On the decision threshold of Eigenvalue Ratio detector based on moments of joint and marginal distributions of extreme eigenvalues

Muhammad Zeeshan Shakir, Anlei Rao, Mohamed-Slim Alouini

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Eigenvalue Ratio (ER) detector based on the two extreme eigenvalues of the received signal covariance matrix is currently one of the most effective solution for spectrum sensing. However, the analytical results of such scheme often depend on asymptotic assumptions since the distribution of the ratio of two extreme eigenvalues is exceptionally complex to compute. In this paper, a non-asymptotic spectrum sensing approach for ER detector is introduced to approximate the marginal and joint distributions of the two extreme eigenvalues. The two extreme eigenvalues are considered as dependent Gaussian random variables such that their joint probability density function (PDF) is approximated by a bivariate Gaussian distribution function for any number of cooperating secondary users and received samples. The PDF approximation approach is based on the moment matching method where we calculate the exact analytical moments of joint and marginal distributions of the two extreme eigenvalues. The decision threshold is calculated by exploiting the statistical mean and the variance of each of the two extreme eigenvalues and the correlation coefficient between them. The performance analysis of our newly proposed approximation approach is compared with the already published asymptotic Tracy-Widom approximation approach. It has been shown that our results are in perfect agreement with the simulation results for any number of secondary users and received samples.
Original languageEnglish
Pages (from-to)974-983
Number of pages10
JournalIEEE Transactions on Wireless Communications
Volume12
Issue number3
DOIs
Publication statusPublished - 18 Jan 2013
Externally publishedYes

Keywords

  • Spectrum sensing
  • eigenvalue ratio based detection
  • non-asymptotic Gaussian approximation
  • correlation coefficient
  • Copula

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