On microphone array beamforming and insights into the underlying signal models in the short-time-Fourier-transform domain

This paper studies signal models for microphone array beamforming in the short-time-Fourier-transform (STFT) domain with long acoustic impulse responses. The major contributions are as follows. First, the signal modeling problem is investigated in the STFT domain and a general decomposition is proposed for the convolved source signal. Second, new insights into the array manifold are presented: the STFT of the windowed acoustic impulse response from the source to the sensors. Third, the structure of the reference signal is analyzed: it can be viewed as the output of a beamformer without considering the noise in the observation signal. Fourth, based on the new perspectives and decomposition, a signal model is derived based on the use of the superdirective beamformer. Finally, three performance measures are defined, based on which three optimal/suboptimal signal models are derived and their performance is assessed under different acoustic environments and analysis window lengths. The performance of the well-known minimum variance distortionless response (MVDR) beamformer is evaluated, which justifies the properties of the developed signal models.