  Besides suppressing all undesired sound sources, an important objective of a
binaural noise reduction algorithm for hearing devices is the preservation of
the binaural cues, aiming at preserving the spatial perception of the acoustic
scene. 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) vector of the desired source, relating the
acoustic transfer functions between the desired source and all microphones to a
reference microphone. In this paper, we propose a computationally efficient
method to estimate the RTF vector in a diffuse noise field, requiring an
additional microphone that is spatially separated from the head-mounted
microphones. Assuming that the spatial coherence between the noise components
in the head-mounted microphone signals and the additional microphone signal is
zero, we show that an unbiased estimate of the RTF vector can be obtained.
Based on real-world recordings, experimental results for several reverberation
times show that the proposed RTF estimator outperforms the widely used RTF
estimator based on covariance whitening and a simple biased RTF estimator in
terms of noise reduction and binaural cue preservation performance.
