division" procedure, the flexible EP symbols 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 nonlinear exponential 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 certain implementations, the flexible demodulator / modulator may provide the equalizer / detector with the outputs xf and ie the AP flexible symbols and their average AP variance, instead of the EP flexible symbols and their average EP variance, for example when the observations are considered poor or not representative, and only the prior information from the decoder is present (for example, this may be the case after a decoding attempt made by the decoder).

[0038] 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 C: those of the current auto-iteration and previous ones and / or those of the current turbo-iteration and 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 soft feedback 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 block diagram form an embodiment of the method for estimating a feedback signal described in this patent application.

[0040] This turbo receiver differs from the state of the art in several respects, allowing for a simplification of its implementation and a reduction in its memory footprint.

[0041] First, soft APP LLR bits are obtained (in 403) from extrinsic LLR bits (obtained in 402) and AP LLR bits for the decoder. These APP LLR bits are then converted (in 404) into soft APP symbols using a technique called "bitwise soft mapping" (English term k equivalent to generating soft symbols from LLR bits), unlike prior art which directly computes APP LLR symbols by implementing functions that are difficult to implement (see equation (2)). This approach avoids the implementation of the steps described above in equations (1) to (4), in particular the computation of exponential functions, and is therefore much less complex and computationally expensive.

[0042] Next, the Gaussian division 405 is performed using the following coefficient cep: CEP^CEp{^^) = (10) in order to simplify the calculations.

[0043] The calculation of the flexible symbols xk of the output signal can then be written as: 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 coefficient EP cep 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] French patent application FR2315402 uses a two-dimensional table 407 for obtain directly and without calculations the value of the coefficient cep 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 mean AP variance v* from the variance of the input samples only.

[0048] This table establishes a "relationship" between the input residual noise variance and an estimate of the average AP variance y? at the output. It is called a "relationship" because there is no one-to-one correspondence or function between these two quantities. The lookup table must therefore suitably represent (i.e., the receiver performance must not be significantly degraded compared to the exact reference receiver) the behavior of the soft demodulator (with regard to the calculation of extrinsic bit LLRs), the decoder (with the possible deinterlacing and interleaving and punching / repeating steps), and the soft modulator that generates AP soft symbols.

[0049] Each table is therefore specific to a combination of error-correcting code (type, size, efficiency), decoder parameters (for example, number of internal turbo iterations for a turbo code or an LDPC code (Low Density Parity Check code, or code with low-density parity checking equations), method for calculating the decoder's internal metrics, etc.) and the constellation used in the system. However, the same table can be used for several different configurations (for example, for similar codeword sizes).

[0050] It is necessary to define a method for establishing these one-dimensional lookup tables (LUTs) to establish the relationship between the average AP variance v? of the soft AP 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 mean AP variance v£- Some suggest evaluating the variance of the a priori soft symbols 14 by its MSE (Mean Square Error): MSExP e[|a / (L“)-x|2]. (13)

[0052] In this formula, the expected value is calculated based on the statistics of the symbols sent and the LLR bits a priori (these random variables may 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 does not reveal how many parameters the MSExP metric should be described for, 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 the fact that its calculation, performed with good precision, may prove too complex or time-consuming. Therefore, it is possible to find different parametric descriptions of equation (13) in the literature, as well as different ways of approximating and calculating it.

[0053] This problem was investigated in the article by J. Ma, L. Liu, X. Yuan, and 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 suppression (known as turbo LMMSE-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 solely from the LLR AP bits provided by the decoder.

[0054] In this article, the LLR bits AP La from the decoder are considered a simple function of Xe and Ve, because the extrinsic LLRs calculated by the demodulator / soft modulator do not take into account prior information from any previous turbo iterations and are calculated solely from Xe. Thus, under 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 effectively reduces the implementation complexity of the calculations, its drawback is that it only works well for long codewords. The predictions are less accurate for small or medium-sized codewords (on the order of a few hundred bits).

