Method for estimating an impulse response of a reception channel, device and corresponding program.

Abstract

Method for estimating an impulse response of a reception channel, device and corresponding program. The present invention relates to a device and a method for calculating an estimate of an impulse response of a signal reception channel. Such a method comprises at least one iteration of the following steps: obtaining (E1) a signal comprising at least p sequences of Np pilots received; predicting (E2), as a function of said at least p sequences of Np pilots received and of a first previously trained neural network NN1, a covariance matrix of the process noise of a Kalman filter at a current time step k; calculating (E4), from the covariance matrix of the process noise and parameters of the current time step k of the Kalman filter, said estimate of the channel impulse response. Figure for abstract: Fig 2.

Description

Title of the invention: Method for estimating an impulse response of a reception channel, device and corresponding program. Domain

[0001] The invention relates to the field of telecommunications. The invention relates more particularly to the field of reception for wireless communication systems. More specifically still, the invention relates to the estimation, by a receiver, of a propagation channel of a radiocommunication signal. Prior art

[0002] A transfer of information from a source to a destination involves propagation through a channel, which may be, for example, a radio channel, a wired channel (e.g., coaxial cable), etc. Certain propagation means generate so-called intersymbol 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, does not contain only the symbol sent and noise, but a mixture of symbols sent and noise.

[0003] To reduce the effects of inter-symbol interference (ISI), equalization and detection algorithms are used. These algorithms, which are responsible for reducing the ISI, require a prior estimate of the channel which is used when calculating the filters and other parameters related to equalization and detection. The closer this channel estimate is to the actual realization of the channel impulse response (also called CIR and also called impulse response hereinafter) which takes place during transmission, the more efficient the reception algorithms are in their tasks.

[0004] Technically, at an instant k, the propagation channel is characterized by its impulse response h(k) defined by fyk) — [ / z0(fe), ..., with L the number of paths between the transmitter and the receiver.

[0005] Channel estimation algorithms play an important role in communication system receivers, and even more so in situations of significant channel variability (transmitters / receivers in motion, movements relative to obstacles such as buildings, walls, mountains, and other mobiles) which cause the channel to vary significantly over time. It is necessary to use algorithms capable of estimating the channel as best as possible in order to suffer the least possible degradation in communications.

[0006] The usual operating diagram of these channel estimation algorithms consists of exploiting the transmission of “pilot” or “learning sequences”, which accompany the data during transmission, and which are also perfectly known to the receiver, by design.

[0007] Thus, to estimate the channel, pilot symbols are used whose observation model is given by z = s*h + v with y ~ CN( 0, Gyl ), z being the observation, h the impulse response, r the additive noise which follows a complex normal law (with mean 0 and covariance matrix proportional to the identity I) and s the corresponding known pilot sequence (conventionally, the pilot sequences are known in advance by the receiver, which makes it possible precisely to compare the pilots that are received with the known pilots and to deduce certain channel characteristics, in particular).

[0008] Channel estimation algorithms exploit the receiver's prior knowledge of these pilot sequences to obtain an estimate of the impulse response that fully characterizes the channel, as well as the signal-to-noise and interference ratio (SINR) of the channel. Among the known estimators of the impulse response, we can cite the least-squares (LS) algorithm and the Kalman filter (KF) which is an optimal algorithm in terms of minimum mean square error under certain assumptions on the additive noise.

[0009] The advantage of the least-squares algorithm LS is that it is computationally efficient. This is the main reason why LS is the algorithm most commonly used in receivers with high real-time constraints. However, the LS algorithm is very sensitive to additive noise, which leads in particular to a low signal-to-noise ratio (SNR) in a poor estimation of the impulse response. This can significantly limit the performance of the following processing operations.

