arXiv subjects

Rémy Boyer

Publications and source records attributed to Rémy Boyer.

16 recordsLinked to original sources

arXiv2022

Semi-Blind Joint Channel and Symbol Estimation for IRS-Assisted MIMO Systems

Intelligent reflecting surface (IRS) is a promising technology for the 6th generation of wireless systems, realizing the smart radio environment concept. In this paper, we present a novel tensor-based receiver for IRS-assisted multiple-input multiple-output communications capable of jointly estimating the channels and the transmitted data streams in a semi-blind fashion. Assuming a fully passive IRS architecture and introducing a simple space-time coding scheme at the transmitter, the received signal model can be advantageously built using the PARATUCK tensor model, which can be seen as a hybrid of parallel factor analysis and Tucker models. Exploiting the algebraic structure of the PARATUCK tensor model, a semi-blind receiver is derived. The proposed receiver is based on a trilinear alternating least squares method that iteratively estimates the two involved - IRS- base station and user terminal-IRS-communication channels and the transmitted symbol matrix. We discuss identifiability conditions that ensure the joint semi-blind recovery of the involved channel and symbol matrices, and propose a joint design of the coding and IRS reflection matrices to optimize the receiver performance. For the proposed semi-blind receiver, the derivation of the expected Cramér-Rao lower bound is also provided. A numerical performance evaluation of the proposed receiver design corroborates its superior performance in terms of the normalized mean squared error of the estimated channels and the achieved symbol error rate.

cs.IT↗

arXiv2021

Channel Estimation for Intelligent Reflecting Surface Assisted MIMO Systems: A Tensor Modeling Approach

Intelligent reflecting surface (IRS) is an emerging technology for future wireless communications including 5G and especially 6G. It consists of a large 2D array of (semi-)passive scattering elements that control the electromagnetic properties of radio-frequency waves so that the reflected signals add coherently at the intended receiver or destructively to reduce co-channel interference. The promised gains of IRS-assisted communications depend on the accuracy of the channel state information. In this paper, we address the receiver design for an IRS-assisted multiple-input multiple-output (MIMO) communication system via a tensor modeling approach aiming at the channel estimation problem using supervised (pilot-assisted) methods. Considering a structured time-domain pattern of pilots and IRS phase shifts, we present two channel estimation methods that rely on a parallel factor (PARAFAC) tensor modeling of the received signals. The first one has a closed-form solution based on a Khatri-Rao factorization of the cascaded MIMO channel, by solving rank-1 matrix approximation problems, while the second one is an iterative alternating estimation scheme. The common feature of both methods is the decoupling of the estimates of the involved MIMO channel matrices (base station-IRS and IRS-user terminal), which provides performance enhancements in comparison to competing methods that are based on unstructured LS estimates of the cascaded channel. Design recommendations for both methods that guide the choice of the system parameters are discussed. Numerical results show the effectiveness of the proposed receivers, highlight the involved trade-offs, and corroborate their superior performance compared to competing LS-based solutions.

eess.SP↗

arXiv2020

Multi-frequency calibration for DOA estimation with distributed sensors

In this work, we investigate direction finding in the presence of sensor gain uncertainties and directional perturbations for sensor array processing in a multi-frequency scenario. Specifically, we adopt a distributed optimization scheme in which coherence models are incorporated and local agents exchange information only between connected nodes in the network, i.e., without a fusion center. Numerical simulations highlight the advantages of the proposed parallel iterative technique in terms of statistical and computational efficiency.

eess.SP↗

arXiv2018

Robust distributed calibration of radio interferometers with direction dependent distortions

In radio astronomy, accurate calibration is of crucial importance for the new generation of radio interferometers. More specifically, because of the potential presence of outliers which affect the measured data, robustness needs to be ensured. On the other hand, calibration is improved by taking advantage of these new instruments and exploiting the known structure of parameters of interest across frequency. Therefore, we propose in this paper an iterative robust multi-frequency calibration algorithm based on a distributed and consensus optimization scheme which aims to estimate the complex gains of the receivers and the directional perturbations caused by the ionosphere. Numerical simulations reveal that the proposed distributed calibration technique outperforms the conventional non-robust algorithm and per-channel calibration.

astro-ph.IM↗

arXiv2018

Robust Calibration of Radio Interferometers in Multi-Frequency Scenario

This paper investigates calibration of sensor arrays in the radio astronomy context. Current and future radio telescopes require computationally efficient algorithms to overcome the new technical challenges as large collecting area, wide field of view and huge data volume. Specifically, we study the calibration of radio interferometry stations with significant direction dependent distortions. We propose an iterative robust calibration algorithm based on a relaxed maximum likelihood estimator for a specific context: i) observations are affected by the presence of outliers and ii) parameters of interest have a specific structure depending on frequency. Variation of parameters across frequency is addressed through a distributed procedure, which is consistent with the new radio synthesis arrays where the full observing bandwidth is divided into multiple frequency channels. Numerical simulations reveal that the proposed robust distributed calibration estimator outperforms the conventional non-robust algorithm and/or the mono-frequency case.