[0055] Other works, such as those in the article by S. Šahm, 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 time-domain DFE turbo equalization based on EP. In this article, the values ​​of the mean 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, is used. Indeed, there is a bijective correspondence between the CGA used to generate the LLR bit APs and the mean AP variance v^. However, the CGA becomes progressively worse as the number of turbo iterations of the receiving turbo 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 article 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 mean AP variance by implementing a computer simulation. This implementation makes it possible to use true LLRs generated by a decoder rather than by a consistent Gaussian approximation, thereby avoiding the problems associated with the parametric modeling of the probability density of the LLRs output from the decoder.

[0057] There is therefore a need for the definition of a method for determining the 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 flexible demodulator (204) and an a priori average variance Vx of a priori flexible 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 lookup table is determined by implementing a computer simulation comprising: - a step of generating a vector of K symbols xk with k = 1, ..., K, generated according to a particular modulation and coding scheme, - a step of adding variance noise to the symbols xk, to form a vector of input samples x^ with k = 1, ..., K, - a flexible demodulation step 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 symbols H of the constellation of the modulation and coding scheme, from the LLR symbols AP lognk ( a ), - a step of calculating flexible symbols AP X? and calculating their instantaneous variance from the mass probabilities nfe( a), - a step of calculating an intermediate measure of mean AP variance from the variances - a step of reiterating the previous steps, and determining a final value of the average AP variance v# from the intermediate measures 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 carried out by averaging the largest intermediate values ​​of said average AP variance Nh

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

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

[0063] Advantageously, the steps of the process 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 process 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 of determining a lookup table between a variance *1 of input samples of a soft demodulator and an a priori average 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] 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 of determining a correspondence table between a variance of input samples of a flexible demodulator and an a priori average variance of a priori flexible symbols associated with a priori LLR bits provided by a decoder in a turbo receiver. Brief description of the drawings

[0067] The invention will be better understood and other features, details and advantages will become clearer from the following description, given by way of non-limiting reason, and from the accompanying figures, given by way of example.

[0068] [Fig.1] Fig.1 represents very roughly the key elements of an emission chain for a digital radio communications equipment.

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

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

[0071] [Fig.4] Fig.4 schematically represents the structure of a flexible expectation propagation demodulator / modulator according to patent application FR2315402.

[0072] [Fig.5] The [Fig.5] represents, in the form of a synoptic 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] The [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 refer to identical or comparable elements. Description of the implementation methods

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

[0077] The process is defined in the form of a synoptic 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 means of digital calculation, 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 lookup tables are adapted to a precise configuration of the modulation scheme and coding / decoding of the turbo receiver.

[0080] The method for determining a variance AP lookup table according to an embodiment of the invention comprises a first step 501 of generating a vector, or block, of K symbols x, generated according to a particular modulation and coding scheme (MCS). 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 bit sequences encoded by an error-correcting encoder whose configuration is compatible with that of the turbo receiver's decoder (i.e., same code type, for example turbo code or LDPC code, same codeword size and throughput configuration, etc.), and modulated according to a constellation corresponding to the constellation implemented by the turbo receiver.Optionally, the coded bits can be interleaved, punched, and / or repeated (this is notably the case with rate matching in the 3GPP standard). It is possible for a codeword to occupy several symbol blocks.

