Compared to monaural hearing aids (HAs), binaural hearing aid systems, in which there is a communication link between the two devices, have improved noise reduction capabilities and the ability to preserve binaural spatial information. However, the limited HA battery lifetime puts constraints on the amount of information that can be shared between the two devices. In other words, the rate of transmission between the devices is an important constraint that needs to be considered, while preserving the spatial information. In this article, a linearly constrained noise reduction problem is proposed, which jointly finds the optimal rate allocation and the optimal estimation (beamforming) weights across all sensors and frequencies, while preserving the binaural spatial cues of point sources. The proposed method considers a rate constraint together with linear constraints to preserve the binaural spatial cues of point sources. Minimizing the mean square error on the estimated target speech at the left and the right side beamformers, the optimal weights are found to be rate-constrained linearly constrained minimum variance (LCMV) filters, and the optimal rates are found to be the solutions to a set of reverse water filling problems. The performance of the proposed method is evaluated using the averaged binaural signal-to-noise ratio (SNR), the interaural level difference (ILD) error and the interaural time difference (ITD) error. The results show that the proposed method outperforms spatially correct noise reduction approaches that use naive/random rate allocation strategies.

Wireless acoustic sensor networks (WASNs) can be used for centralized multi-microphone noise reduction, where the processing is done in a fusion center (FC). To perform the noise reduction, the data needs to be transmitted to the FC. Considering the limited battery life of the devices in a WASN, the total data rate at which the FC can communicate with the different network devices should be constrained. In this article, we propose a rate-constrained multi-microphone noise reduction algorithm, which jointly finds the best rate allocation and estimation weights for the microphones across all frequencies. The optimal linear estimators are found to be the quantized Wiener filters, and the rates are the solutions to a filter-dependent reverse water-filling problem. The performance of the proposed framework is evaluated using simulations in terms of mean square error and predicted speech intelligibility. The results show that the proposed method is very close in performance to that of the existing optimal method based on discrete optimization. However, the proposed approach can do this at a much lower complexity, while the existing optimal reference method needs a non-tractable exhaustive search to find the best rate allocation across microphones.

Binaural hearing aids (HAs) can potentially perform advanced noise reduction algorithms, leading to an improvement over monaural/bilateral HAs. Due to the limited transmission capacities between the HAs and given knowledge of the complete joint noisy signal statistics, the optimal rate-constrained beamforming strategy is known from the literature. However, as these joint statistics are unknown in practice, sub-optimal strategies have been presented. In this paper, we present a unified framework to study the performance of these existing optimal and sub-optimal rate-constrained beamforming methods for binaural HAs. Moreover, we propose to use an asymmetric sequential coding scheme to estimate the joint statistics between the microphones in the two HAs. We show that under certain assumptions, this leads to sub-optimal performance in one HA but allows to obtain the truly optimal performance in the second HA. Based on the mean square error distortion measure, we evaluate the performance improvement between monaural beamforming (no communication) and the proposed scheme, as well as the optimal and the existing sub-optimal strategies in terms of the information bit-rate. The results show that the proposed method outperforms existing practical approaches in most scenarios, especially at middle rates and high rates, without having the prior knowledge of the joint statistics.