stat.AP↗

arXiv2018

Bayesian Calibration using Different Prior Distributions: an Iterative Maximum A Posteriori Approach for Radio Interferometers

In this paper, we aim to design robust estimation techniques based on the compound-Gaussian (CG) process and adapted for calibration of radio interferometers. The motivation beyond this is due to the presence of outliers leading to an unrealistic traditional Gaussian noise assumption. Consequently, to achieve robustness, we adopt a maximum a posteriori (MAP) approach which exploits Bayesian statistics and follows a sequential updating procedure here. The proposed algorithm is applied in a multi-frequency scenario in order to enhance the estimation and correction of perturbation effects. Numerical simulations assess the performance of the proposed algorithm for different noise models, Student's t, K, Laplace, Cauchy and inverse-Gaussian compound-Gaussian distributions w.r.t. the classical non-robust Gaussian noise assumption.

stat.AP↗

arXiv2017

Robust Calibration of Radio Interferometers in Non-Gaussian Environment

The development of new phased array systems in radio astronomy, as the low frequency array (LOFAR) and the square kilometre array (SKA), formed of a large number of small and flexible elementary antennas, has led to significant challenges. Among them, model calibration is a crucial step in order to provide accurate and thus meaningful images and requires the estimation of all the perturbation effects introduced along the signal propagation path, for a specific source direction and antenna position. Usually, it is common to perform model calibration using the a priori knowledge regarding a small number of known strong calibrator sources but under the assumption of Gaussianity of the noise. Nevertheless, observations in the context of radio astronomy are known to be affected by the presence of outliers which are due to several causes, e.g., weak non-calibrator sources or man made radio frequency interferences. Consequently, the classical Gaussian noise assumption is violated leading to severe degradation in performances. In order to take into account the outlier effects, we assume that the noise follows a spherically invariant random distribution. Based on this modeling, a robust calibration algorithm is presented in this paper. More precisely, this new scheme is based on the design of an iterative relaxed concentrated maximum likelihood estimation procedure which allows to obtain closed-form expressions for the unknown parameters with a reasonable computational cost. This is of importance as the number of estimated parameters depends on the number of antenna elements, which is large for the new generation of radio interferometers. Numerical simulations reveal that the proposed algorithm outperforms the state-of-the-art calibration techniques.

stat.AP↗

arXiv2017

Bayesian Lower Bounds for Dense or Sparse (Outlier) Noise in the RMT Framework

Robust estimation is an important and timely research subject. In this paper, we investigate performance lower bounds on the mean-square-error (MSE) of any estimator for the Bayesian linear model, corrupted by a noise distributed according to an i.i.d. Student's t-distribution. This class of prior parametrized by its degree of freedom is relevant to modelize either dense or sparse (accounting for outliers) noise. Using the hierarchical Normal-Gamma representation of the Student's t-distribution, the Van Trees' Bayesian Cramér-Rao bound (BCRB) on the amplitude parameters is derived. Furthermore, the random matrix theory (RMT) framework is assumed, i.e., the number of measurements and the number of unknown parameters grow jointly to infinity with an asymptotic finite ratio. Using some powerful results from the RMT, closed-form expressions of the BCRB are derived and studied. Finally, we propose a framework to fairly compare two models corrupted by noises with different degrees of freedom for a fixed common target signal-to-noise ratio (SNR). In particular, we focus our effort on the comparison of the BCRBs associated with two models corrupted by a sparse noise promoting outliers and a dense (Gaussian) noise, respectively.

stat.ME↗

arXiv2017

Sparse-Based Estimation Performance for Partially Known Overcomplete Large-Systems

We assume the direct sum o for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace and the goal is to estimate the LA am- plitudes corresponding to subspace . Taking into account the knowledge of the orthogonal "interfering" subspace \perp, the Bayesian estimation lower bound is de- rivedfortheLA-sparsevectorinthedoublyasymptoticscenario,i.e. N,LA,LB -> \infty with a finite asymptotic ratio. By jointly exploiting the Compressed Sensing (CS) and the Random Matrix Theory (RMT) frameworks, closed-form expressions for the lower bound on the estimation of the non-zero entries of a sparse vector of interest are derived and studied. The derived closed-form expressions enjoy several interesting features: (i) a simple interpretable expression, (ii) a very low computational cost especially in the doubly asymptotic scenario, (iii) an accurate prediction of the mean-square-error (MSE) of popular sparse-based estimators and (iv) the lower bound remains true for any amplitudes vector priors. Finally, several idealized scenarios are compared to the derived bound for a common output signal-to-noise-ratio (SNR) which shows the in- terest of the joint estimation/rejection methodology derived herein.

