On the Probability Distribution of the Outputs of the Diagonally Loaded Capon-MVDR Processor

The Capon-MVDR algorithm has been widely studied by several authors. The famous Capon-Goodman result on the probability distribution of the Capon-MVDR spectral estimator was also used to accurately predict the bias and variance of the Capon-MVDR algorithm due to finite sample effects. The goal of this present analysis is to extend these results to compute the probability distribution, and hence the bias and variance, of the output of the Capon-MVDR processor when the sample covariance matrix is diagonally loaded. Of particular interest is the computation, for the first time, in the snapshot deficient scenario where the diagonal loading is used to combat the ill-conditioned or rank deficient sample covariance matrix.