Eigenvalue Ratio Detection Based on Exact Moments of Smallest and Largest Eigenvalues

Shakir, M. Z., Tang, W., Rao, A., Imran, M. A. and Alouini, M.-S. (2011) Eigenvalue Ratio Detection Based on Exact Moments of Smallest and Largest Eigenvalues. In: 2011 6th International ICST Conference on Cognitive Radio Oriented Wireless Networks and Communications (CROWNCOM), Osaka, Japan, 01-03 Jun 2011, pp. 46-50. ISBN 9781936968190 (doi:10.4108/icst.crowncom.2011.246151)

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Abstract

Detection based on eigenvalues of received signal covariance matrix is currently one of the most effective solution for spectrum sensing problem in cognitive radios. However, the results of these schemes always depend on asymptotic assumptions since the close-formed expression of exact eigenvalues ratio distribution is exceptionally complex to compute in practice. In this paper, non-asymptotic spectrum sensing approach to approximate the extreme eigenvalues is introduced. In this context, the Gaussian approximation approach based on exact analytical moments of extreme eigenvalues is presented. In this approach, the extreme eigenvalues are considered as dependent Gaussian random variables such that the joint probability density function (PDF) is approximated by bivariate Gaussian distribution function for any number of cooperating secondary users and received samples. In this context, the definition of Copula is cited to analyze the extent of the dependency between the extreme eigenvalues. Later, the decision threshold based on the ratio of dependent Gaussian extreme eigenvalues is derived. The performance analysis of our newly proposed approach is compared with the already published asymptotic Tracy-Widom approximation approach.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Imran, Professor Muhammad
Authors: Shakir, M. Z., Tang, W., Rao, A., Imran, M. A., and Alouini, M.-S.
College/School:College of Science and Engineering > School of Engineering
ISBN:9781936968190
Published Online:29 September 2011
Copyright Holders:Copyright © 2011 ICST
First Published:First published in 2011 6th International ICST Conference on Cognitive Radio Oriented Wireless Networks and Communications (CROWNCOM): 46-50
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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