volume | PIER Journals

Abstract

This paper presents a hybrid method that combines the improved sparrow search algorithm (ISSA) and convex programming (CP) to synthesize sparse arrays under multiple design constraints. The proposed method initiates with introducing ISSA, which establishes a sparse array layout while effectively reducing peak sidelobe levels (PSLLs) through optimizing nonuniform element positions. Subsequently, when the position is fixed, the subproblem of minimizing PSLL is transformed into a convex problem with beamwidth constraint, employing CP to determine optimal excitation amplitudes. The PSLL serves as the fitness function in ISSA to simultaneously optimize both element position and excitation amplitude, to achieve PSLL reduction of sparse array. Afterward, some examples of linear and rectangular planar arrays with low sidelobe are simulated and discussed in detail. Numerical experiments show the effectiveness and reliability of ISSA-CP, which can further reduce PSLL while saving array elements. Ultimately, utilizing the numerical simulation results as a foundation, a full-wave simulation is undertaken to verify the practicality of the novel hybrid method.

1. Zhao, Xiaowen, Yunhua Zhang, and Qingshan Yang, "A hybrid algorithm for synthesizing linear sparse arrays," Progress In Electromagnetics Research C, Vol. 63, 75-83, 2016. Google Scholar

2. Aslan, Yanki, Antoine Roederer, and Alexander Yarovoy, "System advantages of using large-scale aperiodic array topologies in future mm-wave 5G/6G base stations: An interdisciplinary look," IEEE Systems Journal, Vol. 16, No. 1, 1239-1248, Mar. 2022. Google Scholar

3. He, Yuanzhi and Changxu Wang, "Optimization design for sparse planar array in satellite communications," Electronics, Vol. 12, No. 8, 1763, Apr. 2023. Google Scholar

4. Roy, Gourab Ghosh, Swagatam Das, Prithwish Chakraborty, and Ponnuthurai N. Suganthan, "Design of non-uniform circular antenna arrays using a modified invasive weed optimization algorithm," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 1, 110-118, Jan. 2011. Google Scholar

5. Kumar, B. P. and G. R. Branner, "Design of unequally spaced arrays for performance improvement," IEEE Transactions on Antennas and Propagation, Vol. 47, No. 3, 511-523, Mar. 1999. Google Scholar

6. Kumar, B. P. and G. R. Branner, "Generalized analytical technique for the synthesis of unequally spaced arrays with linear, planar, cylindrical or spherical geometry," IEEE Transactions on Antennas and Propagation, Vol. 53, No. 2, 621-634, Feb. 2005. Google Scholar

7. Keizer, Will P. M. N., "Linear array thinning using iterative FFT techniques," IEEE Transactions on Antennas and Propagation, Vol. 56, No. 8, 2757-2760, Aug. 2008. Google Scholar

8. Liu, Yanhui, Zaiping Nie, and Qing Huo Liu, "Reducing the number of elements in a linear antenna array by the matrix pencil method," IEEE Transactions on Antennas and Propagation, Vol. 56, No. 9, 2955-2962, Sep. 2008. Google Scholar

9. Echeveste, J. Ignacio, Miguel A. González de Aza, and Juan Zapata, "Shaped beam synthesis of real antenna arrays via finite-element method, floquet modal analysis, and convex programming," IEEE Transactions on Antennas and Propagation, Vol. 64, No. 4, 1279-1286, Apr. 2016. Google Scholar

10. Zhang, Fenggan, Weimin Jia, and Minli Yao, "Linear aperiodic array synthesis using differential evolution algorithm," IEEE Antennas and Wireless Propagation Letters, Vol. 12, 797-800, 2013. Google Scholar

11. Cui, Chao-Yi, Yong-Chang Jiao, Li Zhang, Liang Lu, and Huan Zhang, "Synthesis of subarrayed monopluse arrays with contiguous elements using a DE algorithm," IEEE Transactions on Antennas and Propagation, Vol. 65, No. 8, 4340-4345, Aug. 2017. Google Scholar

12. Liu, Heng, Hongwei Zhao, Weimei Li, and Bo Liu, "Synthesis of sparse planar arrays using matrix mapping and differential evolution," IEEE Antennas and Wireless Propagation Letters, Vol. 15, 1905-1908, 2016. Google Scholar

13. Haupt, R. L., "Thinned arrays using genetic algorithms," IEEE Transactions on Antennas and Propagation, Vol. 42, No. 7, 993-999, Jul. 1994. Google Scholar

14. Chen, Kesong, Zishu He, and Chunlin Han, "A modified real GA for the sparse linear array synthesis with multiple constraints," IEEE Transactions on Antennas and Propagation, Vol. 54, No. 7, 2169-2173, Jul. 2006. Google Scholar

