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Three-Parameter Elliptical Aperture Distributions for Sum and Difference Antenna Patterns Using Particle Swarm Optimization (Invited Paper)

By Arthur Densmore and Yahya Rahmat-Samii
Progress In Electromagnetics Research, Vol. 143, 709-743, 2013


This paper presents a unified analysis of the three-parameter aperture distributions for both sum and difference antenna patterns, suitable for communications or telemetry applications with either a stationary or tracking antenna, and with the parameters automatically determined by Particle-Swarm Optimization (PSO). These distributions can be created, for example, by reflector, phased array, or other antenna systems. The optimizations involve multiple objectives, for which Pareto efficiency concepts apply, and are accelerated by compact, analytical closed-form equations for key metrics of the distributions, including the far-field radiation pattern and detection slope of the difference pattern. The limiting cases of the threeparameter distributions are discussed and shown to generalize other distributions in the literature. A derivation of the generalized vector far fields provides the background for the distribution study and helps clarify the definition of cross-polarization in the far-field. Examples are given to show that the three-parameter (3P) distributions meet a range of system-level constraints for various applications, including a sidelobe mask for satellite ground stations and maximizing pointing error detection sensitivity while minimizing clutter from sidelobes for tracking applications. The equations for the relative angle sensitivity for the difference pattern are derived. A study of the sensitivity of the 3P parameter values is presented.


Arthur Densmore and Yahya Rahmat-Samii, "Three-Parameter Elliptical Aperture Distributions for Sum and Difference Antenna Patterns Using Particle Swarm Optimization (Invited Paper)," Progress In Electromagnetics Research, Vol. 143, 709-743, 2013.


    1. Collin, R. E. and F. J. Zucker, Antenna Theory, Vol. 2, McGraw-Hill Companies, New York, 1969.

    2. Duan, D.-W. and Y. Rahmat-Samii, "A generalized three-parameter (3-P) aperture distribution for antenna applications," IEEE Transactions on Antennas and Propagation, Vol. 40, No. 6, 697-713, 1992.

    3. Hansen, R. C., "Array pattern control and synthesis," Proceedings of the IEEE, Vol. 80, No. 1, 141-151, 1992.

    4. Elliott, R. S., Antenna Theory and Design, Englewood Cliffs, New Jersey, 1981.

    5. Kennedy, J. and R. Eberhart, "Particle swarm optimization," IEEE International Conference on Neural Networks Proceedings, Vol. 4, 1942-1948, 1995.

    6. Robinson, J. and Y. Rahmat-Samii, "Particle swarm optimization in electromagnetics," IEEE Transactions on Antennas and Propagation, Vol. 52, No. 2, 397-407, 2004.

    7. Xu, S., Y. Rahmat-Samii, and D. Gies, "Shaped-reflector antenna designs using particle swarm optimization: An example of a directbroadcast satellite antenna," Microwave and Optical Technology Letters, Vol. 48, No. 7, 1341-1347, 2006.

    8. Yen, G. G. and W.-F. Leong, "Dynamic multiple swarms in multiobjective particle swarm optimization," IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, Vol. 39, No. 4, 890-911, 2009.

    9. Goudos, S. K., Z. D. Zaharis, D. G. Kampitaki, I. T. Rekanos, and C. S. Hilas, "Pareto optimal design of dual-band base station antenna arrays using multi-objective particle swarm optimization with fitness sharing ," IEEE Transactions on Magnetics, Vol. 45, No. 3, 1522-1525, 2009.

    10. Chen, M., "Second generation particle swarm optimization," IEEE Congress on Evolutionary Computation, (IEEE World Congress on Computational Intelligence), CEC 2008, 90-96, 2008.

    11. Balanis, C., Advanced Engineering Electromagnetics, Wiley, 1989.

    12. Schelkunoff , S. A., "Schelkunoff, S. A., \Some equivalence theorems of electromagnetics and their application to radiation problems," Bell System Technical Journal, Vol. 15, No. 1, 92-112, 1936.

    13. Koffman, I., "Feed polarization for parallel currents in reflectors generated by conic sections ," IEEE Transactions on Antennas and Propagation, Vol. 14, No. 1, 37-40, 1966.

    14. Ludwig, A., "The definition of cross polarization," IEEE Transactions on Antennas and Propagation, Vol. 21, No. 1, 116-119, 1973.

    15. Gradshteyn, I. S. and I. M. Ryzhik, Table of Integrals, Series and Products, 2nd Ed., Academic Press Inc., 1980.

    16. Schelkunof, S. A., "A mathematical theory of linear arrays," Bell System Technical Journal, Vol. 22, No. 1, 80-107, 1943.

    17. Taylor, T. T., "Design of circular apertures for narrow beamwidth and low sidelobes," IRE Transactions on Antennas and Propagation, Vol. 8, No. 1, 17-22, 1960.

    18. Bayliss, E. T., "Design of monopulse antenna difference patterns with low sidelobes ," Bell System Technical Journal, Vol. 47, No. 5, 623-650, 1968.

    19. Mostaghim, S. and J. Teich, "Covering Pareto-optimal fronts by subswarms in multi-objective particle swarm optimization," Congress on Evolutionary Computation, CEC2004, Vol. 2, 1404-1411, 2004.

    20. Jin, Y and B. Sendhoff, "Pareto-based multiobjective machine learning: An overview and case studies," IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, Vol. 38, No. 3, 397-415, 2008.

    21. Densmore, A., Y. Rahmat-Samii, and G. Seck, "Corrugated-conical horn analysis using aperture field with quadratic phase," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 9, 3453-3457, 2011.

    22. Guo, Y. and N. Lin, "A three-parameter distribution for difference pattern," Antennas and Propagation Society International Symposium, AP-S. Digest , Vol. 3, 1594-1597, 1993.

    23. Yang, X.-S., , Introduction to Mathematical Optimization: From Linear Programming to Metaheuristics, Cambridge International Science Publishing, 2008.

    24. Dorigo, M., Dorigo, M., M. Birattari, and T. Stutzle, "Ant colony optimization," IEEE Computational Intelligence Magazine, Vol. 1, No. 4, 28-39, 2006.

    25. Gregory, M. D., Z. Bayraktar, and D. H. Werner, "Fast optimization of electromagnetic design problems using the covariance matrix adaptation evolutionary strategy ," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 4, 1275-1285, 2011.

    26. Rahmat-Samii, Y. and E. Michielssen, Electromagnetic Optimization by Genetic Algorithms, J. Wiley, 1999.