Performance of Eigenvalue-Based Spectrum Sensing With Approximate Eigenvalue Estimation Methods

Abstract

This article presents a performance and computational complexity analysis of cooperative spectrum sensing techniques based on the eigenvalues of the received signal sample covariance matrix, under three methods for approximate eigenvalue estimation: the Cholesky iterations algorithm, the Gershgorin theorem with transformed covariance matrix, and the conventional Gershgorin theorem. Widely used eigenvalue-based test statistics are addressed: the generalized likelihood ratio test, the ratio between the maximum and the minimum eigenvalues, and the Roy’s largest root test. Simulation results show that the first two eigenvalue estimation methods can yield comparable performances, whereas the latter may operate satisfactorily only in situations of high signal-to-noise ratios. It is also demonstrated that the test statistics are not equally sensitive to eigenvalue estimation errors. The Cholesky iterations algorithm is attractive in terms of complexity and performance for all spectrum sensing techniques, while the simple Gershgoring method may be attractive for the Roy’s largest root test.