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    On the decision threshold of eigenvalue ratio detector based on moments of joint and marginal distributions of extreme eigenvalues

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    Type
    Article
    Authors
    Shakir, Muhammad Zeeshan
    Rao, Anlei
    Alouini, Mohamed-Slim cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Electrical Engineering Program
    Communication Theory Lab
    Date
    2013-03
    Permanent link to this record
    http://hdl.handle.net/10754/562679
    
    Metadata
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    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. © 2002-2012 IEEE.
    Citation
    Shakir, M. Z., Rao, A., & Alouini, M.-S. (2013). On the Decision Threshold of Eigenvalue Ratio Detector Based on Moments of Joint and Marginal Distributions of Extreme Eigenvalues. IEEE Transactions on Wireless Communications, 12(3), 974–983. doi:10.1109/twc.2012.011513.111486
    Publisher
    Institute of Electrical and Electronics Engineers (IEEE)
    Journal
    IEEE Transactions on Wireless Communications
    DOI
    10.1109/TWC.2012.011513.111486
    ae974a485f413a2113503eed53cd6c53
    10.1109/TWC.2012.011513.111486
    Scopus Count
    Collections
    Articles; Electrical and Computer Engineering Program; Communication Theory Lab; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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