Stochastic model of the LMS volterra filter

This paper presents a statistical model for the LMS-Volterra filter, which is valid for truncated Volterra filters of any order with stationary input signals. Model expressions for the mean-weight behavior and learning curve are derived by considering a slow adaptation condition. The proposed model brings out and discusses the particular structure of the Volterra input autocorrelation matrix, focusing on its impact on the algorithm behavior. Simulation results illustrating the accuracy of the proposed analytical model are presented.