Stochastic-calculus-based numerical evaluation and performance analysis ofchaotic communication systems

Performance evaluation of a self-synchronizing Lorenz chaotic system is for mulated as a stochastic differential equation problem. Based on stochastic calculus, we provide a rigorous formulation of the numerical evaluation and analysis of the self-synchronization capability and error probabilities of two chaotic Lorenz communication systems with additive white Gaussian nois e disturbance. By using the Ito theorem, we are able to analyze the first t wo moments behavior of the self-synchronization error of a drive-response L orenz chaotic system. The moment stability condition of the synchronization error dynamic is explicitly derived. These results provide further underst anding on the robust self-synchronization ability of the Lorenz system to n oise. Various time-scaling factors affecting the speed of system evolution are also discussed. Moreover, an approximate model of the variance of the s ufficient statistic of the chaotic communication is derived, which permits a comparison of the chaotic communication system performance to the convent ional binary pulse amplitude modulation communication system. Due to synchr onization difficulties of chaotic systems, known synchronization-based chao tic communication system performance is quite poor. Thus, alternative synch ronization-free chaotic communication systems are needed in the future. The use of a stochastic calculus approach as considered here, however, is stil l applicable if the considered chaotic communication system is governed by nonlinear stochastic differential equations.