Estimating correlation coefficient between two complex signals without phase observation

Abstract

In this paper, we propose a method to estimate a correlation coefficient of two correlated complex signals on the condition that only the amplitudes are observed and the phases are missing.Our proposed method is based on a maximum likelihood estimation. We assume that the original complex random variables are generated from a zero-mean bivariate complex normal distribution. The likelihood of the correlation coefficient is formulated as a bivariate Rayleigh distribution by marginalization over the phases. Although the maximum likelihood estimator has no analytical form, an expectation-maximization (EM) algorithm can be formulated by treating the phases as hidden variables. We evaluate the accuracy of the estimation using artificial signal, and demonstrate the estimation of narrow-band correlation of a two-channel audio signal.