telecommunication system, broadband pseudo-noise signal, logistic mapping, signal base, radio channel.


Background. Telecommunication systems with a broadband signal have undoubted advantages: increased noise immunity with narrowband and wideband interference, confidentiality of information transmission, as well as improved electromagnetic compatibility with neighboring radio-electronic devices. A broadband signal is usually formed by direct spread spectrum using well-known classical pseudo-random sequences (PRS): m-sequences, Kasami, Gold, Walsh sequences, which can be decoded and received at the receiver.
Objective. The aim of the paper is creating PRS on the basis of chaos, which the subscriber is practically unable to decode, and thus ensure increased confidentiality of information transmission.
Methods. Using the mathematical model of chaotic logistic mapping, which, as shown by preliminary studies, provides the best results, as well as referring to the bifurcation diagram of Feigenbaum, the parameters of 3-secret keys
are defined and the PRS of the selected length is created. Based on the application of the graphical user interface developed in the MATLAB system, a correlation analysis of the resulting PRS is performed and the PRS is determined
with the minimum side lobes of the autocorrelation function.
Results. By empirical decision of 3 secret keys of the dynamic parameter of the Feigenbaum diagram, the initial value of the sequence and the number of the initial pulse of the PRS, as well as the study of the autocorrelation function,
we obtained a PRS with a side lobe level of the autocorrelation function acceptable for practical use of no more than 0.25.
Conclusions. The use of well-known pseudo-random sequence: Walsh’s, Kasami’s, Gold’s, creating a system with a noise-like signal doesn’t ensure complete confidentiality of information transmission, since they can be decoded.
The most acceptable by the criterion of the side lobe minimum of the autocorrelation function – no worse than 0.25 – is the use of chaos based on the Feigenbaum logistic map. When creating pseudo-random sequences based on chaos, the best results are obtained by choosing the maximum value of the dynamic parameter of the Feigenbaum diagram at the level of the boundary value equal to 4, with an accuracy of 0.05.


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