Optimum weighted smoothing in finite data

Abstract

In this correspondence, we consider a generalized smoothing problem and develop a procedure to obtain a set of optimum weights which gives minimum mean-squared error (MSE) in the estimates of directions of arrival of signals in finite data when the signals are arbitrarily correlated. Using the optimum weights, we study the optimum tradeoff between the number of subarrays and the subarray size for a fixed total size of the array. The computation of optimum weights, however, requires full knowledge of the scenario. Since exact DOA's, powers, and correlations of signals are unknown a priori, we give a method to estimate these weights from the observed finite data. We also show through empirical studies that the optimum weights can be approximated with Taylor weights which serve as near-optimum weights. Simulation results are included to support the theoretical assertions.