Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where the dynamics of the underlying phenomenon can be described by a linear operator, based on the Koopman operator theory. However, despite being able to provide reliable long-term predictions for some dynamical systems in ideal situations, the methods proposed so far have limitations, such as requiring to discretize intrinsically continuous dynamical systems, leading to data loss, especially when handling incomplete or sparsely sampled data. Here, we propose a new deep Koopman framework that represents dynamics in an intrinsically continuous way, leading to better performance on limited training data, as exemplified on several datasets arising from dynamical systems.

In this paper, we study blind equalization techniques to mitigate inter-symbol interference (ISI), and mainly, we are focused on generic blind equalizer (GBE). A GBE has no prior information about the transmission channel or the used constellation. To solve this challenge, a joint generic blind equalizer, based on a new multi-criteria cost function and automatic modulation classification (AMC) is proposed. The new multi-criteria cost function is based on the probability density fitting (PDF) and the k-nearest neighbor (KNN) algorithm is used for the AMC stage. Thus, using a neural architecture, the new criterion is demonstrated in its linear and nonlinear context. Simulation results support our claims with Quadrature Amplitude Modulation (QAM) transmitted signals in single input single output (SISO) communication system and they show a better performance in terms of mean square error (MSE) and symbol error rate (SER) compared to other GBE from the literature.

In this paper, we design an iterative channel estimation and data detection algorithm in delay-Doppler domain for orthogonal time frequency space (OTFS) system by taking advantage of the sparse nature of the channel in this domain. The proposed algorithm iterates between message-passing-aided data detection and data-aided channel estimation. This sparse channel estimation is reformulated as a specific marginalization of maximum a posteriori (MAP) problem. To deal with the intractability of this problem, we provide a Bayesian approach based on the variational mean-field approximation via the variational Bayesian expectation maximization (VB-EM) algorithm. Finally, we compare the complexity and performance in term of Bit Error Rate (BER) and Normalized Mean Square Error (NMSE) of the proposed solution to a reference solution in the literature (SP-I).

In this paper, we study blind equalization techniques to reduce the intersymbol interference (ISI) and we are particularly interested in equalizers based on probability density fitting (PDF). The PDF criterion was used with conventional linear equalizers. So we try in this paper to use this criterion in a nonlinear context using a neural network architecture. The network weights are updated by minimizing, at first, the stochastic quadratic distance, then the Multimodulus quadratic distance between the equalized PDF and some target distribution. Our approach shows a better performance in terms of mean square error (MSE) and symbol error rate (SER).

Abstract Orthogonal time‐frequency space (OTFS) modulation, which has recently been proposed in the literature, is one of the promising techniques designed in the 2D Delay‐Doppler domain adapted to combat high Doppler fading channels. However, channel estimation in high Doppler scenarios in advanced mobile‐communication systems is still a challenging task. In this paper, the problem of channel estimation in the Delay‐Doppler domain of the OTFS is focused on. First, a simple adaptation of the generalized orthogonal matching pursuit procedure, which will serve as a baseline method in this work, is proposed. Then, iterative algorithms are derived beneficiating from the sparsity of the channel. The unknown channel vector is separated into an unknown sparse support vector corresponding to the delay and Doppler taps, and an unknown vector of channel gains. These algorithms involve ℓ 1 ‐norm minimization and a two‐stage iterative procedure to recover alternatively the channel support and its coefficients. The estimation problem is also addressed from a Bayesian point of view. The sparse representation is reformulated as a specific marginalization of the maximum a posteriori problem on the support of the channel. To deal with the intractability of this problem, two existing techniques are adapted to this context, namely: The Monte Carlo Markov chain with the Gibbs sampler and variational mean‐field approximation with the variational Bayesian expectation‐maximization procedure. Finally, to assess the performance of the proposed algorithms, their complexity and performance are compared against existing methods. Experimental tests, conducted in high‐mobility scenarios and low‐latency applications, show that the proposed schemes are slightly more expensive in terms of complexity load but perform significantly better in terms of normalized mean square error and bit error rate.

Kalman filters are widely used for real-time estimation of dynamic systems, and they sometimes need to be implemented on energy-constrained devices. A Kalman filter implementation from unreliable memories is considered, where the flipping probability of a bit in a memory cell directly depends on its energy consumption. The degradation in estimation performance caused by the noise in the memory is theoretically investigated. Updated equations are then developed for the Kalman filter, taking into account the new source of noise from the unreliable memory. Finally, a method is proposed to optimize the bit energy allocation in the memory, and it is shown from numerical simulations that this method allows for important energy gains.

