The Capon-MVDR Algorithm Threshold Region Performance Prediction and Its Probability of Resolution

The Capon-MVDR algorithm exhibits a threshold effect in mean- squared error (MSE) performance (1). Below a specific threshold signal-to-noise ratio (SNR), the MSE of signal parameter estimates derived from the Capon algorithm rises rapidly. Prediction of this threshold SNR point is clearly of practical significance for system design and performance. Via an adaptation of an interval error-based method, referred to herein as the method of interval errors (MIE) (2),(3), the Capon threshold region MSE performance is accurately predicted. The exact pairwise error probabilities for the Capon (and Bartlett) algorithm, derived herein, are given by simple finite sums involving no numerical integration and include finite sample effects for an arbitrary colored data covariance. Combining these probabilities with the large sample MSE predictions of Vaidyanathan and Buckley (4), MIE provides accurate prediction of the threshold SNRs for an arbitrary number of well-separated sources, circumventing the need for numerous Monte Carlo simulations. A new two-point measure of the Capon probability of resolution 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. These results represent very valuable design and analysis tools for any system employing the Capon-MVDR algorithm. Potential to characterize performance in the presence of mismatch is briefly considered.