An unbiased Pisarenko harmonic decomposition estimator for single-tone frequency

In this paper, closed-form frequency estimation of a single real tone in white noise is addressed. Based on the alternative derivation of Pisarenko's frequency estimate using the standard sample covariance of the noisy sinusoid with lags 1 and 2, we have devised novel sample covariance expressions, which are inspired from the modified covariance (MC) method, to achieve unbiased frequency estimation. The variance of the proposed Pisarenko harmonic decomposition (PHD) variant is also derived. Computer simulations are included to corroborate the theoretical development and to demonstrate its superiority over the MC and original PHD algorithms.