Robustness Analysis of the Phase-Phase Correlator to White Impulsive Noise With Applications to Autoregressive Modeling

Using only the phase information and a relationship based on the Gaussian Hypergeometric function, the Phase-Phase Correlator can be utilized to estimate the normalized cross-correlation coefficient between two zero-mean complex Gaussian processes. This estimator naturally introduces a certain robustness to white impulsive observation noise over the Gaussian Maximum Likelihood estimator. This correspondence examines the robustness of the Phase-Phase Correlator in the presence of uncorrelated impulsive noise. We show that its asymptotic bias compares favorably to the robust Schweppe-type GM-estimator with the Huber function termed SHGM at a cost of efficiency. Application of the PPC to autoregressive time series analysis is illustrated with a parametric spectral estimation example.