BOYER , Remy

In this paper, we propose a new MIMO communication system in a time-varying multi-path environment, using a Khatri-Rao space-time (KRST) coding combined with a multiple Khatri-Rao product of symbol matrices (MKRSM). It is shown the signals received at the receiver form a tensor which satisfies a (M + 2)-order nested PARAFAC model, where (M − 1)...

Discrete-time Volterra modeling is a central topic in many application areas and a large class of nonlinear systems can be modeled using high-order Volterra series. The problem with Volterra series is that the number of parameters grows very rapidly with the order of the nonlinearity and the memory in the system. In order to efficiently...

No description

The Higher-Order Singular Value Decomposition (HOSVD) is a possible generalization of the Singular Value Decomposition (SVD) to tensors, which have been successfully applied in various domains. Unfortunately, this decomposition is computationally demanding. Indeed, the HOSVD of a Nth- order tensor involves the computation of the SVD of N...

The canonical polyadic decomposition (CPD) is one of the most popular tensor-based analysis tools due to its usefulness in numerous fields of application. The Q-order CPD is parametrized by Q matrices also called factors which have to be recovered. The factors estimation is usually carried out by means of the alternating least squares (ALS)...

MIMO technology has been subject of increasing interest in both academia and industry for future wireless standards. However, its performance benefits strongly depend on the accuracy of the channel at the base station. In a recent work, a fourth-order channel tensor model was proposed for MIMO systems. In this paper, we extend this model by...

In this paper, we consider a new one-way two-hop amplify-and-forward (AF) relaying scheme with a tensor space-time coding under frequency-selective fading channels. The signals received at the destination of the multi-input multi-output (MIMO) system define a 6-order tensor which satisfies a tensor-train decomposition (TTD). We propose a new...

In the context of big data, high-order tensor decompositions have to face a new challenge in terms of storage and computational costs. The tensor train (TT) decomposition provides a very useful graph-based model reduction, whose storage cost grows linearly with the tensor order D. The computation of the TT-core tensors and TT-ranks can be done...

Multidimensional Harmonic Retrieval (MHR) is at the heart of important signal-based applications. The exploitation of the large number of available measurement diversities for data fusion increases inexorably the tensor order/dimensionality. The need to mitigate the "curse of dimensionality" in this case is crucial. To efficiently cope with...

In this work, equivalence relations between a Tensor Train (TT) decomposition and the Canonical Polyadic Decomposition (CPD)/Tucker Decomposition (TD) are investigated. It is shown that a Q-order tensor following a CPD/TD with Q > 3 can be written using the graph-based formalism as a train of Q tensors of order at most 3 following the same...

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...

The Canonical Polyadic tensor decomposition (CPD), also known as Candecomp/Parafac, is very useful in numerous scientific disciplines. Structured CPDs, i.e. with Toeplitz, circulant, or Hankel factor matrices, are often encountered in signal processing applications. As subsequently pointed out, specialized algorithms were recently proposed for...

In radio astronomy, accurate calibration is of crucial importance for the new generation of radio inter-ferometers. 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...

Robust calibration of next-generation radio-interferometers, as the square kilometer array (SKA) for instance, is a crucial prepro-cessing step for sky imaging. Recently, several robust calibration es-timators based on the use of well known strong sources in the field of view (FOV) have been proposed in the literature. For that, usually a...

This paper investigates calibration of sensor arrays in the radio astronomy context. Current and future radio telescopes require com-putationally 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...

National audience

In this paper, two receivers are proposed for a multiple-input multiple-output (MIMO) relaying multi-hop communication system using a Khatri-Rao space-time (KRST) coding at the source and amplify-and-forward (AF) relays. It is shown that the third-order tensor of signals received at the destination satisfies a PARATUCK-(K+1) tensor model, where...

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...

The canonical polyadic decomposition (CPD) of high-order tensors, also known as Candecomp/Parafac, is very useful for representing and analyzing multidimensional data. This paper considers a CPD model having structured matrix factors, as e.g. Toeplitz, Hankel or circulant matrices, and studies its associated estimation problem. This model...

Over the last two decades, tensor-based methods have received growing attention in the signal processing community. In this work, we propose a comprehensive overview of tensor-based models and methods for multisensor signal processing. We present for instance the Tucker decomposition, the Canonical Polyadic Decomposition (CPD), the Tensor-Train...

In this chapter, we present an algebraic relation between the Tucker model and the Tensor-Train decomposition with structured cores. Exploiting this link, we present a new fast algorithm to compute the dominant singular subspaces of a Q-order tensor. As opposedt o the state of the art methods (usually called HOSVD for high-order SVD), our...