[0010] It is therefore necessary to use other algorithms when one wishes to deal with strong potential additive noise. For this reason, a linear Kalman filter can be used instead of the LS algorithm. The linear Kalman filter has the advantage of providing a follow-up of the impulse response over time (unlike the LS algorithm which gives point estimates), which makes it possible to take into account the previous estimates at each new iteration. It is recalled that a Kalman filter is an infinite impulse response filter which estimates the states of a dynamic system from a series of incomplete or noisy measurements. The Kalman filter is based on a linear state model (which equates the evolution of the useful signal and its relationship to the measured signal) as well as on an optimization criterion which exploits all the observations, from the initial instant to the current instant.It is implemented iteratively and delivers, at each time step, an estimate of a state vector, representing an estimate of the useful signal. An iteration of a Kalman filter includes a so-called prediction phase and a so-called update phase. The . Kalman filter has the advantage of being efficient in monitoring the parameters of a linear system over time and of being optimal in terms of Minimum Mean Square Error (MMSE).

[0011] Although the Kalman filter can provide very good estimates, it is in practice little used in this context of channel estimation. The main reason is that this filter uses a process noise covariance matrix (Q^) which does not correspond to any measurable physical quantity. This process noise covariance matrix (Q^) must be parameterized manually. It corresponds to the degree of variations of the state vector during the update phase of the Kalman filter. Thus, the choice of such a matrix may be suitable in one application case but not in another. For example, if the coefficients of the matrix are too small while the process varies greatly, the estimated parameters will not vary enough to follow the effective (i.e. real) parameters.Otherwise, if the matrix coefficients are too high and the process varies very slowly, the estimated parameters will vary too much between two estimates and this will provide a bad estimate.

[0012] To overcome this problem, the IMM algorithm (from the English "Interacting Multiple Model" for interactive multiple models) consists of using several Kalman filters in parallel, each one being parameterized differently, and consists of combining the outputs of all the Kalman filters to create a single state vector. This makes it possible in particular to benefit from the parameter tracking power of the Kalman filter in multiple cases in exchange for a (much) higher computational cost, which is not necessarily possible for all equipment. In addition, the need for manual parameterization of the process noise covariance matrices of each Kalman filter persists and the performances obtained by the Kalman filters are always likely to vary significantly depending on their parameterization. Also, this solution does not make it possible to respond to the problem of real-time estimation on a digital receiver.

[0013] Document US2021399924 proposes a neural network-based solution for correct a residual error during the iterations of the Kalman filter. This solution, however, is still based on a manual parameterization of the process noise covariance matrices and therefore does not resolve the problem identified above: in fact, the correction of the residual error is not necessarily sufficient to obtain a good channel estimation, if the parameters of the process noise covariance matrix are not adapted to the situation.

[0014] In other words, in a strongly and rapidly varying environment (with different variations over time), with strong real-time constraints, current implementations of the Kalman filter do not necessarily allow surely to obtain better results than the LS algorithm. It is therefore necessary to propose a method for calculating an estimate of an impulse response of a signal reception channel using a Kalman filter which is suitable for these contexts, in particular by parameterizing the process noise covariance matrix more efficiently. Summary

[0015] The invention aims to remedy this drawback. More particularly, the invention relates to a method for calculating an estimate hk of an impulse response of a signal reception channel, a method implemented by an equalization module of a receiver. According to the invention, such a method comprises at least one iteration of the following steps: - obtaining a signal comprising at least p sequences of Np pilots received; - prediction, based on said at least p sequences of Np pilots received and of a first previously trained NNi neural network, of a covariance matrix of the process noise Qk of a Kalman filter at a current time step k; - calculation, from the process noise covariance matrix Qk and parameters of the current time step Æ of the Kalman filter, of said estimate hk of the channel impulse response.

[0016] Thus, the invention offers the possibility of obtaining an evolving version of the process noise covariance matrix at each time step. From then on, this process noise covariance matrix adapts to the variation of the transmission channel.

[0017] According to a particular characteristic, the first NNi neural network comprises at least one recurrent layer.

[0018] According to a particular characteristic, said at least one recurring layer is of the “Gated Recurrent Unit” type.

[0019] According to a particular characteristic, the step of predicting the covariance matrix of the process noise Qk comprises a step of selecting said first neural network NNi, from a set of previously trained neural networks.

