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

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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.

Original languageEnglish (US)
Title of host publicationBayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking
PublisherJohn Wiley and Sons Inc.
Pages289-305
Number of pages17
ISBN (Electronic)9780470544198
ISBN (Print)0470120959, 9780470120958
DOIs
StatePublished - Jan 1 2007
Externally publishedYes

Keywords

  • Algorithm design and analysis
  • Approximation methods
  • Error probability
  • Estimation
  • Prediction algorithms
  • Signal resolution
  • Signal to noise ratio

ASJC Scopus subject areas

  • Computer Science(all)

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    Richmond, C. (2007). Capon Algorithm Mean-Squared Error Threshold SNR Prediction and Probability of Resolution. In Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking (pp. 289-305). John Wiley and Sons Inc.. https://doi.org/10.1109/9780470544198.ch25