{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:33:45Z","timestamp":1760060025503,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,25]],"date-time":"2025-07-25T00:00:00Z","timestamp":1753401600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2023YFB2904804","62394292","62394290"],"award-info":[{"award-number":["2023YFB2904804","62394292","62394290"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["2023YFB2904804","62394292","62394290"],"award-info":[{"award-number":["2023YFB2904804","62394292","62394290"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Terahertz (THz) wireless communications can support ultra-high data rates and secure wireless links with miniaturized devices for unmanned aerial vehicle (UAV) communications. In this paper, a three-dimensional (3D) non-stationary geometry-based stochastic channel model (GSCM) is proposed for multiple-input multiple-output (MIMO) communication links between the UAVs in the THz band. The proposed channel model considers not only the 3D scattering and reflection scenarios (i.e., reflection and scattering fading) but also the atmospheric molecule absorption attenuation, arbitrary 3D trajectory, and antenna arrays of both terminals. In addition, the statistical properties of the proposed GSCM (i.e., the time auto-correlation function (T-ACF), space cross-correlation function (S-CCF), and Doppler power spectrum density (DPSD)) are derived and analyzed under several important UAV-related parameters and different carrier frequencies, including millimeter wave (mmWave) and THz bands. Finally, the good agreement between the simulated results and corresponding theoretical ones demonstrates the correctness of the proposed GSCM, and some useful observations are provided for the system design and performance evaluation of UAV-based air-to-air (A2A) THz-MIMO wireless communications.<\/jats:p>","DOI":"10.3390\/e27080788","type":"journal-article","created":{"date-parts":[[2025,7,25]],"date-time":"2025-07-25T09:35:11Z","timestamp":1753436111000},"page":"788","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Three-Dimensional Non-Stationary MIMO Channel Modeling for UAV-Based Terahertz Wireless Communication Systems"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8266-8316","authenticated-orcid":false,"given":"Kai","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Information and Navigation, Air Force Engineering University, Xi\u2019an 710082, China"}]},{"given":"Yongjun","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information and Navigation, Air Force Engineering University, Xi\u2019an 710082, China"}]},{"given":"Xiang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information and Navigation, Air Force Engineering University, Xi\u2019an 710082, China"}]},{"given":"Zhaohui","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China"}]},{"given":"Fenglei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Information and Navigation, Air Force Engineering University, Xi\u2019an 710082, China"}]},{"given":"Ke","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information and Navigation, Air Force Engineering University, Xi\u2019an 710082, China"}]},{"given":"Zhe","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Information and Navigation, Air Force Engineering University, Xi\u2019an 710082, China"}]},{"given":"Yun","family":"Wang","sequence":"additional","affiliation":[{"name":"The 93135 Armed Force of China PLA, Beijing, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1109\/MVT.2020.3018436","article-title":"6G wireless channel measurements and models trends and challenges","volume":"15","author":"Wang","year":"2020","journal-title":"IEEE Veh. Technol. