Adaptive identification of nonlinear systems with application to chaotic communications

This paper studies the nonlinear system identification problem in a noisy environment using an adaptive algorithm. In particular, nonlinear systems of the polynomial type are considered here. An improved least squares (ILS) objective function is used to reduce the estimation bias caused by measurement noise. Based on this ILS criterion, a novel adaptive filter is developed to track a time-varying polynomial system. Numerical simulations showed that the proposed adaptive algorithm was superior to the conventional identification technique. We applied this new adaptive filter to demodulate the signals of transmission in a chaotic multiuser spread spectrum (SS) communication system. It was observed that the new approach was effective in demodulating a SS signal, even at low signal-to-noise ratios (SNR's).