A nonlinear prediction approach for system identification using chaos symbolic dynamic

In this paper we propose using a nonlinear prediction approach to identify an autoregressive (AR) system with chaos symbolic driven signal. This problem widely exists in many practical situations such as channel equalization for chaos digital communications. Although statistic-based techniques can be used to identify systems driven by chaos symbolic signals, they may not fully exploit the information contained in a deterministic chaos symbolic signal and may not result in an optimal solution. In fact, the nonlinear dynamic of a chaos symbolic signal could be properly approximated by using a radial basis function (RBF) net. Based on the short-term predictability of a chaos symbolic signal, an efficient inverse filtering identification approach is proposed. More precisely, a nonlinear prediction error criterion is used as an objective function in the inverse filtering blind identification method. Compared to the statistically optimal least square (LS) method, the proposed nonlinear predictive method is shown to greatly improve the AR system identification performance. We further apply it to combat channel distortions in a digital chaos communication system. It is found that the proposed method has satisfactory equalization performance even when channel effect is strong.