2022-10-02
Mask-Constrained Synthesis of Domino-Like Tiled Phased Arrays
By
Progress In Electromagnetics Research B, Vol. 96, 173-195, 2022
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.
Citation
Luca Tosi, and Arianna Benoni, "Mask-Constrained Synthesis of Domino-Like Tiled Phased Arrays," Progress In Electromagnetics Research B, Vol. 96, 173-195, 2022.
doi:10.2528/PIERB22061304
References

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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.        Google Scholar

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        Google Scholar

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.        Google Scholar

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        Google Scholar

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        Google Scholar

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.        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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.        Google Scholar