volume | PIER Journals

Abstract

In this work, the mask-constrained synthesis of domino-tiled phased arrays is addressed. By exploiting tiling theorems and theory, optimal and sub-optimal methods for the synthesis of domino arrangements and the corresponding excitations that minimize the deviation of the radiation pattern from a user-defined power mask are presented. A set of numerical examples, carried out with full-wave simulators and concerned with different aperture sizes and various mask shapes, is reported to assess the effectiveness, limitations, and ranges of computationally-admissible applicability of the proposed methods.

1. Rocca, P., G. Oliveri, R. J. Mailloux, and A. Massa, "Unconventional phased array architectures and design Methodologies --- A review," Proc. IEEE, Vol. 104, No. 3, 544-560, Mar. 2016.
doi:10.1109/JPROC.2015.2512389

2. Bucci, O. M., M. D'Urso, T. Isernia, P. Angeletti, and G. Toso, "Deterministic synthesis of uniform amplitude sparse arrays via new density taper techniques," IEEE Trans. Antennas Propag., Vol. 58, No. 6, 1949-1958, Jun. 2010.
doi:10.1109/TAP.2010.2046831

3. Haupt, R. L., "Adaptively thinned arrays," IEEE Trans. Antennas Propag., Vol. 63, No. 4, 1626-1632, Apr. 2015.
doi:10.1109/TAP.2015.2394785

4. Salucci, M., G. Gottardi, N. Anselmi, and G. Oliveri, "Planar thinned array design by hybrid analytical-stochastic optimization," IET Microw. Antennas Propag., Vol. 11, No. 13, 1841-1845, Oct. 2017.
doi:10.1049/iet-map.2017.0349

5. Oliveri, G., A. Gelmini, A. Polo, N. Anselmi, and A. Massa, "System-by-design multi-scale synthesis of task-oriented reflectarrays," IEEE Trans. Antennas Propag., Vol. 68, No. 4, 2867-2882, Apr. 2020.
doi:10.1109/TAP.2019.2955217

6. Salucci, M., A. Gelmini, G. Oliveri, N. Anselmi, and A. Massa, "Synthesis of shaped beam reflectarrays with constrained geometry by exploiting non-radiating surface currents," IEEE Trans. Antennas Propag., Vol. 66, No. 11, 5805-5817, Nov. 2018.
doi:10.1109/TAP.2018.2869036

7. Guan, D., Z. Qian, Y. Zhang, and J. Jin, "High-gain SIW cavity-backed array antenna with wideband and low sidelobe characteristics," IEEE Antennas Wireless Propag. Lett., Vol. 14, 1774-1777, 2015.
doi:10.1109/LAWP.2015.2423497

8. Rocca, P., L. Manica, and A. Massa, "Synthesis of monopulse antennas through iterative contiguous partition method," Electron. Lett., Vol. 43, No. 16, 854-856, 2007.
doi:10.1049/el:20071336

9. Manica, L., P. Rocca, A. Martini, and A. Massa, "An innovative approach based on a tree-searching algorithm for the optimal matching of independently optimum sum and difference excitations," IEEE Trans. Antennas Propag., Vol. 56, No. 1, 58-66, Jan. 2008.
doi:10.1109/TAP.2007.913037

10. D' Urso, M., T. Isernia, and E. F. Meliado, "An effective hybrid approach for the optimal synthesis of monopulse antennas," IEEE Trans. Antennas Propag., Vol. 55, No. 4, 1059-1066, 2007.
doi:10.1109/TAP.2007.893374

11. Rocca, P., M. H. Hannan, L. Poli, N. Anselmi, and A. Massa, "Optimal phase-matching strategy for beam scanning of sub-arrayed phased arrays," IEEE Trans. Antennas Propag., Vol. 67, No. 2, 951-959, Feb. 2019.
doi:10.1109/TAP.2018.2879778

12. Mailloux, R. J., S. G. Santarelli, and T. M. Roberts, "Wideband arrays using irregular (polyomino) shaped subarrays," Electronics Lett., Vol. 42, No. 18, 1019-1020, Aug. 2006.
doi:10.1049/el:20062252

13. Mailloux, R. J., S. G. Santarelli, T. M. Roberts, and D. Lu, "Irregular polyomino-shaped subarrays for space-based active arrays," Int. J. Antennas Propag., Vol. 2009, Article ID 956524, 2009.

14. Morabito, A. F., T. Isernia, M. G. Labate, M. Durso, and O. M. Bucci, "Direct radiating arrays for satellite communications via aperiodic tilings," Progress In Electromagnetics Research, Vol. 93, 107-124, 2009.
doi:10.2528/PIER09040908

15. Yang, X., W. Xi, Y. Su, T. Zeng, T. Long, and T. K. Sarkar, "Optimization of subarray partition for large planar phased array radar based on weighted K-means clustering method," IEEE Trans. Antennas Propag., Vol. 9, No. 8, 1460-1468, Dec. 2015.

16. Rocca, P., R. J. Mailloux, and G. Toso, "GA-based optimization of irregular sub-array layouts for wideband phased arrays design," IEEE Antennas Wireless Propag. Lett., Vol. 14, 131-134, 2015.
doi:10.1109/LAWP.2014.2356855

17. Oppermann, M. and R. Rieger, "RF modules (Tx-Rx) with multifunctional MMICs," 2017 IMAPS Nordic Conference on Microelectronics Packaging (NordPac), 57-60, IEEE, Jun. 2017.
doi:10.1109/NORDPAC.2017.7993164

18. Lyon, R., A. Kinghorn, G. Morrison, A. Stonehouse, G. Byrne, and M. Dugan, "Active electronically scanned tiled array antenna," IEEE International Symposium on Phased Array Systems and Technology, 160-164, Oct. 2013.

