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    • 专利摘要:
    Real time method of blind separation and demodulation of digital telecommunication signals, called channels, from the observation by means of a single sensor of a composite signal comprising these signals, the parameters of these channels including their type of modulation , their amplification, their phase shift, their delay time at the sensor, their frequency and their modulation speed, these parameters for the different channels being different, substantially or perfectly equal, this method comprising the following steps: - preprocessing of the signal sum; estimating the parameters of the Maximum Likelihood channels by an adapted EM algorithm, in which the calculation of the conditional expectation of the log-likelihood is performed recursively by a particulate filtering-smoothing method; - joint demodulation of the channels according to a stochastic Viterbi algorithm; - monitoring the temporal evolution of the parameters of each channel.
    公开号:FR3030964A1
    申请号:FR1402936
    申请日:2014-12-19
    公开日:2016-06-24
    发明作者:Thomas Courtat；Philippe Ciblat；Pascal Bianchi；Bianco Miguel Fernandez
    申请人:Amesys SAS；
    IPC主号:
    专利说明:

    [0001] The present invention relates generally to methods and systems for signal processing in digital telecommunications, and more particularly to those for the blind separation of such signals or signals of similar characteristics. In digital telecommunications, a transmitter seeks to transmit a sequence of information bits to one (or more) receiver (s). The transmitter performs a series of coding operations in order to make possible the transmission of the information on a physical medium which is also called a propagation channel (such as an optical fiber, or such as more particularly the case here, by unstressed propagation in space). This propagation channel is generally not perfect in the sense that the signal received is not an exact replica of the transmitted signal (thermal disturbances, reverberations, dispersion). At the transmitter, a constellation (ASK, M-PSK, MQAM) is given which is a finite set of symbols in the complex plane and a function with a defined number of consecutive bits associates a symbol of the constellation.
    [0002] Each symbol in the sequence is multiplied by a continuous waveform (or shaping filter), shifted in time to form the baseband signal. This baseband signal is transposed at a certain frequency, called the carrier frequency, and then transmitted by a radio interface (an antenna in the case of a wireless transmission). On reception, reverse operations are performed to reconstruct the information bits from the signal measured on the radio interface. In particular, the demodulation is the operation that identifies on reception the symbols actually transmitted by the transmitter from the received signal.
    [0003] We speak of blind demodulation as soon as one of the parameters of the transmission is unknown to the transmitter. In cooperative telecommunications, most parameters are contractually defined between transmitter and receiver (carrier frequency, constellation type, time lag between waveforms, transmit power). The only remaining unknowns are possible synchronization errors and the effect of the propagation channel. These parameters are, in general, estimated by regular transmission of sequences known as pilots known to both parties. The operation compensating the effects of the channel before demodulation is called equalization. In non-cooperative telecommunications, on the other hand, all parameters are unknown - or only known in order of magnitude - and there are no pilot sequences to facilitate equalization. Source separation is a generic problem where one seeks to extract from a composite signal the source signals that constitute it. Blind source separation refers to the subclass of separation problems when the characteristics of the source signals and their mixture are unknown or very partially known a priori. Statistical assumptions about the source signals and / or the nature of their mixture are necessary for this problem to be soluble. It is, for example, commonly assumed: that the sources are mutually independent; the maximum number of constituent sources is known; that the mixture is linear; that there are discriminating statistics between the constituent sources. We are interested here in the separation and the blind demodulation of digital telecommunication signals in a non-cooperative setting. We are more specifically interested in a case where there are no clear discriminant statistics between the sources. As an example, mention is made of the identification of signals transmitted according to the "DoubleTalk Carrier-in-Carrier®" satellite transmission protocol. This satellite transmission technique uses the same frequency band for the continuous exchange of information between two peers. An intercepted DoubleTalk signal consists, therefore, in the time and frequency overlap of two signals of the same characteristics. The identification of these signals is a problem of separation and blind demodulation of sources.
    [0004] Among the methods of blind demodulation in digital telecommunications, we are interested in those based on: the Expectation-Maximization (EM) classification algorithm for the estimation of the parameters of the signal; and on the Viterbi algorithm for demodulation. Documents (S. Barembruch, "Approximate Maximum Likelihood Methods for Blind Classification and Identification in Digital Communications", Thesis Report, Telecom ParisTech, March 7, 2011) and (E. Punskaya, "Sequential Monte Carlo Methods for Digital Communications" ", Thesis report, Cambridge University, 2003) disclose two close methods that combine particulate filtering with EM and Viterbi algorithms. In these two documents, the model of the signal to be demodulated is written as follows: y (i) = + (i) j = 0 or again: y (i) = <h I 5 (i)> +77 (i) where S (i) is the vectorized version of the symbols s (iJ) to s (i) which belong to a constellation C, h is a linear filter modeling the propagation channel, and n is a Gaussian white noise of 0-2 variance . The EM algorithm makes it possible to estimate the filter h and the variance 0-2 according to a probabilistic paradigm and the Viterbi algorithm then makes it possible to reconstruct the sequence g of vectorized symbols which maximizes the probability of the observations of the composite signal y. The EM algorithm makes it possible to approach iteratively the value of the parameter vector 61 = (h, o-2) which maximizes the likelihood of the observed signal. At each iteration, a step E (for expectation) and a step M (for maximization) are successively applied. At the iteration k, there is an estimate 19 (k) = (h (k), 0-2 (k),) of the system parameters. Step E: this step seeks to evaluate the conditional expectation of the log-Likelihood of the observations: The (k) (0) = Etlog P0 ((y (1: 0.5 (1: I) = X (1: I)) IX (1: I) - 0 (k) (. Ly (1: /))) which is rewritten Lek (0) =, o (k) (x) - L 'e (y (01X (i ) = X) (+ cste (6)) i xeci With for any time i, X (i) is the vector variable in CI which designates a possible value for the vector of symbols S (i) actually emitted, the writing y (1: 1) denotes the sequence of observations (y (1),, y (I)) of the composite signal y, f3i, e (k) (X) = Pek) (X (i) = X ly (1) : /)) is the smoothing distribution and L 'e (y (i) IX = X) = log 13 6, (y (i) IX = X) = IY - (111X) I2 / 2o-2. it does not depend on O. It does not need to be calculated, and is omitted in the definition of the conditional expectation of the log-Likelihood The (k) .The stakes of step E are calculate the smoothing distributions / 30 (k) (X), which is done by successively computing the so-called filtering distributions (Pek) (X (i) = X ly (1: i))). s of smoothing (igi, e (k) (X)), by means for example of the Forward-Backard algorithm of Baum and Welch. Step M: once the calculated quantities / (k) (X), step M updates the parameters 61 (k) at 19 (k + 1) according to 6.0c + 1) = argmax The (k) ) (0) In theory, the vector sequence 0 (k) converges to the vector 61 which maximizes the likelihood of the observations. However, applied to the demodulation of a digital communication signal, the EM algorithm is faulty in terms of computational complexity rather quickly with the size of the filter h and / or the size of the constellation C. The contribution of the two documents cited above is to overcome this limitation of complexity with the notions of filtering and particle smoothing which allow to approximate the calculation of the smoothing distribution / 3900 (X) by limiting the number of states X to evaluate.
