volume | PIER Journals

Abstract

In this paper, a method is proposed for solving the one-hop sky-wave propagation problems of an arbitrarily oriented lowfrequency (LF) electric dipole within a planar layered Earth-ionosphere waveguide. The purpose of this study is to clarify the relationship between the radiation field and the direction of the electric dipole source in a planar-layered Earth-ionosphere waveguide. In deriving the specific formulas, we employed the ideal far-field approximation idea for an arbitrarily oriented electric dipole in free space and the method of images in layered media. The reflection characteristics of different polarized plane waves at the interface were also taken into account. Based on the improved wave-hop theory, the expressions for the one-hop sky-wave field excited by dipole sources with different directions suitable for an irregular surface are further derived. Using the proposed method, we calculated the sky-wave fields of electric dipoles operating at 100 kHz with various orientations at different receiver altitudes. The results show that the proposed method can be conveniently used to analyze the one-hop sky-wave field of the electric dipole sources with various orientations in a planar stratified Earth-ionosphere waveguide and provides an efficient modeling tool for LF communication system design and signal prediction over complex terrain.

1. Zhou, L., Y. Zheng, Z. Mu, X. Hu, X. Zhu, and L. He, "Distinction and characteristic analysis of different modes of low-frequency one-hop sky wave in the day-night transition area," Acta Electronica Sinica, Vol. 51, No. 7, 1964-1969, 2023.
doi:10.12263/DZXB.20220659 Google Scholar

2. Kim, Woohyun, Pyo-Woong Son, Sul Gee Park, Sang Hyun Park, and Jiwon Seo, "First demonstration of the Korean eLoran accuracy in a narrow waterway using improved ASF maps," IEEE Transactions on Aerospace and Electronic Systems, Vol. 58, No. 2, 1492-1496, 2022.
doi:10.1109/taes.2021.3114272 Google Scholar

3. Fan, Xiangpeng, Yijun Zhang, Paul R. Krehbiel, Yang Zhang, Dong Zheng, Wen Yao, Liangtao Xu, Hengyi Liu, and Weitao Lyu, "Application of ensemble empirical mode decomposition in low-frequency lightning electric field signal analysis and lightning location," IEEE Transactions on Geoscience and Remote Sensing, Vol. 59, No. 1, 86-100, 2021.
doi:10.1109/tgrs.2020.2991724 Google Scholar

4. Lü, Xiaozhou, Xi Chen, Weiqiang Zhang, Long Gu, and Weimin Bao, "Acoustically actuated compact magnetoelectric antenna for low-frequency underwater communication," IEEE Transactions on Antennas and Propagation, Vol. 71, No. 11, 8493-8503, 2023.
doi:10.1109/tap.2023.3307711 Google Scholar

5. Niknam, Kaiser and Jamesina J. Simpson, "A review of grid-based, time-domain modeling of electromagnetic wave propagation involving the ionosphere," IEEE Journal on Multiscale and Multiphysics Computational Techniques, Vol. 6, 214-228, 2021.
doi:10.1109/jmmct.2021.3136128 Google Scholar

6. Bérenger, Jean-Pierre, "FDTD propagation of VLF-LF waves in the presence of ions in the Earth-ionosphere waveguide," Annals of Telecommunications, Vol. 75, No. 7, 437-446, 2020.
doi:10.1007/s12243-020-00756-5 Google Scholar

7. Panyukov, Anatoly V., "Estimation of the location of an arbitrarily oriented dipole under single-point direction finding," Journal of Geophysical Research: Atmospheres, Vol. 101, No. D10, 14977-14982, 1996.
doi:10.1029/96jd00067 Google Scholar

8. Wakai, N., N. Kurihara, and A. Otsuka, "Numerical method for calculating LF sky-wave, ground-wave and their resultant wave field strengths," Electronics Letters, Vol. 40, No. 5, 288-290, 2004.
doi:10.1049/el:20040207 Google Scholar

9. Wait, James R., "A diffraction theory for LF sky-wave propagation," Journal of Geophysical Research, Vol. 66, No. 6, 1713-1724, 1961.
doi:10.1029/JZ066i006p01713 Google Scholar

