### Abstract

The asymptotic local mean squared error (MSB) performance of the Capon algorithm, a.k.a the minimum variance distortionless response (MVDR) spectral estimator, has been studied extensively by several authors. Stoica et al. [21], Vaidyanathan and Buckley [23], and Hawkes and Nehorai [11] have exploited Taylor's theorem and complex gradient methods to provide accurate prediction of the Capon algorithm signal parameter estimate MSB performance. These predictions are valid (i) above the estimation threshold signal-to-noise ratio (SNR) and (ii) provided a sufficient number of training samples is available for covariance estimation. The goal of this present analysis is to extend these results to the case in which the sample covariance matrix is diagonally loaded, as is often done in practice for regularization, stabilizing matrix inversion, and white noise gain control [7]. Recent advances in the theory of random matrices with large dimensions facilitate simple calculation of the required moments of the eigenvalues of several modified complex Wishart matrices including the inverse of the diagonally loaded case [14, 16]. This initial work focuses on the MSB prediction of angle estimates derived for the canonical case of single and multiple planewave signals in white noise.

Original language | English (US) |
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Title of host publication | Conference Record of The Thirty-Ninth Asilomar Conference on Signals, Systems and Computers |

Pages | 1711-1716 |

Number of pages | 6 |

Volume | 2005 |

State | Published - Dec 1 2005 |

Externally published | Yes |

Event | 39th Asilomar Conference on Signals, Systems and Computers - Pacific Grove, CA, United States Duration: Oct 28 2005 → Nov 1 2005 |

### Other

Other | 39th Asilomar Conference on Signals, Systems and Computers |
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Country | United States |

City | Pacific Grove, CA |

Period | 10/28/05 → 11/1/05 |

### Fingerprint

### ASJC Scopus subject areas

- Signal Processing
- Computer Networks and Communications

### Cite this

*Conference Record of The Thirty-Ninth Asilomar Conference on Signals, Systems and Computers*(Vol. 2005, pp. 1711-1716). [1600062]

**Asymptotic mean squared error performance of diagonally loaded Capon-MVDR processor.** / Richmond, Christ; Rao Nadakuditi, Raj; Edelman, Alan.

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

*Conference Record of The Thirty-Ninth Asilomar Conference on Signals, Systems and Computers.*vol. 2005, 1600062, pp. 1711-1716, 39th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, United States, 10/28/05.

}

TY - GEN

T1 - Asymptotic mean squared error performance of diagonally loaded Capon-MVDR processor

AU - Richmond, Christ

AU - Rao Nadakuditi, Raj

AU - Edelman, Alan

PY - 2005/12/1

Y1 - 2005/12/1

N2 - The asymptotic local mean squared error (MSB) performance of the Capon algorithm, a.k.a the minimum variance distortionless response (MVDR) spectral estimator, has been studied extensively by several authors. Stoica et al. [21], Vaidyanathan and Buckley [23], and Hawkes and Nehorai [11] have exploited Taylor's theorem and complex gradient methods to provide accurate prediction of the Capon algorithm signal parameter estimate MSB performance. These predictions are valid (i) above the estimation threshold signal-to-noise ratio (SNR) and (ii) provided a sufficient number of training samples is available for covariance estimation. The goal of this present analysis is to extend these results to the case in which the sample covariance matrix is diagonally loaded, as is often done in practice for regularization, stabilizing matrix inversion, and white noise gain control [7]. Recent advances in the theory of random matrices with large dimensions facilitate simple calculation of the required moments of the eigenvalues of several modified complex Wishart matrices including the inverse of the diagonally loaded case [14, 16]. This initial work focuses on the MSB prediction of angle estimates derived for the canonical case of single and multiple planewave signals in white noise.

AB - The asymptotic local mean squared error (MSB) performance of the Capon algorithm, a.k.a the minimum variance distortionless response (MVDR) spectral estimator, has been studied extensively by several authors. Stoica et al. [21], Vaidyanathan and Buckley [23], and Hawkes and Nehorai [11] have exploited Taylor's theorem and complex gradient methods to provide accurate prediction of the Capon algorithm signal parameter estimate MSB performance. These predictions are valid (i) above the estimation threshold signal-to-noise ratio (SNR) and (ii) provided a sufficient number of training samples is available for covariance estimation. The goal of this present analysis is to extend these results to the case in which the sample covariance matrix is diagonally loaded, as is often done in practice for regularization, stabilizing matrix inversion, and white noise gain control [7]. Recent advances in the theory of random matrices with large dimensions facilitate simple calculation of the required moments of the eigenvalues of several modified complex Wishart matrices including the inverse of the diagonally loaded case [14, 16]. This initial work focuses on the MSB prediction of angle estimates derived for the canonical case of single and multiple planewave signals in white noise.

UR - http://www.scopus.com/inward/record.url?scp=33847622079&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33847622079&partnerID=8YFLogxK

M3 - Conference contribution

SN - 1424401313

SN - 9781424401314

VL - 2005

SP - 1711

EP - 1716

BT - Conference Record of The Thirty-Ninth Asilomar Conference on Signals, Systems and Computers

ER -