Proportionate NLMS with Variable Step-Size for Adaptive Feedback Cancellation in Hearing Aids

It is known that the Proportionate Normalized Least-Mean-Squares (PNLMS) algorithm is an efficient solution applicable to both Adaptive Echo Cancellation (AEC) and Adaptive Feedback Cancellation (AFC) systems. It enhances the performance by individually assigning step sizes to each filter coefficient, resulting in superior initial convergence and tracking rates compared to the NLMS. The Improved PNLMS (IPNLMS) surpasses the PNLMS by incorporating a novel rule that optimally leverages the predicted feedback channel's characteristics to compute tap-specific step sizes. In this paper, we introduce an enhancement strategy aimed at improving the performance of the IPNLMS algorithm on the prediction error method (PEM) in the context of Adaptive Feedback Cancellation for hearing aids. This enhancement involves the implementation of variable step-size control. We introduce the Improved Practical Variable Step-Size (IPVSS) built upon the Practical Variable Step-Size (PVSS) approach that incorporates upper and lower fixed step sizes to define a bounded range for step-size adjustments. We evaluate the proposed approach using incoming signals containing both speech and music. We also employ real-world feedback channel measurements. Our simulation outcomes clearly indicate that our method delivers an important enhancement in performance when compared to the PEM-IPNLMS approach, irrespective of whether we utilize the upper or lower step-size bounds. Furthermore, our method outperforms the PEM approach when employing the NLMS and IPVSS while preserving a good signal quality.