volume | PIER Journals

Abstract

This paper presents a paattern synthesis method to generate dual-beam patterns of a rectangular planar array of isotropic antennas in a particular scanning angle using Evolution Algorithms. The dual-beam patterns are cosec₂ pattern and pencil beam pattern, and both the patterns are steered to an elevation angle of 20 degrees (θ = 20˚). Moreover, each pattern is synthesized in three azimuth planes (φ = 0˚, 5˚, and 10˚). The isotropic elements are uniformly spaced, and nonuniform excitations are applied to achieve the desired patterns. These patterns are obtained by applying the optimum set of common elements amplitude and phases for the cosecant-squared pattern only. The optimum 4-bit discrete amplitudes and 5-bit discrete phases are produced using using Differential Evolutionary (DE) Algorithm, Genetic Algorithm (GA), Particle Swarm Optimization (PSO) Algorithm, and Firefly Algorithm (FA). These discrete excitations are helpful to reduce the Dynamic Range Ratio (DRR) and the design complexity of the feed networks. The excitations are also verified in a range of arbitrarily chosen azimuth planes. The patterns are generated in the same steering angle with minor variations of the desired parameters. The outcomes established the superiority of DE over PSO, GA, and the effectiveness of the proposed method.

1. Balanis, C. A., Antenna Theory, Analysis and Design, 2nd Ed., Jhon Willy & sons, New York, 1997.

2. Elliott, R. S., Antenna Theory & Design, Revised Edition, Wiley-IEEE Press, Dec. 2002.

3. Hansen, R. C., Phased Array Antennas, 2nd Ed., Jhon Wiley & Sons, Canada, 2009.
doi:10.1002/9780470529188

4. Mailloux, R. J., Phased Array Antenna Handbook, 2nd Ed., Artech House Antennas and Propagation Library, Boston, 2009.

5. Diaz, X., J. A. Rodriguez, F. Ares, and E. Moreno, "Design of phase-differentiated multiple pattern antenna arrays," Microwave and Optical Technology Letters, Vol. 26, No. 1, 52-53, 2000.
doi:10.1002/(SICI)1098-2760(20000705)26:1<52::AID-MOP16>3.0.CO;2-0

6. Lei, J., G. Fu, L. Yang, and D. M. Fu, "Wide band linear printed antenna array with low sidelobe cosecant square-shaped beam pattern," Progress In Electromagnetics Research C, Vol. 15, 233-241, 2010.
doi:10.2528/PIERC10072506

7. Durr, M., A. Trastoy, and F. Ares, "Multiple-pattern linear antenna arrays with single prexed amplitude distributions: Modified Woodward-Lawson synthesis," Electronics Letters, Vol. 36, No. 16, 1345-1346, 2000.
doi:10.1049/el:20000980

8. Chatterjee, A., G. K. Mahanti, and R. P. S. Mahapatra, "Design of fully digital controlled recongurable dual-beam concentric ring array antenna using gravitational search algorithm," Progress In Electromagnetics Research B, Vol. 18, 59-59, 2011.
doi:10.2528/PIERC10101806

9. Chatterjee, A., G. K. Mahanti, and A. Chatterjee, "Design of a fully digital controlled recongurable switched beam concentric ring array antenna using re y and particle swarm optimization algorithm," Progress In Electromagnetics Research B, Vol. 36, 113-131, 2012.
doi:10.2528/PIERB11083005

10. Mandal, D., J. Tewary, K. S. Kola, and V. P. Roy, "Synthesis of dual beam pattern of planar array antenna in a range of azimuth plane using Evolutionary Algorithm," Progress In Electromagnetics Research Letters, Vol. 62, 65-70, 2016.
doi:10.2528/PIERL16060802

11. Mandal, D., V. P. Roy, A. Chatterjee, and A. K. Bhattacharjee, "Synthesis of dual radiation pattern of rectangular planar array antenna using Evolutionary Algorithm," ICTACT Journal on Communication Technology, Vol. 06, No. 03, 1146-1149, 2015.
doi:10.21917/ijct.2015.0167

12. Kenane, E., F. Benmeddour, and F. Djahli, "Nonuniform circular array synthesis for low side lobe level using dynamic invasive weeds optimization," Progress In Electromagnetics Research C, Vol. 111, 147-162, 2021.
doi:10.2528/PIERC21020402

13. Storn, R. and K. Price, "Differential evolution: A simple and efficient heuristic for global optimization over continuous spaces," Journal of Global Optimization, Vol. 11, No. 04, 341-359, 1997.
doi:10.1023/A:1008202821328

14. Price, K. V., R. M. Storn, and J. A. Lampinen, Differential Evolution --- A Practical Approach to Global Optimization. Natural Computing, Springer, New York, USA, 2005.

