Design of Multilevel Signals for Identifying the Best Linear Approximation of Nonlinear Systems

The best linear approximation (BLA) of a nonlinear system minimizes the difference between the actual output of the system and the modeled output in a least square sense. It depends on the power and amplitude distribution of the excitation sequences used to identify it. The theory of the BLA for Gaussian input sequences (including random phased multisines) has been widely studied. It has recently been shown that the BLA when using a binary input sequence is biased with respect to that obtained using a Gaussian input sequence, and expressions for this bias have been obtained. In this paper, it is shown that it is possible to design discrete multilevel input sequences to mimic Gaussianity as closely as possible, thus reducing the bias, by adjusting sequence levels and the probability of the sequence being at these levels. Their performance is compared with true Gaussian sequences in simulation experiments.