Nonlinear System Identification with Multilevel Perturbation Signals

Abstract Measures of perturbation signal quality developed for the identification of linear systems are extended to the identification of nonlinear systems. It is shown that performance depends on the nonlinear system structure, and extreme structures in the form of Wiener and Hammerstein models with quadratic nonlinearities are used for illustration. For the Wiener model, the performance is the same as for a linear system, so a binary perturbation signal is suitable, but the dynamics associated with the nonlinearity cannot be identified directly. For the Hammerstein model, it is necessary to involve the performance of the square of the signal, but the dynamics associated with the nonlinearity can be identified directly. Investigation of the different kinds of multilevel perturbation signals available shows that a three-level pseudo-random signal obtained from a maximum-length sequence in Galois field GF(3) is ideal for this application.