Theoretical Analysis of Linearly Constrained Multi-Channel Wiener Filtering Algorithms for Combined Noise Reduction and Binaural Cue Preservation in Binaural Hearing Aids

Besides noise reduction, an important objective of binaural speech enhancement algorithms is the preservation of the binaural cues of all sound sources. For the desired speech source and the interfering sources, e.g., competing speakers, this can be achieved by preserving their relative transfer functions (RTFs). It has been shown that the binaural multi-channel Wiener filter (MWF) preserves the RTF of the desired speech source, but typically distorts the RTF of the interfering sources. To this end, in this paper we propose two extensions of the binaural MWF, i.e., the binaural MWF with RTF preservation (MWF-RTF) aiming to preserve the RTF of the interfering source and the binaural MWF with interference rejection (MWF-IR) aiming to completely suppress the interfering source. Analytical expressions for the performance of the binaural MWF, MWF-RTF and MWF-IR in terms of noise reduction, speech distortion and binaural cue preservation are derived, showing that the proposed extensions yield a better performance in terms of the signal-to-interference ratio and preservation of the binaural cues of the directional interference, while the overall noise reduction performance is degraded compared to the binaural MWF. Simulation results using binaural behind-the-ear impulse responses measured in a reverberant environment validate the derived analytical expressions for the theoretically achievable performance of the binaural MWF, MWF-RTF, and MWF-IR, showing that the performance highly depends on the position of the interfering source and the number of microphones. Furthermore, the simulation results show that the MWF-RTF yields a very similar overall noise reduction performance as the binaural MWF, while preserving the binaural cues of both the speech and the interfering source.