P. V. Romanov1, Yu. I. Choni2
1, 2 Kazan National Research Technical University n.a. A.N. Tupolev (Kazan, Russia)

Ensuring a working coverage area for telecommunication systems via a geostationary satellite is associated with solving a number of complex technical problems. One of them is stabilization of the beams of a satellite multibeam hybrid reflector antenna (MBHRA) under conditions when the profile of its reflector is distorted due to the variability of the heat flux and mechanical factors. The severity of this problem is because in order to provide the necessary energy parameters, the gain of the beams must be at least 40–50 dB. To do this, it is necessary to form needle-like beams in fractions of a degree and, therefore, to comply with very strict requirements for the stability of their orientation.

Systems of optical or photometric control of the reflector surface and mechanical drives to compensate for deformations are cumbersome in terms of design. It is no accident, therefore, that in recent years there has been an ever-increasing interest in radio technical means for monitoring the current state of the reflector and electronic stabilization of the MBHRA’s beams.

This paper describes a heuristic algorithm for reconstructing the current reflector profile of a satellite MBHRA by processing signals received by elements of its antenna array (AA) from a ground-based beacon.

It has been found that if the distances between the elements of the antenna array are not too large, and the dimensions of the antenna array are sufficient to intercept the lion's share of the power of the field reflected by the reflector, then the following takes place. The excitation of the antenna array in accordance with the complex-conjugate amplitudes of the received signals leads to the formation of a field on the actual surface of the reflector, the phase distribution of which coincides with the phase distribution of a plane wave propagating towards the beacon. Taking into account this feature of the field emitted by the antenna array, the current profile of the reflector is a surface at the points of which the phase difference of the compared fields is constant.

Within the framework of a simplified model of physical optics, simulation of the process of receiving signals from a beacon and reconstruction of the reflector profile with various types of its surface distortions has been carried out. The results of the calculations confirmed that the discussed algorithm is operable under two easily feasible conditions: the elements of the antenna array should not be located too sparsely, and its dimensions should be sufficient to intercept the lion's share of the power of the ground-based beacon field reflected by the reflector. The given examples of reconstructing the profile of a reflector subjected to characteristic deformations demonstrate not only the operability of the proposed algorithm, but also the possibility of achieving high accuracy corresponding to deviations of the reconstructed reflector surface from the true one within hundredths of a wavelength at the operating frequency.

Dependences characterizing the algorithmic features of the analyzed method for reconstructing the profile of the MBHRA’s reflector have been given.

Romanov P.V., Choni Yu.I. Reconstruction of the reflector geometry of a satellite multibeam hybrid reflector antenna by processing antenna array signals. Antennas. 2022. № 4. P. 5–17. DOI: https://doi.org/10.18127/j03209601-202204-01 (in Russian)

