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  5. Analysis of IID-stealthiness of continuous chaotic signals

Analysis of IID-stealthiness of continuous chaotic signals

P. Kostenko, V. Slobodyanuk, S. Volynec, M. Kryuchka
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Description: When developing modern radio engineering systems for the transmission of confidential information there is a tendency to use signals of properties which are close to the properties of "white" noise. These signals include chaotic sequences. It is important to note that the use of mathematical chaos for constructing discrete chaotic signals possessing the necessary secrecy is limited only to their use in telecommunication networks. Physical chaos is used to transmit information over a radio channel, when a chaotic signal is generated directly in the radio or microwave range of wavelengths (direct-chaotic communication systems).Information is entered either by modulating the parameters of the transmitter, or at the expense of its imposing on a chaotic carrier after its generation. However, direct-chaotic communication systems operate at relatively small distances. Currently, due to the development of digital methods of forming and processing signals, the possibility of creating sources of chaotic signals on the basis of digital-analog devices of different degrees of integration, allowing the formation of broadband and bandwidths with a large operating range for navigation, telecommunication and radar systems. One of the important characteristics of radio engineering information transmission systems, which operate under conditions of radio-electronic suppression and in the conditions of unauthorized access to information, is their stealthiness. Under the stealthiness sense of the ability of radio engineering systems to transmit confidential information and counteract the means of radio-intelligence with a given probability. In the article, under the stealthiness understand the proximity of many points in the attractor of the signal in the phase space to the attractor of "white" noise, that is, the degree of its masking to noise. A numerical measure of the quality of masking (stealthiness of the signal) is determined by the value of the BDS-statistics of the signal. Its value for independent and equally distributed random variables (white noise) are in the range (-1.96; 1.96). Deviations of BDS signal statistics from this interval can be characterized by the degree of stealthiness that we call IID- stealthiness. The method of constructing chaotic sequences possessing statistical and dynamic characteristics close to the characteristics of "white" noise is considered in the article. The phase portraits of the constructed sequences and their interpolations are studied to obtain continuous signals transmitted over the radio channel. A comparative analysis of the IID- stealthiness of discrete and continuous chaotic signals is carried out. The results of the article can be used to assess the stealthiness of radio communication systems.

Keywords: chaotic sequences, discrete chaotic signal, phase space, continuous chaotic signal, IID- stealthiness, BDS statistic

 Kostenko, P.Yu., Slobodianiuk, V.V., Volynets, S.V. and Kriuchka, M.L. (2018), “Analiz IID-skrytnosti bezperervnykh khaotychnykh syhnaliv” [Analysis of IID-stealthiness of continuous chaotic signals], Information Processing Systems, Vol. 1(152), pp. 20-26. https://doi.org/10.30748/soi.2018.152.03.