Steady-state performance analysis of the LMS adaptive time-varying second order Volterra filter

In this paper, the steady-state performance of the Least Mean Square (LMS) adaptive second order Volterra filter, with constant step-sizeμ, in a time-varying setting, is analysed. The quantitative evaluation of the steady-state Excess Mean Square Error (EMSE), where the contribution of the gradient misadjustment and the tracking error are well characterized, is established. The optimum step-size for time-varying second order Volterra filter is then given. Thus, we can study the correlation between the Excess MSE and the optimum step-size in one hand and the parameters of the time-varying nonlinear system, in the other hand. Furthermore, the steady-state behavior predicted by the analysis is in good agreement with the experimental results. The adaptive filter was used in a second order Volterra system identification in a non stationary environment.