The problem of the synthesis of optimal continuous aperture sources to optimally realize the satellite multibeam coverage of Earth is stated and solved. The design approach relies on a far-field representation which exploits at best the degrees of freedom arising from the geometrical structure of the well-known four-colors colour coverage map. The overall synthesis is stated as a convex-programming problem wherein the fast achievement of the (unique) globally optimal solution is guaranteed. The introduced tools allow stating the ultimate theoretical radiation performances achievable by any circular-aperture antenna of fixed size and, at the same time, can be exploited as a reference in the synthesis of isophoric direct-radiating arrays. Numerical examples concerning a mission scenario recently proposed by the European Space Agency are provided.
2. Bolt, R. J., D. Cavallo, G. Gerini, D. Deurloo, R. Grooters, A. Neto, and G. Toso, "Characterization of a dual-polarized connected-dipole array for Ku-band mobile terminals," IEEE Transactions on Antennas and Propagation, Vol. 64, No. 2, 591-598, 2016.
3. Morabito, A. F., T. Isernia, and L. Di Donato, "Optimal synthesis of phase-only reconfigurable linear sparse arrays having uniform-amplitude excitations," Progress In Electromagnetics Research, Vol. 124, 405-423, 2012.
4. Fonseca, N. J. G., J.-C. Angevain, and C. Mangenot, "Toward the terabit/s satellite: Antenna design trade-offs and analyses," Proceedings of the 33rd European Space Agency Antenna Workshop, 2011.
5. Rao, S. K., "Parametric design and analysis of multiple-beam reflector antennas for satellite communications," IEEE Antennas and Propagation Magazine, Vol. 45, No. 4, 26-34, 2003.
6. Fonseca, N. J. G. and J. Sombrin, "Multi-beam reflector antenna system combining beam hopping and size reduction of effectively used spots," IEEE Antennas and Propagation Magazine, Vol. 54, No. 2, 88-99, 2012.
7. Appel, K. and W. Haken, "Every planar map is four colourable, Part I: Discharging," Illinois Journal of Mathematics, Vol. 21, 429-490, 1977.
8. Bucci, O. M., T. Isernia, and A. F. Morabito, "Optimal synthesis of directivity constrained pencil beams by means of circularly symmetric aperture fields," IEEE Antennas and Wireless Propagation Letters, Vol. 8, 1386-1389, 2009.
9. Bucci, O. M., T. Isernia, A. F. Morabito, S. Perna, and D. Pinchera, "Density and element-size tapering for the design of arrays with a reduced number of control points and high efficiency," Proceedings of the Fourth European Conference on Antennas and Propagation, EuCAP 2010, Barcelona, Spain, April 12-16, 2010.
10. Bucci, O. M., T. Isernia, and A. F. Morabito, "A deterministic approach to the synthesis of pencil beams through planar thinned arrays," Progress In Electromagnetics Research, Vol. 101, 217-230, 2010.
11. Morabito, A. F., T. Isernia, M. G. Labate, M. D’Urso, and O. M. Bucci, "Direct radiating arrays for satellite communications via aperiodic tilings," Progress In Electromagnetics Research, Vol. 93, 107-124, 2009.
12. Rhodes, D. R., "On the quality factor of strip and line source antennas and its relationship to superdirectivity ratio," IEEE Transactions on Antennas and Propagation, Vol. 20, No. 3, 318-325, 1972.
13. Bucci, O. M., C. Gennarelli, and C. Savarese, "Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples," IEEE Transactions on Antennas and Propagation, Vol. 46, No. 3, 351-359, 1998.
14. Bucci, O. M. and G. Franceschetti, "On the degrees of freedom of scattered fields," IEEE Transactions on Antennas and Propagation, Vol. 37, No. 7, 918-926, 1989.
15. Bertero, M. and P. Boccacci, "Singular value decomposition," Introduction to Inverse Problems in Imaging, 1st Edition, Section 9, 220-246, CRC Press, 1998.
16. Collin, R. E., "Circular waveguides," Foundations of Microwave Engineering, 2nd Edition, 194-198, IEEE Press, Wiley Interscience, New York, 1992.
17. Gradshteyn, I. S. and I. M. Ryzhik, Table of Integrals, Series and Products, 6th Ed., 653-662, Academic Press, USA, 2000.
18. Isernia, T. and G. Panariello, "Optimal focusing of scalar fields subject to arbitrary upper bounds," Electronics Letters, Vol. 34, No. 2, 162-164, 1998.
19. Bucci, O. M., T. Isernia, and A. F. Morabito, "Optimal synthesis of circularly symmetric shaped beams," IEEE Transactions on Antennas and Propagation, Vol. 62, No. 4, 1954-1964, 2014.
20. Vigano, M. C., G. Toso, G. Caille, C. Mangenot, and I. E. Lager, "Sunflower array antenna with adjustable density taper," International Journal of Antennas and Propagation, Vol. 2009, 10 pages, Article ID 624035, doi:10.1155/2009/624035, 2009.
21. Angeletti, P., G. Toso, and G. Ruggerini, "Array antennas with jointly optimized elements positions and dimensions, Part II: Planar circular arrays," IEEE Transactions on Antennas and Propagation, Vol. 62, No. 4, 1627-1639, 2013.