Blind Identification of Autoregressive System Using Chaos

The problem of identifying an autoregressive (AR) model using chaos is investigated here. Based on the Cramer–Rao bound (CRB) analysis, it is proved here that when chaos is used to drive an AR system, identification using only the output signal can be as good as that based on using both input and output signals, that is, blind identification is equivalent to nonblind identification. A deterministic maximum likelihood (ML) is, therefore, developed to blindly identify an AR system driven by chaos. Combined with the global search technique genetic algorithm (GA), the proposed GA-ML method is found to achieve the optimal identification performance imposed by the CRB. The theoretical mean square error (MSE) performance of the proposed GA-ML method is derived, and the result is validated using computer simulations. Compared to conventional methods based on white Gaussian driving signal, the chaos approach is shown to have superior performance. The improvement is proved to be the result of the positive and finite Lyapunov exponent of the chaotic signal. The proposed chaos identification method is applied to blind equalization of a spread spectrum (SS) communication system where chaos is used to modulate the information signal. Computer simulations show that the proposed chaos approach has a satisfactory equalization performance even under strong channel effects.