Optimum weighted smoothing in finite data

The authors consider a generalized smoothing problem and develop a procedure to obtain a set of optimum weights which gives minimum mean-squared error in the estimates of directions of arrival (DOAs) of signals in finite data when the signals are arbitrarily correlated. Using the optimum weights, they 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 DOAs, powers, and correlations of signals are unknown a priori, a method for estimating these weights from the observed finite data is given. It is shown through empirical studies that the optimum weights can be approximated by Taylor weights, which serve as near-optimum weights. Simulation results are included to support the theoretical assertions