Reduced Complexity Volterra Models for Nonlinear System Identification

A broad class of nonlinear systems and filters can be modeled by the Volterra series representation. However, its practical use in nonlinear system identification is sometimes limited due to the large number of parameters associated with the Volterra filter’s structure. The parametric complexity also complicates design procedures based upon such a model. This limitation for system identification is addressed in this paper using a fixed pole expansion technique (FPET) within the Volterra model structure. The FPET approach employs orthonormal basis functions derived from fixed (real or complex) pole locations to expand the Volterra kernels and reduce the number of estimated parameters. That the performance of FPET can considerably reduce the number of estimated parameters is demonstrated by a digital satellite channel example in which we use the proposed method to identify the channel dynamics. Furthermore, a gradient-descent procedure that adaptively selects the pole locations in the FPET structure is developed.