volume | PIER Journals

Abstract

In this paper, a novel measurement matrix construction method based on adaptive cross-approximation (ACA) is proposed to improve the performance of the compressive sensing-based method of moments (CS-MoM) for analyzing electromagnetic scattering problems. ACA is based on a weight scheme and is able to recognize the rows and columns that contribute significantly to the matrix. Thus, the object is divided into multiple blocks, and the impedance matrix is partitioned into near-field and far-field groups to establish the condition for applying ACA. Then, the row indexes are extracted from the group with the highest number of ACA recognized rows in the far-field groups of each block. Finally, by combining all row indexes to extract the impedance matrix, a lower-dimensional and deterministic measurement matrix is constructed, thereby improving computational efficiency. Numerical simulation results validate the accuracy and effectiveness of the proposed method.

1. Harrington, R. F., "Field computation by moment methods," The Macmillan Comp., Vol. 130, No. 6, 276-280, 1968. Google Scholar

2. Gibson, Walton C., The Method of Moments in Electromagnetics, Boca Raton, FL, USA: CRC Press, 2007.

3. Coifman, Ronald, Vladimir Rokhlin, and Stephen Wandzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas and Propagation Magazine, Vol. 35, No. 3, 7-12, 1993. Google Scholar

4. Song, Jiming, Cai-Cheng Lu, and Weng Cho Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Transactions on Antennas and Propagation, Vol. 45, No. 10, 1488-1493, 1997. Google Scholar

5. Prakash, V. V. S., Raj and Mittra, "Characteristic basis function method: A new technique for efficient solution of method of moments matrix equations," Microwave and Optical Technology Letters, Vol. 36, No. 2, 95-100, 2003. Google Scholar

6. Garcia, Eliseo, Carlos Delgado, IvÁn GonzÁlez Diego, and Manuel Felipe Catedra, "An iterative solution for electrically large problems combining the characteristic basis function method and the multilevel fast multipole algorithm," IEEE Transactions on Antennas and Propagation, Vol. 56, No. 8, 2363-2371, 2008. Google Scholar

7. Donoho, David L., "Compressed sensing," IEEE Transactions on Information Theory, Vol. 52, No. 4, 1289-1306, 2006. Google Scholar

8. Candes, E. J., J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Transactions on Information Theory, Vol. 52, No. 2, 489-509, 2006. Google Scholar

9. Kong, Meng, Mingsheng Chen, Xinyuan Cao, Liang Zhang, Qi Qi, and Xianliang Wu, "Fast analysis of local current distribution for electromagnetic scattering problems of electrically large objects," IEEE Access, Vol. 8, 127640-127647, 2020. Google Scholar

10. Kong, Meng, Ming Sheng Chen, Xin Yuan Cao, Jia Bing Zhu, Xiao Jing Kuang, Qi Qi, and Xian Liang Wu, "Fast electromagnetic scattering analysis of inhomogeneous dielectric objects over a wide incident angle," IEEE Antennas and Wireless Propagation Letters, Vol. 20, No. 8, 1527-1531, 2021. Google Scholar

11. Chai, Shui-Rong and Li-Xin Guo, "Compressive sensing for monostatic scattering from 3-D NURBS geometries," IEEE Transactions on Antennas and Propagation, Vol. 64, No. 8, 3545-3553, 2016. Google Scholar

12. Chai, Shui-Rong and Li-Xin Guo, "Integration of CS into MoM for efficiently solving of bistatic scattering problems," IEEE Antennas and Wireless Propagation Letters, Vol. 15, 1771-1774, 2016. Google Scholar

13. Wang, Zhe, Bing-Zhong Wang, and Wei Shao, "Efficient construction and solution of MoM matrix equation with compressed sensing technique," Journal of Electromagnetic Waves and Applications, Vol. 29, No. 5, 683-692, 2015. Google Scholar

14. Chai, Shui-Rong and Li-Xin Guo, "Fast analysis of bistatic scattering problems with compressive sensing technique," Journal of Electromagnetic Waves and Applications, Vol. 30, No. 13, 1755-1762, 2016. Google Scholar