Millimeter-wave (mmWave) and multiple-input multiple-output (MIMO) combination technologies have at-tracted extensive attention from both academia and industry for meeting future communication challenges and requirements. As a viable option to deal with the trade-off between hardware complexity and system performance, hybrid analog/digital architectures are regarded as efficient mmWave MIMO transceivers. While acquiring channel state information (CSI) is a challenging task to design the optimal beamformers/combiners, especially in mmWave communications due to a lot of challenges. Fortunately, the sparse nature of the channel allows to leverage the compressed sensing (CS) tools and theories. However, the critical challenge to develop a CS-based formulation for estimating the mmWave channel is the codebook design (sensing matrices) and its pilot symbol numbers. In this paper, we proposed a multistage CS-based algorithm to estimate the channel explicitly using pilot and data symbols which enable increasing the number of measurements to enhance the estimation accuracy and maximize the spatial diversity by reducing the overlapping between training beams. Simulations confirmed that our proposed method has the best results compared to the existing methods based on codebook schemes.

This paper addresses the problem of adaptive blind sparse source separation in the time domain of an over-determined instantaneous noisy mixture. A two-step approach is proposed: first, the data are projected on the signal subspace estimated using the principal subspace tracker FAPI. In the second step, an ℓ1criterion is used to represent the sparsity property of the signal sources. For the optimization of this cost function, an adaptive method based on Givens and Shear rotations is used. This algorithm, referred to SGDS-FAPI, guarantees low computational complexity which is essential in the adaptive context. Numerical simulations have been performed, and showed that the proposed algorithm outperforms existing solutions in both convergence speed and estimation quality.

The ever increasing availability of in situ, remote sensing and simulation data supports the development of data-driven alternatives to classical model-driven methods for the interpolation of sea surface geophysical fields from partial satellite-derived observations. In this respect, we recently introduced the Analog Data Assimilation (AnDA), which exploits patch-based analog forecasting operators within a classic Kalman-based data assimilation framework. In this work, we consider the application of AnDA to the spatio-temporal interpolation of SLA (Sea Level Anomalies) from two types of satellite altimetry data, namely from along-track nadir data [1] and data from the upcoming wide-swath SWOT mission [2]. We report a sensitivity analysis w.r.t. the main parameters of the proposed AnDA scheme. Overall, the reported benchmarking analysis supports the relevance of the proposed AnDA scheme for an improved reconstruction of mescoscale structures for horizontal scales ranging from ~ 20km to ~ 100km, with an gain of 42% (12%) in terms of SLA RMSE (correlation) with respect to Optimal Interpolation (OI) [3]. Results suggest an additional potential improvement from the joint assimilation of SWOT and along-track nadir observations.

In this paper, we address the problem of large MIMO detection assuming QAM constellations. We show that the QAM signal becomes a simple signal (that is to say a bounded signal with extreme elements equal to the inferior and superior bounds [1]) after a real transformation. Based on this property, we present a low complexity detection algorithm which significantly outperforms classic algorithms such as zero forcing (ZF) and minimum mean square error (MMSE) algorithms. The proposed detection technique is based on a quadratic programming criterion whose constraints ensure that the detected vector is simple. We implement it successfully in an underdetermined MIMO system (the number of observations is less than the number of sources) and we show the necessary conditions of success detection. Then we consider an outer forward error correcting (FEC) code and we propose a turbo detection scheme. Based on the investigation of the output detector statistics in [2], we propose a symbol to binary converter (SBC) which can feed the FEC decoder with reliable output. On the other side, from the second iteration, the detection scheme resorts to a regularized quadratic criterion so that the searched vector draws near to the estimate resulting from the FEC decoder output. Simulation results show the efficiency of the proposed scheme.

Super-resolution is a classical problem in image processing, with numerous applications to remote sensing image enhancement. Here, we address the super-resolution of irregularly-sampled remote sensing images. Using an optimal interpolation as the low-resolution reconstruction, we explore locally-adapted multimodal convolutional models and investigate different dictionary-based decompositions, namely based on principal component analysis (PCA), sparse priors and non-negativity constraints. We consider an application to the reconstruction of sea surface height (SSH) fields from two information sources, along-track altimeter data and sea surface temperature (SST) data. The reported experiments demonstrate the relevance of the proposed model, especially locally-adapted parametrizations with non-negativity constraints, to outperform optimally-interpolated reconstructions.

Canonical correlation analysis (CCA) is a well-known technique used to characterize the relationship between two sets of multidimensional variables by finding linear combinations of variables with maximal correlation. Sparse CCA or regularized CCA are two widely used variants of CCA because of the improved interpretability of the former and the better performance of the later. So far the cross-matrix product of the two sets of multidimensional variables has been widely used for the derivation of these variants. In this paper a new algorithm for sparse CCA is proposed. This algorithm differs from the existing ones in their derivation which is based on penalized rank one matrix approximation and the orthogonal projectors onto the space spanned by the two sets of multidimensional variables instead of the simple cross-matrix product. The performance and effectiveness of the proposed algorithm are tested on simulated experiments. On these results it can be observed that they outperform the state of the art sparse CCA algorithms.

