Distribution of the ratio of an unordered eigenvalue to the trace of a complex central Wishart matrix and its application to cooperative spectrum sensing

Abstract

In this paper, we derive the closed-form expressions of the probability distribution function (PDF) and cumulative distribution function (CDF) of the ratio of an unordered eigenvalue to the trace of a complex central Wishart matrix. Using the random matrix result, we study the eigenvalue-based spectrum sensing algorithm for cognitive ratio. We apply the goodness of fit test to the ratio of an unordered eigenvalue to the trace of the sample covariance matrix. Finally, we compare the performances between the proposed algorithm and the well-known eigenvalue-based spectrum sensing algorithms in cooperative systems.