15. Wang, Zhonggen, Pan Wang, Yufa Sun, and Wenyan Nie, "Fast analysis of bistatic scattering problems for three-dimensional objects using compressive sensing and characteristic modes," IEEE Antennas and Wireless Propagation Letters, Vol. 21, No. 9, 1817-1821, 2022. Google Scholar

16. Gao, Yalan, Muhammad Firdaus Akbar, and Ghassan Nihad Jawad, "Stabilized and fast method for compressive sensing-based method of moments," IEEE Antennas and Wireless Propagation Letters, Vol. 22, No. 12, 2915-2919, 2023. Google Scholar

17. Rao, Sadasiva, Donald Wilton, and Allen Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Transactions on Antennas and Propagation, Vol. 30, No. 3, 409-418, 1982. Google Scholar

18. Wang, Zhong-Gen, Wen-Yan Nie, and Han Lin, "Characteristic basis functions enhanced compressive sensing for solving the bistatic scattering problems of three-dimensional targets," Microwave and Optical Technology Letters, Vol. 62, No. 10, 3132-3138, 2020. Google Scholar

19. Wang, Pan, Zhong-Gen Wang, Yu-Fa Sun, and Wen-Yan Nie, "Novel compressive sensing computing model used for analyzing electromagnetic scattering characteristics of three-dimensional electrically large objects," Acta Physica Sinica, Vol. 72, No. 3, 54-61, 2023. Google Scholar

20. Chen, Yikai and Chao-Fu Wang, Characteristic Modes: Theory and Applications in Antenna Engineering, John Wiley & Sons, 2015.

21. Cao, Xinyuan, Mingsheng Chen, Qi Qi, Meng Kong, Jinhua Hu, Liang Zhang, and Xianliang Wu, "Solving electromagnetic scattering problems by underdetermined equations and Krylov subspace," IEEE Microwave and Wireless Components Letters, Vol. 30, No. 6, 541-544, 2020. Google Scholar

22. Wang, Zhonggen, Haoran Yuan, Yufa Sun, Wenyan Nie, and Pan Wang, "Block-based krylov subspace basis functions for solving bistatic scattering problems," IEEE Antennas and Wireless Propagation Letters, Vol. 22, No. 10, 2561-2565, 2023. Google Scholar

23. Kurz, Stefan, Oliver Rain, and Sergej Rjasanow, "The adaptive cross-approximation technique for the 3D boundary-element method," IEEE Transactions on Magnetics, Vol. 38, No. 2, 421-424, 2002. Google Scholar

24. Zhao, Kezhong, Marinos N. Vouvakis, and Jin-Fa Lee, "The adaptive cross approximation algorithm for accelerated method of moments computations of EMC problems," IEEE Transactions on Electromagnetic Compatibility, Vol. 47, No. 4, 763-773, 2005. Google Scholar

25. Lloyd, Stuart, "Least squares quantization in PCM," IEEE Transactions on Information Theory, Vol. 28, No. 2, 129-137, 1982. Google Scholar

26. Candès, Emmanuel J., "The restricted isometry property and its implications for compressed sensing," Comptes Rendus. Mathematique, Vol. 346, No. 9-10, 589-592, 2008. Google Scholar

27. Baraniuk, Richard G., "Compressive sensing," IEEE Signal Process. Mag., Vol. 24, No. 4, 118-121, 2007. Google Scholar

28. Tropp, Joel A. and Anna C. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Transactions on Information Theory, Vol. 53, No. 12, 4655-4666, 2007. Google Scholar

29. Wang, Jian, Seokbeop Kwon, and Byonghyo Shim, "Generalized orthogonal matching pursuit," IEEE Transactions on Signal Processing, Vol. 60, No. 12, 6202-6216, 2012. Google Scholar

30. Harrington, R. and J. Mautz, "Theory of characteristic modes for conducting bodies," IEEE Transactions on Antennas and Propagation, Vol. 19, No. 5, 622-628, 1971. Google Scholar

Dr. Dai Dong

Professor Zhonggen Wang

Professor Wenyan Nie

Mr. Fei Guo

Dr. Yufa Sun

Dr. Pan Wang

Dr. Chenlu Li