    [0005] Thus, they consider that igi, e (k) (X) .-- Er <R COni - 8 (X - Zni) where S () is the Dirac distribution on state space C1; for all i, the (Zni) iSrERs are R representatives of the state space well chosen and in small numbers compared to the size of this space; for all i, r, coni E [0,1] and for all i, Erconi = 1. The sets ent, coni) li, r are called particles and the stake of the particle method and to formulate an algorithm allowing to calculate them recursively on the index of time i. To do this, we proceed in two stages: firstly, in a so-called filtering step, we calculate for all i the filter distribution Po (k) (X (i) = XI y (1), --- , y (i)) in the form P6 (k) (X (i) = Xy (1), -, y (i)) r, i. - zr, i) rER with for all i, r, E [0,1] and for all Er 4, i - = 1; then, a so-called smoothing step where the coefficients are transformed into coni coefficients which integrate the observations after the time i to obtain 9 (k) (X) = P0 (k) (X (i) = X ly (1), - -, y (I)) coni - 6 (X - Zr, i) r <R We give ourselves a number called threshold and a transition kernel x -> [0,1] which depends on the sample y ( i); the computation of the filtering distribution Po (k) (X (i) = X ly (1), -, y (0) is carried out recursively, according to the steps: - In input, let t ((zr, i_ ,, er, i_i)) 1, a particle approximation of P 9 (k) - = X ly (1), -, y (i - 1)); - s rj1, r threshold o ask for all r, ii-1, r = Zi_ix and ei-1, r = - 51 Er> threshold o draw a multinomial variable: (Y1, -, YR) (The Yr are variables integer random variables whose sum is R and the expectation of each variable is R -) o is E: -> e (t) = inf fr, '.21 <r' <r Yr / 1-1 o for any re = Zi-1, e (r) and = 1 / R - for each 1 <r <R: o draw Zix according to Ai (, Z-1, r) O pose: Ei, r - ti-1, r - (Po (k) (Zix IY (0, 2i-1, r) / Ai (2i, r P 2i-1, r)) O normalize the weights: - Ei = Er Eu. - ii = At the output, fi ,, r ) Ir is a particle approximation of P9 (k) (X (i) = X ly (1), ---, y (0). The success of this method depends on the choice of a nucleus Ai (.,.) adapted to the particularities of the problem dealt with.
    [0006] The cited documents propose and compare different methods to derive the smoothing coefficients from filter coefficients. We particularly remember the so-called "Fixed Lag Smoothing" method. After estimating the parameters of the model of the composite signal by this EM-particulate algorithm, the prior art techniques mentioned above use an adaptation of the Viterbi algorithm to perform the demodulation. This adaptation - called Stochastic Viterbi - limits the exploration of the lattice of the signal to the states of the particles obtained during the last iteration of the EM algorithm.
    [0007] This approach thus solves the problem of digital demodulation with a complexity applicable to filters and / or large constellations. These states of the art have several limitations to be directly adapted to the problem of blind separation and demodulation of digital signals because, among other things, their formalization is limited to a single source; they assume that a synchronization is acquired between the transmitter and the receiver. However, it is impossible for an interceptor to synchronize on multiple signals at the same time. It follows that in the case of signal mixing, it can not be assumed that a synchronization is acquired, thus compromising the exploitation of the purely sequential model of the methods mentioned; they consider a channel of causal propagation. However, the synchronization fault induces on each channel (ie on each signal of the mixture) an equivalent non-causal filter. In addition, a problem specific to the example of the "DoubleTalk Carrier-in-Carrier" digital communications cited above is that the signals to be separated are, theoretically, transmitted at the same frequency, at the same times and with the same bit rate. However, in practice, the time-frequency characteristics of these signals may differ slightly due to a non-perfect synchronization of the emitters of these signals. The operating point of this system is based on synchronization parameters very similar (but not strictly identical) which are, in this case, unknown or at best known by their order of magnitude. It follows that it is impossible to claim to separate in all cases the signals by conventional techniques of time-frequency filtering or by neglecting one of the two signals in favor of the other. An object of the present invention is to provide blind methods of separation and demodulation in digital telecommunications of signals included in a composite signal. Another object of the present invention is to provide methods for blindly separating and demodulating digital signals operating both with signals of different parameters and with very similar or even identical modulation parameter signals. Another object of the present invention is to propose methods for blindly separating and demodulating digital signals in real time, that is to say with complexities in processing time and storage of linear data according to the number samples of the composite signal taken. Another object of the present invention is to provide methods for blindly separating and demodulating two numerically stable digital signals. Another object of the present invention is to provide methods for blindly separating and demodulating two digital signals with a channel and parameters evolving over time. Another object of the present invention is the blind and joint demodulation of the different channels of a "DoubleTalk 0 Carrier-in-Carrier" signal. For these purposes, the invention relates, in a first aspect, to a real-time method of blind separation and demodulation of digital telecommunication signals, called channels, from the observation by means of a single sensor. a composite signal comprising these signals, the parameters of these channels including their type of modulation, their amplification, their phase shift, their delay time at the sensor, their frequency and their symbol time, these parameters for the different channels being different, substantially or perfectly equal, this method comprising the following steps: acquiring a first plurality of observations of the composite signal made using the single sensor; estimating, from the first plurality of observations acquired, the parameters of the paths in the sense of the Maximum Likelihood by an expectation-maximization algorithm, the conditional expectation of the log-likelihood being calculated, in this algorithm, recursively by a method particulate filter-smoothing; joint demodulation of channels according to a stochastic Viterbi algorithm. The particulate filtering-smoothing method includes a particle size approximation of the filtering distribution, which particle approximation assigns, in addition to weights, multiplicities to the particles of this approximation, a multiplicity being the number of particles representing the same state. The particulate filtering-smoothing method includes a particle approximation of the smoothing distribution, wherein the particle approximation assigns, in addition to weights, multiplicities to the particles of this approximation, a multiplicity being the number of particles representing the same state. This method further comprises a step of acquiring a second plurality of observations of the composite signal made by means of the single sensor; a step of estimating, from the second plurality of observations acquired, the parameters of the paths in the sense of the Maximum Likelihood by an Expect-Maximization algorithm, the conditional expectation of the log-likelihood being calculated, in this algorithm, recursively by a particulate filtering-smoothing method; a long-term estimation step of the parameters, this long-term estimation of the parameters being associated with the second plurality of observations and being a linear combination of the estimated parameters from the first plurality of observations and the estimated parameters of the second plurality of observations. According to a second aspect, the invention relates to a computer program product implemented on a memory medium that can be implemented in a computer processing unit and includes instructions for implementing a computer program. a method as presented above. Other objects and advantages of the invention will emerge in the light of the description of embodiments, given below with reference to the accompanying drawings in which: FIGS. 1-6 schematically illustrate various steps of a blind separation method sources according to various embodiments; Figures 7-15 schematically illustrate the results obtained at different stages of the separation method applied to a "DoubleTalk Carrier-in-Carrier®" composite signal.
