Non-Iterative Identification of IIR Wiener Systems with Non-Invertible Nonlinearities

In this paper, a non-iterative method for identifying a single input single output Wiener model consisting of an IIR digital filter in cascade with a potentially non-invertible static non-linearity is developed. Initially, the linear and nonlinear elements are expanded onto bases consisting of IIR Laguerre filters and polynomials, respectively. Extensions to other bases are also considered. The parameters of the linear subsystem and the coefficients of the non-linearity are estimated by using an over-parameterized linear regression generated using a multi-index based approach. The initial over-paramerized solution is projected onto the class of Wiener models using an approach based on singular value decomposition. Finally, simulation examples and results discussions are provided.