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

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.