Null-Steering Beamformer-Based Feedback Cancellation for Multi-Microphone Hearing Aids With Incoming Signal Preservation

In hearing aids, acoustic feedback occurs 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 converges to an optimal solution that is typically biased due to the closed-loop acoustical system of the hearing aid. In order to avoid the adaptation to a biased optimal solution, in this paper we propose to use a fixed beamformer to cancel the acoustic feedback contribution for an earpiece with multiple integrated microphones and loudspeakers. By steering a spatial null in the direction of the hearing aid loudspeaker, we show that theoretically perfect feedback cancellation can be achieved. While previous null-steering beamforming approaches did not control for distortions of the incoming signal, in this paper we propose to incorporate a constraint based on the relative transfer function (RTF) of the incoming signal, aiming to perfectly preserve this signal. 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 results using measured acoustic feedback paths from a custom earpiece with two microphones in the vent and a third microphone in the concha show that the proposed fixed null-steering beamformer using the RTF-based constraint provides a reduction of the acoustic feedback and substantially increases the added stable gain while preserving the incoming signal. This can even be achieved for unknown acoustic feedback paths and incoming signal directions.