Phase dependence mitigation for autocorrelation-based frequency estimation

The sinusoidal frequency estimation from short data records based on Toeplitz autocorrelation (AC) matrix estimates suffer from the dependence on the initial phases of the sinusoid(s). This effect becomes prominent when the impact of additive noise vanishes, that is at high signal-to-noise ratios (SNR). Based on both analytic derivation of the AC lag terms and simulation experiments we show that data windowing can mitigate the limitations caused by the phase dependence. Thus with proper windowing, the variance of the frequency estimate is no more eclipsed by phase dependence, but it continues to decrease linearly with increasing SNR. The study covers both the cases of a single sinusoid and two sinusoids closely spaced in the frequency with the Pisarenko frequency estimator, MUSIC and principal component autoregressive frequency estimators. The trade-offs between the spectral broadening and the achieved minimum variance level due to the data window are analyzed in detail