球谐域混叠消除最优波束形成方法

Optimal beamforming with aliasing cancellation in the spherical harmonics domain

为解决现有的球谐域混叠消除波束形成方法设计目标单一、难以很好地兼容多变的应用场景的问题,提出了球谐域混叠消除最优波束形成方法,并建立了其二阶锥规划形式的多重约束凸优化数学模型。得益于该数学模型,提出了旁瓣约束的混叠消除最大指向性波束形成器、鲁棒的混叠消除最大指向性波束形成器、混叠消除最小方差无失真响应波束形成器、零点约束的混叠消除最大指向性波束形成器。提出方法继承了现有球谐域混叠消除波束形成方法的混叠消除功能,且能够在指向性指数、白噪声增益、旁瓣水平等多个冲突的性能指标之间寻求适宜折中,便于用户根据实际应用需求灵活地调整约束参数得到特定场景下综合性能最优的波束形成器。

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.