arXiv subjects

Abla Kammoun

Publications and source records attributed to Abla Kammoun.

78 records · Page 5Linked to original sources

arXiv2013

Robust blind methods using $\ell_p$ quasi norms

It was shown in a previous work that some blind methods can be made robust to channel order overmodeling by using the $\ell_1$ or $\ell_p$ quasi-norms. However, no theoretical argument has been provided to support this statement. In this work, we study the robustness of subspace blind based methods using $\ell_1$ or $\ell_p$ quasi-norms. For the $\ell_1$ norm, we provide the sufficient and necessary condition that the channel should satisfy in order to ensure its identifiability in the noise-less case. We then study its frequency of occurrence, and deduce the effect of channel parameters on the robustness of blind subspace methods using $\ell_1$ norms.

cs.IT↗

arXiv2012

Performance of mutual information inference methods under unknown interference

The problem of fast point-to-point MIMO channel mutual information estimation is addressed, in the situation where the receiver undergoes unknown colored interference, whereas the channel with the transmitter is perfectly known. The considered scenario assumes that the estimation is based on a few channel use observations during a short sensing period. Using large dimensional random matrix theory, an estimator referred to as {\em G-estimator} is derived. This estimator is proved to be consistent as the number of antennas and observations grow large and its asymptotic performance is analyzed. In particular, the G-estimator satisfies a central limit theorem with asymptotic Gaussian fluctuations. Simulations are provided which strongly support the theoretical results, even for small system dimensions.

math.PR↗

arXiv2012

Estimation of the Covariance Matrix of Large Dimensional Data

This paper deals with the problem of estimating the covariance matrix of a series of independent multivariate observations, in the case where the dimension of each observation is of the same order as the number of observations. Although such a regime is of interest for many current statistical signal processing and wireless communication issues, traditional methods fail to produce consistent estimators and only recently results relying on large random matrix theory have been unveiled. In this paper, we develop the parametric framework proposed by Mestre, and consider a model where the covariance matrix to be estimated has a (known) finite number of eigenvalues, each of it with an unknown multiplicity. The main contributions of this work are essentially threefold with respect to existing results, and in particular to Mestre's work: To relax the (restrictive) separability assumption, to provide joint consistent estimates for the eigenvalues and their multiplicities, and to study the variance error by means of a Central Limit theorem.

cs.IT↗

arXiv2008

BER and Outage Probability Approximations for LMMSE Detectors on Correlated MIMO Channels

This paper is devoted to the study of the performance of the Linear Minimum Mean-Square Error receiver for (receive) correlated Multiple-Input Multiple-Output systems. By the random matrix theory, it is well-known that the Signal-to-Noise Ratio (SNR) at the output of this receiver behaves asymptotically like a Gaussian random variable as the number of receive and transmit antennas converge to +$\infty$ at the same rate. However, this approximation being inaccurate for the estimation of some performance metrics such as the Bit Error Rate and the outage probability, especially for small system dimensions, Li et al. proposed convincingly to assume that the SNR follows a generalized Gamma distribution which parameters are tuned by computing the first three asymptotic moments of the SNR. In this article, this technique is generalized to (receive) correlated channels, and closed-form expressions for the first three asymptotic moments of the SNR are provided. To obtain these results, a random matrix theory technique adapted to matrices with Gaussian elements is used. This technique is believed to be simple, efficient, and of broad interest in wireless communications. Simulations are provided, and show that the proposed technique yields in general a good accuracy, even for small system dimensions.

cs.IT↗

arXiv2008

A Central Limit Theorem for the SINR at the LMMSE Estimator Output for Large Dimensional Signals

This paper is devoted to the performance study of the Linear Minimum Mean Squared Error estimator for multidimensional signals in the large dimension regime. Such an estimator is frequently encountered in wireless communications and in array processing, and the Signal to Interference and Noise Ratio (SINR) at its output is a popular performance index. The SINR can be modeled as a random quadratic form which can be studied with the help of large random matrix theory, if one assumes that the dimension of the received and transmitted signals go to infinity at the same pace. This paper considers the asymptotic behavior of the SINR for a wide class of multidimensional signal models that includes general multi-antenna as well as spread spectrum transmission models. The expression of the deterministic approximation of the SINR in the large dimension regime is recalled and the SINR fluctuations around this deterministic approximation are studied. These fluctuations are shown to converge in distribution to the Gaussian law in the large dimension regime, and their variance is shown to decrease as the inverse of the signal dimension.

cs.IT↗

arXiv2008

A Central Limit Theorem for the SNR at the Wiener Filter Output for Large Dimensional Signals

Consider the quadratic form $β= {\bf y}^* ({\bf YY}^* + ρ{\bf I})^{-1} {\bf y}$ where $ρ$ is a positive number, where ${\bf y}$ is a random vector and ${\bf Y}$ is a $N \times K$ random matrix both having independent elements with different variances, and where ${\bf y}$ and ${\bf Y}$ are independent. Such quadratic forms represent the Signal to Noise Ratio at the output of the linear Wiener receiver for multi dimensional signals frequently encountered in wireless communications and in array processing. Using well known results of Random Matrix Theory, the quadratic form $β$ can be approximated with a known deterministic real number $\barβ_K$ in the asymptotic regime where $K\to\infty$ and $K/N \to α> 0$. This paper addresses the problem of convergence of $β$. More specifically, it is shown here that $\sqrt{K}(β- \barβ_K)$ behaves for large $K$ like a Gaussian random variable which variance is provided.

cs.IT↗