High-SNR asymptotics for signal-subspace methods in sinusoidal frequency estimation

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 are discussed. An alternative to large-sample analysis of the methods is presented. 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 linear prediction, and the more complex one is based on the idea of a forward-backward prediction. Explicit expressions for the high-SNR covariance elements of the estimation errors associated with all the methods are derived. The expressions for the covariances are used to analyze and compare the statistical performances of MUSIC, MN, and SUR estimation methods in both of the variants, to discuss the problem of the optimal dimension of the data covariance matrix, and to study the limit statistical efficiency of the methods. Performances of the large-sample and high-SNR asymptotics derived using Monte Carlo simulations are presented