A superdirective beamforming method for linear sensor arrays

A general superdirective beamforming method which is suitable for arbitrary-shape sensor arrays is proposed, and its performance for linear arrays is studied in this paper. Based on Gram-Schmidt orthogonalization, the optimal solutions of superdirectivity are all expressed in closed-form without any approximations. The optimal beampattern and the maximum directivity factor are decomposed into mode-beams and their associated directivity factors respectively. For linear arrays, the directivity factor of mode-beam increases as its order number increases, but the robustness decreases. Thus, the robust superdirective beampattern can be easily obtained by adopting a reduced-rank treatment which can remove the error sensitive high order modes and remain robust ones. Simulations and experimental results show the good performance of this approach.