[0081] The method for determining a lookup table for the variance AP according to an embodiment of the invention comprises a second step 502 of adding 602 noise ne to the symbols x, for example, white noise following a Gaussian model where all the elements of the vector are independent and identically distributed (i.i.d.), and have a mean of zero 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 emitted symbols are equal to x, and thus models the variance of the residual noise that affects the emitted symbols x at the input of the soft demodulator. In the following, we will use a more concise designation 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 flexible demodulator is the only input parameter of the lookup tables sought. The simulation therefore operates successively for precise values ​​of variance. To determine a The variance value ^x can be measured on the symbols Xe. That is, the program generates or reads noisy samples (or symbols) from a database and, based on knowledge of the corresponding emitted symbols x, calculates an estimate of it as JT* । „ i2 possibly by averaging also 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) appropriately 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 as input to 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 lookup table for the variance AP according to an embodiment of the invention then comprises a step 503 of flexible 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 Figure 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 nullified during the first iteration). However, not taking these LLR bits AP into account does not significantly impact performance when the constellation considered is a Gray or quasi-Gray type constellation. This omission also simplifies the procedure for generating the lookup tables.In practice, it is common for these AP bit LLRs not to be taken into account when determining extrinsic LLRs. Furthermore, there is no dependency when the receiving turbo iteration does not perform any turbo iterations, i.e., when T = T = 0, where T is the index of the current turbo iteration and T is the number of turbo iterations to be performed, which is a sensible configuration in practice. Indeed, at iteration T = 0, there is no prior information. If the AP bit LLRs have a significant effect on the calculation of the extrinsic bit LLRs Le(dk), then in the Nr realizations, care must be taken to vary them in such a way as to sufficiently cover the space of possible realizations for the current value of T, which can lead to a significant increase in the value of Nr.

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

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

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

[0088] - either by considering each of the code words independently, in order to determine a mean AP variance v? specific to each codeword,

[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 issued.

[0090] In the rest of the description, the first option has been chosen, but the process can easily be adapted to operate according to the second option.

[0091] Step 504 of the process 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 * and for all input sample vectors occupied by the codeword.

[0092] The continuation of the process of determining a variance AP correspondence table according to an embodiment of the invention corresponds to flexible modulation processing 605 of the LLR bits AP Lu(d^ f°urnis Pæ" Ie decoder for the whole of the codeword.

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

[0094] V«eE,€ € v£=Y.,K

[0095] It then includes a step 506 of calculation 607 of mass probabilities H / J a) of the prior 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 variance AP lookup table according to an embodiment of the invention then comprises a calculation step 507 608 flexible AP symbols and calculation 609 of their instantaneous variance according to the formulas of equation (6).

[0098] The method for determining a variance AP lookup table according to an embodiment of the invention also includes a step 508 of calculating the average variance AP v£ over the whole codeword by the formula given in equation (7).

[0099] The preceding steps allow us to establish the value of the average AP variance on a realization of the codeword.

[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 performance close to that of the exact receiver.

[0101] Assuming that a codeword is contained in Nb input sample vectors, after simulation of NbNr vectors, corresponding thus to Nr codewords, there are Nr realizations of the mean AP variance, denoted with n ~ , Nr- These achievements are stored, for example, in a database.

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

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

[0105] This method therefore makes it possible to establish, through empirical measurements obtained by means of a numerical simulation, a reliable relationship between the 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 provided 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 MSExP(vJ) function thus evaluated, tabulated and used in the soft modulator of a turbo receiver as an estimator of the mean 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 code words are shorter (a few hundred bits or less).

[0107] The problem of turbo receiver performance when short codewords are used is illustrated in Figure 7 by the packet error rate performance. Considered here is a system using a turbo code of the 3GPP LTE (Long Term Evolution) 4G standard, with a 1 / 2 efficiency, 128 bits of information per packet, and a 4-QAM (Quadrature Amplitude Modulation) constellation. The signal passes through a highly 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 line curve 700 represents the PER of a traditional LMMSE equalizer without turbo iterations (T = 0) and without self-iterations (£ — ()), therefore it is not a turbo equalizer but a simple linear equalizer designed according to the mean squared error minimization criterion.The solid line 701 represents the PER of a traditional IC LMMSE turbo equalizer with one turbo iteration (T = 1) and no self-iterations (μ - μ). The decoder is configured to perform 3 internal iterations in 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 in 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 AP MSE, MSErp(vJ), described earlier, is used to estimate v*. We observe that performance degrades, even for a relatively low SNR.

