SVD-based information theoretic criteria for detection of the number of damped/undamped sinusoids and their performance analysis

Abstract

Recently, Wax and Kailath developed information theoretic criteria for detection of the number of signals received by a sensor array. More recently, Fuchs developed a criterion, based on the perturbation analysis of the data autocorrelation matrix, for detecting the number of sinusoids. In this paper, following the information theoretic approach to model selection, we first develop criteria for detection of the number of dampedlundamped sinusoids. These criteria are matched to the singular value decomposition (SVD) based methods, such as modified forwardlhackward and forwardbackward linear prediction, so well that the extra computations needed over and above those required for computing the SVD are marginal. Next, we develop an analytical framework for analyzing the performance of these criteria, following the assumptions made by Wang and Kaveh and the corrections given by Zhang et al. In the development of the analysis, we make some approximations which become better for large signal-tonoise ratio. Simulations are used to verify the usefulness of the analysis, and to compare the performance of our method with that of Fuchs.