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Aleksei A. Gavrishev, Stavropol, Russia, alexxx.2008@inbox.ru
Aleksandr P. Zhuk, Stavropol, Russia, alekszhuk@mail.ru

Currently, one of the promising areas in the field of secure communication systems is the use of chaotic signals. Great interest are the analysis of communication systems based on chaotic signals. Among the basic methods of analysis, linear and nonlinear methods are distinguished. Among promising methods for analyzing transmitted chaotic signals, one of the nonlinear methods, BDS statistics, is considered, which is based on the statistical properties of the correlation dimension of the process under study in phase space, which in turn is determined by the correlation integral. The mathematical apparatus of BDS-statistics is described. It is noted that many publications do not explicitly indicate the software used to calculate BDS statistics. This circumstance restricts the use of BDS statistics for solving various problems, for example, analysis of communication systems based on chaotic signals. The authors indicate software implementations, with the help of which it is possible to calculate BDS statistics. As the software for calculating BDS-statistics, the econometric package of programs EViews 10 Student Version Lite was chosen. Using the example of modeling one of the communication systems based on chaotic signals in the ScicosLab environment and analyzing the received data in the EViews 10 Student Version Lite software package, it is confirmed that the BDS-statistics is a powerful tool for the analysis of chaotic signals. To do this, using the scheme of the communication system under consideration and two generators of chaotic signals (the Ressler attractor and the perturbed Van der Pol oscillator), various temporal realizations of the signals transmitted in the communication channel were obtained. Based on these temporal realizations, phase portraits and BDS statistics are obtained. An analysis of the obtained data shows that the signals formed generally refer to chaotic processes. To reduce the likelihood of successful use of BDS statistics as a method of analyzing communication systems based on chaotic signals, one should either complicate the structure of the transmitted signal, making it similar to white noise, or use a potentially infinite number of sets of different classes of chaotic sequences and their periodic change.

Keywords: wireless link, BDS-statistics, secure communication systems, chaotic signals.


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Information about authors:
Aleksei A. Gavrishev, Ph. D. Student, North-Caucasus Federal University, Stavropol, Russia
Aleksandr P. Zhuk, Ph. D., professor, North-Caucasus Federal University, Stavropol, Russia