### 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 language | English (US) |
---|---|

Title of host publication | Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking |

Publisher | John Wiley and Sons Inc. |

Pages | 289-305 |

Number of pages | 17 |

ISBN (Electronic) | 9780470544198 |

ISBN (Print) | 0470120959, 9780470120958 |

DOIs | |

State | Published - Jan 1 2007 |

Externally published | Yes |

### Fingerprint

### 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)

### Cite this

*Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking*(pp. 289-305). John Wiley and Sons Inc.. https://doi.org/10.1109/9780470544198.ch25

**Capon Algorithm Mean-Squared Error Threshold SNR Prediction and Probability of Resolution.** / Richmond, Christ.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking.*John Wiley and Sons Inc., pp. 289-305. https://doi.org/10.1109/9780470544198.ch25

}

TY - CHAP

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

AU - Richmond, Christ

PY - 2007/1/1

Y1 - 2007/1/1

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 - Algorithm design and analysis

KW - Approximation methods

KW - Error probability

KW - Estimation

KW - Prediction algorithms

KW - Signal resolution

KW - Signal to noise ratio

UR - http://www.scopus.com/inward/record.url?scp=85036515168&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85036515168&partnerID=8YFLogxK

U2 - 10.1109/9780470544198.ch25

DO - 10.1109/9780470544198.ch25

M3 - Chapter

SN - 0470120959

SN - 9780470120958

SP - 289

EP - 305

BT - Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking

PB - John Wiley and Sons Inc.

ER -