    [0008] In one embodiment, a composite sensor y (t) comprising a mixture of N source signals (sn (t)) '= 1..N is recorded by means of a single sensor. The signals (.97, (0). ', .. LN, called in the following pathways, contain the information symbols (sn (i)) i = 1..oe respectively derived from the constellations C n = (CO g = 1..Gn and carried respectively by wave functions hn (.) The composite signal y (t) is written in theory: i = + c ° y (t) = An. El2 '5 flit hn ( t - jT, - ± (t) n = 1 where: An is the complex gain of the source signal sn (ie An = lAnle'21r9n with lAI the amplification (or gain) and cp 'the phase shift (or the phase error) on channel n); hn is the analytic form of the n-channel shaping filter (for example, a raised Cosine filter); sn is the sequence of symbols in the Cn constellation emitted on channel n and s (i) is the i-th symbol transmitted on channel n; 8fn is the carrier residue (or more generally, the frequency) on channel n. In particular, these residues may be substantially equal. Tn is the symbol time on channel n In particular, these symbol times can be substantially equal (T1 = T2 = - - - TN); rn and the delay time on the channel level of the single sensor. These times are chosen, without loss of generality, between -Tn and 0; no is a random disturbance.
    [0009] The composite signal y (t) is sampled at the period Te: j = + 09 Y (i) Y (iTe) = 1An. e1271-8fnTei hn (iTe iTn - Tn) sn (i) n (i) n = 1 Te is chosen less than twice the symbol times Tn, that is to say that for all 1 <n <N, Te < 2T. Digital noise is a white, Gaussian noise of 0-2 variance. The set of parameters of the model of the composite signal y (t) above is noted in the form of a parameter vector 61 = ([An, Tn, 8fn, Tnk = 1..N, a2). For each channel, we consider the J symbols directly subsequent to i and the J + 1 symbols directly preceding or concomitant with i. We denote by 2J + 1 the vector consisting of these for any path n, Sn (0 = [sni (01j = 1.-2J + 1 E Cn symbols and [Sn (i)] n E Ci2J + 1 x --- x CN2J + 1 the grouping of these vectors.
    [0010] We denote tn (i, j) (= tn, 1i (Tn, T71)) the temporal gap between the intercepted sample et and the jth component of the vector Xn (i).
    [0011] The signal y approximates by truncating the wave functions according to the equation y (i) rie, = 1 An. Ei27n5fnTei (Eii == 21j + 1 hn (tn (i, n, j (0) + n ( i) We add to each constellation Cn a noted order relation <n We denote Ci2J + 1 x ..- x CN2J + 1 to (Ci xx Cn) 2J + 1 via the bijection 0: Ci2J + 1 xx CN2J + 1 -> (Ci xx Cn) 21 + 1, [Xn] '((01.1 ([4]), ..., OLN ([4])), ..., (02j + 1.1 ( [Xn1), ..., 021 + 1, n ([4]))), with all n, Xn = [Xnili = 1 ... 2 j + i and OLni ([Xn] n) = Xnrj. .. We define the order relation on C1.21 xx c.N2J + 1 by +1 for U1 c Ci2j + 1 r2J + 1 "r2J + 1 xx c.2J + 1 .UN u2 N 'U2 (te, ## EQU1 ##, ## EQU1 ## and ## EQU1 ## and ## EQU1 ## no (U2) The separation and demodulation of the source signals (sn) n = 1..N are intended to extract the information symbols (sn (j)) n from each signal (sn) '=. 1..N to from the composite signal y (i) observed on a sensor Referring to Figure 1, samples (or observations) y (i) of the composite signal are fired therein The blind separation system 10 extracts from the observations y (i) of the composite signal the information symbols (§n (t)) n = 1..N of each of the N signals (sn) n = 1 ... N included in the composite signal y. This estimate is in the sense of Maximum likelihood; i.e., the blind separation system 10 minimizes the following function: log P 0 (y (1: n, s1 (1: I), - -, sn (1: according to the parameter vector 19 = ( [An, v fn, Tn] n = 1..Ne 0-2) and the sequences (sn (1: .0) n = 1..N (where I is a natural integer greater than or equal to one), this optimization is performed, inter alia, using an EM algorithm performed on particle approximations of the log-likelihood expectancy Referring now to Figure 2, the blind separation system 10 includes the preprocessing module 1 configured to filter, downsample and cut, the samples y (i) of the composite signal y, in frames 371, -, ym, -, ym of length I. It follows that frames yi, ..-, ym , ..-, ym are successively obtained at the output of the preprocessing module 1. This preprocessing module 1 can also produce a pre-estimation Oir of the parameter vector 0 when it is applied to the frame the modules 2-4 are configured for e to stimulate from each frame ym the information symbol (g. ) of the signal (sn) '=, ... h, transmitted during the duration of the frame ym.
    [0012] Module 2 implements the EM algorithm by filtering and particle smoothing. This module 2 operates on K iterations per frame ym and gives a vector output parameter OZ) = ([Anacm), Tn (mk), 6fn (m ", Tn (km) in = 1..1 ^ 1, 0- 72 // ")) estimated on the frame ym of the composite signal y. This module 2 requires the definition of two additional parameters: Om to initialize the recursive estimation of the parameter vector 0; and Pa (m, 0) which corresponds to a "particle approximation" of the last sample of the signal directly preceding the first sample of the yin frame (i.e., the sample ym_i (I), I being the number samples per frame). In the case where m = 1, this approximation can, for example, result from a uniform draw of the possible states. Module 3 carries out long-term recursive monitoring of the signal parameters. This module 3 takes as input the vector Om (K) delivered by the module 2 for the frame m and a vector 0m-1, giving a long-term estimation of the signal parameters up to the frame m-1. This parameter Om_i generally comes from this same module 3 in the frame m-1. Module 3 produces the long-term estimation of the parameters Om by linearly combining Om (K) and Om_i. A demodulation module 4 implements a variant of the Viterbi Stochastic algorithm from the current ym frame of the composite signal and the parameter vector Om estimated in the long term by the module 3. This demodulation module 4 provides an output an estimate .§1, m, -.-, 'N, m of the information symbols si, m, ..-, sN, m transmitted over the duration of the frame ym by each of the channels .51, -, sN . The information symbols estimated .§1, m, ---,: ssN, m over the frames yi, ..-, ym, respectively, on the channels, are respectively loaded into buffers (see " buffer "in FIG. 2) to form at the output of the blind separation system 10 flows of parallel information symbols corresponding to the signals si, ..-, sN. FIG. 3 details the module 2 for the implementation of the EM algorithm by filtering and particle smoothing and, in particular, the interactions between the step E implemented by the module 2.1 and the step M implemented by the module 2.2 over the iterations k = 1, -, K on a frame ym. The module 2 encapsulating the EM algorithm outputs an estimate of the parameter vector Or) on the frame ym after K iterations from: the current frame yn; a set of particles denoted by Pa (m, O) approximating the signal to the sample preceding the first sample of the frame ym; and an initialization parameter vector OZ initializing the EM algorithm. At the iteration k, the module 2.1 for the implementation of step E calculates from Pa (m, 0) and the parameter vector Om (k-1) (that is, that obtained at 1 previous iteration) a set of particles noted P-6, - (ma: /) deriving from the smoothing distribution over the whole of the ym frame. In the case where k = 1 and m> 1, 07 (nic-1) = om-1 (given by the module 3 on the ym-i frame); if k = 1 and m = em (k-i.) = Oc, is a parameter vector of initialization of the EM algorithm.
