Enhanced Improved Proportionate Set-Membership Fast NLMS Using the ℓ0 Norm

developed the Improved Proportionate Normalized Least Mean Square algorithm using the 0 norm (IPNLMS-L0) to fully leverage the sparsity of impulse responses in echo cancellation scenarios.This algorithm delivered satisfactory outcomes, surpassing the IPNLMS algorithm, especially when addressing sparse impulse responses.However, its utility was limited by its poor performance in non-stationary or dispersive systems and practical constraints associated with evaluating the exponential expression and aligning the parameter with the impulse response's sparsity.In the initial phase of our research, we aimed to overcome these practical hurdles.To do so, we introduced an approach that employs a sparseness measure grounded in the 1 , 2 , and norms to determine the value of the parameter .We also applied an approximation method based on a Maclaurin expansion of the exponential term.The integration of these two strategies resulted in the development of an efficient gain control matrix.We seamlessly integrated this matrix into the framework of Improved Set-Membership Fast NLMS (ISMFNLMS).This led to a substantial reduction in computational complexity and an enhanced ability to address nonstationary conditions.Our proposed algorithm, named Enhanced Improved Proportionate Set-Membership Fast NLMS using the 0 norm (EIPSMFNLMS-L0), aims to address the challenges of acoustic echo cancellation (AEC) by adeptly handling varying degrees of impulse response sparsity.Simulation results validate that our algorithm, regardless of whether the impulse response is sparse or dispersive, exhibits improved convergence speed, enhanced tracking capability, and achieves lower mean square error (MSE) levels, all while maintaining cost-effective computational performance, outperforming all recent variants of the IPNLMS and ISMFNLMS algorithms.