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• W158045392 abstract "ABSTRACTBased on stochastic calculus, we provide a rigorous formu-lation for the numerical evaluation of the error probabilitiesof two modulation techniques for the chaotic Lorenz com-munication system with AWGN disturbance. These resultsprovidefurtherunderstandingon the robust synchronizationability of the Lorenz system to noise. The synchronizationrobustness of Lorenz systems for various time scaling fac-tors is also discussed. An approximate model of the vari-ance of the sufficient statistic of the chaotic communicationis derived, which permits a comparison of the chaotic com-munication system performance to a conventional commu-nication system.1. INTRODUCTIONSince Pecora and Carroll [1] have theoretically and experi-mentally shown that two identical chaotic dynamic systemscan be synchronized, chaotic signals with inherently broad-band,noise-likeandunpredictablepropertieshavebeenpro-posedforpossiblecommunicationmodulation/codingwave-forms[2][3]. A chaotic system possess self-synchronizationproperty if it can be decomposed into two subsystems: adrive system and a conditionally stable response subsystemthat synchronize when driven with a common signal. Basedon the drive-responseconfigurationofsynchronization,spe-cific chaoticcommunicationtechniques,suchaschaoticsig-nal masking, chaotic switching modulation [2][3][4], anddynamicfeedbackmodulationofinformationsignal[5], havebeen considered. As the basic operation of those techniquesis highly dependent on the self-synchronization property ofthe chaotic systems, the robust ability of the systems to per-turbationin the drivesignal is a crucialfactorin determiningthe system performance. Since the AWGN channel consti-tutes the most basic component of a communication link,the understanding of the robust self-synchronization abilityof a chaotic communication system to WGN is necessaryfor system design. However, because of the inherent non-linearity of a chaotic system, it is generally difficult to ob-tain an analytic solution and thus numerical simulations areneeded.Cuomo et al [2] have addressed the numerical evalua-tion of the SNR improvement of the Lorenz chaotic com-munication system based on deterministic numerical algo-rithms. It is known that commercial numerical computa-tionalpackagesusingthestandardEulerorRunge-Kutta(RK)algorithmsfordeterministicdifferentialequationstoapprox-imate the solution to nonlinear stochastic differential equa-tion(SDE) will incur significant errors [6]. This is partic-ularly true for a nonlinear chaotic dynamical system mod-eling the transmitter inputting into an AWGN channel andfollowed by another nonlinear chaotic dynamical system.In this paper, we use the stochastic calculus approachto perform the integration algorithm for the sample func-tions of nonlinear dynamic systems excited by the stochas-tic white noise. Depending on the precise interpretation ofthe white noise, there are two different solutions to the SDEbased on the Stratonovich or Ito integral [9]. Using the con-version between them, a correct numerical integration algo-rithm in the Ito sense is introduced. With this algorithm, thecorrect error probability of the robust self-synchronizationLorenz communication system with AWGN perturbation ispresented. The self-synchronization robustness of Lorenzsystems for varioustime scaling factors, changing the speedof system evolution, is also discussed. Furthermore, weexplicitly demonstrate the performance evaluation of thismodel using deterministic numerical algorithms yields in-correct results. Finally, the numerical evaluation and com-parison of error probabilities among dynamic feedback andchaotic switching modulation for a Lorenz system and aconventional communication system are provided.2. PROBLEM DESCRIPTIONThe modified Lorenz system [2] is given by" @default.
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• W158045392 date "1999-01-01" @default.
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• W158045392 title "Stochastic calculus numerical evaluation of chaotic communication system performance." @default.
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