TY - JOUR

T1 - Capon Algorithm Mean-Squared Error Threshold SNR Prediction and Probability of Resolution

AU - Richmond, Christ D.

N1 - Funding Information:
Manuscript received October 20, 2003; revised August 23, 2004. This work was sponsored by the Defense Advanced Research Projects Agency under Air Force contract F19628-00-C-0002. Opinions, interpretations, conclusions, and recommendations are those of the author and are not necessarily endorsed by the United States Government. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Jian Li.

PY - 2005/8

Y1 - 2005/8

N2 - Below a specific threshold signal-to-noise ratio (SNR), the mean-squared error (MSE) performance of signal parameter 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, derived herein, are given by simple finite sums involving no numerical integration, include finite sample effects, and hold for an arbitrary colored data covariance. 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 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 threshold SNR is provided for uniform linear arrays. A new, exact, two-point measure of the probability of resolution for the Capon algorithm, that includes the deleterious effects of signal model mismatch, is a serendipitous byproduct of this analysis that predicts the SNRs required for closely spaced sources to be mutually resolvable by the Capon algorithm. Last, a general strategy is provided for obtaining accurate MSE predictions that account for signal model mismatch.

AB - Below a specific threshold signal-to-noise ratio (SNR), the mean-squared error (MSE) performance of signal parameter 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, derived herein, are given by simple finite sums involving no numerical integration, include finite sample effects, and hold for an arbitrary colored data covariance. 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 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 threshold SNR is provided for uniform linear arrays. A new, exact, two-point measure of the probability of resolution for the Capon algorithm, that includes the deleterious effects of signal model mismatch, is a serendipitous byproduct of this analysis that predicts the SNRs required for closely spaced sources to be mutually resolvable by the Capon algorithm. Last, a general strategy is provided for obtaining accurate MSE predictions that account for signal model mismatch.

KW - Adaptive

KW - Bartlett

KW - Capon

KW - DOA estimation

KW - Wishart

KW - beamformer

KW - complex Wishart

KW - direction-of-arrival (DOA)

KW - finite sample

KW - mean-squared error (MSE)

KW - mismatch

KW - probability of resolution

KW - resolution

KW - sensitivity

KW - threshold

KW - threshold signal-to-noise ratio (SNR)

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U2 - 10.1109/TSP.2005.850361

DO - 10.1109/TSP.2005.850361

M3 - Article

AN - SCOPUS:33646065413

VL - 53

SP - 2748

EP - 2764

JO - IEEE Transactions on Acoustics, Speech, and Signal Processing

JF - IEEE Transactions on Acoustics, Speech, and Signal Processing

SN - 1053-587X

IS - 8

ER -