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"11154","DOI":"10.1109\/TVT.2021.3116953","article-title":"3D Non-Stationary Wideband UAV-to-Ground MIMO Channel Models Based on Aeronautic Random Mobility Model","volume":"70","author":"Bian","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"8674","DOI":"10.1109\/JIOT.2020.2995707","article-title":"A 3-D Geometry-Based Stochastic Model for Unmanned Aerial Vehicle MIMO Riciean Fading Channels","volume":"7","author":"Cheng","year":"2020","journal-title":"IEEE Internet Things J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5290","DOI":"10.1109\/JIOT.2021.3108411","article-title":"A Non-Stationary 3-D Wideband Channel Model for Low Altitude UAV-MIMO Communication Systems","volume":"9","author":"Lian","year":"2022","journal-title":"IEEE Internet Things J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"12418","DOI":"10.1109\/TVT.2020.3028301","article-title":"Impact of UAV Rotation on MIMO Channel Characterization for Air-to-Ground Communication Systems","volume":"69","author":"Ma","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Ma, Z., Ai, B., He, R., Wang, G., Zhong, Z., Yang, M., Wang, J., and Li, Y. (December, January 18). Impact of UAV Rotation on MIMO Channel Space-Time Correlation. Proceedings of the 2020 IEEE 92nd Vehicular Technology Conference (VTC2020-Fall), Victoria, BC, Canada.","DOI":"10.1109\/VTC2020-Fall49728.2020.9348811"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Chang, H., Wang, C.X., He, Y., Bai, Z., Sun, J., and Zhang, W. (2022, January 27\u201330). Multi-User UAV Channel Modeling with Massive MIMO Configuration. Proceedings of the 2021 IEEE 94th Vehicular Technology Conference (VTC2021-Fall), Norman, OK, USA.","DOI":"10.1109\/VTC2021-Fall52928.2021.9625218"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5145","DOI":"10.1109\/TWC.2021.3137347","article-title":"Performance Analysis of Multi-antenna UAV Networks with 3D Interference Coordination","volume":"21","author":"Tang","year":"2021","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Zhang, X., and Cheng, X. (2019, January 20\u201324). Second Order Statistics of Simulation Models for UAV-MIMORicean Fading Channels. Proceedings of the 2019 IEEE International Conference on Communication (ICC2019), Shanghai, China.","DOI":"10.1109\/ICC.2019.8761565"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4325","DOI":"10.1109\/TWC.2021.3128970","article-title":"A Non-Stationary 3D Model for 6G Massive MIMO mmWave UAV Channels","volume":"21","author":"Bai","year":"2021","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2960","DOI":"10.1109\/JSAC.2021.3088659","article-title":"A Non-Stationary Geometry-Based MIMO Channels Model for Millimeter-Wave UAV Networks","volume":"39","author":"Ma","year":"2021","journal-title":"IEEE J. Sel. Area Commun."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ma, Z., Ai, B., He, R., Zhong, Z., Yang, M., Wang, J., Pei, L., Li, Y., and Li, J. (2020, January 7\u201311). Three-dimensional Modeling Millimeter-Wave MIMO Channels for UAV-Based Communications. Proceedings of the GLOBECOM 2020-2020 IEEE Global Communications Conference, Taipei, Taiwan.","DOI":"10.1109\/GLOBECOM42002.2020.9322621"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Zhou, Y., Ji, Z., Lin, K., and He, Z. (December, January 18). A Three-Dimensional Geometry-Based Stochastic Model for Air-to-Air UAV Channels. Proceedings of the 2020 IEEE 92nd Vehicular Technology Conference (VTC2020-Fall), Victoria, BC, Canada.","DOI":"10.1109\/VTC2020-Fall49728.2020.9348433"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1109\/MCOM.2018.1701263","article-title":"5G Millimeter Wave Channel Sounders, Measurements, and Models: Recent Developments and Future Challenges","volume":"57","author":"Huang","year":"2019","journal-title":"IEEE Commun. Mag."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"78729","DOI":"10.1109\/ACCESS.2019.2921522","article-title":"Wireless Communicationss and Applications Above 100 GHz: Opportunities and Challenges for 6G and Beyond","volume":"7","author":"Rappaport","year":"2019","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1109\/MNET.2019.1800430","article-title":"Terahertz-Enabled Wireless System for Beyond-5G Ultrafast Networks: A Brief Survey","volume":"33","author":"Huq","year":"2019","journal-title":"IEEE Netw."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Ju, S., and Rappaport, T.S. (2021, January 14\u201323). 