TY - GEN
T1 - Asymptotic mean squared error performance of diagonally loaded Capon-MVDR processor
AU - Richmond, Christ D.
AU - Rao Nadakuditi, Raj
AU - Edelman, Alan
PY - 2005
Y1 - 2005
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.
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M3 - Conference contribution
AN - SCOPUS:33847622079
SN - 1424401313
SN - 9781424401314
T3 - Conference Record - Asilomar Conference on Signals, Systems and Computers
SP - 1711
EP - 1716
BT - Conference Record of The Thirty-Ninth Asilomar Conference on Signals, Systems and Computers
T2 - 39th Asilomar Conference on Signals, Systems and Computers
Y2 - 28 October 2005 through 1 November 2005
ER -