Frequency-invariant beamformer design via ADPM approach

Frequency-invariant (FI) beamformers play an important role in suppressing speech waveform distortions. Due to the perfect FI beampattern (FIB), differential microphone arrays (DMAs) have been widely used in practical applications like voice communication and human-machine interface systems. Superdirective beamforming generated by DMAs have many useful properties but suffer white noise amplification. To address this drawback, we formulate a least squares broadband FI problem, under the white noise output power constraints, to improve robustness of superdirective beamformers. The problem is challenging to solve since FI beamformers are designed on broadband and initialization parameters corresponding to each frequency are different. We devise broadband beampattern synthesis algorithm based on alternating direction penalty method (ADPM), which utilizes the relationship between residuals and penalty terms to reduce the iteration number under the improved framework of alternating direction method of multipliers (ADMM). The proposed ADPM method can decompose the optimization problem into multi-block convex optimization problems and solve them separately. The fast convergence property of our solution is demonstrated via numerical simulations.