D. D. Gabrielyan1, K. M. Zanin2, D. S. Fedorov3
1–3 Federal State Unitary Enterprise “Rostov-on-Don Scientific Research Institute of Radio Communications” FSPC
(Rostov-on-Don, Russia)

The analysis of the directional characteristics of a phased array antenna is one of the main problems in the development of an antenna. The key issue in carrying out this analysis is an adequate representation of the directional characteristics of the phased array antenna with known directional patterns and the set-up as part of the aperture of antenna elements. There are many works considering the directional characteristics of the antenna, taking into account the mutual connection between the antenna elements. A number of works are devoted to the study of the directional characteristics of a phased array antenna in the presence of random errors of the amplitude-phase distribution in the radiating aperture. However, the issues related to the influence of the antenna elements installation error in the radiating aperture on the directional characteristics of the phased array antenna practically did not receive their consideration. With this in mind, this article discusses a mathematical model of the radiating aperture of a phased array antenna in the presence of errors in the antenna elements installation. At the same time, the installation error means not only the displacement of the antenna elements, but also its rotation relative to three axes, due to a violation of the shape of the radiating aperture.

The objective of the article is to investigate the influence of the antenna element installation errors, including the displacement and reversal of the antenna elements in the radiating aperture, on the directional characteristics of the phased array antenna, based on strict consideration of the relationship between the directional characteristics of the phased array antenna and the parameters of the antenna elements installation in the radiating aperture.

The main results obtained in the article are as follows.

1. A mathematical model of the radiating aperture of the phased array antenna, taking into account the errors of installation of the antenna elements in the aperture, including displacement of the phase center of the antenna elements and rotation of the antenna elements relative to the plane of the radiating aperture at three angles.

2. Investigation of the main patterns of changes in the directional characteristics of the phased array antenna due to the presence of errors in the antenna elements installation in the radiating aperture of the phased array antenna. In particular, errors in the installation of antenna elements practically do not lead to a change in the main beam either in width or in level. The most significant changes in the directional characteristics are manifested as follows:

the structure and level of the side lobes of the directional patterns of the phased array antenna change;

there is a cross-polarized component in the directional pattern, which, unlike the main component, is weakly directional.

The developed mathematical model and the obtained simulation results allow us to determine the relationship between the parameters of the antenna elements installation errors as part of the phased array antenna aperture with a change in the amplitude, phase and polarization directional pattern, on the basis of which requirements for the accuracy of the parameters of the radiating aperture and the accuracy of the antenna elements installation can be formulated. These results are most significant for communication and radar systems that use orthogonal polarization signals when receiving and radiating.

Gabrielyan D.D., Zanin K.M., Fedorov D.S. Mathematical model of phased array antenna aperture in the presence of errors in the position of antenna elements. Antennas. 2023. № 2. P. 52–58. DOI: https://doi.org/10.18127/j03209601-202302-06 (in Russian)

