To estimate the direction of arrival (DOA) of multiple speakers with methods that use prototype transfer functions, frequency-dependent spatial spectra (SPS) are usually constructed. To make the DOA estimation robust, SPS from different frequencies can be combined. According to how the SPS are combined, frequency fusion mechanisms are categorized into narrowband, broadband, or speaker-grouped, where the latter mechanism requires a speaker-wise grouping of frequencies. For a binaural hearing aid setup, in this paper we propose an interaural time difference (ITD)-based speaker-grouped frequency fusion mechanism. By exploiting the DOA dependence of ITDs, frequencies can be grouped according to a common ITD and be used for DOA estimation of the respective speaker. We apply the proposed ITD-based speaker-grouped frequency fusion mechanism for different DOA estimation methods, namely the multiple signal classification, steered response power and a recently published method based on relative transfer function (RTF) vectors. In our experiments, we compare DOA estimation with different fusion mechanisms. For all considered DOA estimation methods, the proposed ITD-based speaker-grouped frequency fusion mechanism results in a higher DOA estimation accuracy compared with the narrowband and broadband fusion mechanisms.

The objective of binaural multi-microphone speech enhancement algorithms can be viewed as a multi-criteria design problem as there are several requirements to be met. The objective is not only to extract the target speaker without distortion, but also to suppress interfering sources (e.g., competing speakers) and ambient background noise, while preserving the auditory impression of the complete acoustic scene. Such a multi-objective problem (MOP) can be solved using a Pareto frontier, which provides a useful trade-off between the different criteria. In this paper, we propose a unified Pareto optimization framework, which is achieved by defining a generalized mean squared error (MSE) cost function, derived from a MOP. The solution to the multi-criteria problem is grounded on a solid mathematical foundation. The MSE cost function consists of a weighted sum of speech distortion (SD), partial interference reduction (IR), and partial noise reduction (NR) terms with scaling parameters that control the amount of IR and NR. The filter minimizing this generalized cost function, denoted Pareto optimal binaural multichannel Wiener filter (Pareto-BMWF), constitutes a generalization of various binaural MWF-based and binaural MVDR-based beamformers. This solution is optimal for any set of parameters. The improved speech enhancement capabilities are experimentally demonstrated using real-signal recordings when estimation errors are present and the binaural cue preservation capabilities are analyzed.

In this contribution, a novel maximum likelihood (ML) based direction of arrival (DOA) estimator for concurrent speakers in a noisy reverberant environment is presented. The DOA estimation task is formulated in the short-time Fourier transform (STFT) in two stages. In the first stage, a single local DOA per time-frequency (TF) bin is selected, using the W-disjoint orthogonality property of the speech signal in the STFT domain. The local DOA is obtained as the maximum of the narrow-band likelihood localization spectrum at each TF bin. In addition, for each local DOA, a confidence measure is calculated, determining the confidence in the local estimate. In the second stage, the wide-band localization spectrum is calculated using a weighted histogram of the local DOA estimates with the confidence measures as weights. Finally, the wide-band DOA estimation is obtained by selecting the peaks in the wide-band localization spectrum. The results of our experimental study demonstrate the benefit of the proposed algorithm in a reverberant environment as compared with the classical steered response power phase transform (SRP-PHAT) algorithm.

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).

Beamforming algorithms in binaural hearing aids are crucial to improve speech understanding in background noise for hearing impaired persons. In this study, we compare and evaluate the performance of two recently proposed minimum variance (MV) beamforming approaches for binaural hearing aids. The binaural linearly constrained MV (BLCMV) beamformer applies linear constraints to maintain the target source and mitigate the interfering sources, taking into account the reverberant nature of sound propagation. The inequality constrained MV (ICMV) beamformer applies inequality constraints to maintain the target source and mitigate the interfering sources, utilizing estimates of the direction of arrivals (DOAs) of the target and interfering sources. The similarities and differences between these two approaches is discussed and the performance of both algorithms is evaluated using simulated data and using real-world recordings, particularly focusing on the robustness to estimation errors of the relative transfer functions (RTFs) and DOAs. The BLCMV achieves a good performance if the RTFs are accurately estimated while the ICMV shows a good robustness to DOA estimation errors.

