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.