Causal and Relaxed-Distortionless Response Beamforming for Online Target Source Extraction

In this paper, we propose a low-latency beamforming method for target source extraction. Beamforming has been performed in the time-frequency domain and achieved promising results in offline applications. Meanwhile, it causes a long algorithmic delay due to the frame analysis. Such a delay is unacceptable in various low-latency real-time applications, including hearing aids. To reduce this delay, we propose a causal variant of the minimum power distortionless response (MPDR) beamformer. The proposed method constraints the non-causal components of the spatial filter to be zero in the optimization of the MPDR beamformer. The algorithmic delay is reduced to zero by applying the causal spatial filter in the time domain. We further propose to relax the distortionless constraint regarding the gain, which allows us to improve the extraction performance without a phase delay. The Douglas–Rachford splitting method and its online extension are adopted to solve the optimization problems of the proposed methods. In our experiment, the relaxed method outperformed various low-latency beamforming methods in terms of extraction performance.