The Bias of the MVDR Beamformer Outputs under Diagonal Loading

The MVDR beamformer is the most extensively used array processing algorithm and involves inverting the sample covariance matrix. In the snapshot deficient scenario, when the number of sensors is greater than or approximately equal to the number of snapshots, the eigenvalues of the resulting sample covariance matrix are poorly conditioned. Diagonal loading is then applied to the sample covariance matrix. Expressions for the bias of the resulting MVDR beamformer outputs in the sidelobe region are presented that are exact for asymptotically large arrays. Numerical simulations confirm the accuracy of these asymptotic expressions when predicting the bias of the outputs of moderately large arrays.