A Convex Approximation of the Relaxed Binaural Beamfomring Optimization Problem

The recently proposed relaxed binaural beamforming (RBB) optimization problem provides a flexible tradeoff between noise suppression and binaural-cue preservation of the sound sources in the acoustic scene. It minimizes the output noise power, under the constraints, which guarantee that the target remains unchanged after processing and the binaural-cue distortions of the acoustic sources will be less than a user-defined threshold. However, the RBB problem is a computationally demanding non convex optimization problem. The only existing suboptimal method which approximately solves the RBB is a successive convex optimization (SCO) method which, typically, requires to solve multiple convex optimization problems per frequency bin, in order to converge. Convergence is achieved when all constraints of the RBB optimization problem are satisfied. In this paper, we propose a semidefinite convex relaxation (SDCR) of the RBB optimization problem. The proposed suboptimal SDCR method solves a single convex optimization problem per frequency bin, resulting in a much lower computational complexity than the SCO method. Unlike the SCO method, the SDCR method does not guarantee user-controlled upper-bounded binaural-cue distortions. To tackle this problem, we also propose a suboptimal hybrid method that combines the SDCR and SCO methods. Instrumental measures combined with a listening test show that the SDCR and hybrid methods achieve significantly lower computational complexity than the SCO method, and in most cases better tradeoff between predicted intelligibility and binaural-cue preservation than the SCO method.Circuits and System

Robust Joint Estimation of Multimicrophone Signal Model Parameters

One of the biggest challenges in multimicrophone applications is the estimation of the parameters of the signal model, such as the power spectral densities (PSDs) of the sources, the early (relative) acoustic transfer functions of the sources with respect to the microphones, the PSD of late reverberation, and the PSDs of microphone-self noise. Typically, existing methods estimate subsets of the aforementioned parameters and assume some of the other parameters to be known a priori. This may result in inconsistencies and inaccurately estimated parameters and potential performance degradation in the applications using these estimated parameters. So far, there is no method to jointly estimate all the aforementioned parameters. In this paper, we propose a robust method for jointly estimating all the aforementioned parameters using confirmatory factor analysis. The estimation accuracy of the signal-model parameters thus obtained outperforms existing methods in most cases. We experimentally show significant performance gains in several multimicrophone applications over state-of-the-art methods.Accepted author manuscriptCircuits and System

Relaxed Binaural LCMV Beamforming

In this paper, we propose a new binaural beamforming technique, which can be seen as a relaxation of the linearly constrained minimum variance (LCMV) framework. The proposed method can achieve simultaneous noise reduction and exact binaural cue preservation of the target source, similar to the binaural minimum variance distortionless response (BMVDR) method. However, unlike BMVDR, the proposed method is also able to preserve the binaural cues of multiple interferers to a certain predefined accuracy. Specifically, it is able to control the trade-off between noise reduction and binaural cue preservation of the interferers by using a separate trade-off parameter per-interferer. Moreover, we provide a robust way of selecting these trade-off parameters in such a way that the preservation accuracy for the binaural cues of the interferers is always better than the corresponding ones of the BMVDR. The relaxation of the constraints in the proposed method achieves approximate binaural cue preservation of more interferers than other previously presented LCMV-based binaural beamforming methods that use strict equality constraints.Accepted Author ManuscriptCircuits and System

TDOA-based Self-Calibration of Dual-Microphone Arrays

We consider the problem of determining the relative position of dual-microphone sub-arrays. The proposed solution is mainly developed for binaural hearing aid systems (HASs), where each hearing aid (HA) in the HAS has two microphones at a known distance from each other. However, the proposed algorithm can effortlessly be applied to acoustic sensor network applications. In contrast to most state-of-the-art calibration algorithms, which model the calibration problem as a non-linear problem resulting in high computational complexity, we model the calibration problem as a simple linear system of equations by utilizing a far-field assumption. The proposed model is based on target signals time-difference-of-arrivals (TDOAs) between the HAS microphones. Working with TDOAs avoids clock synchronization between sound sources and microphones, and target signals need not be known beforehand. To solve the calibration problem, we propose a least squares estimator which is simple and does not need any probabilistic assumptions about the observed signals.Circuits and System

DOA Estimation of Audio Sources in Reverberant Environments

Reverberation is well-known to have a detrimental impact on many localization methods for audio sources. We address this problem by imposing a model for the early reflections as well as a model for the audio source itself. Using these models, we propose two iterative localization methods that estimate the direction-of-arrival (DOA) of both the direct path of the audio source and the early reflections. In these methods, the contribution of the early reflections is essentially subtracted from the signal observations before localization of the direct path component, which may reduce the estimation bias. Our simulation results show that we can estimate the DOA of the desired signal more accurately with this procedure compared to state-of-the-art estimator in both synthetic and real data experiments with reverberation.Accepted Author ManuscriptCircuits and System

Spatially Correct Rate-Constrained Noise Reduction For Binaural Hearing Aids in Wireless Acoustic Sensor Networks

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.Circuits and System

Rate-constrained noise reduction in wireless acoustic sensor networks

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.Accepted author manuscriptCircuits and System

On the Impact of Quantization on Binaural MVDR Beamforming

Multi-microphone noise reduction algorithms in binaural hearing aids which cooperate through a wireless link have the potential to become of great importance in future hearing aid systems. However, limited transmission capacity of such devices necessitates the data compression of signals transmitted from one hearing aid to the contralateral one. In this paper we study the impact of quantization as a data compression scheme on the performance of the multi-microphone noise reduction algorithms. Using the binaural minimum variance distortionless response (BMVDR) beamformer as an illustration, we propose a quantization aware beamforming scheme which uses a modified cross power spectral density (CPSD) of the system noise including the quantization noise (QN). Moreover, several assumptions on the QN are investigated in the proposed method. Based on the output SNR, we compare different variations of the proposed method with the conventional BMVDR beamformer. The results confirm the improved performance of the proposed method.Circuits and System