Vol. 168
Latest Volume
All Volumes
PIERC 168 [2026] PIERC 167 [2026] PIERC 166 [2026] PIERC 165 [2026] PIERC 164 [2026] PIERC 163 [2026] PIERC 162 [2025] PIERC 161 [2025] PIERC 160 [2025] PIERC 159 [2025] PIERC 158 [2025] PIERC 157 [2025] PIERC 156 [2025] PIERC 155 [2025] PIERC 154 [2025] PIERC 153 [2025] PIERC 152 [2025] PIERC 151 [2025] PIERC 150 [2024] PIERC 149 [2024] PIERC 148 [2024] PIERC 147 [2024] PIERC 146 [2024] PIERC 145 [2024] PIERC 144 [2024] PIERC 143 [2024] PIERC 142 [2024] PIERC 141 [2024] PIERC 140 [2024] PIERC 139 [2024] PIERC 138 [2023] PIERC 137 [2023] PIERC 136 [2023] PIERC 135 [2023] PIERC 134 [2023] PIERC 133 [2023] PIERC 132 [2023] PIERC 131 [2023] PIERC 130 [2023] PIERC 129 [2023] PIERC 128 [2023] PIERC 127 [2022] PIERC 126 [2022] PIERC 125 [2022] PIERC 124 [2022] PIERC 123 [2022] PIERC 122 [2022] PIERC 121 [2022] PIERC 120 [2022] PIERC 119 [2022] PIERC 118 [2022] PIERC 117 [2021] PIERC 116 [2021] PIERC 115 [2021] PIERC 114 [2021] PIERC 113 [2021] PIERC 112 [2021] PIERC 111 [2021] PIERC 110 [2021] PIERC 109 [2021] PIERC 108 [2021] PIERC 107 [2021] PIERC 106 [2020] PIERC 105 [2020] PIERC 104 [2020] PIERC 103 [2020] PIERC 102 [2020] PIERC 101 [2020] PIERC 100 [2020] PIERC 99 [2020] PIERC 98 [2020] PIERC 97 [2019] PIERC 96 [2019] PIERC 95 [2019] PIERC 94 [2019] PIERC 93 [2019] PIERC 92 [2019] PIERC 91 [2019] PIERC 90 [2019] PIERC 89 [2019] PIERC 88 [2018] PIERC 87 [2018] PIERC 86 [2018] PIERC 85 [2018] PIERC 84 [2018] PIERC 83 [2018] PIERC 82 [2018] PIERC 81 [2018] PIERC 80 [2018] PIERC 79 [2017] PIERC 78 [2017] PIERC 77 [2017] PIERC 76 [2017] PIERC 75 [2017] PIERC 74 [2017] PIERC 73 [2017] PIERC 72 [2017] PIERC 71 [2017] PIERC 70 [2016] PIERC 69 [2016] PIERC 68 [2016] PIERC 67 [2016] PIERC 66 [2016] PIERC 65 [2016] PIERC 64 [2016] PIERC 63 [2016] PIERC 62 [2016] PIERC 61 [2016] PIERC 60 [2015] PIERC 59 [2015] PIERC 58 [2015] PIERC 57 [2015] PIERC 56 [2015] PIERC 55 [2014] PIERC 54 [2014] PIERC 53 [2014] PIERC 52 [2014] PIERC 51 [2014] PIERC 50 [2014] PIERC 49 [2014] PIERC 48 [2014] PIERC 47 [2014] PIERC 46 [2014] PIERC 45 [2013] PIERC 44 [2013] PIERC 43 [2013] PIERC 42 [2013] PIERC 41 [2013] PIERC 40 [2013] PIERC 39 [2013] PIERC 38 [2013] PIERC 37 [2013] PIERC 36 [2013] PIERC 35 [2013] PIERC 34 [2013] PIERC 33 [2012] PIERC 32 [2012] PIERC 31 [2012] PIERC 30 [2012] PIERC 29 [2012] PIERC 28 [2012] PIERC 27 [2012] PIERC 26 [2012] PIERC 25 [2012] PIERC 24 [2011] PIERC 23 [2011] PIERC 22 [2011] PIERC 21 [2011] PIERC 20 [2011] PIERC 19 [2011] PIERC 18 [2011] PIERC 17 [2010] PIERC 16 [2010] PIERC 15 [2010] PIERC 14 [2010] PIERC 13 [2010] PIERC 12 [2010] PIERC 11 [2009] PIERC 10 [2009] PIERC 9 [2009] PIERC 8 [2009] PIERC 7 [2009] PIERC 6 [2009] PIERC 5 [2008] PIERC 4 [2008] PIERC 3 [2008] PIERC 2 [2008] PIERC 1 [2008]
2026-03-28
An Integrated Ray Tracing and Variable-Step Fourier Transform-Based Split-Step Parabolic Equation Modeling Approach for UAV-Assisted Channel Characterization in Mountainous Environments
By
Progress In Electromagnetics Research C, Vol. 168, 1-10, 2026
Abstract
To enhance communication performance in mountainous environments, unmanned aerial vehicle (UAV)-assisted communication systems have emerged as a mainstream solution. Channel modeling for UAV-assisted communication is a critical research focus, confronting prominent challenges, including balancing computational efficiency and modeling accuracy. This paper proposes a hybrid modeling approach that combines ray tracing (RT) and the variable-step Fourier transform-based Split-Step Parabolic Equation (V-FSSPE) to address the issue. The proposed method fully leverages the strengths of RT in accurately calculating direct, reflected, and diffracted propagation paths, as well as the advantages of V-FSSPE in efficiently modeling long-distance and large-scale areas. A hierarchical model suitable for low-altitude UAV communication is thereby established. Simulation results demonstrate that, compared with traditional modeling methods, the proposed method in this study effectively balances accuracy and efficiency in terrain-dominated air-to-ground channels, making it suitable for millimeter wave (mmWave) communication and emergency communication network planning in terrain-dominated propagation environments. Since factors such as vegetation and atmospheric effects have not yet been incorporated, practical deployment requires case-specific corrections based on the actual environment. Nonetheless, this framework is expected to provide important theoretical references and foundational support for the design and optimization of communication systems in related fields.
Citation
Jihui Shi, and Jian Song, "An Integrated Ray Tracing and Variable-Step Fourier Transform-Based Split-Step Parabolic Equation Modeling Approach for UAV-Assisted Channel Characterization in Mountainous Environments," Progress In Electromagnetics Research C, Vol. 168, 1-10, 2026.
doi:10.2528/PIERC26012006
References

