Sylvie Icart

Canonical Polyadic Decomposition with a columnwise orthonormal factor matrix

Canonical polyadic decomposition (CPD) of a higher-order tensor is an important tool in mathematical engineering. In many applications at least one of the matrix factors is constrained to be columnwise orthonormal. We first derive a relaxed condition that guarantees uniqueness of the CPD under this constraint. Second, we give a simple proof of the existence of the optimal low-rank approximation of a tensor in the case that a factor matrix is columnwise orthonormal. Third, we derive numerical algorithms for the computation of the constrained CPD. In particular, orthogonality-constrained versions of the CPD methods based on simultaneous matrix diagonalization and alternating least squares are presented. Numerical experiments are reported.

Blind separation of convolutive mixtures using second and fourth order moments

This paper deals with the problem of blind identification of p-non Gaussian inputs, q-outputs AR systems in the special case where p<q. In this case, the identification problem is degenerated, therefore as the classical Levinson (Robinson) algorithm cannot be applied, we use the Inouyes (1983) method. As this procedure assumes that the AR model is normalized, it is necessary to split the problem in two parts: first, we estimate the convolutive mixture by means of linear prediction, and second, we estimate the instantaneous mixture. The first one requires second order moments and the second one, high order statistics. Numerical simulations are presented to show the influence of the conditioning of the instantaneous mixture matrix in the identification problem in presence of white Gaussian noise.

A Unified Study of the Fixed Modes of Systems Decoupled via Regular Static State Feedback

It is well known that one cannot always achieve simultaneously block decoupling and complete freedom of pole assignment. The modes that cannot be assigned are called the fixed modes of the decoupled system.Their interest is obvious : their value determines the ability of a system to be decoupled with stability or not.

Blind equalization of MIMO channels

This paper introduces a blind MIMO equalization algorithm for convolutive mixtures. A parametrization of the equalizer is proposed when observations are whitened. From theoretical results, a numerical algorithm is then derived. This algorithm is based on the solution of a polynomial system, which some values of output cumulant multi-correlations enter. Simulations and performance of the numerical algorithm are also included.

Blind MIMO paraunitary equalizer

This paper introduces a new blind source separation algorithm for convolutive mixtures. In addition to separate sources, this algorithm respects the paraunitary property of the model considered, obtained after whitening observations. In order to do this, the equalizer is factorized in a novel manner. After a presentation of theoretical results, a numerical algorithm is then derived. This algorithm is based on the solution of a polynomial system, which some values of output cumulant multi-correlations enter. Simulations and performances of the numerical algorithm are presented in the last section.

Structural results about the interactor

A new form of interactor is established, which directly provides structural information such as infinite zeros structure or essential orders. Moreover, this form makes it possible to link the infinite and the essential structures of a system. The results of this study can play a key role in the polynomial approach for the row-by-row decoupling problem.<<ETX>>

On Jacobi-type methods for blind equalization of paraunitary channels

In this paper a study of the cumulant-based blind equalization algorithms PAJOD and PAFA is conducted. Both algorithms assume that the data have been pre-whitened and hence the problem reduces to the estimation of paraunitary channels. The main contribution of this paper is an efficient implementation of the PAJOD algorithm called PAJOD2. Second, a performance comparison between the PAJOD, PAJOD2 and PAFA algorithms is reported.

Blind paraunitary equalization

In this paper a blind multiple-input/multiple-output (MIMO) space-time equalizer is described, dedicated to convolutive mixtures when observations have been pre-whitened. Filters preserving space-time whiteness are paraunitary; a parameterization of such filters with plane rotations is proposed. Theoretical developments then lead to a numerical algorithm that sweeps all pairs of delayed outputs. This algorithm involves the solution of a polynomial system in two unknowns, whose coefficients depend on the output cumulants. Simulations and performance of the numerical algorithm are reported.

Blind equalization in presence of bounded errors

This article presents a new approach to blind equalization of an FIR channel. It is based on a bounded-error assumption and takes into account the fact that the input signal is in a finite alphabet. We show that even in the noisy case, identifiability can be guaranteed in finite time, provided that the support of the noise density is suitably bounded.

Design of a minimal precompensator for the decoupling problem

Abstract For right invertible linear time-invariant systems, which cannot be decoupled row by row using regular static state feedback laws, we propose a new algorithmic procedure for designing a minimal precompensator leading to a compensated system which can be decoupled by regular static state feedback.