    [0013] According to the embodiments, it can be provided by an operator, be chosen randomly or be a by-product of the preprocessing module 1. At the iteration k, the module 2.2 for the implementation of step M refines the estimation of oTn (k) in Om (k + 1) from the frame ym, am (k) and particles P (m, 1: /) obtained by the module 2.1 for the implementation of the step E (see Figure 3). In this respect, at the iteration k, the step E implemented by the module 2.1 evaluates the conditional expectation of the log-likelihood of the observations: L9 (-i) (6) = Esp (log P 0m (( ym (1: I), [Sn (1: I) = X na: pin) I Exn (1: Peoc-i) (. n)} which is rewritten Le-i) (0) =>, Gie-i ) ([4 (i)].) - The emcym (i) I [sn (i) = xn (oin) (+ r (Om)) in xn (DEei where:, gie_i> axnumn) = Pee-, asn (i) = xnuAn iym (i), ---, ymcm is the smoothing distribution and 2 x-11 ^ 1 j = 21 L '0m () I [X (i) = Mn) = 1Ym (i) Ane2n1 fnTel. T n)) / 20-2 n = 1 j = 0 L "is a term not necessary for the variant of the step M implemented by the module 2.2, so this term L" does not need to to be calculated. In the following, the index m of the frame ym is implied to lighten the notations.
    [0014] The (k) (0) is calculated by means of a particle approximation. A particle approximation is a parsimonious writing of the state space adapted to the evaluation of Le (k) (0) in the sense that the number of evaluation points is very small compared to the dimensions of the space of d 'state. Two types of particle approximations are considered.
    [0015] According to a first, so-called simple, particle approximation, a particle approximation of the filter distribution Pek) ([4 (0] 'ly (1), -, y (0) is written x-1R P e (k) ([ Xn (O] fl 13 (1), y (j)) 4, i saxn (i) k- [zn, r (oin) where: R is an integer called maximum number of particles given at the initialization of this method for all i and for all r <R, er, i is a real between 0 and 1 called the filtering weight, for all j, Er = 1, for all n, all i and all r RiZnx (i)] n = Rzn - (0) E Cn2J + 1 is a n symbol vector called support of the particle approximation The particle filtering according to this first particle method is the recursive calculation of Pe (k) ([4 (OL, y (0 ) for all i according to the above approximation.
    [0016] In the same way, a simple particle approximation of the smoothing distribution fli, o (k) ([Xn (O] n) = PemaXn (OLIY (1), -, y (n) is a writing of the form: (k) ([Xn (i) k) Wr, j (Vn (Din [Zi n, r (Oln) where: for all i and for all r <R, coni a real between 0 and 1 called the smoothing weight; for all i, Er = 1, for all n, all i and all r R, [rn, r (i) in = (0) E C2J + 1 is a n vector of symbols called support of the particle approximation.
    [0017] This approximation can, in particular, be obtained from the particle approximation of the filter distribution P ek) ([Xn (i)] n ly (1),, y (0) above. particle, called multiple, the particle approximation of the filter distribution PemaXn (Ok IY (1), -, Y (0) is a writing of the form Reff (i) P e (k) ([Xn (O] IY (1) - - - y (0) - = - 11r, i 8aXn (i) in [Zn, r (017,) where: - R is an integer called maximum number of particles given at the initialization of this particular method for all i, Reff (i) R is an integer called the effective number of particles at the generation i, for every i and for every r Reff (i), er, i is a real between 0 and 1 called the filtering weight for all i and for all r Reff (i), iirj is an integer called the multiplicity of the particle - for all i, Eritr, i4, ti = 1 - for all n, all i and all r Reff (i) , Vn, r (01n = Kzn, r, i (0) E Cn2J + 1 is a n vector of symbols called support of the particle approximation. particulate ligation according to this first particulate method is the recursive calculation of Po (k) ([Xn (O) IY (1), -, Y (0) for all i according to the approximation above. Similarly, a multiple particle approximation of the smoothing distribution 13i, e (k) ([X, i (i)]) = P0ck n (OlnY (1), -, y (I)) is a write of the form: Rieff (i) 130 (k) ([Xn (01n). "" '(13r, i - Vr, i 6 ([Xn (i)] [Zin, r (O] where: for all i and for all r R, cor, i is a real between 0 and 1 called smoothing weight, for all i and for all r Reff (i), vri is an integer called multiplicity of the particle, for all i, Er cor, ivr, i = 1, for all n, all i and all r R, [Z ', (0] (0) E Cn "" is a vector of symbols called support of the particle approximation. to be followed: according to the paradigm of the first particle approximation or according to the paradigm of the second (so-called multiple particle approximation) presented above Advantageously, the above multiple particle approximation of the filtering distribution, as well as that of the Smoothing distribution makes it possible to eliminate the redundancy of the particles. Multiple approximation makes it possible to overcome the redundancy of the particles by collecting the particles representing the same state. This multiple particle approximation, which makes it possible to limit the number of particles actually calculated and therefore to divide the calculation time and the memory space necessary for the execution of the algorithm, is detailed below. The following auxiliary variables are introduced: for all i, we denote Vi: KReff (i)]] 41 [1, Reff (i - 1)] 1 the application which to a particle of the generation i designated by its index r associates a particle of the generation i - 1 called its ancestor Vi (r); for every i and every path n, we give ourselves a variable Trn, i e {0,1} called the jump indicator; for all i and all r E j {1, Reff (011, we introduce an additional weight ani e [0,1] called auxiliary weight, especially as for any EReff (i) r ar, i - = 1 The precise definition these auxiliary quantities will be recurrent in the complete specification of the procedure for the blind separation of signals.
