{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T15:33:42Z","timestamp":1775662422914,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T00:00:00Z","timestamp":1771632000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["No. 62171465."],"award-info":[{"award-number":["No. 62171465."]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Owing to their high flexibility, autonomous operation, and rapid deployment capability, unmanned aerial vehicles (UAVs) serve as effective aerial platforms for sensing and communication in remote and time-critical scenarios. However, their limited onboard energy budget poses a significant bottleneck for sustained operations. This paper investigates an energy-efficient UAV-assisted integrated sensing and communication (ISAC) system, aiming to maximize the sensing energy efficiency (SEE), defined as the ratio of the total radar estimation rate to the total energy consumption. Unlike prior works focused solely on rate maximization or fairness, our design jointly optimizes the UAV\u2019s 3D trajectory, task scheduling, and power allocation under kinematic and coverage constraints to maximize the SEE. To solve the formulated non-convex fractional programming problem, we propose an efficient iterative algorithm based on the Dinkelbach method and block coordinate descent (BCD). Simulation results demonstrate that the proposed scheme achieves a superior trade-off between sensing performance and energy consumption.<\/jats:p>","DOI":"10.3390\/e28020248","type":"journal-article","created":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T10:00:52Z","timestamp":1771840852000},"page":"248","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Energy-Efficient 3D Trajectory Optimization and Resource Allocation for UAV-Enabled ISAC Systems"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-3476-3924","authenticated-orcid":false,"given":"Lulu","family":"Jing","sequence":"first","affiliation":[{"name":"College of Communications Engineering, Army Engineering University, Nanjing 210042, China"},{"name":"Office of Cyber Security and Informatization, Nanjing Forestry University, Nanjing 210037, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hai","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Communications Engineering, Army Engineering University, Nanjing 210042, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5363-6107","authenticated-orcid":false,"given":"Zhen","family":"Qin","sequence":"additional","affiliation":[{"name":"Department of Information and Communication, Noncommissioned Officer Academy of PAP, Hangzhou 310000, China"},{"name":"Academy of Systems Engineering, Academy of Military Sciences, Beijing 100091, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yicheng","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Communications Engineering, Army Engineering University, Nanjing 210042, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Zhu","sequence":"additional","affiliation":[{"name":"College of Communications Engineering, Army Engineering University, Nanjing 210042, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wensheng","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Communications Engineering, Army Engineering University, Nanjing 210042, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3227","DOI":"10.1109\/COMST.2024.3515051","article-title":"A Survey of Security in UAVs and FANETs: Issues, Threats, Analysis of Attacks, and Solutions","volume":"27","author":"Ceviz","year":"2025","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Jing, L., Wang, H., Qin, Z., and Zhu, P. (2025). Entropy-Based Age-Aware Scheduling Strategy for UAV-Assisted IoT Data Transmission. Entropy, 27.","DOI":"10.3390\/e27060578"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1109\/MNET.121.2100320","article-title":"Joint Communication, Sensing, and Computation Enabled 6G Intelligent Machine System","volume":"35","author":"Feng","year":"2022","journal-title":"IEEE Netw."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1728","DOI":"10.1109\/JSAC.2022.3156632","article-title":"Integrated Sensing and Communications: Toward Dual-Functional Wireless Networks for 6G and Beyond","volume":"40","author":"Liu","year":"2022","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"8654","DOI":"10.1109\/TWC.2024.3352985","article-title":"UAV Assisted Integrated Sensing and Communications for Internet of Things: 3D Trajectory Optimization and Resource Allocation","volume":"23","author":"Liu","year":"2024","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6578","DOI":"10.1109\/TWC.2020.3004162","article-title":"Age of Information in a Cellular Internet of UAVs: Sensing and Communication Trade-Off Design","volume":"19","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.23919\/JCC.2020.01.001","article-title":"Joint radar and communication: A survey","volume":"17","author":"Feng","year":"2020","journal-title":"China Commun."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1109\/MNET.010.2100152","article-title":"Integrating Sensing and Communications for Ubiquitous IoT: Applications, Trends, and Challenges","volume":"35","author":"Cui","year":"2021","journal-title":"IEEE Netw."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Li, F., and Liao, B. (2025, January 6\u201311). Massive MIMO-ISAC Beamforming Design Via Sensing Energy Maximization. Proceedings of the ICASSP 2025\u20142025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Hyderabad, India.","DOI":"10.1109\/ICASSP49660.2025.10888130"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Jiang, W., Wang, A., Wei, Z., Lai, M., Pan, C., Feng, Z., and Liu, J. (2021, January 13\u201316). Improve Sensing and Communication Performance of UAV via Integrated Sensing and Communication. Proceedings of the 2021 IEEE 21st International Conference on Communication Technology (ICCT), Tianjin, China.","DOI":"10.1109\/ICCT52962.2021.9657955"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2660","DOI":"10.1109\/TCOMM.2020.3044616","article-title":"Constrained Utility Maximization in Dual-Functional Radar-Communication Multi-UAV Networks","volume":"69","author":"Wang","year":"2021","journal-title":"IEEE Trans. