No Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices

dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
dc.contributor.authorKammoun, Abla
dc.contributor.authorAlouini, Mohamed-Slim
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentElectrical Engineering Program
dc.date.accessioned2016-05-25T08:49:16Z
dc.date.available2016-05-25T08:49:16Z
dc.date.issued2016-05-04
dc.date.published-online2016-05-04
dc.date.published-print2016-07
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.
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 KAUST
dc.eprint.versionPost-print
dc.identifier.citationNo Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices 2016:1 IEEE Transactions on Information Theory
dc.identifier.doi10.1109/TIT.2016.2561998
dc.identifier.issn0018-9448
dc.identifier.issn1557-9654
dc.identifier.journalIEEE Transactions on Information Theory
dc.identifier.urihttp://hdl.handle.net/10754/610651
dc.language.isoen
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)
dc.relation.urlhttp://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7464912
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.
dc.titleNo Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices
dc.typeArticle
display.details.left<span><h5>Type</h5>Article<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0002-0195-3159&spc.sf=dc.date.issued&spc.sd=DESC">Kammoun, Abla</a> <a href="https://orcid.org/0000-0002-0195-3159" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0003-4827-1793&spc.sf=dc.date.issued&spc.sd=DESC">Alouini, Mohamed-Slim</a> <a href="https://orcid.org/0000-0003-4827-1793" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><br><h5>KAUST Department</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division,equals">Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Electrical Engineering Program,equals">Electrical Engineering Program</a><br><br><h5>KAUST Grant Number</h5>CRG 4<br><br><h5>Online Publication Date</h5>2016-05-04<br><br><h5>Print Publication Date</h5>2016-07<br><br><h5>Date</h5>2016-05-04</span>
display.details.right<span><h5>Abstract</h5>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.<br><br><h5>Citation</h5>No Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices 2016:1 IEEE Transactions on Information Theory<br><br><h5>Acknowledgements</h5>The work of A. Kammoun, and M.-S. Alouini was supported by a CRG 4 grant from the Office of Sponsored Research at KAUST<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=Institute of Electrical and Electronics Engineers (IEEE),equals">Institute of Electrical and Electronics Engineers (IEEE)</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=IEEE Transactions on Information Theory,equals">IEEE Transactions on Information Theory</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1109/TIT.2016.2561998">10.1109/TIT.2016.2561998</a><br><br><h5>Additional Links</h5>http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7464912</span>
kaust.acknowledged.supportUnitOffice of Sponsored Research
kaust.grant.numberCRG 4
kaust.personKammoun, Abla
kaust.personAlouini, Mohamed-Slim
orcid.authorKammoun, Abla::0000-0002-0195-3159
orcid.authorAlouini, Mohamed-Slim::0000-0003-4827-1793
orcid.id0000-0003-4827-1793
orcid.id0000-0002-0195-3159
refterms.dateFOA2018-06-13T15:33:52Z
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