Phase-only information loss

In many areas of signal processing, the phases of complex-valued random variables are used to estimate system parameters, the magnitudes being discarded. In this paper, we consider the implications of doing this: the loss of statistical information and subsequent increase in asymptotic variance. Two particular cases, those of estimating the phase of the mean of a complex distribution, and estimating the frequency of a complex sinusoid in white noise, are considered. The estimators are motivated by estimation under von Mises distributional assumptions. The asymptotic distributional properties are obtained under general assumptions, and are tested using a small number of simulations.