    [0018] To ensure the stability of the calculations, the auxiliary weights and the filter weights are replaced, respectively, by their logarithms denoted Lani and the time differences tn (i, j) between the sample i of the composite signal y and the j - th sample of the vector of symbols 4 (0 contributing to ym (i) are computed at the same time as the particles, the jump indicators, nor e {0,1} is 1 if it is necessary to consider the arrival of a new symbol between the vectors Sn (i - 1) and S (i) and 0 otherwise We write the sets: Pc (, k) 0n, = (Reff (0, [Un [(t (i,, (Larj, Lri 4tr, i, [Zn, r (01, Vi (r)) r) (called auxiliary approximation of the sample i); (m, i) = (12 ef f (i), [Tr n, dn , Rt, (gr, i, (01 n, Vi (r)), ..) (called particle approximation of the filter distribution at 0; Pco (k) (111, = (11 eff (0, RtnO, D ), (cor "!, vr [Z nr (01n (called particle approximation of the smoothing distribution in 0. We define in the same format sets of particles s additional multiples: Pe (ck) 011, = (1keff0), [Ttn, d. Rtn (Lécr, i, [2n, r (r)) produced by the module 2.1.1 of figure 4 and used by the module 2.1.2 (called resampled auxiliary approximation); 1), -, k) (rn, = (rZeff (i), Rtn 0, D) in ((T) r, i [2n, r W] jr) produced by the module 2.1.4 of figure 4 and used by module 2.2 (called mixed approximation of the smoothing distribution in j) These sets are the data exchange units between the sub-modules constituting the particulate EM algorithm implemented by the modules 2.1.1-2.1. 4 and 2.2 of Figure 4. Note that in the detail of these sets, the frame indices yni and iteration k have been implied to reduce the notation, using the notation Pe (m, 1: 0 (respectively Pe (m, 1: I)) to denote the set consisting of Pe (m, 1), ---, PC) (m, l) (respectively p (k) (m, p (k) (m, The sets Pa (m, i) and P (m, i) also have the property of being classified in lexicographic order on Ci2J + 1 x --- xCn2J + 1 - = (C1 xx Cri) 21 + 1: for all r, i E [[1, Reff0A, r 5_E [Z ,,, (01n [Z ', t (O] n .In the presented method, a calculation of the form logEiciebi , bi <0 is performed at many A naive realization of this calculation raises cases of divergence. An appropriate numerical procedure is introduced, detailed below. A calculation of the form logEielebi realized with this procedure is in the following represented symbolically by EreIbi. - If I = 0, r; Eibi = 0 - If / # 0, let i * = argmaxie / bi LEI = bi * + log1p (expfliciv * (bi - (log1p (-) is a standard function of numerical computation libraries , accurately realizing the evaluation of log (1+ e) when lei "1).
    [0019] Particle estimation methods involve a transition nucleus (function of squared state space in the interval [0,1]). Since the wave functions may not be causal, the transition nuclei studied and used in the documents cited in the state of the art are therefore not appropriate to the problem that concerns us here. We give ourselves an integer 8 of the order of J- max Tn / Te. We define for all i w1 ([4 (0] 7, [4 (i-1)] n) = [x, i (i + 6)] nPe (k) (Yi, - *, Yi + 8, [ Xn (i, [Xn (i + (Mn), wi ([4 (i = E [xnco] nwi ([4 () 1., [4 (i-1) 1n) and wi ([X, (( 0],. ,, [X, - = WiaXn (Oin, [Xn (i - 1)]) / WiaXn (i -) which is a transition nucleus of C121 + 1 x --- x Cn2J + 1 in it. Monte Carlo approximations are used in practice to evaluate this nucleus.
    [0020] The module 2, and in particular the module 2.1 carrying out the step E, breaks down into sub-modules as detailed in FIG. 4 - for each iteration ko for each sample i - the module 2.1.1 corresponds to a step of resampling the particles which takes as input the set of particles Pe) (m, i -1) and gives at the output the set of resampled particles Pe ((k) (m, i - 1) - the module 2.1.2 corresponds to a particle filtering step which takes as input Pe (ck) (m, i), the frame yin, the estimate of the parameter vector 07 (0 obtained at the previous iteration and which gives at the output the filtering distribution Pe (k) (m, i) for sample i as well as the auxiliary approximation Pc (ck (m, i) for sample i: - module 2.1.3 corresponds to a particle smoothing step. this step of particulate smoothing implements an algorithm called "fixed-lagg smoothing" which takes as input the distribution of filt ragePe (k) (m, i) of the sample i and gives the output of the smoothing distribution Pe) (m, i - d) of the sample i, A being an integer parameter defined at the instantiation of the system; the smoothing distributions PC) (m, i - A) for i = 1, -, / are aggregated in a buffer (see FIG. 4) in order to output the smoothing distribution of the entire frame P <,, k ) (m, 1: /); o Module 2.1.4 corresponds to an optional so-called stochastic mixing step (k) which transforms P (k), (m, 1: I) into Pia (m, 1: I) (possibly Pe (m, 1: / ) = Pe) (m, 1: /)); the module 2.2 performs the step M from the frame ym and the particles Pe (m, 1: /) and provides after K iterations the final output of the parameter vector 0 of the module 2 for the frame ym. In the descriptions of submodules 2.1.1 to 2.1.4, the frame indices 171. and iteration k are implied. The algorithm implemented in the resampling module 2.1.1 comprises: at the input of the module 2.1.1: o 13, (tk) (1-11, i-1) = (Ref. (I-1), Rtn - 1i)) jn [Zn, r - 1) 1n, Vi_i (r)) r) draw the variable (Y1, YRef f 1)) MUlt R'C (1, i-1 -Ri, ji - - - CCReff (i-1), i-1 - IlReff ask fteff (i - 1) = card fr E Il, Reff (i 1) 1, Yr> 0) define: eo: fteff (- 1) 11 -> [ [1, Reff (1 - 1) 1 by eo (i-) = inffr, Er, <r min (Yr '1) for all 1 r 5_ f1eff (i - 1), ask: o for all 1 <n < N, - 2n, r (1 - 1) = Zn, e0 (r) (! - 1) 0 = log 1 / R 0 = YE0 (r) O Lr - gEo (r), i - 1 Laeo = eo ( r) at the output of module 2.1.1: o Pe, (, k) (m, i - 1) = (Éeff,, Zn, ri-ln, V7-1rr The algorithm implemented by module 2.1.2 The new generation sampling system comprises: at the input of module 2.1.2 of the sampling module: O Pe (tk) i - = (itff (i - 1), brn, ii], Rtn (i - 1 n, V 1- 1 rr o the yin o frame the parameter vector, (11) update of the time gaps and jump indicators: o for any lane n and all t index j, D = tn (i D Te o SD 0, for all j, tnO, D = 'G0,0 + e and TEn, i = 1 O otherwise for all j, tn (i, i) = (i4 ) and Trn, i = 0 o put K = ---, KK} = 1 n N, 1Tn, i = 1} and K = = n N, Trn, i = 0. for all r Eeff (i - 1), - for all c / (Ki, ---, KK) = (dKi, ---, of K) E CKi X --- X CKK - for all n E NIL - define Zn, r, d (Ki, ..., KK) (0 = - 1) if n K - = [dice ± n, r, 2 (1 - 1), "- - 1) 1 If n = K. EK - calculate LWi ([Znir, d (Here, -., KK) (01n t4, r - 1)) compute LI / Vi ([Zn, r (i - 1)] n) = ([Zn, r, d (Ki, ..., KK) (01n I - 1)) normalize: for all d (Ki, ---, KI () Lw ([Zn, r, d (Ki, -, KK) ( 0inI - 1)) = LWi ([4, r, d (Ki, -, KK) (0in I 4, r - 1)) - LWi ([4, r (i - 1)]) draw the variable (Pdoci , ..-, K0) Muit (wi ([Zn, r, d (K1, -, K0 (01n I - 1))) ask for all r, Ref f (r, i) = card td (K1, ---, KK), Pdoc1, ..., K0> 0) define the bijection E1, r: [ri Reff (r, -> K = Ki EK, Edoctixdoe) Pd (cry) 1-1 - note for everything n, all 1 [1, Reff (r, 011 (0 = = LWi ([Zn, r (i - 1)] n) 0 = O 1.7. = + log Pe (() (y (i) 1 [Z ', (rj.), i1n) - oV; 0-, = Put Reff (i) = Erea1-1) Reff (r, i) - define the bijection (01,02): 111, Reff () 1 - > Urr_ftieff (i-1) {r} x D, Reff (r,) 1 a permutation such that r1 <r2 [Zn, (01 (ri), o2 (ri)) (O1 -4 [Zn, (01 ( r2), 02 (r2)) (OL for all r Reff (0, O [Zn, r () L = {Zn, (01 (r), 02 (r)) (0t O LAr, i = LA (01 (0,02 (r)), i ## EQU1 ## (01 (0.02 (r)), where V (r) = V1 (O1 (r), O2 (O)) normalize weights: for all r, LA i = LAr, i LEi = Er LEr, i Lani = LAni - LAi = LEni - LEi - output: (m, j) = (Reff (I),, [Zn, r Vi (r))) is the filter distribution of the sample i; P (k) (1111 = (Reff (0, [Zn, r Vi (r))) is the auxiliary distribution of the sample i.
