volume | PIER Journals

Abstract

We investigate the design of Concentric Circular Antenna Arrays (CCAAs) with λ/2 uniform inter-element spacing, non-uniform radial separation, and non-uniform excitation across different rings, from the perspective of Multi-objective Optimization (MO). Unlike the existing single-objective design approaches that try to minimize a weighted sum of the design objectives like Maximum Side Lobe Level (MSLL) and principal lobe Beam-Width (BW), we treat these two objectives individually and use Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) with Differential Evolution (DE), called MOEA/D-DE, to achieve the best tradeoff between the two objectives. Unlike the single-objective approaches, the MO approach provides greater flexibility in the design by yielding a set of equivalent final (non-dominated) solutions, from which the user can choose one that attains a suitable trade-off margin as per requirements. We illustrate that the best compromise solution attained by MOEA/D-DE can comfortably outperform state-of-the-art variants of single-objective algorithms like Particle Swarm Optimization (PSO) and Differential Evolution. In addition, we compared the results obtained by MOEA/D-DE with those obtained by one of the most widely used MO algorithm called NSGA-2 and a multi-objective DE variant, on the basis of the R-indicator, hypervolume indicator, and quality of the best trade-off solutions obtained. Our simulation results clearly indicate the superiority of the design based on MOEA/D-DE.

1. Stearns, C. and A. Stewart, "An investigation of concentric ring antennas with low sidelobes," IEEE Trans. Antennas Propag., Vol. 13, No. 6, 856 -863, Nov. 1965.
doi:10.1109/TAP.1965.1138544

2. Das, R., "Concentric ring array," IEEE Trans. Antennas Propag., Vol. 14, No. 3, 398-400, May 1966.
doi:10.1109/TAP.1966.1138688

3. Dessouky, M. I., H. A. Sharshar, and Y. A. Albagory, "Optimum," normalized-Gaussian tapering window for side lobe reduction in uniform concentric circular arrays, Vol. 69, 35-46, 2007.

4. Bogdan, L. and C. Comsa, "Analysis of circular arrays as smart antennas for cellular networks," Proc. IEEE Int. Symp. Signals Circuits and Systems' 03, Vol. 2, 525-528 , Jul. 2003.

5. Roy, G. G., S. Das, P. Chakraborty, and P. N. Suganthan, "Design of non-uniform circular antenna arrays using a modified invasive weed optimization algorithm," IEEE Trans. Antennas Propag. , Vol. 59, No. 1, 110-118, Jan. 2011.
doi:10.1109/TAP.2010.2090477

6. Chen, T. B., Y. L. Dong, Y. C. Jiao, and F. S. Zhang, "Synthesis of circular antenna array using crossed particle swarm optimization algorithm," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 13, 1785-1795, 2006.
doi:10.1163/156939306779292273

7. Dessouky, M. I., H. A. Sharshar, and Y. A. Albagory, "Effcient sidelobe reduction technique for small-sized concentric circular arrays," Progress in Electromagnetics Research, Vol. 65, 187-200, 2006.
doi:10.2528/PIER06092503

8. Dessouky, M., H. Sharshar, and Y. Albagory, "A novel tapered beam forming window for uniform concentric circular arrays," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 14, 2077-2089, 2006.
doi:10.1163/156939306779322701

9. Li, , Y. and K. C. Ho, "3-D array pattern synthesis with frequency invariant property for concentric ring array," IEEE Transactions Signal Processing, Vol. 54, No. 2, 780-784, Feb. 2006.
doi:10.1109/TSP.2005.861897

10. Kennedy, J. and R. Eberhart, "Particle swarm optimization ," Proc. IEEE Int. Conf. Neur. Net., 1942-1948, 1995.
doi:10.1109/ICNN.1995.488968

11. Mandal, D., S. P. Ghoshal, and A. K. Bhattacharjee, "Radiation pattern optimization for concentric circular antenna array with central element feeding using craziness-based particle swarm optimization," International Journal of RF and Microwave International Journal of RF and Microwave, Vol. 20, No. 5, 577-586, Sep. 2010.
doi:10.1002/mmce.20467

12. Mandal, D., S. P. Ghoshal, and A. K. Bhattacharjee, "Optimal design of concentric circular antenna array using particle swarm optimization with constriction factor approach," International Journal of Computer Applications, Vol. 1, No. 17, 112-116, 2010.
doi:10.5120/353-534

13. Pathak, N., G. K. Mahanti, S. K. Singh, J. K. Mishra, and A. Chakraborty, "Synthesis of thinned planar circular array antennas using modi¯ed particle swarm optimization," Progress In Electromagnetics Research Letters, Vol. 12, 87-97, 2009.
doi:10.2528/PIERL09090606

14. Li, H. and Q. Zhang, "Multiobjective optimization problems with complicated pareto sets, MOEA/D and NSGA-II," IEEE Trans. on Evolutionary Computation, Vol. 12, No. 2, 284-302, 2009.
doi:10.1109/TEVC.2008.925798

15. Zhang, Q., W. Liu, and H. Li, "The performance of a new MOEA/D on CEC09 MOP test instances," Proceedings of the Eleventh Conference on Congress on Evolutionary Computation, 203-208, 2009.

