Identification of FIR Wiener systems with unknown, noninvertible, polynomial nonlinearities

Wiener systems consist of a linear dynamic system whose output is measured through a static nonlinearity. In this paper we study the identification of single-input single-output Wiener systems with finite impulse response and polynomial nonlinearities. Our approach is to use multi-index notation to first solve a least squares problem to estimate products of the coefficients of the nonlinearity and the impulse response of the linear system. We then present four methods to extract the coefficients of the nonlinearity and impulse response: direct algebraic solutions, a singular value decomposition, a multi-dimensional singular value decomposition, and a prediction error optimization approach.