V. V. Demshevsky1, G. S. Anikin2
1, 2 JSC RPC «Istok» named after Shokin (Fryazino, Moscow region, Russia)
2 Moscow Aviation Institute (National Research University) (Moscow, Russia)

2 r0ai@bk.ru

The paper demonstrates that for compact active phased antenna arrays, the clustering problem should not be treated as an isolated combinatorial tiling problem of the aperture, but rather as a synthesis problem of a physically optimal structure of phase centers that ensures wide-angle electronic scanning.

The proposed two-level scheme, in which algorithm “X” is used to generate aperture coverings with clusters while the final selection is made based on physical criteria, has enabled a transition from a set of formally admissible solutions to a set of functional configurations.

For compact antenna arrays with an aperture electrical size D = (4…15)λ, a system of quantitative constraints on the admissibility of clustering has been derived. For the central case of D ≈ 8λ, a configuration consisting of 112 two-element domino clusters has been justified and verified; this configuration provides a two-fold reduction in the number of transmit-receive modules compared to a traditional uniform array.

Thus, the region has been established where clustering for apertures with a characteristic size of approximately 8λ is not only combinatorially admissible but also physically rational.

Demshevsky V.V., Anikin G.S. Clustered antenna array for compact APAA with wide-angle electronic scanning // Antennas. 2026. № 3. P. 37–54. DOI: https://doi.org/10.18127/j03209601-202603-04

1. Rocca P., Oliveri G., Mailloux R.J. et al. Unconventional phased array architectures and design methodologies – A review. Proceedings of the IEEE. 2016. V. 104. № 3. P. 544–560.
2. Antennye reshetki. Metody rascheta i proektirovaniya. Pod red. L.S. Benensona. M.: Sov. radio. 1966. (in Russian)
3. Trifonov D.A. Razrabotka rekomendatsij po proektirovaniyu antennoj sistemy dlya aerologicheskikh issledovanij atmosfery. Magisterskaya dissertatsiya. Ekaterinburg. 2020. (in Russian)
4. Golomb S.V. Polimino: Per. s angl. V. Firsova. M.: Mir. 1975. (in Russian)
5. Kasteleyn P.W. The statistics of dimers on a lattice. I. The number of dimer arrangements on a quadratic lattice. Physica. 1961. V. 27. P. 1209–1225.
6. Karp R.M. Reducibility among combinatorial problems. In Complexity of Computer Computations. R.E. Miller, J.W. Thatcher (Eds.). New York: Plenum Press. 1972. P. 85–103.
7. Anselmi N., Rocca P., Salucci M. et al. Irregular phased array tiling by beans of analytic schemata-driven optimization. IEEE Transactions on Antennas and Propagation. 2017. V. 65. № 9.
8. Korn M., Pak I. Tilings of rectangles with T-tetrominoes [Elektronnyj resurs]. URL: https://www.math.ucla.edu/~pak/papers/ttet11.pdf (data obrashcheniya: 11.12.2025).
9. Rocca P., Anselmi N., Polo A. et al. Pareto-optimal domino-tiling of orthogonal polygon phased arrays. IEEE Transactions on Antennas and Propagation. 2022. V. 70. № 5.
10. Mailloux R.J., Santarelli S.G., Roberts T.M. et al. Irregular polyomino-shaped subarrays for space-based active arrays. International Journal of Antennas and Propagation. 2009. V. 2009. Art. ID 956524. DOI: 10.1155/2009/956524.
11. Chirikov R.Yu., Roka P., Bagmanov V.Kh. i dr. Algoritm proektirovaniya fazirovannykh antennykh reshetok dlya sputnikovykh sistem svyazi. Vestnik UGATU. 2013. T. 17. № 4 (57). S. 159–166. (in Russian)
12. Chirikov R., Rocca P., Manica L. et al. Innovative GA-based strategy for polyomino tiling in phased array design. 7th European Conference on Antennas and Propagation (EuCAP). 2013.
13. Gwee B.H., Lim M.H. Polyominoes tiling by a genetic algorithm. Computational optimization and applications. 1996. № 6. P. 273–291.
14. Dicandia F.A., Genovesi S. Wide-scan and energy-saving phased arrays by exploiting Penrose tiling subarrays. IEEE Transactions on Antennas and Propagation. 2022. V. 70. № 9. P. 7524–7537.
15. Spence T.G., Werner D.H. Design of broadband planar arrays based on the optimization of aperiodic tilings. IEEE Transactions on Antennas and Propagation. 2008. V. 56. № 1. P. 76–86.
16. Dicandia F.A., Genovesi S. Analysis of performance enhancement of clustered-based phased arrays employing mixed antenna element factor. IEEE Transactions on Antennas and Propagation. 2024. V. 72. № 2. P. 1439–1448.
17. Bagno D.V. Analiz fazovoj kharakteristiki napravlennosti i opredelenie fazovogo tsentra antenn s ispol'zovaniem metoda preobrazovaniya Fur'e. Antenny. 2024. № 5. S. 58–71. (in Russian)
18. Klarner D.A. Packing a rectangle with congruent N-ominoes. Journal of Combinatorial Theory. 1969. V. 7. № 2. P. 107–115.
19. Knuth D.E. Dancing links. arXiv:cs/0011047v1 [cs.DS]. 2000.
20. Xiong Z.-Y., Xu Z.-H., Chen S.-W. et al. Subarray partition in array antenna based on the algorithm X. IEEE Antennas and Wireless Propagation Letters. 2013. V. 12.
21. Markov G.T., Sazonov D.M. Antenny. M.: Energiya. 1975. (in Russian)
22. Lotov A.V., Pospelova I.I. Konspekt lektsij po teorii i metodam mnogokriterial'noj optimizatsii: Ucheb. posobie. M.: VMIK MGU. 2014. (in Russian)