19. Xiong, Z. Y., Z. H. Xu, S. W. Chen, and S. P. Xiao, "Subarray partition in array antenna based on the algorithm X," IEEE Antennas Wireless Propag. Lett., Vol. 12, 906-909, 2013.
doi:10.1109/LAWP.2013.2272793

20. Anselmi, N., P. Rocca, and A. Massa, "Irregular phased array tiling by means of analytic schemata-driven optimization," IEEE Trans. Antennas Propag., Vol. 65, No. 9, 4495-4510, Sep. 201.
doi:10.1109/TAP.2017.2722539

21. Diao, J., J. W. Kunzler, and K. F. Warnick, "Sidelobe level and aperture efficiency optimization for tiled aperiodic array antennas," IEEE Trans. Antennas Propag., Vol. 65, No. 12, 7083-7090, Jan. 2017.
doi:10.1109/TAP.2017.2766679

22. Ma, Y., S. Yang, Y. Chen, S. Qu, and J. Hu, "Pattern synthesis of 4-D irregular antenna arrays based on maximum-entropy model," IEEE Trans. Antennas Propag., Vol. 67, No. 5, 3048-3057, May 2019.
doi:10.1109/TAP.2019.2896730

23. Dong, W., Z.-H. Xu, X.-H. Liu, L.-S.-B. Wang, and S.-P. Xiao, "Modular subarrayed phased-array design by means of iterative convex relaxation optimization," IEEE Antennas Wireless Propag. Lett., Vol. 18, No. 3, 447-451, Jan. 2019.
doi:10.1109/LAWP.2019.2893946

24. Rocca, P., N. Anselmi, A. Polo, and A. Massa, "Modular design of hexagonal phased arrays through diamond tiles," IEEE Trans. Antennas Propag., Vol. 68, No. 5, 3598-3612, May 2020.
doi:10.1109/TAP.2019.2963561

25. Rocca, P., N. Anselmi, A. Polo, and A. Massa, "Pareto-optimal domino-tiling of orthogonal polygon phased arrays," IEEE Trans. Antennas Propag., Vol. 70, No. 5, 3329-3342, May 2022.
doi:10.1109/TAP.2021.3137298

26. Avser, B., J. Pierro, and G. M. Rebeiz, "Random feeding networks for reducing the number of phase shifters in limited-scan arrays," IEEE Trans. Antennas Propag., Vol. 64, No. 11, 4648-4658, Nov. 2016.
doi:10.1109/TAP.2016.2600861

27. Rocca, P., N. Anselmi, A. Polo, and A. Massa, "An irregular two-sizes square tiling method for the design of isophoric phased arrays," IEEE Trans. Antennas Propag., Vol. 68, No. 6, 4437-4449, Jun. 2020.
doi:10.1109/TAP.2020.2970088

28. Conwey, J. H. and J. C. Lagarias, "Tiling with polyominoes and combinatorial group theory," J. Combinatorial Theory, Series A, Vol. 53, 183-208, 1990.
doi:10.1016/0097-3165(90)90057-4

29. Klarner, D. A., "Packing a rectangle with congruent N-ominoes," J. Combinatorial Theory, Vol. 7, 107-115, 1969.
doi:10.1016/S0021-9800(69)80044-X

30. Brualdi, R. A. and T. H. Foregger, "Packing boxes with harmonic bricks," J. Combinatorial Theory, Vol. 17, 81-114, 1974.
doi:10.1016/0095-8956(74)90078-1

31. Barnes, F. W., "Packing the maximum number of m × n tiles in a large p × q rectangle," Discrete Math., Vol. 26, 93-100, 1979.
doi:10.1016/0012-365X(79)90115-8

32. Kasteleyn, P., "The statistics of dimers on a lattice I. The number of dimer arrangements on a quadratic lattice," Physica, Vol. 27, 1209-1225, 1961.
doi:10.1016/0031-8914(61)90063-5

33. Thurston, W. P., "Conway's tiling groups," The American Mathematical Monthly, Vol. 97, No. 8, 757-773, Oct. 1990.
doi:10.1080/00029890.1990.11995660

34. Desreux, S. and E. Remila, "An optimal algorithm to generate tilings," J. Discrete Alg., Vol. 4, 168-180, 2006.
doi:10.1016/j.jda.2005.01.003

35. Gottardi, G., L. Poli, P. Rocca, A. Montanari, A. Aprile, and A. Massa, "Optimal monopulse beamforming for side-looking airborne radars," IEEE Antennas Wireless Propag. Lett., Vol. 16, 1221-1224, 2017.
doi:10.1109/LAWP.2016.2628881

36. Wachter, A. and L. Biegler, "On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming," Math. Program., Vol. 106, 25-57, Mar. 2006.
doi:10.1007/s10107-004-0559-y

37. Rocca, P., M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, "Evolutionary optimization as applied to inverse scattering problems," Inv. Prob., Vol. 24, 1-41, 2009.

Dr. Luca Tosi

Dr. Arianna Benoni