Sparsity promoting LMS for adaptive feedback cancellation

Abstract

Abstract-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 lp 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).

On Mitigating Acoustic Feedback in Hearing Aids with Frequency Warping by All-Pass Networks

“…We adopt the AFC framework used in [14] as depicted in Figure 4. The AFC filter W (z, n), placed in parallel with the HA processing G(z, n), is the transfer function of an L-tap adaptive filter w(n) = [w0(n), w1(n), ..., wL−1(n)] T that continuously adjusts its coefficients to capture the time-varying nature of the acoustic feedback path F (z, n).…”

“…The update rule (3) is actually the "modified" LMS using the sum method [28] and has been widely used in AFC works [7,11,12,14]. An advanced AFC algorithm, based on the LMS (3), is the sparsity promoting LMS (SLMS) proposed in [14] which leverages the sparsity of the feedback path impulse response to achieve faster convergence for improvement. The SLMS update rule includes an additional sparsity promoting term S(n) as:…”

“…For the AFC, we used L = 100, µ = 0.005, ρ = 0.985, and δ = 10 −6 for both LMS and SLMS. For the SLMS we used p = 1.5 and c = 10 −6 as suggested in [14]. In all simulations, the AFC filter coefficients were initialized as all zeros.…”

“…For evaluation, we compare the feedback-compensated signal e(n) with the clean signal x(n), using the hearing-aid speech quality index (HASQI) [32] which has been adopted in prior AFC works [14,10,33]. The HASQI score ranges from 0 to 1, where a higher value indicates better quality.…”

“…Adaptive feedback cancellation (AFC) has been the work horse for breaking NSC to avoid instabilities in many audio applications [6], including HAs [7,8,9,10]. Typically, the AFC deploys the least mean square (LMS) based approaches to mitigate the magnitude condition in NSC [11,12,13,14]. On the other hand, frequency shifting (FS) [15,16,17] and other ad hoc methods [18,19,20] mainly deal with the phase condition.…”