Joint Maximum Likelihood Estimation of Power Spectral Densities and Relative Acoustic Transfer Functions for Acoustic Beamforming

Acoustic beamforming is crucial for many applications where ex-traction of a target signal from a noisy environment is required. In order to implement practical beamformers, e.g. the multichannel Wiener filter (MWF), estimation of the target and noise power spectral densities (PSDs), and the relative acoustic transfer functions (RATFs) is essential. Several methods, e.g. the so-called covariance whitening (CW) approach, have been proposed for estimating these parameters. However, it seems largely unknown that the CW approach in fact leads to maximum likelihood (ML) estimates of the RATFs. We use historical results to derive joint ML estimates (MLEs) of the RATFs and PSDs in the context of acoustic beam-forming. In addition, based on the MLEs, we propose a basic VAD framework using concentrated likelihood ratios. We use the joint MLEs of the PSDs, RATFs, and the proposed VAD to implement beamformers in a hearing aid application, and compare its performance to competing methods. Simulation results show that the pro-posed scheme can outperform competing methods, in particular in realistic situations where highly accurate prior RATF knowledge is not available or at higher signal-to-noise ratios.