[0020] According to a particular characteristic, the selection step is carried out as a function of an estimated value of a current signal / noise ratio and of a signal / noise ratio used for training each neural network of the set of neural networks.

[0021] According to a particular characteristic, the calculation method further comprises an estimation step, as a function of the last group of Np pilots received from the at least p groups of Np pilots received, and of the corresponding sequence of Np known pilots, and as a function of a second previously trained NN2 neural network, of a measurement noise covariance matrix Rk of the Kalman filter at the current time step k, and in that the step of calculating said estimation hk takes into account the measurement noise covariance matrix Rk.

[0022] According to a particular characteristic, the step of estimating the covariance matrix of the measurement noise Rk comprises: - a step of obtaining, from said second neural network, an initial estimate of an impulse response of the channel, which is obtained by providing the second neural network NN2 with a vector containing the last Np pilots received and the corresponding known Np pilots; - an estimation step, as a function of the initial estimation, of an additive noise vk for each symbol of the pilot vector; - a step of obtaining, as a function of the additive noise vk, the variance of the estimated noise <7?; - a step of constructing the measurement noise covariance matrix Rk using the variance of the estimated noise <7?.

[0023] According to a particular characteristic, the second neural network comprises two groups of fully connected layers so that the second neural network can independently estimate the real part and the imaginary part of each coefficient of the initial estimate. k

[0024] According to another aspect, the invention also relates to a receiver comprising an equalization module for calculating an estimate hk of an impulse response of a signal reception channel. The equalization module of such a receiver comprises: - a module for obtaining a signal comprising at least p sequences of Np pilots received; - a prediction module, as a function of said at least p received pilot Np sequences and a first previously trained NNi neural network, of a covariance matrix of the process noise Qk of a Kalman filter at a current time step k; - a calculation module, from the process noise covariance matrix Qk and parameters of the current time step Æ of the Kalman filter, of said estimation hk of the channel impulse response.

[0025] These modules are implemented iteratively. Brief description of the figures

[0026] The invention will appear more clearly on reading the description which follows, given solely by way of non-limiting example, and made with reference to the drawings in which: - [Fig.l] illustrates a receiver capable of performing a calculation of an impulse response; - [Fig.2] illustrates a method of calculating an impulse response according to the invention; - [Fig.3] represents the structure of a first neural network for the prediction of process noise covariance matrices; - [Fig.4] represents the structure of a second neural network used for estimation of measurement noise covariance matrices. .Description

[0027] In order to benefit, within a digital receiver, from an adaptive Kalman filter which makes it possible to best monitor the coefficients of the impulse response, the inventors have developed a new technique for evaluating, primarily, the covariance matrix Qk of the process noise and, secondarily, the covariance matrix of the measurement noise Rk used for calculating the filter. The method of the invention is implemented by the receiver to calculate the matrix Qk and estimate the impulse response of a channel. This method is carried out using at least one neural network within a hybrid artificial intelligence architecture.

[0028] For the purposes of the present invention, firstly, the modeling of a Kalman filter used in the context of the invention is formulated. It is assumed that the impulse response of the channel evolves linearly from time k-1 to time k according to the following equation:

[0029] — F^k-\+ Bkuk + wk

[0030] With h the channel impulse response vector, Fk the state transition matrix of the model, Bk the control matrix of the control vector and wk the process noise.

[0031] The Kalman filter can be used to track the evolution of the vector h over time using a state vector / j, an estimate of h. This estimate is made using measurements ^k (the pilots) received at each time k. The Kalman filter equations are divided into two parts (corresponding to the two phases of prediction and update) and are given below. The prediction equations are:

[0032] h^i = F^lk.^.i+Blcuk

[0033] Pty^FtP^Fl + Q*

[0034] With Ji^kj the state vector predicted at time k taking into account the observations up to time k-1, P^^ the a priori estimated error covariance matrix, Fk the state change matrix, Bk the control matrix and11 k the control variable and Qk the process noise covariance matrix defined by q _ M,r], w'* [ kk being unknown and unmeasurable. The update equations are given by:

