No Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices

Handle URI:
http://hdl.handle.net/10754/610651
Title:
No Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices
Authors:
Kammoun, Abla ( 0000-0002-0195-3159 ) ; Alouini, Mohamed-Slim ( 0000-0003-4827-1793 )
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
No Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices 2016:1 IEEE Transactions on Information Theory
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
IEEE Transactions on Information Theory
Issue Date:
4-May-2016
DOI:
10.1109/TIT.2016.2561998
Type:
Article
ISSN:
0018-9448; 1557-9654
Sponsors:
The work of A. Kammoun, and M.-S. Alouini was supported by a CRG 4 grant from the Office of Sponsored Research at KAUST
Additional Links:
http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7464912
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorKammoun, Ablaen
dc.contributor.authorAlouini, Mohamed-Slimen
dc.date.accessioned2016-05-25T08:49:16Z-
dc.date.available2016-05-25T08:49:16Z-
dc.date.issued2016-05-04-
dc.identifier.citationNo Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices 2016:1 IEEE Transactions on Information Theoryen
dc.identifier.issn0018-9448-
dc.identifier.issn1557-9654-
dc.identifier.doi10.1109/TIT.2016.2561998-
dc.identifier.urihttp://hdl.handle.net/10754/610651-
dc.description.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 [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.en
dc.description.sponsorshipThe work of A. Kammoun, and M.-S. Alouini was supported by a CRG 4 grant from the Office of Sponsored Research at KAUSTen
dc.language.isoenen
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.relation.urlhttp://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7464912en
dc.rights(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.en
dc.titleNo Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matricesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalIEEE Transactions on Information Theoryen
dc.eprint.versionPost-printen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorKammoun, Ablaen
kaust.authorAlouini, Mohamed-Slimen
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