volume | PIER Journals

Abstract

In this paper, we propose a multi-beam model for antenna array pattern synthesis( AAPS) problem. The model uses a conic trust region algorithm (CTRA) similarly proposed in this paper to optimize its cost function. Undoubtedly, whole algorithm efficiency ultimately lies on the CTRA, thereof, we propose a method to improve the iterative algorithm's efficiency. Unlike traditional trust region methods that resolve sub-problems, the CTRA efficiently searches a region via solving a inequation, by which it identifies new iteration points when a trial step is rejected. Thus, the proposed algorithm improves computational efficiency. Moreover, the CTRA has strong convergence properties with the local superlinear and quadratic convergence rate under mild conditions, and exhibits high efficiency and robustness. Finally, we apply the combinative algorithm to AAPS. Numerical results show that the method is highly robust, and computer simulations indicate that the algorithm excellently performs AAPS problem.

1. Li, X., W.-T. Li, X.-W. Shi, J. Yang, and J.-F. Yu, "Modified differential evolution algorithm for pattern synthesis of antenna arrays," Progress In Electromagnetics Research, Vol. 137, 371-388, 2013.

2. Lin, C., A.-Y. Qing, and Q.-Y. Feng, "Synthesis of unequally spaced antenna arrays by using differential evolution," IEEE Transactions on Antennas and Propagation, Vol. 58, 2553-2561, 2010.
doi:10.1109/TAP.2010.2048864

3. Li, R., L. Xu, X.-W. Shi, N. Zhang, and Z.-Q. Lv, "Improved differential evolution strategy for antenna array pattern synthesis problems," Progress In Electromagnetics Research, Vol. 113, 429-441, 2011.

4. Liu, D., Q.-Y. Feng, W.-B. Wang, and X. Yu, "Synthesis of unequally spaced antenna arrays by using inheritance learning particle swarm optimization," Progress In Electromagnetics Research, Vol. 118, 205-221, 2011.
doi:10.2528/PIER11050502

5. Liu, Y., , Z.-P. Nie, and Q. H. Liu, "A new method for the synthesis of non-uniform linear arrays with shaped power patterns," Progress In Electromagnetics Research, Vol. 107, 349-363, 2010.
doi:10.2528/PIER10060912

6. Wang, W.-B., Q.-Y. Feng, and D. Liu, "Application of chaotic particle swarm optimization algorithm to pattern synthesis of antenna arrays," Progress In Electromagnetics Research, Vol. 115, 173-189, 2011.

7. Zeng, T. J. and Q. Feng, "Penalty function solution to pattern synthesis of antenna array by a descent algorithm," Progress In Electromagnetics Research B, Vol. 49, 281-300, 2013.

8. Caorsi, S., et al. "Peak sidelobe level reduction with a hybrid approach based on GAs and difference sets," IEEE Transactions on Antennas and Propagation, Vol. 52, 1116-1121, 2004.
doi:10.1109/TAP.2004.825689

9. Lizzi, L., G. Oliveri, and A. Massa, "A time-domain approach to the synthesis of UWB antenna systems," Progress In Electromagnetics Research, Vol. 122, 557-575, 2012.
doi:10.2528/PIER11103003

10. Oliveri, G., "Multibeam antenna arrays with common subarray layouts," IEEE Antennas and Wireless Propagation Letters, Vol. 9, 1190-1193, 2010.
doi:10.1109/LAWP.2010.2100073

11. Manica, L., et al. "Synthesis of multi-beam sub-arrayed antennas through an excitation matching strategy," IEEE Transactions on Antennas and Propagation, Vol. 59, 482-492, 2011.
doi:10.1109/TAP.2010.2096383

12. Bregains, J., et al. "Synthesis of multiple-pattern planar antenna arrays with single prefixed or jointly optimized amplitude distributions," Microwave and Optical Technology Letters, Vol. 32, 74-78, 2002.
doi:10.1002/mop.10094

13. Rocca, P., et al. "Differential evolution as applied to electromagnetics," IEEE Antennas and Propagation Magazine, Vol. 53, 38-49, 2011.
doi:10.1109/MAP.2011.5773566

14. Shi, Z. and S. Wang, "Nonmonotone adaptive trust region method," European Journal of Operational Research, Vol. 208, 28-36, 2011.
doi:10.1016/j.ejor.2010.09.007

15. Ahookhosh, M., et al. "A nonmonotone trust-region line search method for large-scale unconstrained optimization," Applied Mathematical Modelling, Vol. 36, 478-487, 2012.
doi:10.1016/j.apm.2011.07.021

16. Zhang, J., et al. "A nonmonotone adaptive trust region method for unconstrained optimization based on conic model," Applied Mathematics and Computation, Vol. 217, 4265-4273, 2010.
doi:10.1016/j.amc.2010.10.043

17. Nocedal, J. and Y.-X. Yuan, Combining trust region and line search techniques, Department of Electrical Engineering and Computer Science, Northwestern University, 1992.

18. Davidon, W. C., "Conic approximations and collinear scalings for optimizers," SIAM Journal on Numerical Analysis, Vol. 17, 268-281, 1980.
doi:10.1137/0717023

19. Di, S. and W. Sun, "A trust region method for conic model to solve unconstraind optimizaions," Optimization Methods and Software, Vol. 6, 237-263, 1996.
doi:10.1080/10556789608805637

20. Ji, Y., et al. "A new nonmonotone trust-region method of conic model for solving unconstrained optimization," Journal of Computational and Applied Mathematics, Vol. 233, 1746-1754, 2010.
doi:10.1016/j.cam.2009.09.011

21. Deng, C., et al. "Modified dynamic differential evolution for 0-1 knapsack problems," International Conference on Computational Intelligence and Software Engineering, CiSE 2009, 1-4, 2009.

22. Luebbers, R. and K. Kunz, "Finite difference time domain calculations of antenna mutual coupling," IEEE Transactions on Electromagnetic Compatibility, Vol. 34, 357-359, 1992.
doi:10.1109/15.155855

23. Ye, Z. and C. Liu, "Non-sensitive adaptive beamforming against mutual coupling," IET Signal Processing, Vol. 3, 1-6, 2009.
doi:10.1049/iet-spr:20070198

24. Liao, B. and S.-C. Chan, "Adaptive beamforming for uniform linear arrays with unknown mutual coupling," IEEE Antennas and Wireless Propagation Letters, Vol. 11, 464-467, 2012.
doi:10.1109/LAWP.2012.2196017

Dr. Tiao Jun Zeng

Prof. Quanyuan Feng