1. Chen, Runfeng, Jin Chen, Hong Li, Xiaojing Chu, Dianxiong Liu, Yuli Zhang, and Yuhua Xu, "Survey on optimizations in coalitions-based unmanned aerial vehicle communication networks for 6G networks," Journal of Electronics & Information Technology, Vol. 44, No. 9, 3126-3135, 2022.
doi:10.11999/JEIT220383        Google Scholar

2. Li, Jing, Yong Niu, Hao Wu, Bo Ai, Sheng Chen, Zhiyong Feng, Zhangdui Zhong, and Ning Wang, "Mobility support for millimeter wave communications: Opportunities and challenges," IEEE Communications Surveys & Tutorials, Vol. 24, No. 3, 1816-1842, 2022.
doi:10.1109/comst.2022.3176802        Google Scholar

3. Zhang, Zhaolei, Yu Liu, Jie Huang, Jingfan Zhang, Jingquan Li, and Ruisi He, "Channel characterization and modeling for 6G UAV-assisted emergency communications in complicated mountainous scenarios," Sensors, Vol. 23, No. 11, 4998, 2023.
doi:10.3390/s23114998        Google Scholar

4. Galvan-Tejada, Giselle M., Jorge E. Aviles-Mejia, Aldo G. Orozco-Lugo, Luis A. Arellano-Cruz, Ruben Flores-Leal, and Rogelio Lozano-Leal, "Propagation characteristics for UAVs operating at short range and low altitude," Progress In Electromagnetics Research C, Vol. 100, 105-120, 2020.
doi:10.2528/pierc19110606        Google Scholar

5. Zhu, Qiuming, Mengtian Yao, Fei Bai, Xiaomin Chen, Weizhi Zhong, Boyu Hua, and Xijuan Ye, "A general altitude-dependent path loss model for UAV-to-ground millimeter-wave communications," Frontiers of Information Technology & Electronic Engineering, Vol. 22, No. 6, 767-776, 2021.
doi:10.1631/fitee.2000497        Google Scholar

6. Guan, Yang-Yang, Peng Zhang, Xu-Long Wang, and Jie Bai, "Compact self-decoupled MIMO antenna based on current cancellation for UAVs," Progress In Electromagnetics Research C, Vol. 158, 85-91, 2025.
doi:10.2528/PIERC25062104        Google Scholar

7. Akram, M. U., U. Saeed, S. A. Hassan, and H. Jung, "UAV-based air-to-ground channel modeling for diverse environments," 2020 IEEE Wireless Communications and Networking Conference (WCNC), 1-6, Seoul, Korea (South), 2020.
doi:10.1109/wcnc45663.2020.9120659

8. Salman, Alaa, Shokri Almekdad, and Mohamad Alhariri, "Improvement of phase noise performance in tracking array of UAV signal based on mixed phased/retrodirective array," Progress In Electromagnetics Research C, Vol. 95, 195-207, 2019.
doi:10.2528/pierc19062604        Google Scholar

9. He, Yuanfeng, Yufan Wang, Haochuan Yue, Jiahui Chai, Yuzhe Sun, Yue Lyu, Qinghui Wu, and Wei Wang, "Analysis of low-altitude UAV-to-ground channel characteristics in rural environment," 2024 IEEE 7th International Conference on Electronic Information and Communication Technology (ICEICT), 1081-1085, Xi’an, China, 2024.
doi:10.1109/ICEICT61637.2024.10671069

10. Semkin, Vasilii, Seongjoon Kang, Jaakko Haarla, William Xia, Ismo Huhtinen, Giovanni Geraci, Angel Lozano, Giuseppe Loianno, Marco Mezzavilla, and Sundeep Rangan, "Lightweight UAV-based measurement system for air-to-ground channels at 28 GHz," 2021 IEEE 32nd Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), 848-853, Helsinki, Finland, 2021.
doi:10.1109/PIMRC50174.2021.9569561