Recently, an extension of the binaural multichannel Wiener filter (BMWF), referred to as BMWF-IRo, was presented in which an interference rejection constraint was added to the BMWF cost function. Although the BMWF-IRo aims to entirely suppress the interfering source, residual interfering sources (as well as unconstrained noise sources) are undesirably perceived as impinging the array from the desired source direction. In this paper, we propose two extensions of the BMWF-IRo that address this issue by preserving the spatial impression of the interfering source. In the first extension, the binaural cues of the interfering source are preserved, while those of the desired source may be slightly distorted. In the second extension, the binaural cues of both the desired and interfering sources are preserved. Simulation results show that the noise reduction performance of both proposed extensions is comparable to the BMWF-, IRo.

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 an interfering source, e.g., competing speaker, 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 source. To this end, in this paper we propose an extension of the binaural MWF, i.e. the binaural MWF with RTF preservation (MWF-RTF) aiming to preserve the RTF of the interfering source. Analytical expressions for the performance of the binaural MWF and the MWF-RTF in terms of noise reduction and binaural cue preservation are derived, using which their performance is thoroughly compared. Simulation results using binaural behind-the-ear impulse responses measured in a reverberant environment validate the derived analytical expressions, showing that the MWF-RTF yields a better performance than the binaural MWF in terms of the signal-to-interference ratio and binaural cue preservation of the interfering source, while the overall noise reduction performance is slightly degraded.

The recently proposed binaural linearly constrained minimum variance (BLCMV) beamformer is an extension of the well-known binaural minimum variance distortionless response (MVDR) beamformer, imposing constraints for both the desired and the interfering sources. Besides its capabilities to reduce interference and noise, it also enables to preserve the binaural cues of both the desired and interfering sources, hence making it particularly suitable for binaural hearing aid applications. In this paper, a theoretical analysis of the BLCMV beamformer is presented. In order to gain insights into the performance of the BLCMV beamformer, several decompositions are introduced that reveal its capabilities in terms of interference and noise reduction, while controlling the binaural cues of the desired and the interfering sources. When setting the parameters of the BLCMV beamformer, various considerations need to be taken into account, e.g. based on the amount of interference and noise reduction and the presence of estimation errors of the required relative transfer functions (RTFs). Analytical expressions for the performance of the BLCMV beamformer in terms of noise reduction, interference reduction, and cue preservation are derived. Comprehensive simulation experiments, using measured acoustic transfer functions as well as real recordings on binaural hearing aids, demonstrate the capabilities of the BLCMV beamformer in various noise environments.

In this paper we consider an acoustic scenario with a desired source and a directional interference picked up by hearing devices in a noisy and reverberant environment. We present an extension of the binaural multichannel Wiener filter (BMWF), by adding an interference rejection constraint to its cost function, in order to combine the advantages of spatial and spectral filtering while mitigating directional interferences. We prove that this algorithm can be decomposed into the binaural linearly constrained minimum variance (BLCMV) algorithm followed by a single channel Wiener post-filter. The proposed algorithm yields improved interference rejection capabilities, as compared with the BMWF. Moreover, by utilizing the spectral information on the sources, it is demonstrating better SNR measures, as compared with the BLCMV.

The objective of binaural noise reduction algorithms is not only to selectively extract the desired speaker and to suppress interfering sources (e.g., competing speakers) and ambient background noise, but also to preserve the auditory impression of the complete acoustic scene. For directional sources this can be achieved by preserving the relative transfer function (RTF) which is defined as the ratio of the acoustical transfer functions relating the source and the two ears and corresponds to the binaural cues. In this paper, we theoretically analyze the performance of three algorithms that are based on the binaural minimum variance distortionless response (BMVDR) beamformer, and hence, process the desired source without distortion. The BMVDR beamformer preserves the binaural cues of the desired source but distorts the binaural cues of the interfering source. By adding an interference reduction (IR) constraint, the recently proposed BMVDR-IR beamformer is able to preserve the binaural cues of both the desired source and the interfering source. We further propose a novel algorithm for preserving the binaural cues of both the desired source and the interfering source by adding a constraint preserving the RTF of the interfering source, which will be referred to as the BMVDR-RTF beamformer. We analytically evaluate the performance in terms of binaural signal-to-interference-and-noise ratio (SINR), signal-to-interference ratio (SIR), and signal-to-noise ratio (SNR) of the three considered beamformers. It can be shown that the BMVDR-RTF beamformer outperforms the BMVDR-IR beamformer in terms of SINR and outperforms the BMVDR beamformer in terms of SIR. Among all beamformers which are distortionless with respect to the desired source and preserve the binaural cues of the interfering source, the newly proposed BMVDR-RTF beamformer is optimal in terms of SINR. Simulations using acoustic transfer functions measured on a binaural hearing aid validate our theoretical results.

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.