{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T16:06:09Z","timestamp":1774454769523,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,5,29]],"date-time":"2025-05-29T00:00:00Z","timestamp":1748476800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China (NSFC)","award":["62171465"],"award-info":[{"award-number":["62171465"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper investigates data transmission in an Internet of Things (IoT) network, where multiple devices send environmental data to a remote base station through an unmanned aerial vehicle (UAV) relay. The UAV serves as an airborne intermediary that collects status information from distributed IoT devices (e.g., temperature readings in a real-time forest fire monitoring system) and forwards it to the base station. To capture the impact of data staleness, a novel Age of Information (AoI) and entropy-aware system loss is defined in terms of L-conditional cross-entropy, which quantifies the expected penalty caused by state misestimation. The scheduling problem, which aims to minimize the system loss defined by L-conditional cross-entropy, is formulated as a Restless Multi-Armed Bandit (RMAB) problem. By applying Lagrange relaxation, the objective function is decomposed into tractable sub-problems, enabling a low-complexity, gain-index-based scheduling strategy. Numerical simulations validate the effectiveness of the proposed algorithm in reducing the long-term average system loss. In particular, the gain-index-based policy achieves a significant reduction in average penalty compared to random, round-robin, periodic update, and MAX-AoI scheduling strategies, demonstrating its superior performance over these baselines.<\/jats:p>","DOI":"10.3390\/e27060578","type":"journal-article","created":{"date-parts":[[2025,5,29]],"date-time":"2025-05-29T07:46:26Z","timestamp":1748504786000},"page":"578","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Entropy-Based Age-Aware Scheduling Strategy for UAV-Assisted IoT Data Transmission"],"prefix":"10.3390","volume":"27","author":[{"given":"Lulu","family":"Jing","sequence":"first","affiliation":[{"name":"College of Communication Engineering, Army Engineering University of PLA, Nanjing 210000, China"}]},{"given":"Hai","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Communication Engineering, Army Engineering University of PLA, Nanjing 210000, China"}]},{"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 100000, China"}]},{"given":"Peng","family":"Zhu","sequence":"additional","affiliation":[{"name":"College of Communication Engineering, Army Engineering University of PLA, Nanjing 210000, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,29]]},"reference":[{"key":"ref_1","unstructured":"(2022, November 01). ITU Internet Reports 2005: The Internet of Things. Available online: http:\/\/handle.itu.int\/11.1002\/pub\/800eae6f-en."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Shah, S.K., Joshi, K., Khantwal, S., Bisht, Y.S., Chander, H., and Gupta, A. (2022, January 17\u201319). IoT and WSN integration for data acquisition and supervisory control. Proceedings of the 2022 IEEE World Conference on Applied Intelligence and Computing, Sonbhadra, India.","DOI":"10.1109\/AIC55036.2022.9848933"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2740","DOI":"10.1109\/TCOMM.2023.3255240","article-title":"Cooperative Data Collection with Multiple UAVs for Information Freshness in the Internet of Things","volume":"71","author":"Wang","year":"2023","journal-title":"IEEE Trans. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Kaul, S., Yates, R., and Gruteser, M. (2012, January 25\u201330). Real-time status: How often should one update?. Proceedings of the 2012 Proceedings IEEE INFOCOM, Orlando, FL, USA.","DOI":"10.1109\/INFCOM.2012.6195689"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Qian, Z., Wu, F., Pan, J., Srinivasan, K., and Shroff, N.B. (2020, January 6\u20139). Minimizing age of information in multi-channel time-sensitive information update systems. Proceedings of the IEEE Conference on Computer Communications, Toronto, ON, Canada.","DOI":"10.1109\/INFOCOM41043.2020.9155420"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.1109\/TWC.2022.3204438","article-title":"UAV Trajectory Planning for AoI-Minimal Data Collection in UAV-Aided IoT Networks by Transformer","volume":"22","author":"Zhu","year":"2023","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Liu, J., Wang, X., Bai, B., and Dai, H. (2018, January 15\u201319). Age-optimal trajectory planning for UAV-assisted data collection. Proceedings of the IEEE INFOCOM 2018\u2014IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS), Honolulu, HI, USA.","DOI":"10.1109\/INFCOMW.2018.8406973"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Mao, C., Liu, J., and Xie, L. (2020, January 21\u201323). Multi-UAV Aided Data Collection for Age Minimization in Wireless Sensor Networks. Proceedings of the 2020 International Conference on Wireless Communications and Signal Processing (WCSP), Nanjing, China.","DOI":"10.1109\/WCSP49889.2020.9299804"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Jia, Z., Qin, X., Wang, Z., and Liu, B. (2019, January 20\u201324). Age-Based Path Planning and Data Acquisition in UAV-Assisted IoT Networks. Proceedings of the 2019 IEEE International Conference on Communications Workshops (ICC Workshops), Shanghai, China.","DOI":"10.1109\/ICCW.2019.8756751"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhang, J., Kang, K., Yang, M., Zhu, H., and Qian, H. (2022, January 10\u201313). AoI-minimization in UAV-assisted IoT Network with Massive Devices. Proceedings of the 2022 IEEE Wireless Communications and Networking Conference (WCNC), Austin, TX, USA.","DOI":"10.1109\/WCNC51071.2022.9771857"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Emami, Y., Li, K., Niu, Y., and Tovar, E. (June, January 28). AoI Minimization Using Multi-Agent Proximal Policy Optimization in UAVs-Assisted Sensor Networks. Proceedings of the ICC 2023\u2014IEEE International Conference on