Sensitivity of complex response zeros of linear power inversion arrays in the presence of random amplitude and phase errors

This paper investigates the variation of the complex response zeros, commonly used for source location purposes, of a linear power inversion array with random amplitude and phase errors. In particular, after deriving the zero variances in terms of the optimal weights and the variances of the amplitude and phase errors, a simple guideline relating the zero variances to the number of elements and the amplitude and phase variances is obtained for situations when the sources are well separated and resolvable by the array. Some simulation results are then presented to verify the theoretical derivations