The identification and separation of contributions associated with different sources or processes is a general problem in signal and image processing. Here, we focus on the decomposition of multiple linear relationships and introduce a non-negative formulation. The proposed models can be viewed as generalizations of latent class regression models and account for possibly varying magnitudes of the linear transfer functions. Along with these models, we present model calibration algorithms. We first demonstrate their performance on simulated data. We also report an application to the analysis of upper ocean dynamics from remote sensing data (namely, satellite-derived Sea Surface Height (SSH) and Sea Surface temperature (SST) image series). This application further stresses the proposed formulation's relevance compared to state-of-the-art regression models.

In this paper, a blind equalizer based on probability density function (pdf) fitting is proposed. It does not require any prior information about the transmission channel or the emitted constellation. We also investigate Automatic Modulation Classification (AMC) for Quadrature Amplitude Modulation (QAM) based on the pdf of the equalized signal. We propose three new approaches for AMC. The first employs maximum likelihood functions (ML) of the modulus of real and imaginary parts of the equalized signal. The second is based on the lowest quadratic or Bhattacharyya distance between the estimated pdf of the real and imaginary parts of the equalizer output and the theoretical pdfs of M-QAM modulations. The third approach is based on theoretical pdf dictionnary learning. The performance of the identification scheme is investigated through simulations.

We propose a novel method for noise power spectrum estimation in speech enhancement. This method called extended-DATE (E-DATE) extends the d-dimensional amplitude trimmed estimator (DATE), originally introduced for additive white gaussian noise power spectrum estimation in “Robust estimation of noise standard deviation in presence of signals with unknown distributions and occurrences” (D. Pastor and F. Socheleau, IEEE Trans. Signal Processing, vol. 60, no. 4, pp. 1545-1555, Apr. 2012) to the more challenging scenario of non-stationary noise. The key idea is that, in each frequency bin and within a sufficiently short time period, the noise instantaneous power spectrum can be considered as approximately constant and estimated as the variance of a complex gaussian noise process possibly observed in the presence of the signal of interest. The proposed method relies on the fact that the Short-Time Fourier Transform (STFT) of noisy speech signals is sparse in the sense that transformed speech signals can be represented by a relatively small number of coefficients with large amplitudes in the time-frequency domain. The E-DATE estimator is robust in that it does not require prior information about the signal probability distribution except for the weak-sparseness property. In comparison to other state-of-the-art methods, the E-DATE is found to require the smallest number of parameters (only two). The performance of the proposed estimator has been evaluated in combination with noise reduction and compared to alternative methods. This evaluation involves objective as well as pseudo-subjective criteria.

We consider the problem of estimating a deterministic finite alphabet vector f from underdetermined measurements y = A f , where A is a given (random) n × N matrix. Two new convex optimization methods are introduced for the recovery of finite alphabet signals via ℓ1-norm minimization. The first method is based on regularization. In the second approach, the problem is formulated as the recovery of sparse signals after a suitable sparse transform. The regularization-based method is less complex than the transform-based one. When the alphabet size p equals 2 and (n, N) grows proportionally, the conditions under which the signal will be recovered with high probability are the same for the two methods. When p > 2, the behavior of the transform-based method is established. Experimental results support this theoretical result and show that the transform method outperforms the regularization-based one.

This paper addresses the problem of decoding and precoding in the K-user MIMO interference channels. At the receiver side, a joint decoding of the interference and the desired signal is able to improve the receive diversity order. At the transmitter side, we introduce a joint linear precoding design that maximizes the joint cut-off rate, known as a tight lower bound on the joint mutual information for high signal-to-noise ratio (SNR). We also derive a closed-form solution of the precoding matrices that maximizes the mutual information when the SNR is close to zero. This solution is characterized by its low computational complexity, and only requires a local channel state information knowledge at the transmitters. Our simulation results show that decoding interference jointly with the desired signal results in a significant improvement of the receive diversity order. Also a substantial bit error rate and sum-rate improvements are illustrated using the proposed precoding designs.

This paper deals with a new challenge for cognitive opportunistic receivers : base station number of antennas estimation. This knowledge allows to get a better understanding of the Signal to Noise Ratio and of the achievable bit-rate with the BS. This task is achieved by taking benefits of the orthogonality between the pilots patterns used by the base station antennas and making use of a the Pilot Induced Cyclo-stationarity detector proposed in [1]. To the best of our knowledge our proposed algorithm is the first technique that can estimate any number of antennas using only one antenna at reception and without any knowledge of the pilot sequence.

