Preprocessing for direction finding with minimal variance degradation

Numerous authors have advocated the use of preprocessing in high-resolution direction of arrival (DOA) algorithms. The benefits cited include reduced computation, improved performance in spatially colored noise, and enhanced resolution. The authors identify the preprocessing matrices that provide minimum variance estimates of DOA for a number of models and algorithms. They examine the Cramer-Rao bound (CRB) for Gaussian signals, the CRB for deterministic signals, and the asymptotic variance of the MUSIC estimator for preprocessed data. They also study the effect of array manifold errors on the direction estimates. As expected, the optimal preprocessor requires knowledge of the source directions. However, they show that performance that is close to optimal can be obtained with only approximate knowledge of the source directions (with an error not exceeding the array beamwidth) if the design rules outlined in this paper are used