11. Thakur, Ekta, Anupma Gupta, Muhannad K. Abdulhameed, Aymen D. Khaleel, and Ahmed Jamal Abdullah Al-Gburi, "Microstrip antenna with two elements and defected ground structure for 5G mobile applications at 28/38 GHz," Progress In Electromagnetics Research C, Vol. 146, 177-185, 2024.
doi:10.2528/pierc24062403        Google Scholar

12. Kohli, Manav, Abhishek Adhikari, Gulnur Avci, Sienna Brent, Jared Moser, Sabbir Hossain, Aditya Dash, Igor Kadota, Rodolfo Feick, Dmitry Chizhik, Jinfeng Du, Reinaldo A. Valenzuela, and Gil Zussman, "Outdoor-to-indoor 28 GHz wireless measurements in manhattan: Path Loss, location impacts, and 90% coverage," Proceedings of the Twenty-Third International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Networks and Mobile Computing, 201-210, 2022.
doi:10.1145/3492866.3549728

13. Maccartney, George R., Theodore S. Rappaport, Shu Sun, and Sijia Deng, "Indoor office wideband millimeter-wave propagation measurements and channel models at 28 and 73 GHz for ultra-dense 5G wireless networks," IEEE Access, Vol. 3, 2388-2424, 2015.
doi:10.1109/access.2015.2486778        Google Scholar

14. Chuan, Lee Loo, Mardeni Roslee, Chilakala Sudhamani, Sufian M. I. Mitani, Athar Waseem, Anwar F. Osman, Fatimah Z. Ali, and Yasir Ullah, "Impact of rainfall on 5G millimeter wave channels," Progress In Electromagnetics Research C, Vol. 148, 97-107, 2024.
doi:10.2528/pierc24052501        Google Scholar

15. Ju, Shihao, Yunchou Xing, Ojas Kanhere, and Theodore S. Rappaport, "Millimeter wave and sub-terahertz spatial statistical channel model for an indoor office building," IEEE Journal on Selected Areas in Communications, Vol. 39, No. 6, 1561-1575, 2021.
doi:10.1109/jsac.2021.3071844        Google Scholar

16. Lee, Jae-Hyun, Jeong-Sik Choi, and Seong-Cheol Kim, "Cell coverage analysis of 28 GHz millimeter wave in urban microcell environment using 3-D ray tracing," IEEE Transactions on Antennas and Propagation, Vol. 66, No. 3, 1479-1487, 2018.
doi:10.1109/tap.2018.2797531        Google Scholar

17. Huang, Jie, Cheng-Xiang Wang, Yuqian Yang, Yu Liu, Jian Sun, and Wensheng Zhang, "Channel measurements and modeling for 400-600-MHz bands in urban and suburban scenarios," IEEE Internet of Things Journal, Vol. 8, No. 7, 5531-5543, 2021.
doi:10.1109/jiot.2020.3032615        Google Scholar

18. Mehrnia, Niloofar and Mehmet Kemal Ozdemir, "Ray tracing-based maritime channel analysis for millimeter radiowaves," Journal of Infrared, Millimeter, and Terahertz Waves, Vol. 40, No. 1, 108-130, 2019.
doi:10.1007/s10762-018-0536-9        Google Scholar

19. Zeng, Yong, Rui Zhang, and Teng Joon Lim, "Wireless communications with unmanned aerial vehicles: Opportunities and challenges," IEEE Communications Magazine, Vol. 54, No. 5, 36-42, 2016.
doi:10.1109/mcom.2016.7470933        Google Scholar

20. Khuwaja, Aziz Altaf, Yunfei Chen, Nan Zhao, Mohamed-Slim Alouini, and Paul Dobbins, "A survey of channel modeling for UAV communications," IEEE Communications Surveys & Tutorials, Vol. 20, No. 4, 2804-2821, 2018.
doi:10.1109/comst.2018.2856587        Google Scholar

21. Gao, Ying, Qun Shao, Binzhou Yan, Jufei Chen, and Shuxia Guo, "Variable step size technique for the parabolic equation in complex environmental conditions," IEEE Access, Vol. 7, 137305-137316, 2019.
doi:10.1109/access.2019.2942369        Google Scholar

22. (ITU-R), I. T. U., "Propagation data and prediction methods required for the design of earth-space telecommunication systems," https://www.itu.int/rec/R-REC-P.526-15-202312-I/en, 2023.

23. Calculation of Free-Space Attenuation, 11th ed., ITU-R, Geneva, Switzerland, Available: https://www.itu.int/rec/R-REC-P.525-5-202411-I/en, Nov. 2024.

24. Chen, Ying and Weiping Qin, "A variable range step technique for propagation predictions over large irregular terrain using the fourier split-step parabolic equation," 2015 Asia-Pacific Microwave Conference (APMC), 1-3, Nanjing, China, 2015.
doi:10.1109/APMC.2015.7413103