HIGH-SNR ASYMPTOTICS FOR SIGNAL-SUBSPACE METHODS IN SINUSOIDAL FREQUENCY ESTIMATION

This paper is concerned with the analysis of high-SNR-limit second-order properties of multiple signal classification (MUSIC), Minimum-Norm (MN), and subspace rotation (SUR) signal-subspace methods for sinusoidal frequency estimation. It presents an alternative to large-sample analysis of the methods, recently provided by Stoica, Soderstrom, and Tichavsky. The two most important variants of these methods are considered in connection with the choice of the sample covariance matrix: the simpler technique follows the principle of a simple linear prediction (LP), and the more complex one is based on the idea of a forward-backward prediction (FB). Explicit expressions for the high-SNR covariance elements of the estimation errors associated with all the methods are derived first. These expressions of covariances are used 1) to analyze and compare the statistical performances of MUSIC, MN, and SUR estimation methods in both of the variants; 2) to discuss the problem of the optimal dimension of the data covariance matrix; and 3) to study the limit statistical efficiency of the methods. Finally, performances of the large-sample and high-SNR asymptotics are documented by aid of Monte Carlo simulations.