16. Zhang, Q., A. Zhou, S. Z. Zhao, P. N. Suganthan W. Liu, and S. Tiwari , "Multiobjective optimization test instances for the CEC 2009 special session and competition," Technical Report CES-887,, 2008.

17. Storn, , R. and K. Price, "Differential evolution --- A simple and effcient heuristic for global optimization over continuous spaces," Journal of Global Optimization, Vol. 11, No. 4, 34111-359, 1997.
doi:10.1023/A:1008202821328

18. Price, K., R. Storn, and J. Lampinen, Differential Evolution --- A Practical Approach to Global Optimization, Springer, Berlin, 2005.

19. Panduroa, M. A., D. H. Covarrubiasa, C. A. Brizuelaa, and F. R. Maranteb, "A multi-objective approach in the linear antenna array design ," Int. J. Electron. Commun. (AEU) , Vol. 59, 205-212, 2005.
doi:10.1016/j.aeue.2004.11.017

20. Pal, S., B. Qu, S. Das, and P. N. Suganthan, "Optimal synthesis of linear antenna arrays with multi-objective differential evolution," Progress In Electromagnetics Research , Vol. 21, 87-111, 2010.

21. Pal, S., S. Das, and A. Basak, "Design of time modulated linear arrays with a multi-objective optimization approach," Progress In Electromagnetics Research, Vol. 23, 83-107, 2010.

22. Pal, S., S. Das, A. Basak, and P. N. Suganthan, "Synthesis of difference patterns for monopulse antennas with optimal combination of array-size and number of subarrays --- A multiobjective optimization approach," Progress In Electromagnetics Research, Vol. 21, 257-280, 2010.

23. Abido, M. A., "A novel multiobjective evolutionary algorithm for environmental/economic power dispatch," Electric Power Systems Research, Vol. 65, 71-81, 2003.
doi:10.1016/S0378-7796(02)00221-3

24. Tapia , C. G. and B. A. Murtagh, "Interactive fuzzy programming with preference criteria in multiobjective decision making," Comput. Oper. Res., Vol. 18, 307-316, 1991.
doi:10.1016/0305-0548(91)90032-M

25. Liang, J. J., A. K. Qin, P. N. Suganthan, and S. Baskar, "Comprehensive learning particle swarm optimizer for global optimization of multimodal functions," IEEE Trans. on Evolutionary Computation, Vol. 10, No. 3, 281-295, Jun. 2006.
doi:10.1109/TEVC.2005.857610

26. Das, S., A. Abraham, U. K. Chakraborty, and A. Konar, "Differential evolution using a neighborhood based mutation operator," IEEE Trans. on Evolutionary Computation, Vol. 13, No. 3, 526-553, Jun. 2009.
doi:10.1109/TEVC.2008.2009457

27. Deb, K., A. Pratap, S. Agarwal, and T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGA-II," IEEE Trans. on Evolutionary Computation, Vol. 6, No. 2, 182-197, 2002.
doi:10.1109/4235.996017

28. Xue, F., A. C. Sanderson, and R. J. Graves, "Pareto-based multi-objective differential evolution," Proceedings of the 2003 Congress Proceedings of the 2003 Congress, Vol. 2, 862-869, 2003.

29. Knowles, J., L. Thiele, and E. Zitzler, A tutorial on the performance assessment of stochastic multiobjective optimizers Computer Engineering and Networks Laboratory, ETH Zurich, Switzerland, Feb. 2006.

30. Coello Coello, C. A., G. B. Lamont, and D. A. Van Veldhuizen, Evolutionary Algorithms for Solving Multi-objective Problems, Springer, 2007.

31. Deb, K., Multi-objective Optimization Using Evolutionary Algorithms , John Wiley & Sons, 2001.

32. Zhang, Q. and H. Li, MOEA/D: A multi-objective evolutionary algorithm based on decomposition, Vol. 11, No. 6, 712-731, IEEE Trans. on Evolutionary Computation, 2007.

33. Miettinen, K., Nonlinear Multiobjective Optimization, Kuluwer Academic Publishers, 1999.

34. Yang, S., Y. B. Gan, and A. Qing, Antenna-array pattern nulling using a differential evolution algorithm, Vol. 14, No. 1, 57-63, International Journal of RF and Microwave Computer-Aided Engineering, Jan. 2004.

35. Wu, H., J. Geng, R. Jin, J. Qiu, W. Liu, J. Chen, and S. Liu, "An improved comprehensive learning particle swarm optimization and its application to the semiautomatic design of antennas," IEEE Trans. Antennas Propag. , Vol. 57, No. 9, 3018-3028, Oct. 2009.
doi:10.1109/TAP.2009.2028608

36. 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 Antennas and Wireless Propagation Letters, Vol. 5, 155-158, 2006.
doi:10.1109/LAWP.2006.872435

37. Haupt, R. L., "Optimized element spacing for low sidelobe concentric ring arrays," IEEE Trans. Antennas Propag., Vol. 56, No. 1, 266-268, 2008.
doi:10.1109/TAP.2007.913176

Mr. Subhodip Biswas

Dr. Digbalay Bose

Dr. Swagatam Das

Dr. Souvik Kundu