Stochastic-calculus-based numerical evaluation and performance analysis of chaotic communication systems

Performance evaluation of a self-synchronizing Lorenz chaotic system is formulated 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 noise disturbance. By using the Ito theorem, we are able to analyze the first two moments behavior of the self-synchronization error of a drive-response Lorenz chaotic system. The moment stability condition of the synchronization error dynamic is explicitly derived. These results provide further understanding on the robust self-synchronization ability of the Lorenz system to noise. Various time-scaling factors affecting the speed of system evolution are also discussed. Moreover, an approximate model of the variance of the sufficient statistic of the chaotic communication is derived, which permits a comparison of the chaotic communication system performance to the conventional binary pulse amplitude modulation communication system. Due to synchronization difficulties of chaotic systems, known synchronization-based chaotic communication system performance is quite poor. Thus, alternative synchronization-free chaotic communication systems are needed in the future. The use of a stochastic calculus approach as considered here, however, is still applicable if the considered chaotic communication system is governed by nonlinear stochastic differential equations.