An exact analysis of Pisarenko's single-tone frequency estimation algorithm

Abstract

A number of statistical analyses of the Pisarenko harmonic decomposition (PHD) method for single-tone frequency estimation were carried out in the literature. Based on asymptotic derivations, however, none of them can provide an accurate frequency variance expression for arbitrary data record lengths and/or signal-to-noise ratios (SNRs). With the use of a simple variance analysis technique, a new closed form expression of the PHD variance is derived in this paper. An approximate PHD variance formula for sufficiently large data lengths and SNRs, as well as the upper and lower performance bounds are also included.