How Nonlinear Parametric Wiener System Identification is Under Gaussian Inputs?

A number of methods exist for identifying nonlinear Wiener systems. However, there is no attempt to address the fundamental question of how nonlinear these identification problems really are? In this technical note, we try to address this question by investigating the average squared error cost function used in identification. By a proper normalization and a clever characterization of the cost function in terms of the angle between the true but unknown parameter vector and its estimate, it is shown in the technical note that under iid Gaussian inputs for parametric Wiener systems with polynomial nonlinear parts and FIR linear parts, the cost function is globally monotonic and has one and only one (local and global) minimum. The implication is that identification of such systems is nonlinear but very close to linear. Further, any local search based identification algorithms would converge globally for such systems.