Yu. I. Choni1, P. V. Romanov2
1, 2 Kazan National Research Technical University n.a. A.N. Tupolev (Kazan, Russia)

A large multi-beam hybrid reflector antenna (MBHRA), located on a geostationary satellite, plays an important role in providing the required energy potential of modern high-capacity satellite communication systems. These antennas form a plurality of narrow beams (fractions of a degree wide) that cover the operational service area within its boundary. Due to the uneven and variable heat flux, the reflector profile is subject to distortion. Even at a relatively low level, this leads to a deterioration in the energy coverage of the working areas, mainly due to the displacement of the beams.

In modern MBHRA, each beam is formed by a corresponding cluster of feeds, which opens up the opportunity for stabilizing the state of the beams by adaptively correcting the weight vectors (WV) of the clusters. To do this, it is necessary to control the current state of the reflector, calculate the focal spots from plane wave incident from the required directions, and excite the WVs in accordance with the complex conjugate focal spots on the cluster elements.

At the stage of reflector distortion control, direct measurements using laser scanning of a certain number of marker points on the reflector surface, as well as photogrammetric control of the surface, are widely used. A useful alternative to these methods is the reconstruction of the reflector profile from, as we say, the signal imprint of a ground beacon on the MBHRA antenna array. A similar line of research includes a system that includes measuring deviations of the reflector’s optical axis in two perpendicular planes, which implements the principle of sum-difference direction finding of a ground-based beacon by processing antenna array signals. In the same row, there are works on approximating the current profile by the so-called paraboloid of the best fit (PNS), which is more informative. In the same rank, there are works on approximating the current profile by the so-called the best-fit paraboloid (BFP), which is more informative. In this case, six parameters of the BFP are retrieving from the cluster signals: the deviation of the optical axis in two planes, the change in the focal length, and the displacement of the top of the paraboloid along three axes.

Postgraduate Romanov P.V. came up with an original way of reconstructing a reflector without any a priori restrictions on its profile. The ideology comes down to the search for such coordinates of the profile points at which the field emitted by the cluster is transformed into a section of a plane wave propagating towards the beacon. Within the framework of this approach, an unexpected opportunity opens up to calculate the coordinates of the reflector points directly, according to the corresponding formulas, the derivation of which is the subject of this article.

In contrast to the real situation, at the stage of computer simulation, the reflector distortions are set, i.e. are known, and together with them, the optimal WVs corresponding to the current state of the reflector are also known. Calculations show that the deviations from the WVs and the beams generated by them from the optimal ones are very small, which confirms the efficiency of the presented algorithm, which is not related to the use of gradient descent or other search recursions.

Choni Yu.I., Romanov P.V. Searchless algorithm for reconstruction of the reflector profile of a hybrid reflector antenna from antenna array signals. Antennas. 2022. № 2. P. 12–20. DOI: https://doi.org/10.18127/j03209601-202202-02 (in Russian)

1. Cherette A.R., Acosta R.J., Lam P.T., Lee S.W. Compensation of reflector antenna surface distortion using an array feed. IEEE Transactions on Antennas and Propagation. 1989. V. 37. № 8. P. 966–978.
2. Smith W.T., Stutzman W.L. A pattern synthesis technique for array feeds to improve radiation performance of large distorted reflector antennas. IEEE Transactions on Antennas and Propagation. 1992. V. 40. № 1. P. 57–62.
3. Lavrent'eva A.S., Morozov O.A., Chumankin Yu.E. Vliyanie deformatsii reflektora antenny na diagrammu napravlennosti. Izvestiya vysshikh uchebnykh zavedenij. Povolzhskij region. Tekhnicheskie nauki. 2020. № 1 (53). S. 78–89. DOI 10.21685/2072-3059-2020-1-8. (in Russian)
4. Chen Yu., Chi Yu.,  Fan J., Ma C. Gradient descent with random initialization: fast global convergence for nonconvex phase retrieval. Mathematical programming. 2019. V. 176. P. 5–37.
5. Kalabegashvili G.I., Bikeev E.V., Matylenko M.G. Poisk minimal'nogo kolichestva tochek otrazhayushchej poverkhnosti reflektora, neobkhodimogo dlya otsenki otkloneniya diagrammy napravlennosti krupnogabaritnykh transformiruemykh antenn. Sibirskij zhurnal nauki i tekhnologij. 2018. T. 19. № 1. S. 66–75. (in Russian)
6. Titarenko S.A., Dvirnyj V.V. Primenenie opticheskikh markerov dlya izmereniya profilya krupnogabaritnykh reflektorov. Reshetnevskie chteniya. 2014. S. 106–108. (in Russian)
7. Goldobin N.N. Metodika otsenki formy radiootrazhayushchej poverkhnosti krupnogabaritnogo transformiruemogo reflektora kosmicheskogo apparata. Vestnik SibGAU. 2013. № 1 (47). S. 206–2011. (in Russian)
8. 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.
9. Goldobin N.N. Analiz effektivnosti orbital'noj yustirovki krupnogabaritnogo reflektora. Reshetnevskie chteniya. 2018. S. 97–99. (in Russian)
10. Huang J., Jin H., Ye Q., Meng G. Surface deformation recovery algorithm for reflector antennas based on geometric optics. Optics Express. 2017. V. 25. № 20. P. 24346–24361.
11. Suzuki Yo., Harada S., Kobayashi K., Ueba M., Ohara K. Deformed antenna pattern compensation method for onboard multi-beam antennas. 25th AIAA International Communications Satellite Systems Conference (APSCC). AIAA 2007-3269. P. 1–7.
12. Yoshinori S., Satoshi H., Kiyoshi K., Masazumi U. Deformed antenna pattern compensation technique for multi-beam antennas for broadband and scalable mobile communications satellite. International Symposium on Antennas and Propagation. 2006. P. 1–6.
13. Choni Y.I., Dardymov A.V., Romanov A.G., Danilov I.Yu. 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). 2021. Kazan, Russia. P. 1–5.
14. 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). 2021. Kazan, Russia. P. 1–5.
15. Choni Yu.I. Lokal'nyj fazovyj tsentr antenny i ego godograf: metodologiya, tekhnika vychislenij. Antenny. 2017. № 10. S. 36–45. (in Russian)