    [0021] For the smoothing step implemented by the module 2.1.3 (FIG. 4), the method known under the name of "fixed-lag smoothing" is for example used. We get an integer A, - at the input, the filtering distribution of the sample i Pt (m, i) = (Reff (i), [un, dri, (gr, i 41-r, i, [Zn , r (01n, Vi (r)) put V1,0 (r) - = V1 (r) for all 1 <j <A oij (r) = - ask Kif (i - A) = Reff (i) - ask for all r Reff (i), O Vr, iP = lir, i O = O [Zin, r - = [Zn, Vi, A (r) Win - at the output, the set POE, (m, iA) = (Rieff0 - (c) r, iA, Vr, i-Ae [ZI n, r - Jr) is a particle approximation of the smoothing distribution at iA.
    [0022] The module 2.1.4 is configured to implement a step of stochastic mixing of the particles obtained by the module 2.1.3. It takes, therefore, as input the set of smoothed particles P, (m, 1: /) returns a new set of particles noted Pia (m, 1: /). This module 2.1.4 makes it possible to be immunized against the risks of convergences towards a local optimum of the algorithm EM. For all i, it consists in retaining from P '(m, 0 only one particle drawn by lot.) It should be noted that, if this step is applied to each iteration k of each yin frame, the algorithm becomes It is thus applied only to certain pairs (m, k), those belonging to a set It, this set being to be less and less dense with the evolution of (m, k). For example, we can consider It such that (m, k) E It ssi -1) - K + k is the square of an integer. The procedure implemented in this module is: at the input: P (k) (m, 1: 1) = ((R ef f, {(tri (i, l)) .1, (cor i, vr [Z )) is the approximation of the smoothing distribution, if (m, k) It o for all ieo ask peff (i) = 1 o draw an index ro in [[1, Re'ff (i)]] with a probability proportional to coi, r, o, to set t ,, i = 1, = 1 and [2a (i)] n = [Znixo (O) - if (m, k) It o for all i E ft1, I, o ask eff (i) ---- Re'ff (i) o for all ref (0]] o to set ior, i = 1, -er, i = 1 and [2n, r (0) = [4, r (0] 7. 'At the output: P (m, 1: 1) = ((P' ff, l (tn (i, fin, fr) r, i [2n, r (Oljr) ) is the mixed approximation of the smoothing distribution The module 2.2, highlighted in Figures 3 and 4, corresponds to the step M of the EM algorithm At the iteration k, it takes as input the frame of signal ym, the parameter vector em (k-1) estimated at the previous iteration and the mixed particles P (m, 1: 0 obtained at the end of step E (ie by the module 2.1 and especially the sub module 2.1.4) It outputs a refined estimate (k) em of the parameter vector. This estimate is chosen to decrease the conditional expectation of the log-likelihood of observations according to the parameter vector 61: (k) n (k-1) (k-i) (uni) e (k-1) (Uni). Many methods can be envisaged for this purpose. In one embodiment, the following procedure is implemented: Note the parameter vector Om (k) estimated at the k-th iteration on the m-th oc) = (mn (krn), Tn (rnk), fn (ink) Tem)] n = 1..N, 0_711 (k)) em field in the form 61m (k) = (em (9) where L 'is the total number of parameters to be estimated. and the indices I can be any, even random and different at each iteration, we denote e = for all 1.1 <1 <L 10 we update the 1-th parameter according to L 'I (y (01 [21i, ) oc = 9 = (k-1) v: 201,1, 01 0.0 (k, 1-1) Ei Er iiiniVr, 1 a 07 9 = 0 (k, 1-1) = ofior efk-1), ef + k; i), ..., 0, k-1)) and we put: 0 (1 ('1) we get at the output Ce = The derivatives of order 1 and 2 are computed analytically. 0.1] makes it possible to adjust the speed of convergence of the algorithm, it is possibly different for each parameter, and if certain parameters of the system are known a priori with certainty, they can be considered. are used as constants in the algorithm and are not updated in the step M. In this case, the convergence of the algorithm is accelerated and the residual variance due to the estimation of these parameters is neutralized. FIG. 5 details the interactions between the module 3 for the long-term monitoring of the parameter vector 0 of the composite signal y and the demodulation module 4. Module 3 for the long-term monitoring of the parameter vector 0 forms an estimate 0 of the parameter vector 0 by linearly combining all the Y (01 [2n, r, i] estimates obtained from the parameter vectors 6 +; _ 1 (), e0 , em (10 by the EM algorithm (implemented by the module 2) on the frames Yi to ym This estimation can be made recursively from: 61m (K) the parameter vector estimated for the frame ym on K iterations by the module 2 and in particular by the module 2.2, and by 19m-1 the long-term parameter vector estimated by the module 3 for the long-term monitoring of the parameter vector O on the previous frame if m> 1 or possibly by the priming module 1.3 if m = 1. At the convergence of the EM algorithm on the yin frame, all the parameter estimators have a variance proportional to 0-2m (K), so we put: Pm = 2 (K ) -2 Y - am -2 1 - 2 = cro = +00 Y1 '-2, 2 (K) am-1 0 "m Then we update the parameters according to: em = + (1 - fm) - (Or) - cm-1) The tracking parameter set by the user between 0 and 1 allows to give elasticity to take into account the evolution of the channel. The quantities fm and eirl, respectively, are a modified tracking parameter and variance in order to linearly optimally combine the estimation on the m-frame of the EM Om (k) algorithm and the long-term estimation up to the frame m-1.8m_i. The demodulation module 4, detailed in FIG. 5, demodulates the channels. This module 4 implements a stochastic Viterbi algorithm. This demodulation module 4 essentially produces the estimated symbol frames .1, m, 2, m, -, N, in for each of the channels. 2 (K) Y - a m The demodulation module 4 comprises two functional blocks. The submodule 4.1 is an instantiation of the step E of the EM algorithm, limited to the reproduction of the modules 2.1.1 and 2.1.2 corresponding to the particulate filtering step. This submodule 4.1 II takes as input: the frameym; the long-term parameter vector Om estimated on the frame ym by the module 3 for the long-term monitoring of the parameter vector O. The submodule 4.1 realizes with this parameter vector Om a new filtering step and produces an output: a set of particles fi (m, 1: /) to sub-module 4.2. This set may, depending on the particle approximation used, be a set of particles or a set of multiple particles. It should be noted that in this output, the weights of filtering obtained are not used in the following; an auxiliary particle approximation Pa (m, I) of the last sample of the frame ym. It is this approximation which serves to initialize the module 2 and in particular the 2.1.1 module of the ym + i frame via their input parameter Pa (m +1.0). The sub-module 4.2 realizes the demodulation of the channels. by a stochastic Viterbi algorithm. It takes as input: the parameter vector Om estimated in the long term up to the frame ym by the module 3 for the long-term monitoring of the parameter vector e; the support of the particle / 5 (m, 1: 0) approximation of the frame given by the submodule 4.1.