[0035] yk = zk-Skh^

[0036] Nk = SkP^tSTk+Rk

[0037] Kk = P^STkNl

[0038] + Kkÿk

[0039] Pk / l=(I-KtSll)Pif,.t

[0040] With %k the observation of the process at time k, and ÿk is called the innovation. Nk is the covariance matrix of the innovation, and Rk is the covariance matrix of the measurement noise defined by Rk = F^ykv£\, not known in practice. The matrix Kk is called the Kalman gain.

[0041] These two phases ("prediction and update") are iterated throughout the reception, by the receiver, in order to have what is the predicted state vector at k knowing k, in other words predicted according to the observation. For simplicity, hk is also noted.

[0042] [Fig. 1] illustrates the receiver for implementing a method for estimating an impulse response of a signal reception channel according to the invention.

[0043] In the example of [Fig.l], the receiver 2 comprises a communication interface 10 with remote devices adapted to communicate via a communication bus 15 to an electronic memory unit 40 and at least one calculation processor 50. The communication interface 10 uses a chosen communication protocol, for example a wired protocol and / or a radio communication protocol.

[0044] In the example of [Fig.l], the receiver comprises an analog communication chain 20, a digital communication chain 30, which notably comprises a synchronization module 301 (in charge of filtering and time / frequency synchronization), an equalization module 302 (in charge of frame extraction, channel estimation and equalization), a detection module 303 (which performs demodulation) and an error correction module 304 (which, from the demodulated signal, performs deinterlacing and decoding). The equalization module 302 implements the method for estimating an impulse response of a channel according to the invention. The digital communication chain 30 can be implemented in whole or in part within the calculation processor 50. In the example of [Fig.l] these modules are each produced in the form of software, or a software brick, executable by the calculation processor 50. The memory of the receiver 2 is then able to store synchronization software, equalization software, detection software and error correction software. The processor is then able to execute each of these software programs.

[0045] In the example of Figure 1, for implementing the method, the receiver 2 (or the equalization module 302) comprises a module for obtaining a signal comprising at least p sequences of Np pilots received, a module for predicting, as a function of the p sequences of Np pilots received and of a first previously trained neural network NNi, the covariance matrix of the process noise Qk of the Kalman filter at a current time step Æ and a module for calculating, from the covariance matrix of the process noise Qk and parameters of the current time step k of the Kalman filter, the estimation hk of the channel impulse response.

[0046] In a variant not shown, these modules are produced in whole or in part in the form of a programmable logic component, such as an FPGA (from the English "Field Programmable Gate Array"), or even an integrated circuit, such as an ASIC (from the English "Application Specific Integrated Circuit"), this or these components being able to be coupled to the calculation processor as described previously.

[0047] When the receiver 2 is produced at least in part in the form of one or more software programs, that is to say in the form of a computer program, also called a computer program product, it is also capable of being recorded on a medium, not shown, that is readable by a computer. The computer-readable medium is, for example, a medium capable of storing electronic instructions and of being coupled to a bus of a computer system. By way of example, the readable medium is an optical disk, a magneto-optical disk, a ROM memory, a RAM memory, any type of non-volatile memory (for example FLASH or NVRAM) or a magnetic card. A computer program comprising software instructions is then stored on the readable medium.

[0048] In relation to Figure 2, the different steps of the method, implemented by the equalization module 302 of the receiver 2, for calculating the hk estimate of the impulse response of the reception channel of a signal are presented. According to the invention, this method comprises at least one iteration of the following steps: - obtaining El of the signal (a radio electric signal) comprising at least p sequences of Np pilots received; - prediction E2, as a function of the p sequences of Np pilots received and of a first previously trained NNi neural network, of the covariance matrix of the process noise Qk of the Kalman filter at a current time step k; - calculation E4, from the covariance matrix of the process noise Qk and parameters of the current time step Æ of the Kalman filter, of the hk estimation of the channel impulse response.