140 GHz Urban Microcell Propagation Measurements for Spatial Consistency Modeling. Proceedings of the 2021 IEEE International Conference on Communication (ICC2021), Montreal, QC, Canada.","DOI":"10.1109\/ICC42927.2021.9500677"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"8163","DOI":"10.1109\/TWC.2021.3090781","article-title":"Channel Measurement and Ray-Tracing-Statistical Hybrid Modeling for Low-Terahertz Indoor Communications","volume":"20","author":"Chen","year":"2021","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2843","DOI":"10.1109\/TVT.2016.2543139","article-title":"Investigation of Prediction Accuracy, Sensitivity, and Parameter Stability of Large-Scale Propagation Path Loss Models for 5G Wireless Communications","volume":"65","author":"Sun","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3151","DOI":"10.1109\/LCOMM.2021.3088264","article-title":"Millimeter Wave and Sub-THz Indoor Radio Propagation Channel Measurements, Models, and Comparisons in an Office Environment","volume":"25","author":"Xing","year":"2021","journal-title":"IEEE Commun. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Xing, Y., and Rappaport, T.S. (2021, January 14\u201323). Propagation Measurements and Path Loss Models for sub-THz in Urban Microcells. Proceedings of the 2021 IEEE International Conference on Communications (ICC2021), Montreal, QC, Canada.","DOI":"10.1109\/ICC42927.2021.9500385"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.23919\/JCC.2021.05.001","article-title":"Towards 6G: Paradigm of Realistic Terahertz Channel Modeling","volume":"18","author":"Guan","year":"2021","journal-title":"China Commun."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/s11276-017-1548-4","article-title":"Terahertz wireless data communication","volume":"25","author":"Akkas","year":"2017","journal-title":"Springer Wirel. Netw."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Khalid, N., and Akan, O.B. (2016, January 22\u201327). Wideband THz Communication Channel Measurements for 5G Indoor Wireless Networks. Proceedings of the 2016 IEEE International Conference on Communications (ICC2016), Kuala Lumpur, Malaysia.","DOI":"10.1109\/ICC.2016.7511280"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1576","DOI":"10.1109\/JSAC.2021.3071850","article-title":"A General 3D Space-TimeFrequency Non-Stationary THz Channel Model for 6G Ultra-Massive MIMO Wireless Communication Systems","volume":"39","author":"Wang","year":"2021","journal-title":"IEEE J. Sel. areas Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3142","DOI":"10.1109\/COMST.2018.2862141","article-title":"A survey of 5G channel measurements and models","volume":"20","author":"Wang","year":"2018","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"12312","DOI":"10.1109\/TVT.2021.3117239","article-title":"A novel 3D non-stationary GBSM for 6G THz ultra-massive MIMO wireless systems","volume":"70","author":"Wang","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1688","DOI":"10.1109\/TAP.2011.2122294","article-title":"Channel and Propagation Measurements at 300 GHz","volume":"59","author":"Priebe","year":"2011","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1109\/MCOM.2018.1700898","article-title":"Propagation Modeling for Wireless Communications in the Terahertz Band","volume":"56","author":"Han","year":"2018","journal-title":"IEEE Commun. Mag."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2402","DOI":"10.1109\/TWC.2014.2386335","article-title":"Multi-ray channel modeling and wideband characterization for wireless communications in the terahertz band","volume":"14","author":"Han","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"He, D., Guan, K., Ai, B., Fricke, A., He, R., Zhong, Z., Kasamatsu, A., Hosako, I., and Kurner, T. (2017, January 19\u201324). Channel modeling for Kiosk downloading communication system at 300 GHz. Proceedings of the 2017 European Conference on Antennas and Propagation (EUCAP 2017), Paris, France.","DOI":"10.23919\/EuCAP.2017.7928447"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Gureev, A., Cherniakov, M., Marchetti, E., and Gureev, I. (2017, January 1\u20133). Channel description in the low-THz wireless communications. Proceedings of the 2017 IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (EIConRus 2017), St. Petersburg and Moscow, Russia.","DOI":"10.1109\/EIConRus.2017.7910787"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"5626","DOI":"10.1109\/TVT.2016.2614335","article-title":"Three-Dimensional End-to-End Modeling and Analysis for Graphene-Enabled Terahertz Band Communications","volume":"66","author":"Han","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1109\/TTHZ.2017.2720962","article-title":"Stochastic Channel Modeling for Kiosk Applications in the Terahertz