    [0023] The vectorized sequence of maximum a posteriori (P, (0)) is obtained by the stochastic Viterbi algorithm.The symbols emitted on each channel are estimated by the sequence ((in)) according to the procedure: 15in5In - input: the vector sequences of maximum a posteriori: ([] n) and the jump indicators [n] for all 1 i I and all 1 <n 5_ N; - for all n ER, N1 o ask In = o for all in EO " és (in) = infti E [1,11 in} O gnOn) = - at the output, the sequences -n, m = U'n (WiED., / nl are an estimate of the symbols emitted by the n-way on the The preprocessing module 1 (see FIG. 2) provides, in particular, the formation of the ym frames This pretreatment module 1 takes the information flow y in. In the case of the identification of Double Talk signals by For example, the signals of this composite signal y are not emitted according to raised cosine filters h but according to a raised cosine root filter F. In this case, there is the signal directly o bservated and modulated by elevated cosine root filters and y the filtered signal that is manipulated by the downstream modules. It is therefore up to pretreatment module 1 to filter the signal picked up by to obtain a signal shaped by h. In addition, at the time of the interception, the symbol times are unknown, it is necessary to oversample the signal widely in order to be sure to respect the condition of Shannon. Once the known symbol times, it is no longer necessary to manipulate a largely oversampled signal.
    [0024] As shown in FIG. 6, the module 1 comprises three submodules. the submodule 1.1 ensures the "buffering" of the signal y observed at its input to form the ym frames; the sub-module 1.2 jointly performs the subsampling and filtering of the frame ym to output the frame ym which is the signal directly manipulated by the other modules of the blind separation system 10. This submodule 1.2 uses the knowledge more or less precise symbol times Tn available in the system through the vector 0, -1 delivered by the module 3 for the long-term monitoring of the parameter vector O. For the first frame, the parameter vector Bo is estimated for example in blinded by submodule 1.3; sub-module 1.3 makes it possible to make a rough first estimate of the parameter vector O. This step is used only on the first frame of the signal and is called the boot step. For example, the frequencies can be initiated from the circularity property of the considered constellations, the symbol times by the spectral line method, the amplifications by an equitable sharing of the energy of the intercepted signal, the delay times and the errors. of phase which are a priori bounded can be taken equal to 0 or values drawn randomly. The procedure for joint filtering and decimation of the signal implemented in the adaptation sub-module 1.2 is as follows: at the input: the frame ym (i) = Einv = iAn. ei2n8 f N (Eiii + cecoitn (iTe .- j Tn - inbn (n) (i) sampled at the rate Teo; -lin is a raised root cosine filter of symbol time Tn, the Tn are substantially equal; sampling times of each channel Ti, -, TN via the parameter Om_1, we set T, min Tn and fi the raised cosine root filter of symbol time 2T, ym is filtered and subsampled together in ym at the rate T, according to the equation Ym (i) = Ijirn (j) - ri UT e0 iTe) e0 - at the output, the frame ym is given at the input of the downstream processing chain The proposed separation algorithm is a generalization of the EM algorithm computed on a particle approximation This algorithm is applied to an analytical model of the composite signal to extract the source signals Decoding is provided by a Stochastic Viterbi algorithm The real-time term is justified here since the signal is "buffered" in frames of I (100 to a few thousand) symbols and that the temporal complexity of the separation algorithm and its memory resource requirements are linear depending on the size of the frame. Thus, it is possible to implement it in such a way that the processing time of a frame is equal to the transmission time of its I samples regardless of the value of the size. Thus the size of the frames can be adapted to signals whose parameters are constant in time (long frames) or to signals whose parameters vary rapidly in time (short frames), the long-term monitoring module is loaded in the latter case of composing an estimate of the parameters of less variance. Advantageously, the systems and methods described above introduce the notion of particles with multiplicity which makes it possible to greatly limit the number of particles to be treated and therefore to greatly accelerate the execution of the algorithm. Indeed, with this paradigm, the effective number of particles used for a frame during an iteration EM automatically adapts to the difficulty of this treatment. Thus, on the first iterations of the first frames, many particles are actually used; when the convergence of the parameters is initiated, this number gradually decreases before stabilizing at a much smaller number of particles than would be necessary in the classical paradigm of particulate filtering when the convergence is acquired.
