volume | PIER Journals

Abstract

A worst-case tolerance synthesis problem for low-sidelobe sparse linear arrays is solved by using a novel self-adaptive hybrid differential evolution (SAHDE) algorithm. First, we establish a worst-case tolerance synthesis model for low-sidelobe sparse linear arrays, in which random position errors are considered and assumed to obey the Gaussian distributions. Through the random sampling, the random model is converted to a deterministic optimization problem. Then, a novel SAHDE algorithm is presented for solving the problem. As a modification to the existing hybrid differential evolution algorithm, a simplified quadratic interpolation (SQI) operator is used to tune the control parameters self-adaptively, establishing the connections between control parameters and the fitness values. In order to determine appropriate control parameter values quickly, a selection operation is also used. Detailed implementation procedure for the SAHDE algorithm is presented, and some numerical results show its effectiveness. Finally, for the deterministic optimization problem, we present a fast way for calculating its fitness values. The SAHDE algorithm is used to obtain optimal nominal element positions. Simulated results illustrate that the worst-case peak sidelobe levels for the sparse linear arrays are improved evidently. The SAHDE algorithm is efficient for solving the worst-case tolerance synthesis problem.

1. Lo, Y. T. and S. W. Lee, "A study of space-tapered arrays," IEEE Trans. Antennas Propag., Vol. 14, No. 1, 22-30, Jan. 1966.
doi:10.1109/TAP.1966.1138612 Google Scholar

2. Skolnik, M. I., G. Nemhauser, and J. W. Sherman, "Dynamic programming applied to unequally spaced arrays," IEEE Trans. Antennas Propag., Vol. 12, No. 1, 35-43, Jan. 1964.
doi:10.1109/TAP.1964.1138163 Google Scholar

3. Kumar, B. P. and G. R. Branner, "Design of unequally for performance improvement," IEEE Trans. Antennas Propag., Vol. 47, No. 3, 511-523, Mar. 1999.
doi:10.1109/8.768787 Google Scholar

4. Haupt, R. L., "Unit circle representation of aperiodic arrays," IEEE Trans. Antennas Propag., Vol. 43, No. 10, 1152-1155, Oct. 1995.
doi:10.1109/8.467654 Google Scholar

5. Haupt, R. L., "Thinned arrays using genetic algorithms," IEEE Trans. Antennas Propag., Vol. 42, No. 7, 993-999, Jul. 199.
doi:10.1109/8.299602 Google Scholar

6. Cheng, K. S., Z. S. He, and C. L. Han, "A modified real GA for the sparse linear array synthesis with multiple constraints," IEEE Trans. Antennas Propag., Vol. 54, No. 7, 2169-2173, Jul. 2006.
doi:10.1109/TAP.2006.877211 Google Scholar

7. Khodier, M. M. and C. G. Christodoulou, "Linear array geometry synthesis with minimum sidelobe level and null control using particle swarm optimization," IEEE Trans. Antennas Propag., Vol. 53, No. 8, 2674-2679, Aug. 2005.
doi:10.1109/TAP.2005.851762 Google Scholar

8. Rocca, P., G. Oliveri, and A. Massa, "Differential evolution as applied to electromagnetics," IEEE Antennas and Propagation Magazine, Vol. 53, No. 1, 38-49, 2011.
doi:10.1109/MAP.2011.5773566 Google Scholar

9. Cen, L., Z. L. Yu, and W. Ser, "Linear aperiodic array synthesis using an improved genetic algorithm," IEEE Trans. Antennas Propag., Vol. 60, No. 2, 895-902, Feb. 2012.
doi:10.1109/TAP.2011.2173111 Google Scholar

10. Zhang, L., Y. C. Jiao, B. Chen, and F. S. Zhang, "Synthesis of linear aperiodic arrays using a self- adaptive hybrid differential evolution algorithm," IET Microwaves, Antennas & Propag., Vol. 5, No. 12, 1524-1528, Dec. 2011.
doi:10.1049/iet-map.2010.0429 Google Scholar

11. Goudos, S. K., K. Siakavara, T. Samaras, E. E. Vafiadis, and J. N. Sahalos, "Sparse linear array synthesis with multiple constraints using differential evolution with strategy adaptation," IEEE Antennas and Wire. Propag. Lett., Vol. 10, 670-673, 2011.
doi:10.1109/LAWP.2011.2161256 Google Scholar

12. Schjaer-Jacobsen, H. and K. Madsen, "Algorithms for worst case tolerance optimization," IEEE Trans. Circuits & Systems, Vol. 26, No. 9, 775-783, Sep. 1979.
doi:10.1109/TCS.1979.1084700 Google Scholar

13. Schjaer-Jacobsen, H., "Worst-case tolerance optimization of antenna system," IEEE Trans. Antennas Propag., Vol. 28, No. 2, 247-250, Mar. 1980.
doi:10.1109/TAP.1980.1142296 Google Scholar

14. Jiao, Y. C., Y. H. Qi, and L.-Y. Zhang, "Tolerance optimization design for low sidelobe linear arrays," IEEE Antennas and Propagation Society International Symposium, 736-739, 1993.
doi:10.1109/APS.1993.385242 Google Scholar

15. Anselmi, N., L. Manica, P. Rocca, and A. Massa, "Tolerance analysis of antenna arrays through interval arithmetic," IEEE Trans. Antennas Propag., Vol. 61, No. 11, 5496-5507, Nov. 2013.
doi:10.1109/TAP.2013.2276927 Google Scholar

16. Krischuk, V., G. Shilo, and B. Artyushenko, "Tolerable linear antenna array design with genetic algorithm," 9th International Conference onthe Experience of Designing and Applications of CAD Systems in Microelectronics, 167-169, 2007. Google Scholar

