volume | PIER Journals

Abstract

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.

1. Bailleul, P. K., "A new era in elemental digital beamforming for spaceborne communications phased arrays," Proceedings of the IEEE, Vol. 104, No. 3, 623-632, 2016.
doi:10.1109/JPROC.2015.2511661 Google Scholar

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.
doi:10.1109/TAP.2015.2509505 Google Scholar

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.
doi:10.2528/PIER11112210 Google Scholar

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. Google Scholar

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.
doi:10.1109/MAP.2003.1241308 Google Scholar

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.
doi:10.1109/MAP.2012.6230720 Google Scholar

7. Appel, K. and W. Haken, "Every planar map is four colourable, Part I: Discharging," Illinois Journal of Mathematics, Vol. 21, 429-490, 1977. Google Scholar

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.
doi:10.1109/LAWP.2009.2039189 Google Scholar

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. Google Scholar

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.
doi:10.2528/PIER10010104 Google Scholar

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.
doi:10.2528/PIER09040908 Google Scholar

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.
doi:10.1109/TAP.1972.1140191 Google Scholar

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.
doi:10.1109/8.662654 Google Scholar

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.
doi:10.1109/8.29386 Google Scholar

15. Bertero, M. and P. Boccacci, "Singular value decomposition," Introduction to Inverse Problems in Imaging, 1st Edition, Section 9, 220-246, CRC Press, 1998. Google Scholar

16. Collin, R. E., "Circular waveguides," Foundations of Microwave Engineering, 2nd Edition, 194-198, IEEE Press, Wiley Interscience, New York, 1992. Google Scholar

17. Gradshteyn, I. S. and I. M. Ryzhik, Table of Integrals, Series and Products, 6th Ed., 653-662, Academic Press, 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.
doi:10.1049/el:19980212 Google Scholar

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.
doi:10.1109/TAP.2014.2302842 Google Scholar

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. Google Scholar

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.
doi:10.1109/TAP.2013.2281519 Google Scholar

Prof. Andrea Francesco Morabito

Dr. Antonia Rita Lagana

Dr. Loreto Di Donato