Subspace-based blind identification of IIR wiener systems

A new subspace method for the blind (i.e., based only on output data) identification of Single Input Single Output Wiener models is presented in this paper. The Wiener model consists of the cascade of a Linear Time Invariant (LTI) system followed by a zero-memory nonlinear element. The linear block in the Wiener model is given an Infinite Impulse Response (IIR) representation using orthonormal bases with fixed poles, while the static nonlinearity is represented using nonlinear basis functions. Basis coefficients (both of the linear and nonlinear blocks) are estimated in closed form, up to a scalar factor, by first computing the column space of an equivalent output Hankel matrix using Singular Value Decomposition (SVD), and then solving two Least Squares problems also resorting to SVDs. The performance of the proposed algorithm is illustrated through a simulation example.