Please use this identifier to cite or link to this item: http://localhost/handle/Hannan/643618
Title: No Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices
Authors: Abla Kammoun;Mohamed-Slim Alouini
subject: Science & Technology
Year: 2016
Publisher: IEEE
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 by Vallet et al., 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.
URI: http://localhost/handle/Hannan/149882
http://localhost/handle/Hannan/643618
ISSN: 0018-9448
1557-9654
volume: 62
issue: 7
Appears in Collections:2016

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Title: No Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices
Authors: Abla Kammoun;Mohamed-Slim Alouini
subject: Science & Technology
Year: 2016
Publisher: IEEE
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 by Vallet et al., 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.
URI: http://localhost/handle/Hannan/149882
http://localhost/handle/Hannan/643618
ISSN: 0018-9448
1557-9654
volume: 62
issue: 7
Appears in Collections:2016

Files in This Item:
File Description SizeFormat 
7464912.pdf308.1 kBAdobe PDFThumbnail
Preview File
Title: No Eigenvalues Outside the Limiting Support of Generally Correlated Gaussian Matrices
Authors: Abla Kammoun;Mohamed-Slim Alouini
subject: Science & Technology
Year: 2016
Publisher: IEEE
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 by Vallet et al., 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.
URI: http://localhost/handle/Hannan/149882
http://localhost/handle/Hannan/643618
ISSN: 0018-9448
1557-9654
volume: 62
issue: 7
Appears in Collections:2016

Files in This Item:
File Description SizeFormat 
7464912.pdf308.1 kBAdobe PDFThumbnail
Preview File