volume | PIER Journals

Abstract

In this paper, a covariance matrix adaptation evolutionary strategy (CMA-ES) is employed for optimization design of non-uniform circular antenna arrays. To achieve minimum sidelobe levels with the constraint of a specific first null beamwidth, the CMA-ES is utilized to find out the optimal weights and geometry of the circular array. The three various circular ring arrays are solved via CMA-ES, and the results are presented for arrays of varying configurations. The design results obtained with CMA-ES are compared to the existing array designs in the literature and to those found by the other evolutionary algorithms. Comparison with the results of other algorithms reveals the superiority of the CMA-ES.

1. Balanis, C. A., Antenna Theory: Analysis and Design, Wiley, New York, 2005.

2. Du, K. L., "Pattern analysis of uniform circular array," IEEE Trans. Antennas Propag., Vol. 52, No. 4, 1125-1129, 2004.
doi:10.1109/TAP.2004.825802 Google Scholar

3. Pesik, L. J., D. L. Paul, C. J. Railton, G. S. Hilton, and M. A. Beach, "FDTD technique for modeling eight element circular antenna array," Electronics Letters, Vol. 42, No. 14, 787-788, 2006.
doi:10.1049/el:20061215 Google Scholar

4. Goto, N. and Y. Tsunoda, "Sidelobe reduction of circular arrays with a constant excitation amplitude," IEEE Trans. Antennas Propag., Vol. 25, No. 6, 896-898, 1977.
doi:10.1109/TAP.1977.1141700 Google Scholar

5. Watanabe, F., N. Goto, A. Nagayama, and G. Yoshida, "A pattern synthesis of circular arrays by phase adjustment," IEEE Trans. Antennas Propag., Vol. 28, No. 6, 857-863, 1980.
doi:10.1109/TAP.1980.1142424 Google Scholar

6. Vescovo, R., "Constrained and unconstrained synthesis of array factor for circular arrays," IEEE Trans. Antennas Propag., Vol. 43, No. 12, 1405-1410, 1995.
doi:10.1109/8.475929 Google Scholar

7. Barkat, O. and A. Benghalia, "Synthesis of superconducting circular antennas placed on circular array using a particle swarm optimisation and the full-wave method," Progress In Electromagnetics Research B, Vol. 22, 103-119, 2010.
doi:10.2528/PIERB10042404 Google Scholar

8. Panduro, M., 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," Int. J. Electron. Commun., Vol. 60, 713-717, 2006.
doi:10.1016/j.aeue.2006.03.006 Google Scholar

9. Shihab, M., Y. Najjar, N. Dib, and M. Khodier, "Design of non-uniform circular antenna arrays using particle swarm optimization," Journal of Electrical Engineering, Vol. 59, 216-220, 2008. Google Scholar

10. 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, 2011.
doi:10.1109/TAP.2010.2090477 Google Scholar

11. 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 Google Scholar

12. 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

13. Chatterjee, A., G. K. Mahanti, and N. N. Pathak, "Comparative performance of gravitational search algorithm and modified particle swarm optimization algorithm for synthesis of thinned scanned concentric ring array antenna," Progress In Electromagnetics Research B, Vol. 25, 331-348, 2010.
doi:10.2528/PIERB10080405 Google Scholar

14. Ghosh, P. and S. Das, "Synthesis of thinned planar concentric circular antenna arrays - A differential evolutionary approach," Progress In Electromagnetics Research B, Vol. 29, 63-82, 2011.
doi:10.2528/PIERB11020204 Google Scholar

15. Wang, J., B. Yang, S. H. Wu, and J. S. Chen, "A novel binary particle swarm optimization with feedback for synthesizing thinned planar arrays," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 14-15, 1985-1998, 2011.
doi:10.1163/156939311798071965 Google Scholar

16. Li, F., Y.-C. Jiao, L.-S. Ren, Y.-Y. Chen, and L. Zhang, "Pattern synthesis of concentric ring array antennas by differential evolution algorithm," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 2-3, 421-430, 2011.
doi:10.1163/156939311794362777 Google Scholar

17. Elasidy, S., M. Dessouky, S. Khamis, and Y. Albagory, "Concentric circular antenna array synthesis using comprehensive learning particle swarm optimizer," Progress In Electromagnetics Research Letter, Vol. 29, 1-13, 2012.
doi:10.2528/PIERL11112506 Google Scholar

18. Hansen, N. and A. Ostermeier, "Completely derandomized self-adaptation in evolutionary strategies," Evol. Comput., Vol. 9, No. 2, 159-195, 2001.
doi:10.1162/106365601750190398 Google Scholar

19. Hansen, N., S. D. MÄuller, and P. Koumoutsakos, "Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES)," Evol. Comput., Vol. 11, No. 1, 1-18, 2003.
doi:10.1162/106365603321828970 Google Scholar

20. Gregory, M. D., Z. Bayraktar, and D. H. Werner, "Fast optimization of electromagnetic design problems using the covariance matrix adaptation evolutionary strategy," IEEE Trans. Antennas Propag., Vol. 59, No. 4, 1275-1285, 2011.
doi:10.1109/TAP.2011.2109350 Google Scholar

21. Coello, C. A. C., "Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: A survey of the state of the art," Comput. Methods Appl. Mechan. Eng., Vol. 191, No. 11-12, 1245-1287, 2002.
doi:10.1016/S0045-7825(01)00323-1 Google Scholar

22. Storn, R. and K. Price, "Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces," J. Global Optim., Vol. 11, 341-359, 1997.
doi:10.1023/A:1008202821328 Google Scholar

Dr. Li Zhang

Dr. Yong-Chang Jiao

Dr. Bo Chen

Professor Zibin Weng