10. Nazari, Mohsen Eslami and Weimin Huang, "An analytical solution of electromagnetic radiation of a vertical dipole over a layered half-space," IEEE Transactions on Antennas and Propagation, Vol. 68, No. 2, 1181-1185, 2020.
doi:10.1109/tap.2019.2938675 Google Scholar

11. Karami, Hamidreza, Keyhan Sheshyekani, and Farhad Rachidi, "Mixed-potential integral equation for full-wave modeling of grounding systems buried in a lossy multilayer stratified ground," IEEE Transactions on Electromagnetic Compatibility, Vol. 59, No. 5, 1505-1513, 2017.
doi:10.1109/temc.2017.2655497 Google Scholar

12. Mu, Zhonglin, Qiaoqiao Wang, Lili Zhou, Xinyue Hu, and Lifeng He, "Comparison of low frequency multi-hop sky wave delay estimation algorithms," Chinese Journal of Radio Science, Vol. 37, No. 2, 244-250, 2022.
doi:10.12265/j.cjors.2021262 Google Scholar

13. Wait, J. R., "The ancient and modern history of EM ground-wave propagation," IEEE Antennas and Propagation Magazine, Vol. 40, No. 5, 7-24, 1998.
doi:10.1109/74.735961 Google Scholar

14. Li, Kai, Electromagnetic Fields in Stratified Media, Zhejiang University Press, Hangzhou, China, 2009.
doi:10.1007/978-3-540-95964-9

15. Li, Zheng Xu, Hui Ran Zeng, and Kai Li, "Near field generated by a VLF magnetic dipole with arbitrary orientation in an anisotropic magnetoplasma," IEEE Transactions on Plasma Science, Vol. 51, No. 6, 1527-1539, 2023.
doi:10.1109/tps.2023.3277280 Google Scholar

16. Xu, Honglei, Tingting Gu, Juan Zheng, and Kai Li, "LF sky wave propagation excited by a horizontal electric dipole towards understanding of its radiation mechanism," Applied Computational Electromagnetics Society Journal (ACES), Vol. 33, No. 6, 657-664, 2018. Google Scholar

17. Cao, Le, Bing Wei, and De-Biao Ge, "Computation of far radiation field of an arbitrarily oriented dipole above layered anisotropic half space," Waves in Random and Complex Media, Vol. 23, No. 4, 446-460, 2013.
doi:10.1080/17455030.2013.850551 Google Scholar

18. Zhou, Li-Li, Xin-Yue Hu, Zhong-Lin Mu, Rui Zhang, and Yue Zheng, "Far-field calculation of an arbitrarily oriented electric dipole in horizontal layered confined space," Acta Physica Sinica, Vol. 71, No. 20, 1-7, 2022.
doi:10.7498/aps.71.20220545 Google Scholar

19. Zhou, Lili, Yuhong Jiang, Zhonglin Mu, Qiaoqiao Wang, Xinyue Hu, and Lifeng He, "Study of Loran-C one-hop sky-wave fields at different altitudes above the ground," IEEE Antennas and Wireless Propagation Letters, Vol. 20, No. 12, 2368-2371, 2021.
doi:10.1109/lawp.2021.3111690 Google Scholar

20. Xi, Xiaoli, Lili Zhou, Jinsheng Zhang, Jiangfan Liu, and Lili Wang, "Combined IE-FDTD algorithm for long-range Loran-C ground-wave propagation," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 8, 3802-3808, 2012.
doi:10.1109/tap.2012.2201102 Google Scholar

21. Zhou, L., Y. Zhang, Z. Mu, and X. Hu, "The calculation of the far-field radiation field of an electric dipole in anisotropic layered confined space," Journal of Shaanxi University of Science & Technology, Vol. 23, No. 4, 209-214, 2025.
doi:10.3969/j.issn.1000-5811.2025.04.024 Google Scholar

Dr. Xinyue Hu

Dr. Lili Zhou

Dr. Zhonglin Mu

Dr. Ying Zhang

Dr. Jinsheng Zhang