Abdelouahab Boudjellal

Constant modulus algorithms using hyperbolic Givens rotations

We propose two new algorithms to minimize the constant modulus (CM) criterion in the context of blind source separation. The first algorithm, referred to as Givens CMA (G-CMA), uses unitary Givens rotations and proceeds in two stages: prewhitening step, which reduces the channel matrix to a unitary one followed by a separation step where the resulting unitary matrix is computed as a product of Givens rotations. However, for small sample sizes, the prewhitening does not make the channel matrix close enough to unitary and hence applying Givens rotations alone does not provide satisfactory performance. To remediate to this problem, we propose to use Hyperbolic rotations in conjunction with Givens rotations. This second algorithm, referred to as Hyperbolic G-CMA (HG-CMA), is shown to outperform the G-CMA as well as the Analytical CMA (ACMA). The last part of this paper is dedicated to an efficient adaptive implementation of the HG-CMA and to performance assessment through numerical experiments.

Adaptive Constant Modulus Algorithm based oncomplex Givens rotations

This paper deals with adaptive Constant Modulus Algorithm (CMA) for the blind separation of communication signals. Ikhlef et al. proposed in 2010 an efficient block implementation of the CMA using Givens rotations. We introduce herein a fast adaptive implementation of this method which exploits recent developments on whitening techniques together with appropriate updating of the used statistics and efficient selection of the Givens rotation parameters. The proposed algorithm shows significantly improved performance with respect to existing techniques as illustrated by the simulation results.

A new methodology for optimal delay detection in mobile localization context

In this paper, we address the problem of delay detection in mobile localization context. A new methodology for delay detection is introduced, namely the Cell-Averaging Minimum Error Rate CA-MER detector, based on the minimization of the true error probability instead of minimizing only the miss probability for a constant false alarm rate. Simulation results show that the CA-MER detector operates better than the classical ones especially for low SNR values.

Sparsity-based algorithms for blind separation of convolutive mixtures with application to EMG signals

In this paper we propose two iterative algorithms for the blind separation of convolutive mixtures of sparse signals. The first one, called Iterative Sparse Blind Separation (ISBS), minimizes a sparsity cost function using an approximate Newton technique. The second algorithm, referred to as Givens-based Sparse Blind Separation (GSBS) computes the separation matrix as a product of a whitening matrix and a unitary matrix estimated, via a Jacobi-like process, as the product of Givens rotations which minimize the sparsity cost function. The two sparsity based algorithms show significantly improved performance with respect to the time coherence based SOBI algorithm as illustrated by the simulation results and comparative study provided at the end of the paper.

Minimum error rate detection: An adaptive bayesian approach

Abstract This paper addresses the thresholding problem which is an important issue in detection theory. A new thresholding methodology is proposed, namely the Minimum Error Rate (MER), related to the minimization of the error probability instead of minimizing only the miss probability for a Constant False Alarm Rate (CFAR). In an adaptive detection scheme, the proposed thresholding technique is combined with Cell Averaging (CA) and Order-Statistics OS estimation methods giving birth to the (CA-MER) and (OS-MER) detectors. Their performance statistics are analyzed for both homogeneous and heterogeneous environments. Moreover, a simplified approximate threshold expression is proposed and its effect on the whole detection process is studied. Theoretical and numerical results show that the MER-based detectors operate better than the classical CFAR-based ones. In particular, the proposed method is shown to be robust w.r.t. estimation errors on the different parameters (priors). Comparative study of MER versus CFAR-based detectors used for the delay detection in multipath context show that OS-MER detector outperforms the OS-CFAR which induces more accurate mobile positioning.

On the impact of signals time-frequency sparsity on the localization performance

In this paper, we investigate the localization performance of far field sources that have sparse time-frequency (T-F) representations. The Cramér-Rao Bound (CRB) under the sparsity assumption is developed and the impact of the T-F sparsity prior on the localization performance is analyzed. In particular, one studies how the different T-F sparsity properties i.e. local SNR level, source supports spreading and source overlapping and orthogonality affect the CRB of the Direction-of-Arrival (DoA) estimation. The obtained results show that the sources T-F orthogonality has the most significant impact on the localization performance. Simulation results are provided to illustrate the concluding remarks made out of this study.