Christophe De Luigi

A General Algebraic Algorithm for Blind Extraction of One Source in a MIMO Convolutive Mixture

The paper deals with the problem of blind source extraction from a multiple-input/multiple-output (MIMO) convolutive mixture. We define a new criterion for source extraction which uses higher-order contrast functions based on so called reference signals. It generalizes existing reference-based contrasts. In order to optimize the new criterion, we propose a general algebraic algorithm based on best rank-1 tensor approximation. Computer simulations illustrate the good behavior and the interest of our algorithm in comparison with other approaches.

Wigner-Ville and polynomial Wigner-Ville Transforms in the estimation of nonlinear FM signal parameters

In this paper, we consider the estimation problem of the frequency characteristics of a nonlinear FM and monocomponent signal. The instantaneous frequency (IF) of such a signal can be highlighted by a Time-Frequency Transform (TFT). Using the properties of the cross TFT, we develop an iterative algorithm taking into consideration the presence of wrong frequencies in the estimated IF sequence of the signal. Finally, a computer simulation is performed to illustrate the behavior of this iterative scheme with different TFT.

Cubic higher-order criterion and algorithm for blind extraction of a source signal

The paper deals with the problem of the blind extraction of a source signal after a MIMO convolutive mixture. The extraction is performed using a MISO equalizer. A contrast function based on high order statistics is first proposed. It is more general than the existing contrast in the same context and exhibits a cubic dependence w.r.t. the unknown equalizer parameters. This allows us to propose a new extraction algorithm based on a third order tensor decomposition. Computer simulations illustrate the good behavior and the usefulness of our algorithm.

Optimal joint diagonalization of complex symmetric third-order tensors: application to separation of non circular signals

In this paper, we address the problem of blind source separation of non circular digital communication signals. A new Jacobi-like algorithm that achieves the joint diagonalization of a set of symmetric third-order tensors is proposed. The application to the separation of non-gaussian sources using fourth order cumulants is particularly investigated. Finally, computer simulations on synthetic signals show that this new algorithm improves the STOTD algorithm.

A PARAFAC decomposition based algorithm for blind MIMO source separation

The paper deals with the problem of blind source separation after a MIMO convolutive mixture. We propose an algorithm for the simultaneous extraction of all the sources. It is based on the PARAFAC decomposition of a tensor built from the observations and from so called reference signals. In particular this algorithm allows to overcome the classical drawbacks of the deflation approach in the sequential separation scheme. The order of the PARAFAC decomposition depends on the mixture parameters, the extraction filter length and the number of sources. Then a selection among these PARAFAC factors is proposed, in order to obtain the different sources. A fixed point method improves then the estimation performances iteratively. Computer simulations illustrate the good behavior and the interest of our algorithm in comparison with other approaches.

Gradient algorithm for reference-based cubic contrast function in a deflation scenario

The paper deals with the problem of blind source separation of a MIMO convolutive mixture by a deflation procedure. A criterion based on high order statistics and showing a cubic dependence w.r.t. the unknown equalizer parameters has been recently proposed. In order to optimize efficiently this criterion in a classical deflation scenario, we propose a new algorithm based on a fixed step size gradient. Computer simulations illustrate the good behavior and the usefulness of our algorithm in comparison with other approaches.

Radar modulation classification using time-frequency representation and nonlinear regression

In naval electronic environment, pulses emitted by radars are collected by ESM receivers. For most of them the intrapulse signal is modulated by a particular law. To help the classical identification process, a classification and estimation of this modulation law is applied on the intrapulse signal measurements. To estimate with a good accuracy the time-varying frequency of a signal corrupted by an additive noise, one method has been chosen. This method consists on the Wigner distribution calculation, the instantaneous frequency is then estimated by the peak location of the distribution. Bias and variance of the estimator are performed by computed simulations. In a estimated sequence of frequencies, we assume the presence of false and good estimated ones, the hypothesis of Gaussian distribution is made on the errors. A robust non linear regression method, based on the Levenberg-Marquardt algorithm, is thus applied on these estimated frequencies using a Maximum Likelihood Estimator. The performances of the method are tested by using varied modulation laws and different signal to noise ratios.