TY - JOUR
T1 - No Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices
AU - Kammoun, Abla
AU - Alouini, Mohamed-Slim
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): CRG 4
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
PY - 2016/5/4
Y1 - 2016/5/4
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/610651
UR - http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7464912
UR - http://www.scopus.com/inward/record.url?scp=84976494823&partnerID=8YFLogxK
U2 - 10.1109/TIT.2016.2561998
DO - 10.1109/TIT.2016.2561998
M3 - Article
SN - 0018-9448
VL - 62
SP - 4312
EP - 4326
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 7
ER -