Nonparametric identification of Wiener system with a subclass of wide-sense cyclostationary excitations

The paper identifies a Wiener system, which is excited by a cyclostationary time series. To estimate the first subsystem's linear dynamic impulse response: this proposed algorithm first kernel-windows the Wiener system's input measurements, then cross-correlates with the output time series. To identify the second subsystem's static nonlinearity: this proposed algorithm first estimates the unobservable inter-block internal signal (consistently in the statistical sense), and then kernel-windows these estimates with the Wiener system output. This estimator provides the unusual capability to identify non-invertible nonlinearities. This strategy removes any restrictive requirement for a Gaussian random excitation or a sinusoidal deterministic excitation. This paper further proves the estimator's asymptotic consistency and determines the kernel bandwidth for algorithmic convergence. The proposed algorithm's efficacy is verified in the context of two common applications: a servo mechanical system and a telecommunication channel.