Phase estimation in heavy-tailed noise for co-prime arrays

A phase estimator appropriate for use in the product-processing of co-prime sub-array pairs is described and analyzed. The estimator is a unit-circle average (UCA) of the phase estimates from each sub-array. A Fourier-series representation of the probability density function (PDF) of a single phase estimate is used to simplify evaluation of the PDF of the UCA estimator and its circular variance. The UCA estimator, which can be described as trading signal-to-noise ratio (SNR) for multiple observations, is seen to suffer a performance loss relative to the fully coherent, angle of the sum AoS, phase estimator of no more than 1-dB SNR in Gaussian noise. When the noise PDF tails are high enough, however, the UCA estimator is seen to outperform the AoS estimator.