Improved proportionate affine projection sign algorithms for adaptive feedback cancellation using pre-filters in hearing aids

An open-fitting hearing aid often experiences acoustic feedback, limiting the achievable amplification gain and degrading sound quality. Prediction-error-method-based adaptive feedback cancellation (PEM-AFC) is a widely recognized approach for mitigating the adverse effects of acoustic feedback. Proportionate-type algorithms combined with affine projection sign algorithms, known as PAPSA, along with its variants such as improved PAPSA (IPAPSA), memory IPAPSA (MIPAPSA), and block-sparse MIPAPSA (BS-MIPAPSA), have been successfully applied to network echo cancellation applications. However, using these fast adaptive algorithms for acoustic feedback cancellation remains limited due to the inherent correlation between the incoming and the loudspeaker signals. To address this challenge, we propose integrating these adaptive algorithms with PEM-AFC, resulting in a new class of AFC methods for hearing aids, including PEM-IPAPSA, PEM-MIPAPSA, and PEM-BSMIPAPSA. The proposed AFC methods leverage the pre-filter, the sparse nature of the feedback path, and fast adaptive filtering techniques to enhance convergence rate and tracking ability while maintaining similar steady-state error levels. We provide a detailed derivation of the proposed AFC methods and evaluate their performance using recorded speech as the incoming signal, with abrupt changes in the feedback path. Simulations were conducted in environments with/without background noise and impulsive noise. Simulation results show that the proposed methods are robust against impulsive interference and colored input, achieving higher convergence and tracking rates while maintaining similar steady-state errors compared to state-of-the-art competing methods. Additionally, the proposed methods offer low computational complexity, which is crucial for hearing aids where low power consumption is a significant concern.