1. Skobelev S.P. Fazirovannye antennye reshetki s sektornymi partsial'nymi diagrammami napravlennosti. M.: Fizmatlit. 2010. (in Russian)
2. Verba V.S., Neronskij L.B., Osipov I.G. i dr. Radiolokatsionnye sistemy zemleobzora kosmicheskogo bazirovaniya. Pod red. V.S. Verby. M.: Radiotekhnika. 2010. (in Russian)
3. Shishlov A.V., Denisenko V.V., Levitan B.A., Topchiev S.A., Shitikov A.M. Aktivnye fazirovannye antennye reshetki – sostoyanie i tendentsii razvitiya. Zhurnal radioelektroniki [elektronnyj zhurnal]. 2023. № 1. DOI: https://doi.org/10.30898/1684-1719.2023.1.5. (in Russian)
4. 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)
5. Mailloux R.J. Phased array antenna handbook. 2nd Edition. Boston–London: Artech House. 2005.
6. Rebeiz G.M. SiGe and CMOS for advanced phased array communication and radar systems. Proceedings of 2016 Phased Array Symposium. Boston. 2016. P. 1–107.
7. Obukhovets V.A. Some new trends in phased antenna array designing. Conference Proceedings «Radiation and Scattering of Elec-tromagnetic Waves». 2019.
8. Gültepe G., Kanar T., Zihir S., Rebeiz G.M. A 1024-element Ku-band SATCOM phased-array transmitter with 45-dBW single-polarization EIRP. IEEE Transactions on Microwave Theory and Techniques. 2021. V. 69. № 9.
9. Bankov S.E., Kaloshin V.A., Frolova E.V. Sintez i analiz planarnoj volnovodnoj reshetki s chastotnym skanirovaniem, sfokusirovannoj v zone Frenelya. Radiotekhnika i elektronika. 2016. T. 61. № 6. S. 547–557. DOI: 10.7868/S0033849416060036. (in Russian)
10. Denisenko V.V., Kozlov V.N., Kolesnikov R.A., Korchemkin Yu.B., Krivosheev Yu.V., Levitan B.A., Shitikov A.M., Shishlov A.V., Yanuk'yan Z.A., Uhm M.S., Yun S.H. Printsipy sozdaniya aktivnoj fazirovannoj antennoj reshetki dlya terminalov sputnikovoj svyazi na osnove mnogoslojnoj pechatnoj platy. Radiotekhnika. 2021. T. 85. № 10. S. 42–52. DOI: https://doi.org/10.18127/j00338486-202110-05. (in Russian)
11. Anpilogov V., Pekhterev S., Shishlov A. Antennaya reshetka i abonentskij terminal Starlink. Tekhnologii i sredstva svyazi. 2020. № S1. S. 69–76. (in Russian)
12. Bankov S.E., Kaloshin V.A., Frolova E.V. Issledovanie chastotno-fazovykh kharakteristik skanirovaniya sfokusirovannoj volnovodno-shchelevoj reshetki. Zhurnal radioelektroniki [elektronnyj zhurnal]. 2017. № 5. URL: http://jre.cplire.ru/jre/may17/9/text.pdf. (in Russian)
13. Nekrasov A.V., Khachaturian A., Abramov E.S., Popov D., Markelov O., Obukhovets V.A., Veremyev V., Bogachev M. Optimization of the airborne antenna geometry for the ocean surface scatterometric measurements. Remote Sensing. 2018. V. 10. № 10.
14. Delos P. Digital beamforming accelerates the evolution to next-generation radar. Microwave Journal. 2017. V. 60. № 1.
15. Fulton C., Yeary M., Thompson D., Lake J., Mitchell A. Digital phased arrays: Challenges and opportunities. Proceedings of the IEEE. 2016. V. 104. № 3. DOI: https://doi.org/10.1109/JPROC.2015.2501804.
16. Ku B.J., Ahn D.-S., Lee S.-P., Shishlov A.V., Reutov A.S., Ganin S.A., Shubov A.G. Radiation pattern of multibeam array antenna with digital beamforming for stratospheric communication System: Statistical simulation. ETRI Journal. 2002. V. 24. № 3. DOI: https://doi.org/ 10.4218/etrij.02.0102.0303.
17. Shishlov A.V. Teoriya i tekhnika aktivnykh fazirovannykh antennykh reshetok. M.: MFTI. 2013. (in Russian)
18. Borisov S.N., Denisenko V.V., Levitan B.A., Shishlov A.V. Antenny dlya shirokopolosnoj sputnikovoj svyazi na dvizhushchemsya transporte. Analiticheskij obzor. Radiotekhnika. 2015. № 10. (in Russian)
19. Shishlov A.V., Levitan B.A., Topchiev S.A., Anpilogov V.R., Denisenko V.V. Mnogoluchevye antenny dlya sistem radiolokatsii i svyazi. Zhurnal radioelektroniki. 2018. № 7. (in Russian)
20. Vi U.N., Kaloshin V.A., Le D.T. Mnogoluchevye volnovodno-shchelevye antennye reshetki s bifokal'nymi diagrammo-obrazuyushchimi sistemami. Zhurnal radioelektroniki [elektronnyj zhurnal]. 2020. № 3. URL: http://jre.cplire.ru/jre/mar20/13/text.pdf. (in Russian)
21. Shifrin Ya.S. Voprosy statisticheskoj teorii antenn. M.: Sov. radio. 1970. (in Russian)
22. Rocca P. Analysis of the pattern tolerances in linear arrays with arbitrary amplitude errors. IEEE Antennas and Wireless Propagation Letters. 2013. V. 12.
23. Maslov O.N., Rakov A.S., Silkin A.A. Statisticheskie kharakteristiki polya reshetki aperturnykh sluchajnykh antenn. Radiotekhnika i elektronika. 2013. T. 58. № 11. (in Russian)
24. Krasil'nikova E.P., Maslov O.N., Rakov A.S. Modelirovanie statisticheskikh kharakteristik elektromagnitnogo polya aperturnoj sluchajnoj antenny. Infokommunikatsionnye tekhnologii. 2014. T. 12. № 2. (in Russian)
25. Zimina S.V. Vliyanie fluktuatsij vesovogo vektora na statisticheskie kharakteristiki adaptivnoj antennoj reshetki s nelinejnoj fluktuatsiej v tsepi obratnoj svyazi, nastraivaemoj po algoritmu LMS s kvadratichnym ogranicheniem. Fizika volnovykh protsessov i radiotekhnicheskie sistemy. 2014. T. 17. № 4. (in Russian)
26. Korn G., Korn T. Spravochnik po matematike (dlya nauchnykh rabotnikov i inzhenerov). M.: Nauka. 1977. (in Russian)