Causal Distortionless Response Beamforming by Alternating Direction Method of Multipliers

We present a low-latency beamforming method by extending the well-known minimum power distortionless re-sponse (MPDR) beamformer. Beamforming has been widely used to extract a target signal arriving from a specific direction. It is often conducted in the time-frequency domain, which causes an algorithmic delay for frame analysis. To reduce this delay, it was proposed to truncate the non-causal components of a spatial filter in the time domain and convolve it with audio mixtures. This method can reduce the algorithmic delay, but the truncated filter was not optimal. To address this problem, we optimize the spatial filter so that the power of the extracted signal is minimized under the distortionless and causality constraints. We further propose a relaxation of the distortionless constraint to improve the extraction performance. The alternating direction method of multipliers (ADMM) is used to solve the exact and relaxed optimization problems. Through numerical experiments, we investigate the performance of the causal MPDR beamforming and demonstrate the effectiveness of the relaxation.