Sparsity promoting LMS for adaptive feedback cancellation

In hearing aids (HAs), the acoustic coupling between the microphone and the receiver results in the system becoming unstable under certain conditions and causes artifacts commonly referred to as whistling or howling. The least mean square (LMS) class of algorithms is commonly used to mitigate this by providing adaptive feedback cancellation (AFC). The speech quality after AFC and the amount of added stable gain (ASG) with AFC are used to assess these algorithms. In this paper, we introduce a variant of the LMS that promotes sparsity in estimating the acoustic feedback path. By using the l_p norm as a diversity measure, the approach does not enforce, but takes advantage of sparsity when it exists. The performance in terms of speech quality, misalignment, and ASG of the proposed algorithm is compared with other proportionate-type LMS algorithms which also leverage sparsity in the feedback path. We demonstrate faster convergence compared with those algorithms, quality improvement of about 0.25 (on a 0-1 objective scale of the hearing-aid speech quality index (HASQI)), and about 5 dB ASG improvement compared with the normalized LMS (NLMS).