[0049] Thus, the proposed solution allows the estimation of the impulse response in contexts where the channel is likely to vary strongly and in very different ways over time. Thanks to this solution, a prediction of the matrix Qk of the Kalman filter can be carried out, by the receiver 2, for a lower computational cost and in a real-time context. In particular, a neural network based on recurrent layers is used to carry out the prediction of the matrix Qk and thus avoids relying on one or more predefined manual settings. It may also be noted that, depending on the embodiments, several (first) NNi neural networks may be available, for the receiver, for the prediction of the matrix Qk, for example depending on a signal / noise ratio used for training the neural network.In this case, the signal-to-noise ratio measured or calculated using the received signal makes it possible to select, from a plurality of (first) available NNi neural networks, a particular NNi neural network for predicting the matrix Qk. In addition, the use of the last p pilot sequences received as input to the NNi neural network to predict the matrix Qk also makes it possible to obtain convincing results in the context of the implementation of the invention. The matrix Qk itself no longer constitutes a parameter fixed in advance for the Kalman filter and it evolves over time with the variations encountered by the channel.

[0050] A second neural network NN2 can optionally be used to estimate the matrix R / over time. This estimation is carried out from an initial pre-estimation £ of the impulse response which makes it possible to calculate the noise k- additive and extract its variance. Other methodologies for estimating the Rk matrix can also be used.

[0051] More particularly, still in relation to Figure 2, the method then comprises an estimation step E3, as a function of the last group of Np pilots received (i.e. NpObservations corresponding to the Np known pilot symbols, not shown in the figure), of the corresponding Np known pilot symbols and as a function of the second neural network NN2, of the covariance matrix of the measurement noise Rk of the Kalman filter at the current time step. In this case, the calculation step E4 of the estimation hk takes into account the covariance matrix of the measurement noise Rk, obtained using the second neural network.

[0052] The use of this second neural network makes it possible to further increase the performance of the filter, but it is not essential.

[0053] We describe, subsequently, an implementation by the receiver 2 of the estimation method as presented previously. In this example, the two neural networks are used by receiver 2: the first neural network NNi allowing the prediction of the matrix Qk and the second neural network NN2, allowing the estimation of the matrix Rk. Thanks to this particular implementation, the equalization module 302 (implementing the Kalman filter) performs improved tracking of the channel regardless of its variations.

[0054] In this example, the matrices and Qk are obtained at each instant k, that is to say at each iteration on the Kalman filter.

[0055] The first neural network NNi uses the last p received pilot symbol sequences to directly predict the matrix Qk. In this example, p is equal to two and a sequence contains five pilot symbols. In other words, two sequences of five received pilots (one at the current time step Æ and one at the time step k-1) are used to form an input vector of the neural network NNb. In the next iteration, the sequence received at the current time step Æ becomes the sequence of the previous time step).

[0056] The second neural network NN2 is used by the receiver 2 to make an initial estimate of the impulse response, noted from the pilot sequence received at time k. This initial estimate is then used to estimate the variance of the additive noise in order to construct the matrix R. The initial estimate is thus directly used only to make an estimate of the noise, and not to produce the final estimate.

[0057] This makes it possible to obtain a Kalman filter whose matrices Rk and Qk vary and adapt over time. The implemented architecture thus offers the possibility of carrying out the (final) hk estimation of the impulse response, using this correctly parameterized Kalman filter. The equalization itself can then be carried out, for example by an MMSE algorithm, from this hk estimation (which is also noted in the following equations), within the equalization module 302 of the receiver 2.

[0058] Prediction of the Ok matrix using the NN network,

[0059] Considering the independence of the coefficients of the impulse response, the (covariance) matrix Qk can be written:

[0060] a2J

[0061] With for all i between 0 and Nl, tr? represents the variance of the ith coefficient, N being the length of the state vector ■ In order to predict the matrix Qk over time, the first neural network NNi is used and its architecture is presented in relation with [Fig.3].