stat.AP↗

arXiv2017

Joint ML calibration and DOA estimation with separated arrays

This paper investigates parametric direction-of-arrival (DOA) estimation in a particular context: i) each sensor is characterized by an unknown complex gain and ii) the array consists of a collection of subarrays which are substantially separated from each other leading to a structured noise covariance matrix. We propose two iterative algorithms based on the maximum likelihood (ML) estimation method adapted to the context of joint array calibration and DOA estimation. Numerical simulations reveal that the two proposed schemes, the iterative ML (IML) and the modified iterative ML (MIML) algorithms for joint array calibration and DOA estimation, outperform the state of the art methods and the MIML algorithm reaches the Cramér-Rao bound for a low number of iterations.

stat.AP↗

arXiv2017

Relaxed concentrated MLE for robust calibration of radio interferometers

In this paper, we investigate the calibration of radio interferometers in which Jones matrices are considered to model the interaction between the incident electromagnetic field and the antennas of each station. Specifically, perturbation effects are introduced along the signal path, leading to the conversion of the plane wave into an electric voltage by the receptor. In order to design a robust estimator, the noise is assumed to follow a spherically invariant random process (SIRP). The derived algorithm is based on an iterative relaxed concentrated maximum likelihood estimator (MLE), for which closed-form expressions are obtained for most of the unknown parameters.

astro-ph.IM↗

arXiv2016

Parallel Calibration for Sensor Array Radio Interferometers

In order to meet the theoretically achievable imaging performance, calibration of modern radio interferometers is a mandatory challenge, especially at low frequencies. In this perspective, we propose a novel parallel iterative multi-wavelength calibration algorithm. The proposed algorithm estimates the apparent directions of the calibration sources, the directional and undirectional complex gains of the array elements and their noise powers, with a reasonable computational complexity. Furthermore, the algorithm takes into account the specific variation of the aforementioned parameter values across wavelength. Realistic numerical simulations reveal that the proposed scheme outperforms the mono-wavelength calibration scheme and approaches the derived constrained Cramér-Rao bound even with the presence of non-calibration sources at unknown directions, in a computationally efficient manner.

astro-ph.IM↗

arXiv2016

Calibration of Radio Interferometers Using a Sparse DoA Estimation Framework

The calibration of modern radio interferometers is a significant challenge, specifically at low frequencies. In this perspective, we propose a novel iterative calibration algorithm, which employs the popular sparse representation framework, in the regime where the propagation conditions shift dissimilarly the directions of the sources. More precisely, our algorithm is designed to estimate the apparent directions of the calibration sources, their powers, the directional and undirectional complex gains of the array elements and their noise powers, with a reasonable computational complexity. Numerical simulations reveal that the proposed scheme is statistically efficient at low SNR and even with additional non-calibration sources at unknown directions.

astro-ph.IM↗

arXiv2015

Statistical efficiency of structured cpd estimation applied to Wiener-Hammerstein modeling

The computation of a structured canonical polyadic decomposition (CPD) is useful to address several important modeling problems in real-world applications. In this paper, we consider the identification of a nonlinear system by means of a Wiener-Hammerstein model, assuming a high-order Volterra kernel of that system has been previously estimated. Such a kernel, viewed as a tensor, admits a CPD with banded circulant factors which comprise the model parameters. To estimate them, we formulate specialized estimators based on recently proposed algorithms for the computation of structured CPDs. Then, considering the presence of additive white Gaussian noise, we derive a closed-form expression for the Cramer-Rao bound (CRB) associated with this estimation problem. Finally, we assess the statistical performance of the proposed estimators via Monte Carlo simulations, by comparing their mean-square error with the CRB.

stat.CO↗

arXiv2013

Coexistence of Near-Field and Far-Field Sources: the Angular Resolution Limit

Passive source localization is a well known inverse problem in which we convert the observed measurements into information about the direction of arrivals. In this paper we focus on the optimal resolution of such problem. More precisely, we propose in this contribution to derive and analyze the Angular Resolution Limit (ARL) for the scenario of mixed Near-Field (NF) and Far-Field (FF) Sources. This scenario is relevant to some realistic situations. We base our analysis on the Smith's equation which involves the Cramér-Rao Bound (CRB). This equation provides the theoretical ARL which is independent of a specific estimator. Our methodology is the following: first, we derive a closed-form expression of the CRB for the considered problem. Using these expressions, we can rewrite the Smith's equation as a 4-th order polynomial by assuming a small separation of the sources. Finally, we derive in closed-form the analytic ARL under or not the assumption of low noise variance. The obtained expression is compact and can provide useful qualitative informations on the behavior of the ARL.

cs.IT↗

arXiv2008

Informed stego-systems in active warden context: statistical undetectability and capacity

Several authors have studied stego-systems based on Costa scheme, but just a few ones gave both theoretical and experimental justifications of these schemes performance in an active warden context. We provide in this paper a steganographic and comparative study of three informed stego-systems in active warden context: scalar Costa scheme, trellis-coded quantization and spread transform scalar Costa scheme. By leading on analytical formulations and on experimental evaluations, we show the advantages and limits of each scheme in term of statistical undetectability and capacity in the case of active warden. Such as the undetectability is given by the distance between the stego-signal and the cover distance. It is measured by the Kullback-Leibler distance.

cs.IT↗