Harmonic retrieval in colored non-Gaussian noise

Abstract

This paper addresses the harmonic retrieval problem in colored linear non-Gaussian noise of unknown covariance and unknown distribution. The assumptions made in the reported studies, that the non-Gaussian noise is asymmetrically distributed and no quadratic phase coupling occurs, are released. Using the elaborately defined fourth-order cumulants of the complex noisy observations which are obtained through the Hilbert transform, we can either estimate the noise correlation nonparametrically via cumulant projections or obtain the AR polynomial of the non-Gaussian noise parametrically through ARMA modeling, then it is shown that the prewhitening or prefiltering techniques can be employed to retrieve harmonics respectively. Simulation results are presented to demonstrate the performance of the proposed algorithms.