[0062] The sizes of the NNi layers were selected by the inventors for the general performance ratio they provide. A first flattening layer is present (FLT). The GRU layer is composed of a GRU cell with a hidden vector of size 128. In particular, the NNi neural network consists of a "Gated Recurrent Unit" (GRU) layer, followed by three fully connected layers, each activated by a sigmoid function (SIG). This architecture is particularly effective for predicting the Qk matrix. Firstly, the use of a GRU layer allows the memory of past data to be retained, and is therefore particularly suitable for predicting the Qk matrix over time. In addition, the GRU layer allows the calculations to be limited during inference and is therefore suitable for real-time constraints.The size of the fully connected layers (FC) is adapted: the size of FC7 is 32, FC8 is of size 16 and FC9 is of size N=5 (size of the state vector equal to the size of the matrix Qk, i.e. 5 in this example of realization).

[0063] In order to take into account the evolution of the channel, the input of the network is a vector composed of the last p pilot sequences received (in a particular example, p=2, as explained previously, i.e. a vector of size 10, if a pilot sequence is composed of 5 pilots, each comprising a real part and an imaginary part, i.e. twenty values in total). The matrix Qk is obtained at the output of the NNb. More particularly, the diagonal coefficients of the matrix Qk are obtained by inference of the first neural network. In this exemplary embodiment, five diagonal coefficients of the matrix Qk are obtained.

[0064] Estimation of the matrix R: using the NN2 network

[0065] The estimation of Rk at each instant k is obtained using the NN2 network which uses the (last) sequence of pilot symbols of length Np received at instant k. The NN2 network is a Multi Layer Perceptron (MLP) neural network, the architecture of which is illustrated in [Fig.4].

[0066] The sizes of the layers of the NN2 network were selected by the inventors for the general performance ratio that they provide. More particularly, these sizes represent a compromise between performance and computational complexity. A first flattening layer is present (FLT). The sizes of the layers FC1 and FC4 are 128, the layers FC2 and FC5 are of size 32 and finally the sizes FC3 and FC6 are of size N=5 (also size of the state vector equal to size of the matrix Qk, i.e. 5 in this exemplary embodiment). These layers are implemented in parallel. The second neural network thus comprises two groups of fully connected layers (FC1, FC2, FC3 and FC4, FC5, FC6) to independently estimate the real part and the imaginary part of each coefficient of the initial estimate.

[0067] However, the structure of the network (type of layers, size of layers) is not fixed and it is possible that other architectures are also suitable to address the problem. In this case, the NN2 neural network is thus made up of fully connected layers. The LeakyReLU activation functions have been added to accelerate training. Other configurations are possible, in particular depending on the number of pilots envisaged.

[0068] The network takes as input the vector of the pilot emitted and the pilot received (table of size 2x2xNp, taking into account the real part and the imaginary part. As output the network provides two vectors of size N, R^hj and which are used to obtain h = Re(h} + / Re being the real part and 7m the imaginary part.

[0069] The neural network NN2 thus provides the initial estimate of the impulse response of the channel h (in the form of two vectors, one for the real part, one for the imaginary part), at time k, which is used to estimate the noise. Using this initial estimate, the equalization module 302 of the receiver 2 performs the following calculation:

[0070] ^)=(^)( / )-^)

[0071] for O i < Np- 1 with N pie number of pilot symbols emitted (for example 5). The vector is the vector of pilot symbols. The vector rk contains the observations of the pilot symbols. More precisely we have Lt — s*hk + vk- With hk the CIR at time k, and vk the additive noise. This calculation provides an estimate of the additive noise vk (also called an estimate of the measurement noise). Using this estimate, the equalization module 302 of the receiver 2 can therefore calculate the variance of the estimated noise rr?: [°°72] + -hf)

[0073] With the arithmetic mean of Re the real part and 7m the imaginary part.

[0074] We then simply construct, using the identity matrix I, the matrix Rk:

[0075]

[0076] This matrix is used at time k as an estimate of noise covariance.