1. Wang C.S., Yuan S., Liu X., Xu Q., Wang M., Zhu M.B., Chen G.D., Duan Y.H. Temperature distribution and influence mechanism on large reflector antennas under solar radiation: solar thermal effect on reflector antenna. Radio science. 2017. V. 52. № 10. P. 1253–1260.
2. Shendalyov D.O. Proektirovanie formoobrazuyushchej struktury zontichnogo reflektora. Vestnik SibGAU. 2013. № 6 (52). S. 164–173. (in Russian)
3. Tajgin V.B., Lopatin A.V. Metod obespecheniya vysokoj tochnosti formy reflektorov zerkal'nykh antenn kosmicheskikh apparatov. Kosmicheskie apparaty i tekhnologii. 2019. T. 3. № 4. S. 200–208. DOI: 10.26732/2618-7957-2019-4-200-208. (in Russian)
4. Sayapin S.N. Analiz i sintez raskryvaemykh na orbite pretsizionnykh krupnogabaritnykh mekhanizmov i konstruktsij kosmicheskikh radioteleskopov lepestkovogo tipa. Diss. … dokt. tekhn. nauk. Moskva. 2003. (in Russian)
5. Sledyashchij opto-elektronnyj monitoring deformatsij v zadache dinamicheskoj yustirovki ustrojstv prostranstvennogo nablyudeniya. Pod red. A.V. Ushakova. SPb.: SPb GU ITMO. 2008. (in Russian)
6. Subrahmanyan R. Photogrammetric measurement of the gravity deformation in a Cassegrain antenna. IEEE Transactions on Antennas and Propagation. 2005. V. 53. № 8. P. 2590–2596.
7. Kalabegashvili G.I., Bikeev E.V., Matylenko M.G. Selection of the device for orbital alignment of a large transformable antenna reflector. Reshetnev readings. 2018. P. 121–122.
8. Scheid R.E. Precision pointing compensation for DSN antennas with optical distance measuring sensors. TDA Progress Report. 1989. P. 127–140.
9. Bikeev E.V., Yakimov E.N., Matylenko M.G., Titov G.P. Sposob kompensatsii deformatsij konstruktsii krupnogabaritnoj antenny kosmicheskogo apparata. Vestnik SibGAU. 2016. T. 17. № 3. S. 673–683. (in Russian)
10. Gryanik M.V., Loman V.I. Razvertyvaemye zerkal'nye antenny zontichnogo tipa. M.: Radio i svyaz'. 1987. (in Russian)
11. Wang C., Li H., Ying K., Xu Q., Wang Na., Duan B., Gao W., Xiao L., Duan Yu. Active surface compensation for large radio telescope antennas. Hindawi International Journal of Antennas and Propagation. 2018. V. 1. P. 1–17. DOI: 10.1155/2018/3903412.
12. Shipilov S.E., Efremov A.A., Yakubov V.P. Vosstanovlenie formy iskrivlenij zerkal'nykh kombinirovannykh antenn. Izv. vuzov. Fizika. 2008. T. 51. № 9/2. S. 103–105. (in Russian)
13. Dai M., Newman T.S., Cao C. Least-squares-based fitting of paraboloids. Pattern recognition. 2007. V. 40. № 2. P. 504–515.
14. Goldobin N.N. Metodika otsenki formy radiootrazhayushchej poverkhnosti krupnogabaritnogo transformiruemogo reflektora kosmicheskogo apparata. Vestnik SibGAU. 2013. № 1 (47). S. 106–111. (in Russian)
15. Li Zh., Zhuo X., Wang J., Lei Ya. Fitting method of rotating paraboloid reflector. IOP Conf. Series: Materials Science and Engineering. 2018. V. 397. № 1. DOI:10.1088/1757-899X/397/1/012047.
16. Alekseenko A.A., Bikeev E.V., Dorofeev M.O., Luk'yanenko M.V., Matylenko M.G. Sistema navedeniya krupnogabaritnoj transformiruemoj antenny. Aviatsionnaya i raketno-kosmicheskaya tekhnika. Vestnik SibGAU. 2014. № 1 (53) S. 104–108. (in Russian)
17. Goldobin N.N. Analiz effektivnosti orbital'noj yustirovki krupnogabaritnogo reflektora. Reshetnevskie chteniya. 2018. S. 97–99. (in Russian)
18. Goldobin N.N. Otsenka tochnosti navedeniya reflektora na osnovanii informatsii ob otkloneniyakh kontsov ego silovykh spits. Reshetnevskie chteniya. 2016. S. 102–104. (in Russian)
19. Suzuki Y., Harada S., Kobayashi K., Ueba M., Ohata K. Deformed antenna pattern compensation method for onboard multi-beam antennas. 25th AIAA International Communications Satellite Systems Conference. 2007. [Elektronnyj resurs]. URL: https://doi.org/10.2514/ 6.2007-3269.
20. Sikri D., Jayasuriya R.M. Multi-beam phased array with full digital beamforming for SATCOM and 5G. Microwave Journal. 2019. [Elektronnyj resurs]. URL: https://www.microwavejournal.com/articles/32053-multi-beam-phased-array-with-full-digital-beamforming-for-satcom-and-5g (data obrashcheniya: 25.02.2022).
21. Ponomarev L.I., Vechtomov V.A., Miloserdov A.S. Bortovye tsifrovye mnogoluchevye antennye reshetki dlya sistem sputnikovoj svyazi. M.: MGTU im. N.E. Baumana. 2016. (in Russian)
22. Romanov A.G., Dardymov A.V., Danilov I.Yu., Choni Yu.I. Retrieving best-fit paraboloid from signals of a ground based beacon for electronic compensation of satellite multi-beam hybrid reflector antenna distortions. 2021 International Siberian Conference on Control and Communications (SIBCON). Kazan, Russia. 2021. P. 1–5. DOI: 10.1109/SIBCON50419.2021.9438869. (in Russian)
23. Romanov P.V., Choni Yu.I. Stabilization of beams of a satellite hybrid reflector antenna via processing signals from the ground beacon. 2021 International Siberian Conference on Control and Communications (SIBCON). Kazan, Russia. 2021. P. 1–5. DOI: 10.1109/SIBCON50419. 2021.9438853. (in Russian)
24. Mochalov V.V. Attestatsiya algoritma akusticheskogo priblizheniya. Uspekhi sovremennoj radioelektroniki. 2019. № 12. S. 124–128. (in Russian)
25. Wenhe Ye, Dajun Yue, Fengqi You. Trust-region methods. Northwestern University Open Text Book on Process Optimization [Elektronnyj resurs]. URL: https://optimization.mccormick.northwestern.edu/index.php/Trust-region_methods (data obrashcheniya: 03.03.2022).