Nonlinear System Identification Using Wiener Basis Functions and Multiple-Variance Perfect Sequences

The paper addresses nonlinear identification using the Wiener series. Differently from the traditional approach, the truncated Wiener series is expressed as a linear combination of basis functions, which are orthogonal for white Gaussian inputs. The coefficients of the basis functions are efficiently estimated with the cross-correlation method, computing the cross-correlation between the basis functions and the system output. Perfect periodic sequences (PPSs), which are periodic sequences guaranteeing the perfect orthogonality of the basis functions over a period, are also developed. The PPSs allow to avoid the estimation problems experienced with the cross-correlation method using stochastic inputs. The Wiener series formulation in terms of basis functions allows also to develop a novel, more efficient, multiple-variance identification method. Multiple-variance methods exploit input signals with multiple variances for estimating the Volterra kernels. They overcome the problem of locality of the solution, i.e., the fact that the identified model well approximates the nonlinear system only for input signal variances close to that used for the identification. Optimal values of the multiple variances are also studied in the paper. Experimental results, involving the identifications of real devices, show that the proposed approach can accurately model the identified system on a wide range of input variances.