The CAPON-MVDR algorithm: threshold SNR prediction and the probability of resolution

The threshold region mean squared error (MSE) performance of the Capon-MVDR algorithm is predicted via an adaptation of an interval error based method referred to herein as the method of interval errors (MIE). MIE requires good approximations of two quantities: (i) interval error probabilities, and (ii) the algorithm asymptotic (SNR → ∞) MSE performance. Exact pairwise error probabilities for the Capon (and Bartlett) algorithm are derived herein that include finite sample effects for an arbitrary colored data covariance; with the union bound, accurate approximations of the interval error probabilities are obtained. Further, with the large sample MSE predictions of Vaidyanathan and Buckley (1995), MIE accurately predicts the signal-to-noise ratio (SNR) threshold point, below which the Capon algorithm MSE performance degrades swiftly. A two-point measure of the probability of resolution is defined for the Capon algorithm that accurately predicts the SNR at which sources of arbitrary closeness become resolvable.