Abstract
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.
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