An LMS adaptive second-order Volterra filter with a zeroth-order term: steady-state performance analysis in a time-varying environment

This article studies the steady-state performance of the least mean square (LMS) adaptive second-order Volterra filter (SOVF) with a zeroth-order term for Gaussian inputs. The mean-square-error (MSE) criterion is evaluated first. Then, SOV LMS algorithm-based updating equations are derived. Next, the steady-state performance of the recursions is analyzed for a random walk model for the unknown system parameters, and the steady-state excess MSE is evaluated. Finally, the theoretical performance predictions are shown to be in good agreement with simulation results, especially for small step sizes.