No Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices
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AbstractThis 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 , 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.
CitationNo Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices 2016:1 IEEE Transactions on Information Theory
SponsorsThe work of A. Kammoun, and M.-S. Alouini was supported by a CRG 4 grant from the Office of Sponsored Research at KAUST