Eigenvalue ratio detection based on exact moments of smallest and largest eigenvalues

Muhammad Shakir, Wuchen Tang, Anlei Rao, Muhammad Ali Imran, Mohamed-Slim Alouini

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

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. © 2011 ICST.
Original languageEnglish (US)
Title of host publicationProceedings of the 6th International ICST Conference on Cognitive Radio Oriented Wireless Networks and Communications
PublisherEuropean Alliance for Innovation n.o.
Pages46-50
Number of pages5
ISBN (Print)9781936968190
DOIs
StatePublished - 2011

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