Communications, Rome, Italy.","DOI":"10.1109\/ICC45041.2023.10278748"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Choudhury, B., Shah, V.K., Ferdowsi, A., Reed, J.H., and Hou, Y.T. (2021, January 4\u20137). AoI-minimizing Scheduling in UAV-relayed IoT Networks. Proceedings of the 2021 IEEE 18th International Conference on Mobile Ad Hoc and Smart Systems (MASS), Denver, CO, USA.","DOI":"10.1109\/MASS52906.2021.00023"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"8810","DOI":"10.1109\/JSEN.2023.3253920","article-title":"Fresh Data Collection for UAV-Assisted IoT Based on Aerial Collaborative Relay","volume":"23","author":"Huang","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Long, Y., Zhang, W., Gong, S., Luo, X., and Niyato, D. (2022, January 4\u20138). AoI-aware Scheduling and Trajectory Optimization for Multi-UAV-assisted Wireless Networks. Proceedings of the GLOBECOM 2022\u20142022 IEEE Global Communications Conference, Rio de Janeiro, Brazil.","DOI":"10.1109\/GLOBECOM48099.2022.10001660"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2415","DOI":"10.1109\/LWC.2022.3205316","article-title":"Regret of Age-of-Information Bandits in Nonstationary Wireless Networks","volume":"11","author":"Song","year":"2022","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2215","DOI":"10.1109\/TNET.2020.3005549","article-title":"The Age of Incorrect Information: A New Performance Metric for Status Updates","volume":"28","author":"Maatouk","year":"2020","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_17","unstructured":"Ismail, C., Ulukus, S., and Akar, N. (2025). Minimizing Functions of Age of Incorrect Information for Remote Estimation. arXiv."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Zhong, J., Yates, R.D., and Soljanin, E. (2018, January 17\u201322). Two Freshness Metrics for Local Cache Refresh. Proceedings of the 2018 IEEE International Symposium on Information Theory (ISIT), Vail, CO, USA.","DOI":"10.1109\/ISIT.2018.8437927"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"7237","DOI":"10.1109\/TWC.2020.3009881","article-title":"Urgency of Information for Context-Aware Timely Status Updates in Remote Control Systems","volume":"19","author":"Zheng","year":"2020","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Ornee, T.Z., Shisher, M.K.C., Kam, C., and Sun, Y. (November, January 30). Context-aware Status Updating: Wireless Scheduling for Maximizing Situational Awareness in Safety-critical Systems. Proceedings of the MILCOM 2023\u20142023 IEEE Military Communications Conference (MILCOM), Boston, MA, USA.","DOI":"10.1109\/MILCOM58377.2023.10356278"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Luo, J., and Pappas, N. (2024, January 14\u201317). Minimizing the Age of Missed and False Alarms in Remote Estimation of Markov Sources. Proceedings of the Twenty-Fifth International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Networks and Mobile Computing (MobiHoc\u201924), Athens, Greece.","DOI":"10.1145\/3641512.3690161"},{"key":"ref_22","unstructured":"Luo, J., and Nikolaos, P. (2024). On the Cost of Consecutive Estimation Error: Significance-Aware Non-linear Aging. arXiv."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Erbayat, E., Maatouk, A., Zou, P., and Subramaniam, S. (2024, January 14\u201317). Age of Information Optimization and State Error Analysis for Correlated Multi-Process Multi-Sensor Systems. Proceedings of the Twenty-fifth International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Networks and Mobile Computing (MobiHoc\u201924), Athens, Greece.","DOI":"10.1145\/3641512.3686378"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Shisher, M.K.C., and Sun, Y. (2022, January 17\u201320). How does data freshness affect real-time supervised learning?. Proceedings of the Twenty-Third International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Networks and Mobile Computing, Seoul, Republic of Korea.","DOI":"10.1145\/3492866.3549711"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On Information and Sufficiency","volume":"22","author":"Kullback","year":"1951","journal-title":"Ann. Math. Stat."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/BF02418571","article-title":"Sur les fonctions convexes et les in\u00e9galit\u00e9s entre les valeurs moyennes","volume":"30","author":"Jensen","year":"1906","journal-title":"Acta Math."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"637","DOI":"10.2307\/3214547","article-title":"On an index policy for restless bandits","volume":"27","author":"Weber","year":"1990","journal-title":"J. Appl. Probab."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"287","DOI":"10.2307\/3214163","article-title":"Restless bandits: Activity allocation in a changing world","volume":"25","author":"Whittle","year":"1988","journal-title":"J. Appl. Probab."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1057\/palgrave.jors.2600425","article-title":"Nonlinear programming","volume":"48","author":"Bertsekas","year":"1997","journal-title":"J. Oper. Res. Soc."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1109\/TIT.2023.3315459","article-title":"An Index Policy for Minimizing the Uncertainty-of-Information of Markov Sources","volume":"70","author":"Chen","year":"2023","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_31","first-page":"1189","article-title":"Subgradient methods in network resource allocation: Rate analysis","volume":"8","author":"Nedic","year":"2008","journal-title":"Annu. Conf. Inf. Sci. Syst."},{"key":"ref_32","unstructured":"Bertsekas, D. (2009). Convex Optimization Theory, Athena Scientific."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Boyd, S. (2004). Convex Optimization, Cambridge University Press.","DOI":"10.1017\/CBO9780511804441"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/6\/578\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:43:03Z","timestamp":1760031783000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/6\/578"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,29]]},"references-count":33,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["e27060578"],"URL":"https:\/\/doi.org\/10.3390\/e27060578","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,29]]}}}