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Acoustic feedback occurs in hearing aids due to the coupling between the hearing aid loudspeaker and microphone(s). In order to reduce the acoustic feedback, adaptive filters are commonly used to estimate the feedback contribution in the microphone(s). While theoretically allowing for perfect feedback cancellation, in practice the adaptive filter typically converges to a biased optimal solution due to the closed-loop acoustical system of the hearing aid. Previously it has therefore been proposed to suppress the acoustic feedback contribution for an earpiece with multiple integrated microphones and loudspeakers using a fixed null-steering beamformer and hence avoiding a biased adaption. While previous null-steering beamforming approaches aimed at perfect preservation of the incoming signal using its relative transfer function (RTF), in this article we propose to use a soft constraint that allows to trade off between incoming signal preservation and feedback suppression. We formulate the computation of the beamformer coefficients both as a least-squares optimization procedure, aiming to minimize the residual feedback power, and as a min-max optimization procedure, aiming to directly maximize the maximum stable gain of the hearing aid. Experimental evaluations were performed using measured acoustic feedback paths from a custom earpiece with two microphones in the vent and a third microphone in the concha. Results show that the proposed fixed null-steering beamformer using the RTF-based soft constraint provides a reduction of the acoustic feedback by 7-8 dB compared to the previously proposed RTF-based hard constraint while limiting the distortions of the incoming signal in the beamformer output.

Acoustic Feedback Suppression for Multi-Microphone Hearing Devices Using a Soft-Constrained Null-Steering Beamformer