The degree of freedom of the Single Input Single Output (SISO) fading interference channel is asymptotically upperbounded by K/2. This upperbound can be achieved using the Interference Alignment approach (IA), proposed by Cadambe et al., In this work, a new optimized design of the IA scheme is presented. It involves introducing, for each user, a combination matrix so as to maximize the sum rate of the network. The optimal design is obtained via an iterative algorithm proposed in the K-user IA network, and a convergence to a local optimum is achieved. Numerical results enable us to evaluate the performance of the new algorithm and to compare it with other designs.

We address the problem of blind source separation in the underdetermined and instantaneous mixture case. The proposed method is based on an algorithm developed by Aissa-El-Bey and al.. This algorithm requires a good choice of the noise threshold and does not take into account the noise contribution in the inversion process. In order to overcome these drawbacks, this paper presents a robust underdetermined blind source separation approach. Robustness is achieved by estimating the noise standard deviation and using this estimate in the inversion process and the expression of the noise threshold. The good performance of the proposed method is shown by comparison with state-of-the-art methods.

In this paper, we are interested in blind and semi-blind identification of multiple-input multiple-output (MIMO) channel for orthogonal frequency division multiplexing (OFDM) systems. Using the sparsity property of wireless channel impulse response, we propose an iterative method which minimizes a cost function to result from the combination of blind or semi-blind criterion and the lp norm. This norm is considered as a good sparsity measure. The simulations show that the proposed method outperforms existing techniques in terms of estimation error and robustness to channel order overestimation.

This paper introduces new hybrid blind equalization algorithms for QAM signals, the first term of which is the constant modulus criterion (CMA) or its extended version (ECMA) and the second are a penalty term that vanishes at constellation points coordinates. Several penalties, based on cosine, Gaussian and polynomial lscr1-norm functions respectively are investigated. Simulations show the effectiveness of these algorithms.

We present two new noise variance estimation methods for OFDMA signals transmitted through an unknown multipath fading channel. We focus on blind estimation as it does not require any pilot sequences and is therefore applicable to contexts, such as cognitive radio for instance, where little prior signal knowledge is available. The two estimators are respectively based on the time-frequency sparsity of OFDMA signals and on the redundancy induced by the cyclic prefix. Numerical simulations compare the performance of the two algorithms and highlight their complementarity.

In the context of cognitive radio, system identification is a crucial step towards radio environment awareness. In this paper, we present a new OFDM system identification method based on m-sequence (MS) specific characteristics. Thanks to their good random properties, m-sequences are commonly used in existing standards (such as Wifi or WiMAX) to modulate pilot tones for channel estimation and/or for synchronization purposes. We demonstrate that such sequences show extra-properties relevant to distinguish systems from each other and therefore advocate to generalize their use in a cognitive context. MS signatures are indeed of interest since they are able to discriminate OFDM based systems that have the same modulation parameters (intercarrier spacing, cyclic prefix duration, etc.). In order to detect these signatures, we conduct a hypothesis test based on the MS high order statistics. Detailed numerical examples demonstrate the efficiency of the proposed identification criterion and especially show its benefits compared to classical correlation based methods.

This paper considers the blind separation of nonstationary sources in the underdetermined convolutive mixture case. We introduce two methods based on the sparsity assumption of the sources in the time-frequency (TF) domain. The first one assumes that the sources are disjoint in the TF domain; i.e. there is at most one source signal present at a given point in the TF domain. In the second method, we relax this assumption by allowing the sources to be TF-nondisjoint to a certain extent. In particular, the number of sources present (active) at a TF point should be strictly less than the number of sensors. In that case, the separation can be achieved thanks to subspace projection which allows us to identify the active sources and to estimate their corresponding time-frequency distribution (TFD) values.

This paper focuses on the blind image separation using their sparse representation in an appropriate transform domain. A new separation method is proposed that proceeds in two steps: (i) an image pre-treatment step to transform the original sources into sparse images and to reduce the mixture matrix to an orthogonal transform (ii) and a separation step that exploits the transformed image sparsity via an lscrp-norm based contrast function. A simple and efficient natural gradient technique is used for the optimization of the contrast function. The resulting algorithm is shown to outperform existing techniques in terms of separation quality and computational cost.

This paper considers the blind separation of nonstationary sources in the underdetermined convolutive mixture case. We introduce, two methods based on the sparsity assumption of the sources in the time-frequency (TF) domain. The first one assumes that the sources are disjoint in the TF domain, i.e., there is at most one source signal present at a given point in the TF domain. In the second method, we relax this assumption by allowing the sources to be TF-nondisjoint to a certain extent. In particular, the number of sources present (active) at a TF point should be strictly less than the number of sensors. In that case, the separation can be achieved thanks to subspace projection which allows us to identify the active sources and to estimate their corresponding time-frequency distribution (TFD) values. Another contribution of this paper is a new estimation procedure for the mixing channel in the underdetermined case. Finally, numerical performance evaluations and comparisons of the proposed methods are provided highlighting their effectiveness.