    [0025] Advantageously, the methods and systems described above allow the processing of a wide range of configuration: of different types of modulations (for example M-ASK, M-PSK, QPSK, M-QAM), the type of modulation can be different on each of the tracks; various frequency bands for the different channels, whether they are different or equal (or substantially equal because of synchronization errors between the channels to be considered for example for the separation of Double Talk signals); various symbol rates for the different channels, whether different or equal (or substantially equal because of synchronization errors between the channels, to consider for example for the separation of signals Double Talk); transmission gains at the different sources, whether different or substantially equal; delay time and phase errors on each channel can be arbitrary. The described systems are capable of automatically detecting, optimally combining and exploiting any asymmetry between the source signals to its advantage. In an illustrative implementation of the blind separation method described above, a composite signal comprising two "DoubleTalk Carrier-in-Carrier" signals is simulated according to the following parameters: the signal y is composed of two paths: N = 2; the interception sampling period is taken as the reference time unit: Te = 1; the shaping filters i and 1-1.2 are raised root cosine filters of roll-off 0.35; the symbol times are T1 = 2 and T2 = 2 in reduced units; the carrier residues are 8f1 = i.i0, 8f2 = 3.10-6 in reduced units; the phase offsets are (pi = 1T / 10 and (p2 = Tr / 4), the delays are -c1 = -0.3 - Ti and T2 = -0.8 - T2, - the two modulations are QPSK, the amplifications are such that 1A21 = 0.95 -1A11 the noise is white, Gaussian, the ratio between the average power of the signals and that of the noise is 20 dB.The simulated composite signal is analyzed on 20 fields of size equivalent to 500 symbols per channel. signal adaptation step, the blind separation method is instantiated with the following settings: the maximum number of particles is fixed at 200, the smoothing parameter is A = 40, the channel is assumed to be quasi-invariant: y = 0.9; there are K = 10 iterations EM per frame The sequence of the separation algorithm on this composite signal is shown in Figures 7 to 14 and in Figure 15. Figures 7 to 14 visually show the results of a few typical iterations of the algorithm, the sub figures respectively represent from left to right and from top to bottom: a reconstruction of lane 1 in the complex plane (this reconstruction is obtained by subtracting from the composite signal the estimate of lane 2 and intersymbol interference on lane 1. Gray represents the local density of measurements on reconstructed track 1). The value of SINR is an estimate in decibels of the ratio between the power of the signal on channel 1 and all the disturbances which are superimposed on it (interference between symbols, channel 2 and noise). a reconstruction of track 2 (this reconstruction is obtained by subtracting from the composite signal the estimate of channel 1 and the inter-symbol interferences on channel 2. The gray levels represent the local density of the measurements on the reconstructed channel 2) . The value of SINR is a decibel estimate of the ratio of the power of the signal on channel 2 and all the disturbances superimposed on it (interference between symbols, channel 1 and noise). a reconstruction of the composite signal (this reconstruction is obtained by subtracting the intersymbol interference on channel 1 and on channel 2 from the composite signal.) The gray levels represent a local density of measurements on the reconstructed composite signal. to what would be the composite signal without noise, the pairs of figures above each point designate the pairs of states of the constellations of the channels 1 and 2 which correspond to this composite signal state). the quantitative data in this sub-figure are: Tr: the number of the processed frame, It: the current iteration, MP: the average effective number of particles used to process the current iteration and SI: the estimated standard deviation of the estimated noise at this iteration. a reconstruction in the frequency domain of channel 1, channel 2 and noise. a reconstruction in the time domain of the shaping filters on each of the channels In FIG. 7, the signals are observed after the adaptation phase (0 iterations). They are indistinguishable. SINRs for lanes 1 and 2 can not yet be estimated; their unknown value is noted " ". FIG. 8 shows the signals after reconstruction with the initialization parameters of the algorithm (that is to say, after a single iteration); the level of noise is high and we do not find at the eye of relevant structures on the different reconstructions. In FIG. 9, after 4 iterations, it is noted that the noise level has decreased, we begin to provide a QPSK on the reconstruction of the channel 2.
    [0026] Figure 10 shows the last iteration of the algorithm on the first frame; on each of the channels, we see a QPSK forming. The noise level is still high, however, the algorithm has not finished converging at the end of the iterations allocated to the first frame. However, we see in FIG. 11 that the convergence continues on the second frame: the change of frame has not created any upheaval in the algorithm, the convergence mode is continuous.
    [0027] It is at the fourth iteration of the second frame (Figure 12) that the convergence of the algorithm is acquired. The QPSKs are well drawn on each of the reconstructed tracks and the estimated noise level is lower than the noise level of the intercepted signal (the adaptation step also gained a few dB of SNR). Figures 13 and 14 are typical of the sequence of the results of the algorithm: the convergence of the parameters remains stable with the time, the algorithm follows the evolution of the channel and corrects the accumulation of the errors of estimation of the residues of carriers by slightly changing phase errors over frames. It should be noted that the paradigm of particles with multiplicity is, in this example, effective in adapting the number of effective particles to the difficulty of the case to be treated. If in the first iterations 88 to 14 effective particles are used (out of the 200 available), this number stabilizes at 4-5 in the following iterations, which is a gain in need of significant time and material resources compared to the state of the art in blind demodulation. Figure 15 shows the evolution of parameter estimation over frames ("global" estimate) and iterations ("local" estimate). In particular, it can be seen that the estimate of phase errors changes slightly to compensate for the variance in the estimate of carrier residues.
    权利要求:
    Claims (5)
    [0001]
    REVENDICATIONS1. Real time method of blind separation and demodulation of digital telecommunication signals, called channels, from the observation by means of a single sensor of a composite signal comprising these signals, the parameters of these channels including their type of modulation , their amplification, their phase shift, their delay time at the sensor, their frequency and their symbol time, these parameters for the different channels being different, substantially or perfectly equal, this method comprising the following steps: acquisition of a first a plurality of composite signal observations made using the single sensor; estimating, from the first plurality of observations acquired, the parameters of the paths in the sense of the Maximum Likelihood by an expectation-maximization algorithm, the conditional expectation of the log-likelihood being calculated, in this algorithm, recursively by a method particulate filter-smoothing; joint demodulation of channels according to a stochastic Viterbi algorithm.
    [0002]
    The method of the preceding claim, wherein the particulate filtering-smoothing method comprises a particle size approximation of the filtering distribution, said particle approximation assigning, in addition to weights, multiplicities to the particles of this approximation, a multiplicity being the number of particles representing the same state.
    [0003]
    The method of claim 1 or 2, wherein the particulate filtering-smoothing method comprises a particle approximation of the smoothing distribution, said particle approximation assigning, in addition to weights, multiplicities to the particles of this approximation, a multiplicity being the number of particles representing the same state.
    [0004]
    The method of any one of the preceding claims, further comprising a step of acquiring a second plurality of composite signal observations made using the single sensor; from the second plurality of observations acquired, the parameters of the Maximum Likelihood channels by an Expectation-Maximization algorithm, the conditional expectation of the log-likelihood being calculated, in this algorithm, recursively by a filtering method- particle smoothing; a long-term estimation step of the parameters, this long-term estimation of the parameters being associated with the second plurality of observations and being a linear combination of the estimated parameters from the first plurality of observations and the estimated parameters of the second plurality of observations.
    [0005]
    5. Computer program product implemented on a memory medium, capable of being implemented within a computer processing unit and comprising instructions for the implementation of a method according to any one of the preceding claims. .
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    引用文献:
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    EP3506173A1|2017-12-29|2019-07-03|Avantix|System for blind demodulation of digital telecommunications signals|
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    FR3076412A1|2017-12-29|2019-07-05|Avantix|System for the blind demodulation of digital telecommunication signals|JPH06350660A|1993-06-08|1994-12-22|Nec Corp|Demodulator|
    US20080253011A1|2004-01-23|2008-10-16|Matusuhita Electric Industrial Co., Ltd.|Signal Processing Device and Signal Processing Method|
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    US8223890B1|2009-10-30|2012-07-17|The United States Of America As Represented By The Secretary Of The Army|Asymptotically optimal modulation classification method for software defined radios|
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