A.N. Abakumov1, R.R. Saniev2, S.S. Semenyuk3, E.Yu. Shilovskiy4

1,3 Military Space Academy named after A.F. Mozhaisky (Saint-Petersburg, Russia)

2,4 Military University of Radio Electronics (Cherepovets, Russia)

With the development of technologies in the field of satellite communications, the reduction in the cost of user equipment, the expansion of the range of services provided by satellite communications systems for private and corporate users, in the conditions of a limited frequency resource of satellite repeaters and a high density of satellites in geostationary orbit, the task of identifying illegitimate users of a satellite system becomes increasingly important. communication, violating the communication regulations, and determining their location. One of the common directions for the effective use of the frequency resource of a satellite transponder is a method based on the technology of combining carrier frequencies. Determining the location of subscriber terminals of a satellite communication system with the reuse of the frequency resource of a satellite repeater using the technology of combining carrier frequencies can be implemented based on a sequence of measurements of frequency shifts of component signals of subscriber terminals due to the Doppler effect due to the changing relative position of the transmitters, the repeater and the receiver of the additive mixture of these signals. Frequency shifts in this case act as coordinate-informative parameters. However, with certain ratios of the mutual space-time position of subscriber terminals, a repeater satellite and a receiver performing radio monitoring, the spectra of carrier oscillations of component signals at the receiving point, obtained as a result of quadratic transformations of the additive mixture, may be indistinguishable, which will not allow estimation of their carriers. frequencies for each component signal separately. Investigation of the conditions under which the spectra of carrier oscillations of component signals obtained as a result of quadratic transformations based on the spectrum convolution effect are distinguishable at the reception point as part of an additive mixture, which means that it is possible to estimate coordinate-informative parameters to solve the problem of geolocation of AT of illegitimate users. A mathematical model of an additive mixture of subscriber signals with overlapping carrier frequencies is presented, taking into account the conditions for dynamic changes in the relative spatial position of transmitters and receivers relative to the repeater satellite. Based on the developed model, the possibility of distinguishing the carrier frequencies of subscriber terminals was evaluated when solving the problem of measuring coordinate-informative parameters and geolocation of illegitimate users. The value of the results obtained is in determining the boundary values of the mutual spatial position of the repeater satellite and user terminals, which provide the ability to distinguish and estimate the coordinate-informative parameters of additive component signals with the alignment of carrier frequencies over the observation interval, which is the basis for solving the problem of geolocation of subscriber terminals of illegitimate users.

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