Optimal beamforming with aliasing cancellation in the spherical harmonics domain

The existing beamforming with aliasing elimination in the spherical harmonics domain usually adopts a single design goal, which is difficult to adapt to diverse application scenarios. To solve this problem, we propose an optimal beamforming with aliasing cancellation in the spherical harmonics domain, and establish a multiply constrained convex optimization model with a second-order cone programming form. Benefiting from the mathematical model, we further propose the maximum directivity beamformer with sidelobe constraint and aliasing cancellation, the robust maximum directivity beamformer with aliasing cancellation, the minimum variance distortionless response beamformer with aliasing elimination, and the maximum directivity beamformer with null constraint and aliasing elimination. The proposed method inherits the aliasing cancellation capability of the existing spherical-harmonics based aliasing-elimination beamforming, and can achieve a proper compromise among multiple contradictory performance measures such as directivity factor, white noise gain and sidelobe level. Therefore, it is convenient for users to flexibly adjust the constraint parameters according to actual application requirements, so as to obtain a beamformer with the best comprehensive performance in a specific scenario.