On robust Capon beamforming and diagonal loading

TLDR: It is shown that a natural extension of the Capon beamformer to the case of uncertain steering vectors also belongs to the class of diagonal loading approaches, but the amount of diagonalloading can be precisely calculated based on the uncertainty set of the steering vector.

Abstract: The Capon (1969) beamformer has better resolution and much better interference rejection capability than the standard (data-independent) beamformer, provided that the array steering vector corresponding to the signal of interest (SOI) is accurately known. However, whenever the knowledge of the SOI steering vector is imprecise (as is often the case in practice), the performance of the Capon beamformer may become worse than that of the standard beamformer. Diagonal loading (including its extended versions) has been a popular approach to improve the robustness of the Capon beamformer. We show that a natural extension of the Capon beamformer to the case of uncertain steering vectors also belongs to the class of diagonal loading approaches, but the amount of diagonal loading can be precisely calculated based on the uncertainty set of the steering vector. The proposed robust Capon beamformer can be efficiently computed at a comparable cost with that of the standard Capon beamformer. Its excellent performance for SOI power estimation is demonstrated via a number of numerical examples.