An accurate variance expression of Pisarenko's method for sinusoidal frequency estimation

Pisarenko harmonic decomposition (PHD) method for sinusoidal frequency estimation has been extensively analyzed in the literature. However, none of the analyses can provide an accurate frequency variance expression particularly for small data, record lengths and/or high signal-to-noise ratios (SNRs). With the use of a simple variance analysis technique, an exact expression of the, PHD variance for single-tone frequency estimation is derived tit this paper. An approximate PHD variance formula, for sufficienty large data, lengths and SNRs, as well as the tippet, and lower performance bounds axe also included.