Title :
Stochastic-calculus-based numerical evaluation and performance analysis of chaotic communication systems
Author :
Chen, Chi-Chung ; Yao, Kung
Author_Institution :
Dept. of Electr. Eng., California Univ., Los Angeles, CA, USA
fDate :
12/1/2000 12:00:00 AM
Abstract :
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
Keywords :
AWGN; chaos; error statistics; nonlinear differential equations; stochastic processes; synchronisation; Ito theorem; additive white Gaussian noise disturbance; chaotic Lorenz communication systems; chaotic communication systems; drive-response Lorenz chaotic system; error probabilities; moment stability condition; nonlinear stochastic differential equations; robust self-synchronization ability; self-synchronization capability; self-synchronization error; self-synchronizing Lorenz chaotic system; stochastic differential equation problem; stochastic-calculus-based numerical evaluation; synchronization error dynamic; time-scaling factors; Additive white noise; Calculus; Chaotic communication; Communication systems; Differential equations; Error probability; Indium tin oxide; Stochastic resonance; Stochastic systems; System performance;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on