Analysis of beamformer directed single-channel noise reduction system for hearing aid applications

We study multi-microphone noise reduction systems consisting of a beamformer and a single-channel (SC) noise reduction stage. In particular, we present and analyse a maximum likelihood (ML) method for jointly estimating the target and noise power spectral densities (psd´s) entering the SC filter. We show that the estimators are minimum variance and unbiased, and provide closed-form expressions for their mean-square error (MSE). Furthermore, we show that the MSE of the noise psd estimator is particularly simple: it is independent of target signal characteristics, frequency, and microphone locations. In a hearing aid context, we analyze the performance of the estimators as a function of target angle-of-arrival and frequency. Finally, we demonstrate the advantage of the proposed method in a hearing aid situation with a target speaker in large-crowd noise.