Second order volterrs filter with formulation and variable step-size LMS adaptation

Nonlinear Adaptive Filtering Techniques for system Identification based on Volterra model are widely used for the time-invariant system. This paper investigates a new implementation for time -varying volterra system identification using LMS adaptive algorithm with variable step-size for the linear and nonlinear part of filters. The purpose of this paper is in twofold. Firstly the minimum mean square error (MMSE) is evaluated, Next Time-varying second orders volterra variable step size LMS algorithm based updating equations and simulations are derived and evaluated. Therefore we develop a method to estimate the unknown quantities. Finally a variable step size LMS filtering scheme is utilized to identify and track the time -varying volterra system and present its convergence characteristics and tracking performance using computer simulation on MATLAB. The computer simulation results are presented to the improvement in its MMSE (minimum mean square error), convergence & tracking performance of volterra second order system under the time varying environment.