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2103","DOI":"10.1109\/JSAC.2022.3157366","article-title":"Integrated Scheduling of Sensing, Communication, and Control for mmWave\/THz Communications in Cellular Connected UAV Networks","volume":"40","author":"Chang","year":"2022","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Orikumhi, I., Lee, N., Kim, J.W., Bae, J., and Kim, S. (2024, January 16\u201318). A Weighted-Sensing Algorithm for UAV-ISAC Enabled Relaying in the Presence of Blockages. Proceedings of the 2024 15th International Conference on Information and Communication Technology Convergence (ICTC), Jeju Island, Republic of Korea.","DOI":"10.1109\/ICTC62082.2024.10827344"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Lin, H., Zhang, Z., Wei, L., Zhou, Z., and Zheng, T. (2023, January 10\u201313). A Deep Reinforcement Learning Based UAV Trajectory Planning Method For Integrated Sensing And Communications Networks. Proceedings of the 2023 IEEE 98th Vehicular Technology Conference (VTC2023-Fall), Hong Kong, China.","DOI":"10.1109\/VTC2023-Fall60731.2023.10333531"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"29546","DOI":"10.1109\/JIOT.2023.3327445","article-title":"Fair Integrated Sensing and Communication for Multi-UAV-Enabled Internet of Things: Joint 3-D Trajectory and Resource Optimization","volume":"11","author":"Liu","year":"2024","journal-title":"IEEE Internet Things J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1109\/TWC.2022.3197623","article-title":"Throughput Maximization for UAV-Enabled Integrated Periodic Sensing and Communication","volume":"22","author":"Meng","year":"2023","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2424","DOI":"10.1109\/TWC.2022.3211533","article-title":"Joint Maneuver and Beamforming Design for UAV-Enabled Integrated Sensing and Communication","volume":"22","author":"Lyu","year":"2023","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"6918","DOI":"10.1109\/OJCOMS.2024.3489873","article-title":"Optimizing Multi-UAV Multi-User System Through Integrated Sensing and Communication for Age of Information (AoI) Analysis","volume":"5","author":"Zhou","year":"2024","journal-title":"IEEE Open J. Commun. Soc."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhu, Q., Liu, R., Lv, X., Meng, Q., and Wang, Y. (2023, January 20\u201322). AoI-Optimal Trajectory Planning in UAV-Assisted ISAC Networks. Proceedings of the 2023 IEEE 23rd International Conference on Communication Technology (ICCT), Wuxi, China.","DOI":"10.1109\/ICCT59356.2023.10419470"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"148826","DOI":"10.1109\/ACCESS.2024.3475630","article-title":"Joint Beamforming, Scheduling, Trajectory, and Transmit Power Optimization in UAV-Assisted ISAC Systems for Information Freshness","volume":"12","author":"He","year":"2024","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"12776","DOI":"10.1109\/TVT.2025.3558061","article-title":"AoI Minimization for Air-Ground Integrated Sensing and Communication Networks with Jamming Attack","volume":"74","author":"Mei","year":"2025","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4440","DOI":"10.1109\/TWC.2025.3539108","article-title":"Joint Sensing and Age of Information Optimization for Energy Constrained UAV Assisted Integrated Sensing, Calculation and Communication","volume":"24","author":"Liu","year":"2025","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2243","DOI":"10.1109\/JSAC.2024.3413973","article-title":"Maximizing the value of service provisioning in multi-user ISAC systems through fairness guaranteed collaborative resource allocation","volume":"42","author":"Li","year":"2024","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"29190","DOI":"10.1109\/JIOT.2024.3406930","article-title":"Integrated sensing and communication enabled multidevice multitarget cooperative sensing: A fairness-aware design","volume":"11","author":"Dou","year":"2024","journal-title":"IEEE Internet Things J."},{"key":"ref_25","unstructured":"Qualcomm Technologies, Inc. (2017). LTE Unmanned Aircraft Systems, Qualcomm Technologies, Inc.. Trial Rep. v.1.0.1."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Richards, M.A., Scheer, J.A., and Holm, W.A. (2010). Principles of Modern Radar: Basic Principles, SciTech Publishing, Inc.","DOI":"10.1049\/SBRA021E"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2572","DOI":"10.1109\/COMST.2025.3584333","article-title":"Advanced Learning Algorithms for Integrated Sensing and Communication (ISAC) Systems in 6G and Beyond: A Comprehensive Survey","volume":"28","author":"Luong","year":"2025","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"17635","DOI":"10.1109\/TWC.2024.3455370","article-title":"Efficient UAV Hovering, Resource Allocation, and Trajectory Design for ISAC With Limited Backhaul Capacity","volume":"23","author":"Khalili","year":"2024","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3747","DOI":"10.1109\/TWC.2017.2688328","article-title":"Energy-Efficient UAV Communication With Trajectory Optimization","volume":"16","author":"Zeng","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/2\/248\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T05:21:43Z","timestamp":1772169703000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/2\/248"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,21]]},"references-count":29,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,2]]}},"alternative-id":["e28020248"],"URL":"https:\/\/doi.org\/10.3390\/e28020248","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,21]]}}}