An Exact Variance Expression of Pisarenko’s Method for Frequency Estimation of a Single Real Sinusoid: Random Phase Case

Several statistical analyses of the Pisarenko harmonic decomposition (PHD) method for frequency estimation of a single real sinusoid in noise have been carried out in the literature. However, all of the analyses consider the phase of the sinusoid as a constant parameter which does not change from one snapshot to another. In this paper, it is assumed that the phase is a random variable uniformly distributed in an interval of length 2 . With the use of a simple variance analysis technique, an exact expression of the PHD frequency variance is derived. An approximate PHD variance formula for sufficiently large data lengths and signal-to-noise ratios is also given. Computer simulations are included to validate the theoretical development