[0077] Initialization and training of neural networks

[0078] An example of initialization and training of neural networks used to perform the prediction of the Qk matrix and, secondarily, the estimation of the Rk-H matrix is presented below. It is understood that the implementations described below are not limiting and that they are only intended to illustrate a way of obtaining usable instances of the neural networks used to perform the estimation of an impulse response of a channel. Thus, it is possible to imagine various neural architectures that could play the roles described above, but the proposed invention provides recommendations on these allowing to obtain more interesting performance-complexity compromises.

[0079] It is recalled for all useful purposes that a neural network of the invention comprises an ordered succession of layers of neurons, each of which takes its inputs from the outputs of the preceding layer. More precisely, each layer comprises neurons taking their inputs from the outputs of the neurons of the preceding layer, or from the input variables for the first layer. Alternatively, more complex neural network structures can be envisaged with a layer that can be connected to a layer further away than the immediately preceding layer, for example if the channel estimation conditions lend themselves to such an architecture.

[0080] Each neuron is also associated with an operation, i.e. a type of processing, to be carried out by said neuron within the corresponding processing layer.

[0081] It is also recalled that each layer is connected to the other layers by a plurality of synapses. A synaptic weight is associated with each synapse, and each synapse forms a connection between two neurons. It is often a real number, which takes both positive and negative values. In certain cases, the synaptic weight is a representation of a complex number. Each neuron is capable of performing a weighted sum of the value(s) received from the neurons of the previous layer, each value then being multiplied by the respective synaptic weight of each synapse, or connection, between said neuron and the neurons of the previous layer, then applying an activation function, typically a non-linear function, to said weighted sum, and delivering as output from said neuron, in particular to the neurons of the following layer which are connected to it, the value resulting from the application of the activation function.The activation function allows us to introduce non-linearity into the processing performed by each neuron. The sigmoid function, presented previously, the hyperbolic tangent function, the Heaviside function are examples of activation functions.

[0082] A fully connected layer of neurons is a layer in which the neurons of said layer are each connected to all the neurons of the previous layer. Such a type of layer is more often referred to as a “fully connected” layer, and sometimes referred to as a “dense layer”.

[0083] The size of the layers is understood by the number of parameters composing this layer. This is for example the number of synaptic weights (and optionally, the number of bais associated with each weight).

[0084] NNi_network which predicts the Qk matrix

[0085] NNi is responsible for estimating Qk over time. For this, the database must be composed of time-varying channels, so that the training can have real-world meaning. The NNi network is trained on correlated Rayleigh channels with Jakes spectrum, which are used to simulate a lack of a direct path between the transmitter and the receiver. The channels were generated using the sinusoid method, based on the Clarke model.

[0086] What mainly characterizes these channels is the normalized maximum Doppler frequency fd. The higher it is, the more rapidly the channels vary over time. The training of the NNi network was carried out on a database of size 2xl06 elements. Each channel of the database contains L=5 paths, and fd varies independently and uniformly every 100 packets in {103, 102, 10 1}. This independent variation reflects an environment in which the channel varies rapidly and abruptly. The value L=5 was selected by the inventors so as to have channels representative of reality, in the sense that it is rare to consider only one path, just as it is rare to consider too many. This makes it possible to obtain a network trained on channels varying very slightly (when fd= 103), moderately (when fd=102), and strongly (when fd=10 '), and abruptly over time.The batch size is 200, an Adam optimizer and the MSE loss function were also used.

[0087] In addition, depending on the embodiments, as indicated previously, it is possible to train several NNi neural networks at several different signal-to-noise ratios. In other words, several NNb neural networks are trained at different signal-to-noise ratios. A plurality of different signal-to-noise ratios are then selected and a specific training database for each selected signal-to-noise ratio is defined. As explained previously, the prediction step, by the equalization module 302 of the receiver 2, then comprises the selection, from among the available NNi neural networks, that which relates to the signal-to-noise ratio closest to that measured (or calculated) at time k, by the receiver 2.

