Capon and Bartlett Beamforming: Threshold Effect in Direction-of- Arrival Estimation Error and On the Probability of Resolution

摘要

Below a specific threshold signal-to-noise ratio (SNR), the mean squared error (MSE) perfor- mance of signal direction-of arrival (DOA) estimates derived from the Capon algorithm degrades swiftly. Prediction of this threshold SNR point is of practical significance for robust system design and analysis. The exact pairwise error probabilities for the Capon (and Bartlett) algorithm are derived herein, given by simple finite sums involving no numerical integration, include finite sample effects, and hold for an arbitrary colored data covariance. An accurate large sample approximation of these error probabilities in terms of the well tabulated complementary error function is also provided. Via an adaptation of an interval error-based method, these error probabilities, along with the local error MSE predictions of Vaidyanathan and Buckley, facilitate accurate prediction of the Capon threshold region DOA MSE performance for an arbitrary number of well separated sources, circumventing the need for numerous Monte Carlo simulations. A large sample closed form approximation for the Capon (and Bartlett) threshold SNR is provided for uniform linear arrays. A new exact two-point measure of the Capon probability of resolution, that includes the deleterious effects of signal model mismatch, is a serendipitous by-product of this analysis that predicts the SNRs required for closely spaced sources to be mutually resolvable by the Capon algorithm. Lastly, a new general strategy is provided for obtaining accurate MSE predictions that account for signal model mismatch.