Deterministic equivalents for certain functionals of large random matrices

Abstract : Consider a $N\times n$ random matrix $Y_n$ where the entries are independent but not identically distributed (matrices with a variance profile) Consider now a deterministic $N\times n$ matrix $A_n$ whose columns and rows are uniformly bounded for the Euclidean norm. Let $\Sigma_n=Y_n+A_n$. We prove in this article that there exists a deterministic equivalent to the empirical Stieltjes transform of the distribution of the eigenvalues of $\Sigma_n \Sigma_n^T$ which is itself the Stieltjes transform of a probability measure. This work is motivated by the context of performance evaluation of Multiple Inputs / Multiple Output (MIMO) wireless digital communication channels. As an application, we derive a deterministic equivalent to the mutual information of a wireless channel.
Type de document :
Pré-publication, Document de travail
39 pages. 2005
Domaine :

https://hal.archives-ouvertes.fr/hal-00014668
Contributeur : Olivier Cappé <>
Soumis le : mardi 29 novembre 2005 - 09:39:14
Dernière modification le : jeudi 9 février 2017 - 15:20:28

Citation

W. Hachem, Philippe Loubaton, J. Najim. Deterministic equivalents for certain functionals of large random matrices. 39 pages. 2005. <hal-00014668>

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