On low rank MVDR beamforming using the conjugate gradient algorithm

In array applications an important task is adaptive beamforming. The minimum variance distortionless response (MVDR) beamformer can only be computed if the true spatial correlation matrix is available. In practice, the correlation matrix has to be estimated from the arriving signals, and in some cases there are only a small number of samples (snapshots) available. When the number of snapshots is small, the MVDR beamformer is no longer optimal, and a low rank MVDR solution can provide a higher SINR. In this work we analyze two methods of finding low rank solutions: steering independent conjugate gradient (SI-CG) and steering dependent conjugate gradient (SD-CG). We also propose a simplified expression to compute the arriving power from any given direction.