Statistical analysis of the LMS algorithm with a zero-memory nonlinearity after the adaptive filter

This paper presents a statistical analysis of the least mean square (LMS) algorithm when a zero-memory nonlinearity appears at the adaptive filter output. The nonlinearity is modelled by a scaled error function. Deterministic nonlinear recursions are derived for the mean weight and mean square error (MSE) behavior for white Gaussian inputs and slow adaptation. Monte Carlo simulations show excellent agreement with the behavior predicted by the theoretical models. The analytical results show that a small nonlinear effect has a significant impact on the converged MSE.