15. Das, S., A. Abraham, U. K. Chakraborty, and A. Konar, "Differential evolution using a neighborhood-based mutation operator," IEEE Transactions on Evolutionary Computation, Vol. 13, No. 03, 526-553, 2009.
doi:10.1109/TEVC.2008.2009457

16. Guo, J. and J. Li, "Pattern synthesis of conformal array antenna in the presence of platformusing differential evolution algorithm," IEEE Transactions on Antennas and Propagation, Vol. 57, No. 09, 2615-2621, 2009.
doi:10.1109/TAP.2009.2027046

17. Qi, X., Z. Huang, and Y. Chen, "An improved differential evolution algorithm based on adaptive parameter," Journal of Control Science and Engineering, Vol. 2013, 2013.

18. Yang, S., Y. B. Gan, and A. Qing, "Sideband suppression in time-modulated linear arrays by the differential evolution algorithm," IEEE Transactions on Antennas and Propagations Letters, Vol. 1, No. 1, 173-175, 2002.
doi:10.1109/LAWP.2002.807789

19. Massa, A., M. Pastorino, and A. Randazzo, "Optimization of the directivity of a monopulse antenna with a subarray weighting by a hybrid differential evolution method," IEEE Transactions on Antennas and Propagations Letters, Vol. 5, No. 1, 155-158, 2006.
doi:10.1109/LAWP.2006.872435

20. Kennedy, J. and R. C. Eberhart, "Particle swarm optimization," Proceedings of the Conference on Neural Networks, 1942-1948, Perth, Australia, 1995.

21. Shi, X. H. and R. C. Eberhart, "Empirical study of particle swarm optimization," Proceedings of the Congress on Evolutionary Computation, 1945-1950, Washington, D.C., USA, 1999.

22. Juang, C. F., "A hybrid of genetic algorithm and particle swarm optimization for recurrent network design," IEEE Trans. Syst., Man, Cybern. --- Part B: Cybern., Vol. 34, 997-1006, 2004.
doi:10.1109/TSMCB.2003.818557

23. Robinson, J. and Y. Rahmat-Samii, "Particle swarm optimization in electromagnetics," IEEE Transactions on Antennas and Propagation, Vol. 52, No. 2, 397-407, 2004.
doi:10.1109/TAP.2004.823969

24. Boeringer, D. W. and D. H. Werner, "Particle swarm optimization versus genetic algorithms for phased array synthesis," IEEE Trans. Antennas Propagat., Vol. 52, 771-779, 2004.
doi:10.1109/TAP.2004.825102

25. Lee, K. C. and J. Y. Jhang, "Application of particle swarm algorithm to the optimization of unequally spaced antenna arrays," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 14, 2001-2012, 2006.
doi:10.1163/156939306779322747

26. Carro Ceballos, P. L., J. De Mingo Sanz, and P. G. Ducar, "Radiation pattern synthesis for maximum mean effective gain with spherical wave expansions and particle swarm techniques," Progress In Electromagnetics Research, Vol. 103, 355-370, 2010.
doi:10.2528/PIER10031808

27. Modiri, A. and K. Kiasaleh, "Modification of real-number and binary PSO algorithms for accelerated convergence," IEEE Transactions on Antennas and Propagation, Vol. 59, 214-224, 2011.
doi:10.1109/TAP.2010.2090460

28. Haupt, R. L., "Introduction to genetic algorithms for electromagnetics," IEEE Antennas and Propagation Magazine, Vol. 37, No. 2, 7-15, 1995.
doi:10.1109/74.382334

29. Man, K. F., K. S. Tang, and S. Kwong, "Genetic algorithms: Concepts and applications," IEEE Transactions on Industrial Electronics, Vol. 43, No. 5, 519-534, 1996.
doi:10.1109/41.538609

30. Johnson, J. M. and Y. Rahmat-Samii, "Genetic algorithms in engineering electromagnetics," IEEE Antennas and Propagation Magazine, Vol. 39, No. 4, 7-21, 1997.
doi:10.1109/74.632992

31. Marcano, D. and F. Duran, "Synthesis of antenna arrays using genetic algorithms," IEEE Antennas and Propagation Magazine, Vol. 42, No. 3, 12-20, 2000.
doi:10.1109/74.848944

32. Panduro, M. A., A. L. Mendez, R. Dominguez, and G. Romero, "Design of non-uniform circular antenna arrays for side lobe reduction using the method of genetic algorithms," International Journal of Electronics and Communications, Vol. 60, No. 10, 713-717, 2006.
doi:10.1016/j.aeue.2006.03.006

Professor Sanjay Kumar Dubey

Professor Debasis Mandal