volume | PIER Journals

Abstract

Time-modulated antenna arrays attracted the attention of researchers for the synthesis of low/ultra-low side lobes in recent past. This article proposes a Multi-objective Optimization (MO) framework for the design of time-modulated linear antenna arrays with ultra low maximum Side Lobe Level (SLL), maximum Side Band Level (SBL) and main lobe Beam Width between the First Nulls (BWFN). In contrast to the conventional optimization-based methods that attempt to minimize a weighted sum of maximum SLL, SBL, and BWFN we treat these as three different objectives that are to be achieved simultaneously and use one of the best known Multi-Objective Evolutionary Algorithms (MOEAs) of current interest called MOEA/D-DE (Decomposition based MOEA with Differential Evolution operator) to determine the best compromise among these three objectives. Unlike the single-objective approaches, the MO approach provides greater flexibility in the design by yielding a set of equivalent final solutions from which the user can choose one that attains a suitable trade-off margin as per requirements. We compared time-modulated antenna structures with other linear array synthesis such as the excitation method and the phase-position synthesis method on the basis of the approximated Pareto Fronts (PFs) yielded by MOEA/D-DE and the best compromise solutions determined from the Pareto optimal set with a fuzzy membership-function based method. The final results obtained with MOEA/D-DE were also compared with the results achieved by three state-of-the-art single objective optimization algorithms. Our simulation studies on three significant instantiations of the design problem reflect the superiority of the MOEA-based design of time-modulated linear arrays.

1. Godara, L. C., Handbook of Antennas in Wireless Communications, CRC, 2002.

2. Kummer, W. H., A. T. Villeneuve, T. S. Fong, and F. G. Terrio, "Ultra-low sidelobes from time-modulated arrays," IEEE Trans. Antennas Propag., Vol. 11, No. 6, 633-639, Nov. 1963.
doi:10.1109/TAP.1963.1138102 Google Scholar

3. Schrank, H. E., "Low sidelobe phased array antennas," IEEE Antennas Propagat. Soc. Newslett., Vol. 25, No. 2, 4-9, Apr. 1983. Google Scholar

4. Yang, S., Y. B. Gan, and A. Qing, "Sideband suppression in time-modulated linear arrays by the differential evolution algorithm," IEEE Antennas and Wireless Propagation Letters, Vol. 1, 2002. Google Scholar

5. Bickmore, R. W., "Time versus space in antenna theory," Microwave Scanning Antennas, Vol. 3, R. C. Hansen (ed.), Academic, New York, 1966. Google Scholar

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

7. Yang, S., Y. Chen, and Z. Nie, "Multiple patterns from time-modulated linear antenna arrays," Electromagnetics, Vol. 28, 562-571, 2008.
doi:10.1080/02726340802428671 Google Scholar

8. Yang, S. and Z. Nie, "Millimeter-wave low sidelobe time modulated linear arrays with uniform amplitude excitations," Int. J. Infrared Milli. Waves, Vol. 28, 531-540, 2007.
doi:10.1007/s10762-007-9244-6 Google Scholar

9. Li, G., S. Yang, Z. Zhao, and Z. Nie, "A study of AM And FM signal reception of time modulated linear antenna arrays," Progress In Electromagnetics Research Letters, Vol. 7, 171-181, 2009.
doi:10.2528/PIERL09030801 Google Scholar

10. Yang, S., Y. B. Gan, A. Qing, and P. K. Tan, "Design of a uniform amplitude time modulated linear array with optimized time sequences," IEEE Trans. Antennas Propagat., Vol. 53, No. 7, 2337-2339, Jul. 2005.
doi:10.1109/TAP.2005.850765 Google Scholar

11. Yang, S., Y. B. Gan, and P. K. Tan, "A new technique for power pattern synthesis in time modulated linear arrays," IEEE Antennas and Wireless Propagation Letters, Vol. 2, 285-287, Dec. 2003.
doi:10.1109/LAWP.2003.821556 Google Scholar

12. Yang, S., Y. B. Gan, and P. K. Tan, "Comparative study of low sidelobe time modulated linear arrays with different time schemes," Journal of Electromagnetic Waves and Applications, Vol. 18, No. 11, 1443-1458, Nov. 2004.
doi:10.1163/1569393042954910 Google Scholar

13. Yang, S., Y. B. Gan, and P. K. Tan, "Linear antenna arrays with bidirectional phase center motion," IEEE Trans. Antennas Propagat., Vol. 53, No. 5, 1829-1835, May 2005.
doi:10.1109/TAP.2005.846754 Google Scholar

14. Zhu, X., S. Yang, and Z. Nie, "Full-wave simulation of time modulated linear antenna arrays in frequency domain," IEEE Trans. Antennas Propagat., Vol. 56, No. 5, 1479-1482, May 2008.
doi:10.1109/TAP.2008.922701 Google Scholar

15. Yang, S. and Z. Nie, "Mutual coupling compensation in time modulated linear antenna arrays," IEEE Trans. Antennas Propagat., Vol. 53, No. 12, 4182-4185, Dec. 2005.
doi:10.1109/TAP.2005.860000 Google Scholar

16. Yang, S. W., Y. K. Chen, and Z. P. Nie, "Simulation of time modulated linear antenna arrays using the FDTD method," Progress In Electromagnetics Research, Vol. 98, 175-190, 2009.
doi:10.2528/PIER09092507 Google Scholar

17. 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 Google Scholar

18. 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, (Trondheim, Norway, May 18{21, 2009), 203-208, IEEE Press, Piscataway, NJ, 2009. Google Scholar

19. 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, University of Essex and Nanyang Technological University, 2008.

