Superdirective Beamforming Robust Against Microphone Mismatch

Fixed superdirective beamformers using small-sized microphone arrays are known to be highly sensitive to errors in the assumed microphone array characteristics (gain, phase, position). This paper discusses the design of robust superdirective beamformers by taking into account the statistics of the microphone characteristics. Different design procedures are considered: applying a white noise gain constraint, trading off the mean noise and distortion energy, minimizing the mean deviation from the desired superdirective directivity pattern, and maximizing the mean or the worst case directivity factor. When computational complexity is not an issue, maximizing the mean or the worst case directivity factor is the preferred design procedure. In addition, it is shown how to determine a suitable parameter range for the other design procedures such that both a high directivity and a high level of robustness are obtained     

GSVD-based optimal filtering for single and multimicrophone speech enhancement

A generalized singular value decomposition (GSVD) based algorithm is proposed for enhancing multimicrophone speech signals degraded by additive colored noise. This GSVD-based multimicrophone algorithm can be considered to be an extension of the single-microphone signal subspace algorithms for enhancing noisy speech signals and amounts to a specific optimal filtering problem when the desired response signal cannot be observed. The optimal filter can be written as a function of the generalized singular vectors and singular values of a speech and noise data matrix. A number of symmetry properties are derived for the single-microphone and multimicrophone optimal filter, which are valid for the white noise case as well as for the colored noise case. In addition, the averaging step of some single-microphone signal subspace algorithms is examined, leading to the conclusion that this averaging operation is unnecessary and even suboptimal. For simple situations, where we consider localized sources and no multipath propagation, the GSVD-based optimal filtering technique exhibits the spatial directivity pattern of a beamformer. When comparing the noise reduction performance for realistic situations, simulations show that the GSVD-based optimal filtering technique has a better performance than standard fixed and adaptive beamforming techniques for all reverberation times and that it is more robust to deviations from the nominal situation, as, e.g., encountered in uncalibrated microphone arrays.     

Reduced-Bandwidth and Distributed MWF-Based Noise Reduction Algorithms for Binaural Hearing Aids

In a binaural hearing aid system, output signals need to be generated for the left and the right ear. Using the binaural multichannel Wiener filter (MWF), which exploits all microphone signals from both hearing aids, a significant reduction of background noise can be achieved. However, due to power and bandwidth limitations of the binaural link, it is typically not possible to transmit all microphone signals between the hearing aids. To limit the amount of transmitted information, this paper presents reduced-bandwidth MWF-based noise reduction algorithms, where a filtered combination of the contralateral microphone signals is transmitted. A first scheme uses a signal-independent beamformer, whereas a second scheme uses the output of a monaural MWF on the contralateral microphone signals and a third scheme involves an iterative distributed MWF (DB-MWF) procedure. It is shown that in the case of a rank-1 speech correlation matrix, corresponding to a single speech source, the DB-MWF procedure converges to the binaural MWF solution. Experimental results compare the noise reduction performance of the reduced-bandwidth algorithms with respect to the benchmark binaural MWF. It is shown that the best performance of the reduced-bandwidth algorithms is obtained by the DB-MWF procedure and that the performance of the DB-MWF procedure approaches quite well the optimal performance of the binaural MWF.     

Design of broadband beamformers robust against gain and phase errors in the microphone array characteristics

Fixed broadband beamformers using small-size microphone arrays are known to be highly sensitive to errors in the microphone array characteristics. The paper describes two design procedures for designing broadband beamformers with an arbitrary spatial directivity pattern, which are robust against gain and phase errors in the microphone array characteristics. The first design procedure optimizes the mean performance of the broadband beamformer and requires knowledge of the gain and the phase probability density functions, whereas the second design procedure optimizes the worst-case performance by using a minimax criterion. Simulations with a small-size microphone array show the performance improvement that can be obtained by using a robust broadband beamformer design procedure.