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.