Band","volume":"7","author":"He","year":"2017","journal-title":"IEEE Trans. Terahertz Sci. Technol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"6423","DOI":"10.1109\/TWC.2016.2585103","article-title":"Statistical Modeling and Simulation of Short-Range Device-to-Device Communication Channels at Sub-THz Frequencies","volume":"15","author":"Kim","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Ekti, A.R., Boyaci, A., Alparslan, A., \u00dcnal, \u0130., Yarkan, S., G\u00f6r\u00e7in, A., Arslan, H., and Uysal, M. (2017, January 18\u201320). Statistical modeling of propagation channels for Terahertz band. Proceedings of the 2017 IEEE Conference on Standards for Communications and Networking (CSCN 2017), Helsinki, Finland.","DOI":"10.1109\/CSCN.2017.8088634"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Nie, S., Nie, I.F.A., and Akyildiz, I.F. (2017, January 8\u201313). Three-dimensional dynamic channel modeling and tracking for terahertz band indoor communications. Proceedings of the 2017 IEEE Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC 2017), Montreal, QC, Canada.","DOI":"10.1109\/PIMRC.2017.8292607"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"50","DOI":"10.23919\/JCC.2021.05.004","article-title":"A 3-D Hybrid Dynamic Channel Model for Indoor THz Communications","volume":"18","author":"Zhang","year":"2021","journal-title":"China Commun."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Zhang, K., Wang, H., Zhang, C., Yu, X., and Dong, Y. (June, January 28). Three-dimensional non-stationary geometry-based modeling of sub-THz MIMO channels for UAV air-to-ground communications. Proceedings of the 2023 IEEE International Conference on Communications (ICC2023), Rome, Italy.","DOI":"10.1109\/ICC45041.2023.10279768"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Zhang, K., Wang, H., Zhang, C., Yu, X., and Dong, Y. (2023, January 10\u201312). Three dimensional geometry based stochastic model for sub-terahertz air-to-air UAV-MIMO channels. Proceedings of the 2023 IEEE\/CIC International Conference on Communications in China (ICCC2023), Dalian, China.","DOI":"10.1109\/ICCC57788.2023.10233307"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Zhang, K., Zhang, F., Li, Y., Wang, X., Yang, Z., Liu, Y., Zhang, C., and Li, X. (2024). A Three-Dimensional Time-Varying Channel Model for THz UAV-Based Dual-Mobility Channels. Entropy, 26.","DOI":"10.3390\/e26110924"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Zhang, K., Zhang, D., Yang, Z., Zhang, F., Li, Y., Wang, X., Wang, G., and Tian, Q. (2024, January 18\u201320). 3D Time-Varying UAV-Based Channel Model for THz Air-to-Air Wireless Communications. Proceedings of the 2024 IEEE 24th International Conference on Communication Technology (ICCT2024), Chengdu, China.","DOI":"10.1109\/ICCT62411.2024.10946478"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"26888","DOI":"10.1109\/JIOT.2024.3381476","article-title":"Non-Stationary Channel Modelling for Wireless Communications Underlaying UAV-Based Relay Assisted IIoT Networks in the Sub-Terahertz Band","volume":"11","author":"Zhang","year":"2024","journal-title":"IEEE Internet Things J."},{"key":"ref_44","unstructured":"International Telecommunication Union (2025, July 15). Radiocommunication Sector (ITU-R), Recommendation P.676-11, Attenuation by Atmospheric Gases. Available online: https:\/\/www.itu.int\/rec\/R-REC-P.676-11-201609-I."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1109\/TAP.2019.2944536","article-title":"A Study of Diffuse Scattering in Massive MIMO Channels at Terahertz Frequencies","volume":"68","author":"Sheikh","year":"2020","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1109\/TTHZ.2011.2153610","article-title":"Diffuse Scattering from Rough Surfaces in THz Communication Channels","volume":"1","author":"Jansen","year":"2011","journal-title":"IEEE Trans. Terahertz Technol."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/8\/788\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:15:52Z","timestamp":1760033752000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/8\/788"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,25]]},"references-count":46,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["e27080788"],"URL":"https:\/\/doi.org\/10.3390\/e27080788","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2025,7,25]]}}}