Resolution of coherent sources by using spatial smoothing technique in power inversion arrays with random amplitude and phase errors

The variances of the complex response zeros of a linear equally spaced power inversion array employing spatial smoothing to locate coherent sources are investigated with respect to random amplitude and phase errors. Specifically, after expressing the variances in terms of the ideal zero positions, a simple guideline, 2M^-3(σ_a²+σ_p ²)(p_T/p_n), giving the variance as a function of the ratio of individual source power p_n to the combined source power p_T, the number of elements 2M, the amplitude variance σ_a² and phase variance σ_p², is derived. Some simulation results are then presented to demonstrate the validity and usefulness of the theoretical results