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 (SNHs). With the use of a simple variance analysis technique, an exact expression of the PHD variance for single-lone frequency estimation is derived in this paper. An approximate PHD variance formula for sufficiently large data lengths and SNHs, as well as the upper and lower performance bounds are also included.