[0108] The inventors of the method for determining an AP variance lookup table according to the invention 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 (falsely) maintaining good reliability, which degrades performance.

[0109] Let VP(vex) = {^(k) : n - 1, ..., TVjpj} be the set of realizations of for a given. Let V^(vJ) be the same set VP(Vx) but with the elements sorted in descending order according to the increasing index n (the v^(w) are all between 0 and 1 for constellations with an energy normalized to 1), therefore ^(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 v₁, by calculating the mean of the largest intermediate Nh values ​​of v₁(n) in V₂(v₁) 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 smallest intermediate values ​​Nh Vx(n) in for each '4, thus providing a The final estimate of the mean AP variance K becomes increasingly optimistic (i.e., closer to 0) as the mean decreases. This method of estimating v? can be used, for example, to compensate for an equalizer that would provide pessimistic input samples.

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

[0116] The inventors also discovered that it was possible to generate an efficient AP variance lookup 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 based on the modulation scheme (i.e., the choice of constellation) and coding (in all its parameters, e.g., code type, codeword size, decoding algorithm type, etc.) used by the system, or MCS. The evaluation of the saturation value by simulation can be done with regard to one or more performance criteria significant for the physical layer system, such as packet error rate, bit error rate, symbol error rate, a percentage of link availability, etc.

[0119] The vP®* value to be used is the one that minimizes the degradation of the chosen metric(s) at 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 requiring 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 be limited over a given SNR interval, or for given SNR points, - by requiring that the mean squared 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 / availability rate 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 done 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, timing offsets, imperfections in the RF chain, impulsive noise, or phase noise, or interference, etc.

[0122] It may be necessary to iterate several times over different values ​​of Nh before finding the correct combination for the lookup table. For example, in the case of Figure 7, we chose = -5 dB, and curve 705 exhibits performance very close to that of 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 performed by saturating the minimum value of the final average AP variance calculated by retaining only the largest realizations of average AP variance. This saturation is also applicable to the embodiment where the average is taken over 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 an AP variance lookup table according to the invention makes it possible to calculate the table for a particular modulation and decoding scheme (for example, the code type, codeword sizes, decoder type and parameters, such as the number of internal iterations for turbo codes or 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 on a logarithmic scale (decibels or base 2 log, which is easier to implement). Indeed, the input dynamic range is between 0 and infinity (i.e., between -infinity and +infinity on a logarithmic scale). A reasonable range is to establish the lookup table for a variance dynamic range of the input signal from -30 dB to 10 dB, for example.

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

[0129] The lookup 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 from 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 changes, a new lookup table for the average AP variance must be calculated, again implementing the method according to the invention. The parameter validation step may involve several trials against 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, the target performance (or performances) can be verified on a plurality of different test propagation channels, such as three channels with low, medium, and high frequency selectivity. This ensures that the lookup table works properly on most propagation channels.

[0130] The method for determining a variance AP lookup table according to the invention applies to the determination of lookup 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 prior 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 process, and to a recording medium, or storage device, such as for example a CD, a USB flash drive (English acronym for Universal Serial Bus, or universal serial bus) or an SSD (English acronym for Solid State Drive), including the code instructions for executing the computer program product.

Claims

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

2. Method of determining a lookup table according to claim 1, wherein the step (509) of determining a final value of the mean AP variance is done by averaging the largest intermediate values ​​of said mean AP variance V%.

3. Method for determining a lookup table according to claim 1, wherein 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 lookup table according to any one of claims 1 to 3, wherein the step (509) of determining a final value of the mean AP variance v* is done by saturating the minimum value of the final mean AP variance v£.

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

6. Method for determining a lookup table according to claim 5, wherein the plurality of input variance values ​​is established according to a logarithmic scale.

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

8. Product computer program comprising program code instructions recorded on a computer-readable medium, to implement the steps of the method for determining a lookup table according to any 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 lookup table according to any one of claims 1 to 7.

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