An improved variable step size LMS adaptive filtering algorithm based on hyperbolic sine function and its application

This paper presents an enhanced variable step-size LMS (VSS-LMS) algorithm using a hyperbolic tangent function to address the poor performance of traditional VSS-LMS algorithms in non-Gaussian environments. The conventional VSS-LMS struggles with adaptability and convergence speed under non-Gaussian noise. To overcome this, a parameter-free VSS-LMS algorithm based on the hyperbolic tangent function is proposed. This new algorithm introduces a nonlinear step-size error model with five adaptive coefficients ($\beta,\text k,\text b,\text a, \text m$). It analyzes convergence and algorithmic complexity and compares performance with traditional LMS, VSS-LMS, and an improved VSS-LMS under various non-Gaussian noise conditions. Simulation results demonstrate that the proposed algorithm significantly improves convergence speed and steady-state characteristics, achieving near-theoretical SNR performance.