Estimating the mode of a phase distribution

If the phase of the theoretical mean of a complex-valued random variable is estimated by the sample mean of observed phases, there is a theoretical bias which results from the fact that phases are only measured on an interval of length 2pi, so that, for example, -pi and pi may represent the same phase. Thus if a true phase or direction is say, near pi, then the observed phases may instead be near -pi. In this paper, a least squares estimator of phase is proposed which accounts for this ";phase-wrapping";. The estimator is shown to be strongly consistent and its central limit theorem is derived. The results of various simulations are described, for different values of sample size, SNR and theoretical phase. The technique and methods of analysis may prove useful in the more complicated estimation of frequency from the phases of a complex sinusoid.