Second-order properties of MUSIC and ESPRIT estimates of sinusoidal frequencies in high SNR scenarios

Abstract

Expressions are presented for the variance of the MUSIC and ESPRIT estimates of sinusoidal frequencies, for situations when the signal-to-noise ratio (SNR) is high and the number of data is limited. The high SNR variance expressions are compared to the large sample variance expressions presented by Stoica and Söderström. The high SNR variance expressions are also valid for reasonable values of the SNR, and should be regarded as a complement to the large sample variance expressions. The theoretical results are supported by Monte Carlo simulations.