S1

The problem of the optimal synthesis of a shaped beam lying in a power mask specified by an ‘upper bound’ function and a ‘lower bound’ function is definitively solved in [1] for the case of uniformly-spaced linear arrays. The approach splits the problem into a feasibility step (amounting to solve a linear programming problem) and actual synthesis (which requires factorization of a polynomial). Notably, in case the feasibility analysis says a solution exists, a large set of equivalent excitations producing the same power pattern is easily found. Such a multiplicity, far from being a problem, allows to eventually optimize some additional performance parameter (such as for instance dynamic range ratio).
The approach has been recently extended to planar arrays radiating ring-shaped patterns [2], to those cases in which the antenna designer needs to maximize the power radiated in a given portion of the visible space [3], to linear equispaced arrays having an even excitation distribution [4], and to completely-arbitrary 1-D and 2-D arrays (including sparseness, mutual coupling, and mounting-platform effects) [5]-[8].

1. T. Isernia, O. M. Bucci, and N. Fiorentino, “Shaped beam antenna synthesis problems: Feasibility criteria and new strategies,” Journal of Electromagnetic Waves and Applications, vol. 12, no. 1, pp. 103-138, 1998. [click here]
2. A. F. Morabito, A: R. Lagana, and T. Isernia, “On the optimal synthesis of ring symmetric shaped patterns by means of uniformly spaced planar arrays,” Progress In Electromagnetics Research,vol. 20, 33-48, 2010. [click here]
3. A. F. Morabito, A: R. Lagana, and T. Isernia, “Optimizing power transmission in given target areas in the presence of protection requirements,” IEEE Antennas and Wireless Propagation Letters,vol. 14, pp. 44-47, 2014. [click here]
4. T. Isernia and A. F. Morabito, “Mask-constrained power synthesis of linear arrays with even excitations,” IEEE Transactions on Antennas and Propagation,vol. 64, no. 7, pp. 3212-3217, 2016. [click here]
5. G. G. Bellizzi, D. A. M. Iero, L. Crocco, and T. Isernia, “Three-dimensional field intensity shaping: The scalar case,”IEEE Antennas and Wireless Propagation Letters, vol. 17, no. 3, pp. 360-363, 2018. [click here]
6. A. F. Morabito, A. Di Carlo, L. Di Donato, T. Isernia, and G. Sorbello, “Extending spectral factorization to array pattern synthesis including sparseness, mutual coupling, and mounting-platform effects,”IEEE Transactions on Antennas and Propagation, vol. 67, no. 7, pp. 4548-4559, 2019. [click here]
7. G. M. Battaglia, G. G. Bellizzi, A. F. Morabito, G. Sorbello, and T. Isernia, “A general effective approach to the synthesis of shaped beams for arbitrary fixed-geometry arrays,”Journal of Electromagnetic Waves and Applications, vol. 33, no. 18, pp. 2404-2422, 2019. [click here]
8. G. M. Battaglia, A. F. Morabito, G. Sorbello, and T. Isernia, “Mask-Constrained Power Synthesis of Large and Arbitrary Arraysas a Few-Samples Global Optimization,”Progress In Electromagnetics Research, vol. 98, pp. 69-81, 2020. [click here]
9. Giada Maria Battaglia, Andrea Francesco Morabito, Gino Sorbello, and Tommaso Isernia, “Mask-Constrained Power Synthesis of Large and Arbitrary Arraysas a Few-Samples Global Optimization,” Progress In Electromagnetics Research C, Vol. 98, 69-81, 2020. [click here]
10. Battaglia, G. M., Bellizzi, G. G., Morabito, A. F., Sorbello, G., & Isernia, T. (2019). A general effective approach to the synthesis of shaped beams for arbitrary fixed-geometry arrays. Journal of Electromagnetic Waves and Applications, 33(18), 2404–2422. [click here]
11. A. F. Morabito, A. Di Carlo, L. Di Donato, T. Isernia and G. Sorbello, “Extending Spectral Factorization to Array Pattern Synthesis Including Sparseness, Mutual Coupling, and Mounting-Platform Effects,” in IEEE Transactions on Antennas and Propagation, vol. 67, no. 7, pp. 4548-4559, July 2019. [click here]
12. G. M. Battaglia, A. F. Morabito, R. Palmeri and T. Isernia, “Extending Spectral Factorization to the 2-D Mask-Constrained Power Synthesis of Shaped Beams with Arbitrary Footprints,” 2024 18th European Conference on Antennas and Propagation (EuCAP), Glasgow, United Kingdom, 2024. [click here]