In this article, we study the fluctuations of the random variable:where Σn = n −1/2 D 1/2 n XnD 1/2 n + An, as the dimensions of the matrices go to infinity at the same pace. Matrices Xn and An are respectively random and deterministic N × n matrices; matrices Dn andDn are deterministic and diagonal, with respective dimensions N ×N and n×n; matrix Xn = (X ij ) has centered, independent and identically distributed entries with unit variance, either real or complex.We prove that when centered and properly rescaled, the random variable In(ρ) satisfies a Central Limit Theorem and has a Gaussian limit. The variance of In(ρ) depends on the moment EX 2 ij of the variables X ij and also on itsThe main motivation comes from the field of wireless communications, where In(ρ) represents the mutual information of a multiple antenna radio channel. This article closely follows the companion article "A CLT for Information-theoretic statistics of Gram random matrices with a given variance profile", Ann. Appl. Probab. (2008) by Hachem et al., however the study of the fluctuations associated to non-centered large random matrices raises specific issues, which are addressed here.2. The Central Limit Theorem for I n (ρ) 2.1. Notations, assumptions and first-order results. Let i = √ −1. As usual, R + = {x ∈ R : x ≥ 0}. Denote by P − → the convergence in probability of random variables and by D − → the convergence in distribution of probability measures. Denote by diag(a i ; 1 ≤ i ≤ k) the k × k diagonal matrix whose diagonal entries are the a i 's. Element (i, j) of matrix M will be either denoted m ij or [M ] ij depending on the notational context. If M is a n × n square matrix, diag(M ) = diag(m ii ; 1 ≤ i ≤ n). Denote by M T the matrix transpose of M ,

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 multiantenna 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.

International audienceLinear mixture models are commonly used to represent a hyperspectral data cube as linear combinations of endmember spectra. However, determining the number of endmembers for images embedded in noise is a crucial task. This paper proposes a fully automatic approach for estimating the number of endmembers in hyperspectral images. The estimation is based on recent results of random matrix theory related to the so-called spiked population model. More precisely, we study the gap between successive eigenvalues of the sample covariance matrix constructed from high-dimensional noisy samples. The resulting estimation strategy is fully automatic and robust to correlated noise owing to the consideration of a noise-whitening step. This strategy is validated on both synthetic and real images. The experimental results are very promising and show the accuracy of this algorithm with respect to state-of-the-art algorithms