Ya.Ya. Levin1

1 St. Petersburg State University of Aerospace Instrumentation (SUAI) (St. Petersburg, Russia)

Interest in the use of chaotic oscillators in modern information transmission technologies is due to the possibility of generating complex non-periodic oscillations by relatively simple electronic circuits; controlling the parameters of chaotic signals by making minor changes in the parameters of the system that generates them and obtaining a signal space of high dimensions, as well as non-traditional approach to multiplexing and demultiplexing methods, based on the phenomenon of synchronization of chaotic collisions

Objective – hardware-software implementation of telecommunication systems models with increased noise immunity by using chaotic and fractal signals.

Further improvement of noise immunity is possible through the use of broadband fractal signals. The theory of interference-resistant information transmission is developing towards the search for new classes of signals, the use of which makes it possible to develop interference-resistant telecommunications systems. Several basic technologies based on synchronization of pseudorandom oscillations and modulation of pseudorandom carrier with information signal have become widespread.

We consider methods of synchronization of autocoincidence systems for generating chaotic oscillations using the similarity function between the signals of the main and the controlled systems. The synchronization of the oscillators of pseudorandom oscillations of the receiving and transmitting sides of the information transmission system depends on the coupling coefficient between them and the cut-off frequency of the low-pass filter that models the communication channel. The values of the Lorentz system parameters describing the generator of chaotic signals used for coding digital information are established. The system of digital information transmission that uses a random process as a pseudo-random carrier, which is a fractal Gaussian noise with different Hearst exponents, is considered.

Levin Ya.Ya. Modeling of telecommunication systems information transmission using pseudorandom fluctuations. Achievements of modern radioelectronics. 2023. V. 77. № 8. P. 66–76. DOI: https://doi.org/10.18127/j20700784-202308-09 [in Russian]

1. Baskakov S.I. Radiotekhnicheskie tsepi i signaly. Moskva. 2022. [in Russian]
2. Romanov B.N., Krasnov S.V. Teoriya elektricheskoy svyazi. Soobshcheniya, signaly, pomekhi, ikh matematicheskie modeli. Ul'yanovsk: Izd-vo Ul'yanovskogo tekhn. un-ta. 2008. [in Russian]
3. Gonzalez J.A., Reyes L.I., Suarez J.J., Guerrero L.E., Gutierez G. Chaos-induced true randomness. Physica A. 2002. V. 316. P. 259–288.
4. Kuznetsov S.P. Dinamicheskiy khaos (kurs lektsiy). M.: Fizmatlit. 2006. [in Russian]
5. Kyarginskiy B.E. Generatory na bipolyarnykh tranzistorakh razlichnoy moshchnosti. Elektronnaya tekhnika. Ser. SVCh-tekhnika. 1993. V. 457. № 3. P. 3–7. [in Russian]
6. Pecora L.M., Carroll T.L., Johnson G.A., Mar D.J. Fundamentals of synchronization in chaotic systems, concepts, and applications. Chaos. 1997. V. 7. № 4. P. 520–543.
7. Shuster G. Determinirovannyy khaos: Vvedenie. M.: Mir. 1988. [in Russian]
8. Kronover R.M. Fraktaly i khaos v dinamicheskikh sistemakh. Osnovy teorii. Per. s angl. L.: Jones and Bartlett Publishers Inc.; M.: Postmarket. 1999. [in Russian]
9. Feder E. Fraktaly. M.: Mir. 1991. [in Russian]
10. Li T.Y., Yorke J.A. Period three implies chaos. The American mathematical monthly. 1975. V. 82. № 10. P. 985–992.
11. Sharkovskiy A.N. Sosushchestvovanie tsiklov nepreryvnogo otobrazheniya pryamoy v sebya. Ukrainskiy matematicheskiy zhurnal. 1964. № 1. P. 61–71. [in Russian]
12. Sharkovskiy A.N. Prityagivayushchie mnozhestva, ne soderzhashchie tsiklov. Ukrainskiy matematicheskiy zhurnal. 1968. № 1. P. 136–142. [in Russian]
13. Gel'fond A.O. Ischislenie konechnykh raznostey. M.: GIFML. 1959. [in Russian]
14. Mitchell J. Feigcnbaum. The Universal Metric Properties of Nonlinear Transformations. Journal of Statistical Physics. 1979. V. 21. № 6. P. 669–706.
15. Pumir A., Manneville P., Pomeau Y. On solitary waves running down an inclined plane. Journal of fluid mechanics. 1983. V. 135. P. 27–50.
16. Pomeau Y., Manneville P. Intermittent Transition to Turbulence in Dissipative Dynamical Systems. Comm. Math. Phys. 1980. № 74. P. 189.
17. Lorenz E.N. Deterministic nonperiodic flow. J. Atmos. Sci. 1963. V. 20. № 2. P. 130–141.
18. Luo Xiao-Hua and etc. Circuitry implementation of a novel four-dimensional nonautonomous hyperchaotic Liu system and its experimental studies on synchronization control. Chinese Physics B. 2009. V. 18. № 6. P. 2168–2175.
19. Benettin G., Galgani L., Giorgilli A., Strelcyn J.-M. Lyapunov characteristic exponents for smoth dynamical systems and for Hamiltonian systems: A method for computing all of them. P. I: Theory. P. II: Numerical application. Meccanica. 1980. V. 15. P. 9–30.
20. Pecora L.M., Carroll T.L. Synchronization in Chaotic Systems. Phys. Rev. Lett. 1990. V. 64. P. 821.
21. Shakhtarin B.I. Sluchaynye protsessy v radiotekhnike. M: Radio i svyaz'. 2000. [in Russian]
22. Hurst H.E. Long-term storage capacity of reservoirs. Transactions of American Society of Civil Engineers. 1951. V. 116. P. 770.
23. Dvornikov S.V., Kryachko A.F., Popov E.A., Dvornikov S.S., Tomashevich S.V. Kompensatsiya strukturnykh pomekh v radiochastotnykh kanalakh upravleniya robototekhnicheskikh sistem. Radiotekhnika. 2021. V. 85. № 11. P. 95–106. DOI: https://doi.org/10.18127/j00338486-202111-15. [in Russian]
24. Kryachko A.F., Yakushenko S.A., Dvornikov S.V., Popov E.A., Zabelo A.N. Metodika otsenki ustoychivosti seti mnogokanal'noy radiosvyazi na osnove reshenie zadachi Koshi dlya sistemy matrichnykh uravneniy Kolmogorova, opisyvayushchikh ee sostoyanie. Radiotekhnika. 2020. V. 84. № 12 (24). P. 112–120. DOI: 10.18127/j00338486-202012(24)-11. [in Russian]