### Abstract

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, 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.

Original language | English (US) |
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Journal | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |

Volume | 2 |

State | Published - Oct 7 2004 |

Externally published | Yes |

Event | Proceedings - IEEE International Conference on Acoustics, Speech, and Signal Processing - Montreal, Que, Canada Duration: May 17 2004 → May 21 2004 |

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### ASJC Scopus subject areas

- Software
- Signal Processing
- Electrical and Electronic Engineering

### Cite this

**The capon-MVDR algorithm : Threshold SNR prediction and the probability of resolution.** / Richmond, Christ.

Research output: Contribution to journal › Conference article

}

TY - JOUR

T1 - The capon-MVDR algorithm

T2 - Threshold SNR prediction and the probability of resolution

AU - Richmond, Christ

PY - 2004/10/7

Y1 - 2004/10/7

N2 - 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, 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.

AB - 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, 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.

UR - http://www.scopus.com/inward/record.url?scp=4644327231&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4644327231&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:4644327231

VL - 2

JO - Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing

JF - Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing

SN - 0736-7791

ER -