A Linear MMSE Filter Using Delayed Remote Microphone Signals for Speech Enhancement in Hearing Aid Applications

Existing methods that use remote microphones with hearing aid (HA) noise reduction systems, assume the wireless transmission to be instantaneous. In practice, however, there exists a time difference of arrival (TDOA) between the wirelessly transmitted target signals and the acoustic signal arriving from the target source to the HA device, which degrades their noise reduction performance. As speech is correlated between consecutive time-frames in the short-time Fourier transform (STFT) domain, we propose a linear minimum mean-square error (MMSE) estimator to estimate the desired signal, by combining multiple HA microphone signals with multiple consecutive time-frames of the remote microphone signal. We derive closed form expressions for the resulting filter weights and interpret them in terms of existing multi-channel and multi-frame methods. The simulation results validate the interpretation and show that using a multi-frame method along with a multi-channel method is an advantage, in the presence of unknown, positive TDOA between the microphone signals.