Karim Abed-Meraim

Fast orthonormal PAST algorithm

Subspace decomposition has proven to be an important tool in adaptive signal processing. A number of algorithms have been proposed for tracking the dominant subspace. Among the most robust and most efficient methods is the projection approximation and subspace tracking (PAST) method. This paper elaborates on an orthonormal version of the PAST algorithm for fast estimation and tracking of the principal subspace or/and principal components of a vector sequence. The orthonormal PAST (OPAST) algorithm guarantees the orthonormality of the weight matrix at each iteration. Moreover, it has a linear complexity like the PAST algorithm and a global convergence property like the natural power (NP) method.

Blind source-separation using second-order cyclostationary statistics

This paper studies the blind source separation (BSS) problem with the assumption that the source signals are cyclostationary. Identifiability and separability criteria based on second-order cyclostationary statistics (SOCS) alone are derived. The identifiability condition is used to define an appropriate contrast function. An iterative algorithm (ATH2) is derived to minimize this contrast function. This algorithm separates the sources even when they do not have distinct cycle frequencies.

Separating more sources than sensors using time-frequency distributions

We examine the problem of blind separation of nonstationary sources in the underdetermined case, where there are more sources than sensors. Since time-frequency (TF) signal processing provides effective tools for dealing with nonstationary signals, we propose a new separation method that is based on time-frequency distributions (TFDs). The underlying assumption is that the original sources are disjoint in the time-frequency (TF) domain. The successful method recovers the sources by performing the following four main procedures. First, the spatial time-frequency distribution (STFD) matrices are computed from the observed mixtures. Next, the auto-source TF points are separated from cross-source TF points thanks to the special structure of these mixture STFD matrices. Then, the vectors that correspond to the selected auto-source points are clustered into different classes according to the spatial directions which differ among different sources; each class, now containing the auto-source points of only one source, gives an estimation of the TFD of this source. Finally, the source waveforms are recovered from their TFD estimates using TF synthesis. Simulated experiments indicate the success of the proposed algorithm in different scenarios. We also contribute with two other modified versions of the algorithm to better deal with auto-source point selection.

Orthogonal Oja algorithm

In this letter, we propose an orthogonalized version of the Oja algorithm (OOja) that can be used for the estimation of minor and principal subspaces of a vector sequence. The new algorithm offers, as compared to Oja, such advantages as orthogonality of the weight matrix, which is ensured at each iteration, numerical stability, and a quite similar computational complexity.

A view on latest audio steganography techniques

Steganography has been proposed as a new alternative technique to enforce data security. Lately, novel and versatile audio steganographic methods have been proposed. A perfect audio Steganographic technique aim at embedding data in an imperceptible, robust and secure way and then extracting it by authorized people. Hence, up to date the main challenge in digital audio steganography is to obtain robust high capacity steganographic systems. Leaning towards designing a system that ensures high capacity or robustness and security of embedded data has led to great diversity in the existing steganographic techniques. In this paper, we present a current state of art literature in digital audio steganographic techniques. We explore their potentials and limitations to ensure secure communication. A comparison and an evaluation for the reviewed techniques is also presented in this paper.

Optimum Ambiguity-Free Directional and Omnidirectional Planar Antenna Arrays for DOA Estimation

This paper studies the antenna array geometry impact on both direction of arrival (DOA) estimation accuracy and array rank ambiguity. Some restrictions are imposed on the array geometry that guarantee first-order ambiguity-free arrays and, at the same time, reduce the cost of a global systematic optimization. The subsequently derived Cramer-Rao bound (CRB) on the DOA estimates shows to be attractive for numerical evaluation. Depending on whether the DOA estimation accuracy is desired to be uniform in all possible directions or is to be enhanced in a given aperture around some privileged direction, two optimization problems are formulated and solved by exhaustive search to compute the optimal array geometries. The obtained optimal arrays significantly outperform their circular counterparts and tend to have a form close to the V shape. We study in details V-shaped arrays and derive asymptotic performance measures that apply for large sized arrays where exhaustive search is unaffordable.

Reduced-rank adaptive filtering using Krylov subspace

A unified view of several recently introduced reduced-rank adaptive filters is presented. As all considered methods use Krylov subspace for rank reduction, the approach taken in this work is inspired from Krylov subspace methods for iterative solutions of linear systems. The alternative interpretation so obtained is used to study the properties of each considered technique and to relate one reduced-rank method to another as well as to algorithms used in computational linear algebra. Practical issues are discussed and low-complexity versions are also included in our study. It is believed that the insight developed in this paper can be further used to improve existing reduced-rank methods according to known results in the domain of Krylov subspace methods.

Algorithms for blind components separation and extraction from the time-frequency distribution of their mixture

We propose novel algorithms to select and extract separately all the components, using the time-frequency distribution (TFD), of a given multicomponent frequency-modulated (FM) signal. These algorithms do not use any a priori information about the various components. However, their performances highly depend on the cross-terms suppression ability and high time-frequency resolution of the considered TFD. To illustrate the usefulness of the proposed algorithms, we applied them for the estimation of the instantaneous frequency coefficients of a multicomponent signal and the results are compared with those of the higher-order ambiguity function (HAF) algorithm. Monte Carlo simulation results show the superiority of the proposed algorithms over the HAF.

Underdetermined blind audio source separation using modal decomposition

This paper introduces new algorithms for the blind separation of audio sources using modal decomposition. Indeed, audio signals and, in particular, musical signals can be well approximated by a sum of damped sinusoidal (modal) components. Based on this representation, we propose a two-step approach consisting of a signal analysis (extraction of the modal components) followed by a signal synthesis (grouping of the components belonging to the same source) using vector clustering. For the signal analysis, two existing algorithms are considered and compared: namely the EMD (empirical mode decomposition) algorithm and a parametric estimation algorithm using ESPRIT technique. A major advantage of the proposed method resides in its validity for both instantaneous and convolutive mixtures and its ability to separate more sources than sensors. Simulation results are given to compare and assess the performance of the proposed algorithms.

Cramer-Rao bounds for MIMO channel estimation

We investigate the performance of pilot-aided channel estimation and data detection for multi-input multi-output (MIMO) systems. We analyze and compare the Cramer-Rao bound (CRB) on channel tap estimation error for different design models of the pilot sequences. Then, the minimum mean square error (MMSE) estimation method with deflation is performed for channel identification for the embedded pilot scheme.