Phase estimation mean square error and threshold effects for windowed and amplitude modulated sinusoidal signals

The problem of estimating the phase of (possibly amplitude modulated) sinusoidal signals arises in a variety of signal processing applications [1]. A closed form expression for the maximum likelihood (ML) estimator exists which achieves the best possible performance given by the Cramer-Rao lower bound (CRLB) asymptotically. However, due to the nonlinear nature of the problem, below a certain level of signal-to-noise ratio (SNR), the so called threshold effect occurs, and the performance of the estimator decreases quickly. In this paper, we investigate this effect, together with the influence of windowing and amplitude modulation on the threshold using the unmodified estimator.