Steady-State Performance Analysis of the Arctangent LMS Algorithm With Gaussian Input

The adaptive filtering algorithms based on the arctangent cost function framework have shown robustness against impulsive noise. In this brief, the standard least mean square (LMS) algorithm under this framework is concentrated on, which is called the arctangent LMS (ATLMS) algorithm. The steady-state excess mean square error (EMSE) and mean square deviation (MSD) of the ATLMS algorithm are analyzed using the energy conservation relation. In stationary environment, both Gaussian and non-Gaussian situations are discussed. The closed-form expressions of the steady-state EMSE and MSD are obtained using Taylor’s expansion. In non-stationary environment, a first-order random-walk model is used for modeling the time-varying optimal weight. Theoretical steady-state performance and the optimal step size are derived. Simulation results under different noise environments verify the validity of our theoretical findings.