Performance analysis of eigenvalue based distributed spectrum sensing

Abstract

In this paper, we consider the performance analysis of the distributed eigenvalue estimation technique based on the decentralized power method (d-PM) and the averaging consensus (AC) protocol. An analytical asymptotic expression of the second order statistics of the eigenvalues obtained from the d-PM is presented. This expression is essential for assessing the performance of estimators which are based on the d-PM. We show that the d-PM is not a consistent estimator of the eigenvalues of the true covariance matrix unless the AC protocol is carried out for a infinitely large number of iterations. However, for a moderately large number of samples a finite number of AC iterations is sufficient to achieve a performance which is comparable to that of the centralized eigendecomposition.