15. Shi, Li, Yun-Kai Deng, Hui-Feng Sun, Robert Wang, Jia-Qiu Ai, and He Yan, "An improved real-coded genetic algorithm for the beam forming of spaceborne SAR," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 6, 3034-3040, Jun. 2012. Google Scholar

16. Yang, Jianhua, Feng Yang, Peng Yang, and Zhiyu Xing, "Synthesis of clustered concentric ring arrays through joint optimization of multi-parameters," IEEE Transactions on Antennas and Propagation, Vol. 71, No. 1, 840-851, Jan. 2023. Google Scholar

17. Jia, Weimin, Zhiqiang Lin, Minli Yao, et al., "A synthesis technique for linear sparse arrays with multiple constraints," Acta Electronica Sinica, Vol. 41, No. 5, 926-930, 2013. Google Scholar

18. Zhao, Heng, Yong-Ling Ban, Yanhui Liu, Jun Hu, and Zaiping Nie, "Go-caterpillar mutation and its optimization algorithm for synthesis of large-scale sparse planar arrays," IEEE Transactions on Antennas and Propagation, Vol. 71, No. 3, 2194-2207, Mar. 2023. Google Scholar

19. Wandale, Steven and Koichi Ichige, "Simulated annealing assisted sparse array selection utilizing deep learning," IEEE Access, Vol. 9, 156907-156914, 2021. Google Scholar

20. Wang, Bin, Xue Tian, and Kui Tao, "Synthesis of sparse uniformly excited concentric ring arrays using the chaos sparrow search algorithm," International Journal of Antennas and Propagation, Vol. 2023, No. 1, 2926111, May 2023. Google Scholar

21. Tian, Xue, Bin Wang, Kui Tao, and Ke Li, "An improved synthesis of sparse planar arrays using density-weighted method and chaos sparrow search algorithm," IEEE Transactions on Antennas and Propagation, Vol. 71, No. 5, 4339-4349, May 2023. Google Scholar

22. Chen, Kesong, Xiaohua Yun, Zishu He, and Chunlin Han, "Synthesis of sparse planar arrays using modified real genetic algorithm," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 4, 1067-1073, Apr. 2007. Google Scholar

23. Dai, Dingcheng, Minli Yao, Hongguang Ma, Wei Jin, and Fenggan Zhang, "An asymmetric mapping method for the synthesis of sparse planar arrays," IEEE Antennas and Wireless Propagation Letters, Vol. 17, No. 1, 70-73, Jan. 2018. Google Scholar

24. Boyd, S. P. and L. Vandenberghe, Convex Optimization, Cambridge University Press, New York, UK, 2004.
doi:10.1017/CBO9780511804441

25. Lebret, H. and S. Boyd, "Antenna array pattern synthesis via convex optimization," IEEE Transactions on Signal Processing, Vol. 45, No. 3, 526-532, Mar. 1997. Google Scholar

26. Nai, Siew Eng, Wee Ser, Zhu Liang Yu, and Huawei Chen, "Beampattern synthesis for linear and planar arrays with antenna selection by convex optimization," IEEE Transactions on Antennas and Propagation, Vol. 58, No. 12, 3923-3930, Dec. 2010. Google Scholar

27. Angeletti, Piero and Giovanni Toso, "Optimal amplitude-density synthesis of linear aperiodic arrays," IEEE Transactions on Antennas and Propagation, Vol. 71, No. 6, 4903-4918, Jun. 2023. Google Scholar

28. Battaglia, Giada M., Gennaro G. Bellizzi, Andrea F. Morabito, Gino Sorbello, and Tommaso Isernia, "A general effective approach to the synthesis of shaped beams for arbitrary fixed-geometry arrays," Journal of Electromagnetic Waves and Applications, Vol. 33, No. 18, 2404-2422, 2019. Google Scholar

29. Isernia, T., F. J. A. Pena, O. M. Bucci, M. D'Urso, J. F. Gomez, and J. A. Rodriguez, "A hybrid approach for the optimal synthesis of pencil beams through array antennas," IEEE Transactions on Antennas and Propagation, Vol. 52, No. 11, 2912-2918, Nov. 2004. Google Scholar

30. Cui, Chao-Yi, Yong-Chang Jiao, and Li Zhang, "Synthesis of some low sidelobe linear arrays using hybrid differential evolution algorithm integrated with convex programming," IEEE Antennas and Wireless Propagation Letters, Vol. 16, 2444-2448, 2017. Google Scholar

31. CVX Research, Inc., "CVX: MATLAB software for disciplined convex programming," Version 2.2, Apr. 2011, http://cvxr.com/cvx.

Ms. Qi Tang

Professor Bin Wang

Dr. Xue Tian