Besides reducing undesired noise sources and limiting speech distortion, another important objective of a binaural noise reduction algorithm is the preservation of the binaural cues of all sound sources in the acoustic scene. In this paper, we consider the binaural minimum variance distortionless response beamformer with partial noise estimation (BMVDR-N), which allows to trade off between noise reduction performance and binaural cue preservation of the noise component by mixing the output signals of the BMVDR beamformer with the noisy reference microphone signals. For a directional noise source, it has been shown that incorporating an external microphone in addition to the head-mounted microphones enables both the noise reduction performance as well as the interaural time and level difference cues of the noise component to be improved in the output signals. In this paper, we consider an arbitrary noise field and analytically show that incorporating an external microphone in the BMVDR-N beamformer enables 1) a larger output signal-to-noise ratio (SNR) for the same mixing parameter, 2) the same output SNR for a larger mixing parameter, and 3) the same desired output magnitude squared coherence (MSC) of the noise component for a smaller mixing parameter to be obtained. The derived analytical expressions are firstly validated using simulated anechoic acoustic transfer functions, where the listener's head is modelled as a rigid sphere. Experimental results using recorded signals for a binaural hearing device setup in a reverberant environment also show that in a realistic scenario incorporating an external microphone in the BMVDR-N beamformer significantly improves the output SNR and reduces the mixing parameter that is required to obtain a desired output MSC of the noise component compared to using only the head-mounted microphones.

Besides reducing undesired sources, i.e., interfering sources and background noise, another important objective of a binaural beamforming algorithm is to preserve the spatial impression of the acoustic scene, which can be achieved by preserving the binaural cues of all sound sources. While the binaural minimum variance distortionless response (BMVDR) beamformer provides a good noise reduction performance and preserves the binaural cues of the desired source, it does not allow to control the reduction of the interfering sources and distorts the binaural cues of the interfering sources and the background noise. Hence, several extensions have been proposed. First, the binaural linearly constrained minimum variance (BLCMV) beamformer uses additional constraints, enabling to control the reduction of the interfering sources while preserving their binaural cues. Second, the BMVDR with partial noise estimation (BMVDR-N) mixes the output signals of the BMVDR with the noisy reference microphone signals, enabling to control the binaural cues of the background noise. Aiming at merging the advantages of both extensions, in this paper we propose the BLCMV with partial noise estimation (BLCMV-N). We show that the output signals of the BLCMV-N can be interpreted as a mixture between the noisy reference microphone signals and the output signals of a BLCMV using an adjusted interference scaling parameter. We provide a theoretical comparison between the BMVDR, the BLCMV, the BMVDR-N and the proposed BLCMV-N in terms of noise and interference reduction performance and binaural cue preservation. Experimental results using recorded signals as well as the results of a perceptual listening test show that the BLCMV-N is able to preserve the binaural cues of an interfering source (like the BLCMV), while enabling to trade off between noise reduction performance and binaural cue preservation of the background noise (like the BMVDR-N).

A well-known binaural noise reduction algorithm is the binaural minimum variance distortionless response beamformer, which can be steered using the relative transfer function (RTF) vectors of the desired source. In this paper, we consider the recently proposed spatial coherence (SC) method to estimate the RTF vectors, requiring an additional external microphone that is spatially separated from the head-mounted microphones. Although the SC method provides a biased estimate of the RTF between the head-mounted microphones and the external microphone, we show that this bias is real-valued and only depends on the SNR in the external microphone. We propose to use the SC method to estimate the extended RTF vectors that also incorporate the external microphone, enabling to filter the external microphone signal in conjunction with the head-mounted microphones. Evaluation results using recorded signals of a moving speaker in diffuse noise show that the SC method yields a slightly better performance than the widely used covariance whitening method at a much lower computational complexity.