37 research outputs found
The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile
Consider a random matrix where the entries are
given by , the
being centered i.i.d. and being a
continuous function called a variance profile. Consider now a deterministic
matrix whose non diagonal elements
are zero. Denote by the non-centered matrix . Then
under the assumption that and where is a probability measure, it is proven
that the empirical distribution of the eigenvalues of
converges almost surely in distribution to a non random probability measure.
This measure is characterized in terms of its Stieltjes transform, which is
obtained with the help of an auxiliary system of equations. This kind of
results is of interest in the field of wireless communication.Comment: 25 pages, revised version. Assumption (A2) has been relaxe
The empirical eigenvalue distribution of a Gram matrix: From independence to stationarity
Consider a random matrix where the
individual entries are a realization of a properly rescaled stationary gaussian
random field.
The purpose of this article is to study the limiting empirical distribution
of the eigenvalues of Gram random matrices such as and where is a deterministic matrix with appropriate
assumptions in the case where and .
The proof relies on related results for matrices with independent but not
identically distributed entries and substantially differs from related works in
the literature (Boutet de Monvel et al., Girko, etc.).Comment: 15 page
Methodes d'estimation spectrale 2D pour le traitement d'antenne bande etroite
eux méthodes d'estimation spectrale haute résolution 2D adaptées au problème de l'imagerie de sources bandes étroites non sinusoïdales en traitement d'antenne sont présentées dans cet article.La première basée sur les propriétés algébriques de la matrice de covariance spatio-temporelle est une extention 2D de Ia méthode du goniomètre.La deuxième: généralisation de la méthode TAM intoduite par Kung exploite la propriété que toute factorisation minimale de la matrice de covariance spatio-temporelle en l'absence de bruit coincide avec la matrice d'observabilité d'un systène linéaire 2D réalisable par un modèle d'Attasi.Des résultats de simulations comparent les performances de l'extension 2D du goniomètre à celles obtenues en exploitant la matrice de covariance spatiale et la matrice interspectrale
On the fluctuations of the mutual information of large dimensional MIMO channels
International audienc