Robust sparse array design for adaptive beamforming against DOA mismatch

The performance of an adaptive beamformer is significantly influenced by its array configuration. The problem of optimum array configuration for minimum variance distortionless response (MVDR) beamformers has been recently investigated under the assumption of accurate estimate or prior exact knowledge of the source direction of arrival (DOA). Inaccuracies in DOA can lead to significant performance degradation. Improving the robustness of MVDR beamformers has commonly been achieved by adding appropriate constraints in the determination of beamforming weights, such as the linearly constrained minimum variance (LCMV) beamformer. This work examines the sensitivity of different sparse array configurations towards uncertainty in the source DOA. It proposes enhancing system robustness through optimizing array configurations. The sparse array design problem is formulated in terms of maximizing the output signal-to-interference-plus-noise ratio (SINR) of the MVDR and LCMV beamformers. The constrained maximization problem is expressed as the fraction of matrix determinants, and a sequential convex programming algorithm is adopted for the solution of the corresponding non-convex problem. Numerical examples are presented to validate the robustness of configured sparse array MVDR and LCMV beamformers for small errors in source directional angles.