No Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices

Type
Article

Authors
Kammoun, Abla
Alouini, Mohamed-Slim

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program

KAUST Grant Number
CRG 4

Online Publication Date
2016-05-04

Print Publication Date
2016-07

Date
2016-05-04

Abstract
This paper investigates the behaviour of the spectrum of generally correlated Gaussian random matrices whose columns are zero-mean independent vectors but have different correlations, under the specific regime where the number of their columns and that of their rows grow at infinity with the same pace. Following the approach proposed in [1], we prove that under some mild conditions, there is no eigenvalue outside the limiting support of generally correlated Gaussian matrices. As an outcome of this result, we establish that the smallest singular value of these matrices is almost surely greater than zero. From a practical perspective, this control of the smallest singular value is paramount to applications from statistical signal processing and wireless communication, in which this kind of matrices naturally arise.

Citation
No Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices 2016:1 IEEE Transactions on Information Theory

Acknowledgements
The work of A. Kammoun, and M.-S. Alouini was supported by a CRG 4 grant from the Office of Sponsored Research at KAUST

Publisher
Institute of Electrical and Electronics Engineers (IEEE)

Journal
IEEE Transactions on Information Theory

DOI
10.1109/TIT.2016.2561998

Additional Links
http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7464912

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