Reduction of variances of source-tracking response zeros of power inversion arrays in the presence of random amplitude and phase errors

A new technique to reduce the variances of the source-tracking response zeros of power inversion arrays in the presence of random amplitude and phase errors is investigated. Essentially, the zero variances are reduced by dividing the original system into several spatially shifted power inversion arrays, averaging the weight vectors of these arrays, and determining the zeros of the spatially averaged weight vector. Equations for the optimal averaging weights and the ensuing variance performance are derived and verified by simulation results. It is found that the new technique may reduce the zero variance substantially when compared with taking the entire system as a single array.