Permutation inconsistency in blind speech separation: Investigation and solutions

Acoustic reverberation severely limits the performance of multiple microphone blind speech separation (BSS) methods. In this paper, we show that the limited performance is due to random permutations of the unmixing filters over frequency. This problem, which we refer to as permutation inconsistency, becomes worse as the length of the room impulse response increases. We explore interesting connections between BSS and ideal beamforming, which leads us to propose a. permutation alignment scheme based on microphone array directivity patterns. Given that the permutations are properly aligned, we show that the blind speech separation method outperforms the nonblind beamformer in a highly reverberant environment. Furthermore, we discover the tradeoff where permutations can be aligned by affording a loss in spectral resolution of the unmixing filters. We then propose a multistage algorithm, which aligns the unmixing filter permutations without sacrificing the spectral resolution. For our study, we perform experiments in both real and simulated environments and compare the results to the ideal performance benchmarks that we derive using prior knowledge of the mixing filters.