Fast Beam Pattern Synthesis Based on Vector Accelerated Alternating Direction Multiplier Method

The alternating direction multiplier method (ADMM) has been employed to iteratively solve convex optimization problems with multiple constraints in be amforming scenarios. Faster beamforming can help improve the response speed of acoustic devices in scenarios such as sound field reconstruction and speech enhancement. In this study, an accelerated ADMM for faster beam pattern synthesis is proposed and compared to traditional ADMMs. Based on the principle of vector acceleration, the computation of dual and auxiliary variables is expedited to improve the computational speed of ADMM beamforming algorithm. Simulation results show that the proposed algorithm reduces the overall computational time by approximately 30<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> and achieves more accurate results in less time compared to traditional ADMM beamforming algorithms.