Identification of polyperiodic Volterra systems by means of input-output noisy measurements

Abstract Identification methods of polyperiodically time-varying Volterra systems of finite order N by input–output measurements are proposed. The presence of additive signal-independent noise on the system input and output signal measurements is taken into account. Two identification methods are presented: both assume that the input signal be amplitude-modulated cyclostationary signal. The former supposes that the modulating sequence be white at least up to 2 N -order; the latter considers a stationary Gaussian sequence. They exploit the higher-order cyclostationarity selectivity property of the input signal to reject noises and interferences. The performance analysis, carried out by computer simulations for a periodically time-varying quadratic Volterra system, shows the capability of the proposed methods to operate satisfactorily in severe noise environments.

[1]  Tadashi Fujino,et al.  An adaptive maximum-likelihood sequence estimator for fast time-varying intersymbol interference channels , 1994, IEEE Trans. Commun..

[2]  M. Schetzen.  The Volterra and Wiener Theories of Nonlinear Systems , 1980 .

[3]  Nicholas Kalouptsidis,et al.  Nonlinear system identification using Gaussian inputs , 1995, IEEE Trans. Signal Process..

[4]  Stephen A. Billings,et al.  Identi cation of nonlinear systems-A survey , 1980 .

[5]  Luigi Paura,et al.  Identification of polyperiodic nonlinear systems , 1995, Signal Process..

[6]  William A. Gardner,et al.  Fraction-of-time probability for time-series that exhibit cyclostationarity , 1991, Signal Process..

[7]  Georgios B. Giannakis,et al.  Asymptotic theory of mixed time averages and k th-order cyclic-moment and cumulant statistics , 1995, IEEE Trans. Inf. Theory.

[8]  Abdelhak M. Zoubir,et al.  Identification of quadratic Volterra systems driven by non-Gaussian processes , 1995, IEEE Trans. Signal Process..

[9]  Enders A. Robinson.  Statistical spectral analysis—a nonprobabilistic theory: by William A. GARDNER, Department of Electrical Engineering, University of California, Davis, U.S.A. Publishers: Prentice-Hall, Inc., Englewood Cliffs, NJ 07632, U.S.A., 1987, 566 pp., ISBN 0-13-844572-9 , 1990 .

[10]  William A. Gardner,et al.  Exploitation of cyclostationarity for identifying the Volterra kernels of nonlinear systems , 1993, IEEE Trans. Inf. Theory.

[11]  William A. Gardner,et al.  The cumulant theory of cyclostationary time-series. I. Foundation , 1994, IEEE Trans. Signal Process..

[12]  Luigi Paura,et al.  Higher-order cyclostationarity-based methods for identifying volterra systems by input-output noisy measurements , 1998, Signal Process..

[13]  C. L. Nikias,et al.  Signal processing with higher-order spectra , 1993, IEEE Signal Processing Magazine.

[14]  M. Schwartz,et al.  Binary Signaling over Channels Containing Quadratic Nonlinearities , 1974, IEEE Trans. Commun..