交替迭代多约束波束优化设计

声学阵列波束形成器的阵增益、旁瓣级、稳健性等多个指标相互关联,对于包含加权向量范数约束和旁瓣控制的高增益波束优化设计问题,针对传统的内点法波束优化算法硬件实现困难及计算复杂度大等问题,提出了多约束交替迭代求解方法。通过引入辅助变量将范数约束和旁瓣约束解耦合,进而将多约束优化转化为两组单约束优化问题。给出了优化子问题的解析或近似解。理论分析表明,与现有内点优化算法相比,所提方法计算量较小,单次迭代复杂度仅为变量及约束个数的二次多项式。采用仿真和实测的阵列流形验证了设计效果,结果表明所提方法可实现旁瓣级,阵增益和稳健性等多个波束设计指标的合理折中,计算精度与二阶锥规划算法相当,但计算量更小。 

Design of multiply constrained beamformer via alternating direction method of multipliers

Design of high array gain beamformer with norm constraints on weight vectors and peak constraints on sidelobes is studied.In view of the difficulties in hardware implementation and high computational complexity of the traditional interior-point based optimization techniques,an alternating iterative method with multiple constraints is proposed.By introducing auxiliary variables to decouple norm constraints and sidelobe constraints,the multiply constrained optimization is transformed into two groups of singly constraint optimization problems.The analytical or approximate solutions of the optimization subproblem are provided.Theoretical analysis shows that the proposed method requires less computation since the computational complexity in one iteration is only quadratic polynomial compared with the existing interior point optimization algorithms.The proposed method is verified by both simulated and measured array manifold.The results show that the proposed method can provide the reasonable tradeoff among the sidelobe level,the array gain and the robustness of the sensor arrays.