20. Abido, M. A., "A novel multiobjective evolutionary algorithm for environmental/economic power dispatch," Electric Power Systems Research, Vol. 65, 71-81, Elsevier, 2003. Google Scholar

21. Panduro, M. A., D. H. Covarrubias, and A. L. Mendez, "Design of phased antenna arrays using evolutionary optimization techniques," Advances in Evolutionary Algorithms, 361-376, W. Kosiński (ed.), I-Tech Education and Publishing, Vienna, Austria, Nov. 2008. Google Scholar

22. Boeringer, D. W. and D. H.Werner, "Particle swarm optimization versus genetic algorithms for phased array synthesis," IEEE Trans. Antennas Propagat., Vol. 52, No. 3, 771-779, Mar. 2004.
doi:10.1109/TAP.2004.825102 Google Scholar

23. Kurup, D. G., M. Himdi, and A. Rydberg, "Synthesis of uniform amplitude unequally spaced antenna arrays using the differential evolution algorithm," IEEE Trans. Antennas Propagat., Vol. 51, No. 9, 2210-2217, Sep. 2003.
doi:10.1109/TAP.2003.816361 Google Scholar

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

25. Kennedy, J., R. C. Eberhart, and Y. Shi, Swarm Intelligence, Morgan Kaufmann, 2001.

26. Jin, N. and Y. Rahmat-Samii, "Advances in particle swarm optimization for antenna designs: Real-number, binary, single-objective and multiobjective implementations," IEEE Trans. Antennas Propagat., Vol. 55, 556-567, 2007.
doi:10.1109/TAP.2007.891552 Google Scholar

27. Das, I. and J. Dennis, "Normal-boundary intersection: A new method for generating pareto optimal points in multicriteria optimization problems," SIAM Journal on Optimization, Vol. 8, No. 3, 631-657, 1998.
doi:10.1137/S1052623496307510 Google Scholar

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

29. Knowles, J. D. and D. W. Corne, "Approximating the non-dominated front using the Pareto archived evolution strategy," Evolutionary Computation, Vol. 8, No. 2, 149-172, 2000.
doi:10.1162/106365600568167 Google Scholar

30. Knowles, J. D. and D. Corne, "The Pareto archived evolution strategy: A new baseline algorithm for pareto multiobjective optimisation," Proceedings of the 1999 IEEE Congress on Evolutionary Computation, IEEE Neural Networks Council, 1999. Google Scholar

31. Zitzler, E., M. Laumanns, and L. Thiele, "SPEA2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization," Evolutionary Methods for Design, Optimisation and Control with Application to Industrial Problems (EUROGEN 2001), 95-100, K. C. Giannakoglou et al. (eds.), International Center for Numerical Methods in Engineering, CIMNE, 2002. Google Scholar

32. Xue, F., A. C. Sanderson, and R. J. Graves, "Pareto-based multi-objective differential evolution," Proceedings of the 2003 Congress on Evolutionary Computation (CEC'2003), Vol. 2, 862-869, IEEE Press, Canberra, Australia, 2003. Google Scholar

33. 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. Google Scholar

34. Yang, S., Y. B. Gan, and A. Qing, "Antenna-array pattern nulling using a differential evolution algorithm," International Journal of RF and Microwave Computer-aided Engineering, Vol. 14, No. 1, 57-63, Jan. 2004.
doi:10.1002/mmce.10118 Google Scholar

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

36. Deb, K., Multi-objective Optimization using Evolutionary Algorithms, John Wiley & Sons, 2001.

37. Zhang, Q. and H. Li, "MOEA/D: A multi-objective evolutionary algorithm based on decomposition," IEEE Trans. on Evolutionary Computation, Vol. 11, No. 6, 712-731, 2007.
doi:10.1109/TEVC.2007.892759 Google Scholar

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

39. 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. 3, 526-553, Jun. 2009.
doi:10.1109/TEVC.2008.2009457 Google Scholar

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

41. 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 Google Scholar

42. Dib, N. I., S. K. Goudos, and H. Muhsen, "Application of Taguchi's optimization method and self-adaptive differential evolution to the synthesis of linear antenna arrays," Progress In Electromagnetics Research, Vol. 102, 159-180, 2010.
doi:10.2528/PIER09122306 Google Scholar

43. Pal, S., B. Qu, S. Das, and P. N. Suganthan, "Linear antenna array synthesis with constrained multi-objective differential evolution," Progress In Electromagnetics Research B, Vol. 21, 87-111, 2010. Google Scholar

44. 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 Propagat., Vol. 57, No. 9, 3018-3028, Oct. 2009. Google Scholar

45. 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. (AEÜ), Vol. 59, 205-212, 2005.
doi:10.1016/j.aeue.2004.11.017 Google Scholar

Dr. Siddharth Pal

Dr. Swagatam Das

Dr. Aniruddha Basak