Robust Adaptive Beamforming Based on Conjugate Gradient Algorithms

TLDR: This paper derives a diagonal loading CGLS algorithm (CG applied to normal equations) and proposes a simple method to choose the loading level based on a coarse estimation of the desired signal power, which can effectively reduce the signal self-cancellation at high signal-to-noise ratio.

Abstract: The mismatches of signal and array geometry will seriously degrade the performance of adaptive beamformer. In this paper, we propose two methods for robust adaptive beamforming based on the conjugate gradient (CG) algorithm. The proposed beamformers offer a significant improvement in the computational complexity while providing the same performance of the best robust beamformers at present. The first method belongs to the diagonal loading technique. We derive a diagonal loading CGLS algorithm (CG applied to normal equations) and propose a simple method to choose the loading level based on a coarse estimation of the desired signal power. This parameter-free method can effectively reduce the signal self-cancellation at high signal-to-noise ratio. The second method belongs to the regularization technique. Since the CG algorithm has a regularizing effect with iteration number being the regularization parameter, the stopping criterion plays an important role on the robustness. We develop three fast stopping criteria for CG iteration, which reduce the stopping complexity from $O(N)$ or $O(N^2)$ to $O(1)$ . The former two are the fast versions of existing methods and the later one is new. Moreover, the new criterion based on fast Ritz value estimation has better performance than others.