17. Qin, A. K. and P. N. Suganthan, "Self-adaptive dfferential evolution algorithm for numerical optimization," 2005 IEEE Congress on Evolutionary Computation, Vol. 2, 1785-1791, 2005.
doi:10.1109/CEC.2005.1554904 Google Scholar

18. Brest, J., S. Greiner, B. Boskovic, and V. Zumer, "Self-adapting control parameters in differential evolution: A comparative study on numerical benchmark problems," IEEE Trans. on Evolutionary Computation, Vol. 10, No. 6, 646-657, Jun. 2006.
doi:10.1109/TEVC.2006.872133 Google Scholar

19. Ali, M. M., A. Torn, and S. Vitanen, "A numerical comparison of some modified controlled random search algorithms," J. Global Optim., Vol. 11, 377-385, 1997.
doi:10.1023/A:1008236920512 Google Scholar

20. Jiao, Y. C., C. Dang, Y. Leung, and Y. Hao, "A modification to the new version of the Price's algorithm for continuous global optimization problems," J. Global Optim., Vol. 36, 609-626, 2006.
doi:10.1007/s10898-006-9030-3 Google Scholar

21. Li, H., Y. C. Jiao, and Y. P. Wang, "Integrating the simplifiedinterpolation into the genetic algorithm for constrained optimization problems," Computational Intelligence and Security, 247-254, Lecture Notes in Artificial Intelligence 3801, Springer-Verlag, Berlin, 2005. Google Scholar

22. Zhang, L., Y. C. Jiao, H. Li, and F. S. Zhang, "Antenna optimization by hybrid differential evolution," Int. J. RF and Microwave Comput. --- Aided Eng., Vol. 20, 51-55, 2010. Google Scholar

23. Massa, A., M. Donelli, F. G. B. De Natale, et al. "Planar antenna array control with genetic algorithms and adaptive array theory," IEEE Trans. Antennas Propag., Vol. 52, No. 11, 2919-2924, Nov. 2004.
doi:10.1109/TAP.2004.837523 Google Scholar

24. Azaro, R., G. Boato, M. Donelli, et al. "Design of a prefractal monopolar antenna for 3.4--3.6 GHz Wi-Max band portable devices," IEEE Antennas and Wire. Propag. Lett., Vol. 5, 116-119, 2007. Google Scholar

25. Carlo, F., D. Massimo, and G. F.Walsh, "Particle-swarm optimization of broadband nanoplasmonic arrays," Optics Letters, Vol. 35, No. 2, 133-135, 2010.
doi:10.1364/OL.35.000133 Google Scholar

26. Azaro, R., F. G. B. De Natale, M. Donelli, et al. "Optimized design of a multifunction/multiband antenna for automotive rescue systems," IEEE Trans. Antennas Propag., Vol. 54, No. 2, 392-400, Feb. 2006.
doi:10.1109/TAP.2005.863387 Google Scholar

27. Donelli, M., I. J. Craddock, D. Gibbins, and M. Sarafianou, "A three-dimensional time domain microwave imaging method for breast cancer detection based on an evolutionary algorithm," Progress In Electromagnetics Research M, Vol. 18, 179-195, 2011.
doi:10.2528/PIERM11040903 Google Scholar

28. Oliveri, G., M. Donelli, and A. Massa, "Linear array thinning exploiting almost difference sets," IEEE Trans. Antennas Propag., Vol. 57, No. 12, 3800-3812, Dec. 2009.
doi:10.1109/TAP.2009.2027243 Google Scholar

29. Oliveri, G., M. Donelli, and A. Massa, "ADS-based guidelines for thinned planar arrays," IEEE Trans. Antennas Propag., Vol. 58, No. 6, 1935-1948, Jun. 2010.
doi:10.1109/TAP.2010.2046858 Google Scholar

30. Oliveri, G., "Bayesian compressive sampling for pattern synthesis with maximally sparse non-uniform linear arrays," IEEE Trans. Antennas Propag., Vol. 59, No. 2, 467-481, Feb. 2011.
doi:10.1109/TAP.2010.2096400 Google Scholar

31. Viani, F., G. Oliveri, and A. Massa, "Compressive sensing pattern matching techniques for synthesizing planar sparse arrays," IEEE Trans. Antennas Propag., Vol. 61, No. 9, 4577-4587, Sep. 2013.
doi:10.1109/TAP.2013.2267195 Google Scholar

32. Poli, L., P. Rocca, N. Anselmi, and A. Massa, "Dealing with uncertainties on phase weighting of linear antenna arrays by means of interval-based tolerance analysis," IEEE Trans. Antennas Propag., Vol. 63, No. 7, 3229-3234, Jul. 2015.
doi:10.1109/TAP.2015.2421952 Google Scholar

33. Rocca, P., N. Anselmi, and A. Massa, "Optimal synthesis of robust arrayconfigurations exploiting interval analysis and convex optimization," IEEE Trans. Antennas Propag., Vol. 62, No. 7, 3603-3612, Jul. 2014.
doi:10.1109/TAP.2014.2318071 Google Scholar

34. Anselmi, N., P. Rocca, M. Salucci, and A. Massa, "Optimization of excitationtolerances for robust beamforming in linear arrays," IET Microwave, Antenna and Propagation, Vol. 10, No. 2, 208-214, 2016.
doi:10.1049/iet-map.2015.0508 Google Scholar

Dr. Tao Ni

Dr. Yong-Chang Jiao

Dr. Li Zhang

Professor Zibin Weng