Statistical performance of the MVDR beamformer in the presence of diagonal loading

New results are derived that describe the statistical performance of the MVDR (minimum variance distortionless response) adaptive beamformer when the weights are computed utilizing the sample covariance matrix and diagonal loading. It is well known that undesirably high sidelobes are generated when the unaugmented sample covariance matrix is used as an estimate of the true covariance matrix in adaptive beamforming algorithms. In practice, diagonal loading is frequently employed to reduce this deleterious effect. However, surprisingly little information is available in the technical literature that enables the user to predict the statistical performance of the MVDR algorithm when the sample covariance matrix and diagonal loading are employed. We help fill this gap by generating an approximate probability density function for the adaptive beam response for the diagonally loaded MVDR algorithm. The approximations are valid for an important class of signal scenarios. The utility of the new analysis is demonstrated via simulation. In particular, the new results are used to estimate the probability density function of the range sidelobe level for a wideband radar system in which adaptive beamforming and pulse compression are implemented in subbands.