Enhanced Noise Cancellation: A Variable Step Size Normalized Least Mean Square Approach

Noise cancellation remains a significant challenge in signal processing, particularly when addressing non-stationary and time-varying noise sources. Traditional approaches, such as the Normalized Least Mean Square (NLMS) algorithm, are often limited by the fixed step size parameter, which dictates the trade-off between convergence rate and system robustness. In this study, an innovative Variable Step Size NLMS (VSS-NLMS) algorithm is introduced, designed to dynamically adjust the step size parameter, thereby optimizing performance criteria including precision, robustness, convergence rate, and tracking ability. Employing system identification techniques within an adaptive filtering framework, this research advances the NLMS algorithm by incorporating a variable step size parameter that adapts in real-time to the noise environment. The proposed VSS-NLMS algorithm is evaluated through extensive simulations, demonstrating a significant enhancement in the balance between Mean Square Error (MSE) reduction and convergence rate over both the conventional NLMS and Recursive Least Squares (RLS) algorithms, whilst maintaining computational simplicity. In the context of adaptive filters, the VSS-NLSM algorithm represents a substantial improvement for noise cancellation applications, particularly in scenarios characterized by variable noise dynamics. The results presented herein confirm that the VSS-NLMS algorithm not only achieves a superior trade-off between accuracy/robustness and convergence rate/tracking but also sets a new benchmark for adaptive noise cancellation strategies in complex acoustic environments.