频率不变波束形成器抽头稀疏化设计的交替方向乘子法

针对具有空间响应变化函数约束的频率不变波束形成器设计问题,提出了采用交替方向乘子法实现抽头稀疏设计的优化算法。该算法利用交替方向乘子法能够将原始优化问题进行分裂处理的特点,通过引入替代变量和指示函数,使得表征波束形成器抽头稀疏度量的非凸L₀范数与阵列响应约束分离,进而将问题分裂到元素层级并给出近邻算子的解。对于指示函数的近邻算子求解,在分裂到元素层级后则退化为简单的双边约束问题,因而降低了优化求解的计算复杂度。仿真分析表明,提出的方法比现有的L₁范数方法在宽频带条件下的抽头稀疏度能够提升6%~13%,通带最大波动误差减小了约2 dB,并且优化消耗时间更短。实验结果进一步验证了所提方法在实现高抽头稀疏度波束形成的同时,对声信号造成的失真更小。因此,所提出的方法在降低传声器阵列波束形成器的实现复杂度以及保持阵列响应的频率不变性能方面更具有优势。 

Design of frequency invariant wideband beamformers with sparse tap coefficients using alternating direction method of multipliers

To design frequency-invariant beamformers with Spatial Response Variation(SRV) constraints,an optimization algorithm with sparse tap coefficients using Alternating Direction Method of Multipliers(ADMM) was proposed.The algorithm takes advantage of the characteristic of the ADMM which can split the original complex optimization problem into simpler ones.By introducing auxiliary variables and indicator functions,the non-convex L₀ norm which indicates the degree of tap sparsity is separated from array response constraints,thereby the problem is separated into element level and the solution of its proximal operator is then derived.As for the proximal operator of indicator function,it degenerates into a simple bilateral constraint problem when splitting to the element level,thus reducing the computational complexity of optimization.Simulation analysis shows that the tap sparsity of the proposed method can be increased by 6%-13% under the wide frequency band condition,the maximum passband fluctuation level is reduced by about 2 dB,and the time consumption is also shorter when compared with the existing L₁ norm method.The experimental results further verify that the proposed method can achieve higher tap sparsity while causing less distortion to the acoustic signal.Therefore,the proposed method performs better in reducing the implementation complexity of the microphone array beamformer and maintaining the frequency-invariant ability of the array response.