LMS/LMF and RLS Volterra system identification based on nonlinear Wiener model

This paper presents the LMS/LMF and RLS adaptive filtering algorithms based on the nonlinear Wiener model for Volterra system identification. This Wiener model contains three sections: a single-input multi-output linear with memory system, a multi-input, multi-output nonlinear no-memory system and a multi-input, single-output amplification and summary system. For Gaussian white input signal, because of the orthogonality of the Q-polynomial, the autocorrelation matrix can be diagonalizable which allows us to apply LMS algorithm without any difficulty. This result can also be extended easily to LMF algorithm family. If we apply RLS, the faster convergence speed can be expected. In certain circumstances, the nonlinear Wiener model allows us to identify a complicated Volterra system with only very few terms but still keep the linear filtering properties which means that we can achieve good performance without sacrificing the computation complexity