[0088] NN network^ which pre-estimates the impulse response in order to obtain R^

[0089] In the context of the example of implementation by the equalization module 302 of the receiver 2, of the method presented previously, the matrix R^ is obtained indirectly using NN2. To be as general as possible (the neural network NN2 is thus able to provide an estimate for any channel) and to adapt to multiple types of channels, the training database is composed of a large number of different impulse responses, whether in terms of channel depth or amplitude of the coefficients.

[0090] The NN2 training database is, in this exemplary embodiment, composed of 5xl04 vectors of size IxN whose first L coefficients are not nuis, L uniformly drawn between 1 and 5. The non-nuis coefficients of these vectors follow a reduced centered complex normal distribution that represents the impulse response. The database is split into 20% test data and 80% training data. The batch size is 128, the Adam optimizer was used, and the loss function is the MSE.

Claims

Claims

1. Method for calculating an estimate hk of an impulse response of a signal reception channel, method implemented by an equalization module (302) of a receiver (2), method characterized in that it comprises at least one iteration of the following steps: - obtaining (El) a signal comprising at least p sequences of N pilots received; - prediction (E2), as a function of said at least p sequences of N pilots received and of a first previously trained NNi neural network, of a process noise covariance matrix Qk of a Kalman filter at a current time step k; - calculation (E4), from the process noise covariance matrix Qk and parameters of the current time step k of the Kalman filter, of said estimate hk of the channel impulse response.

2. Calculation method according to claim 1, characterized in that the first NNi neural network comprises at least one recurrent layer.

3. Calculation method according to claim 2, characterized in that said at least one recurrent layer is of the “Gated Recurrent Unit” (GRU) type.

4. Calculation method according to one of claims 1 to 3, characterized in that the step of predicting the covariance matrix of the process noise Qk comprises a step of selecting said first neural network NNb from a set of previously trained neural networks.

5. Calculation method according to claim 4, characterized in that the selection is made as a function of an estimated value of a current signal / noise ratio and a signal / noise ratio used for training each neural network of the set of neural networks.

6. Calculation method according to one of claims 1 to 5, characterized in that it further comprises an estimation step (E3), as a function of the last group of Np pilots received from the at least p groups of Np pilots received, and the corresponding sequence of known pilot Np, and as a function of a second previously trained neural network NN2, of a covariance matrix of the measurement noise of the Kalman filter at the current time step A; and in that the step of calculating said estimation hk takes into account the covariance matrix of the measurement noise R^.

7. Calculation method according to claim 6, characterized in that the step of estimating (E3) the measurement noise covariance matrix R^ comprises: - a step of obtaining, from said second neural network, an initial estimate of an impulse response of the channel, which is obtained by providing the second neural network NN2 with a vector of the received pilot and a vector of the corresponding transmitted pilot; - a step of estimating, as a function of the initial estimate, an additive noise v,. for each symbol of the pilot vector; - a step of obtaining, as a function of the additive noise vk, the variance of the estimated noise cr?; - a step of constructing the measurement noise covariance matrix R^ using the variance of the estimated noise <7?.

8. Calculation method according to one of claims 6 and 7, characterized in that the second neural network comprises two groups of fully connected layers so that the second neural network can independently estimate the real part and the imaginary part of each coefficient of the initial estimate.

9. Receiver (2) comprising an equalization module (302) for calculating an estimate hk of an impulse response of a signal reception channel, receiver (2) characterized in that the equalization module (302) comprises: - a module for obtaining a signal comprising at least p sequences of N pilots received; - a module for predicting, as a function of said at least p sequences of N pilots received and of a first previously trained NNi neural network, a covariance matrix of the process noise Qk of a Kalman filter at a current time step Æ ; - a calculation module, from the covariance matrix of the process noise Qk and parameters of the current time step k of the Kalman filter, of said estimation hk of the channel impulse response; these modules being implemented iteratively.

10. A computer program comprising software instructions which, when executed by a programmable electronic device, implement a method of calculating an estimate of an impulse response of a channel according to claims 1 to 8.

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