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Null-steering beamformer for acoustic feedback cancellation in a multi-microphone earpiece optimizing the maximum stable gain

Commonly adaptive filters are used to reduce the acoustic feedback in hearing aids. While theoretically allowing for perfect cancellation of the feedback signal, in practice the adaptive filter solution is typically biased due to the closed-loop hearing aid system. In contrast to conventional behind-the-ear hearing aids, in this paper we consider an earpiece with multiple integrated microphones. For such an earpiece it has previously been proposed to use a fixed beamformer to reduce the acoustic feedback in the microphones which has been designed to minimize a least-squares cost function. In this paper we propose to design the beamformer by minimizing a min-max cost function which directly maximizes the maximum stable gain of the earpiece. Furthermore, we propose a robust extension of the min-max cost function maximizing the worst-case maximum stable gain over a set of acoustic feedback paths. Experimental results using measured acoustic feedback paths show that the feedback cancellation performance of the fixed beamformer can be considerably improved by minimizing the proposed min-max optimization problem, while maintaining a high perceptual quality of the incoming signal.