{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T13:46:29Z","timestamp":1761745589207,"version":"3.37.3"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T00:00:00Z","timestamp":1649203200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T00:00:00Z","timestamp":1649203200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62002133","61872158"],"award-info":[{"award-number":["62002133","61872158"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61806083"],"award-info":[{"award-number":["61806083"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013061","name":"Jilin Scientific and Technological Development Program","doi-asserted-by":"publisher","award":["20190701019GH","20190701002GH"],"award-info":[{"award-number":["20190701019GH","20190701002GH"]}],"id":[{"id":"10.13039\/501100013061","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013061","name":"Jilin Scientific and Technological Development Program","doi-asserted-by":"publisher","award":["20210101183JC","20210201072GX"],"award-info":[{"award-number":["20210101183JC","20210201072GX"]}],"id":[{"id":"10.13039\/501100013061","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62172186"],"award-info":[{"award-number":["62172186"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Young Science and Technology Talent Lift Project of Jilin Province","award":["QT202013"],"award-info":[{"award-number":["QT202013"]}]},{"name":"Graduate Innovation Fund of Jilin University","award":["101832020CX176","101832020CX177"],"award-info":[{"award-number":["101832020CX176","101832020CX177"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Wireless Netw"],"published-print":{"date-parts":[[2022,7]]},"DOI":"10.1007\/s11276-022-02954-6","type":"journal-article","created":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T05:02:59Z","timestamp":1649221379000},"page":"2001-2016","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Joint optimization of SNR and motion energy consumption for UAV-enabled collaborative beamforming"],"prefix":"10.1007","volume":"28","author":[{"given":"Tingting","family":"Zheng","sequence":"first","affiliation":[]},{"given":"Yanheng","family":"Liu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7802-4908","authenticated-orcid":false,"given":"Geng","family":"Sun","sequence":"additional","affiliation":[]},{"given":"Jing","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Jiahui","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,4,6]]},"reference":[{"issue":"2","key":"2954_CR1","doi-asserted-by":"publisher","first-page":"2241","DOI":"10.1109\/JIOT.2018.2887086","volume":"6","author":"B Li","year":"2019","unstructured":"Li, B., Fei, Z., & Zhang, Y. (2019). UAV communications for 5G and beyond: Recent advances and future trends. IEEE Internet of Things Journal, 6(2), 2241\u20132263.","journal-title":"IEEE Internet of Things Journal"},{"key":"2954_CR2","doi-asserted-by":"crossref","unstructured":"Garza,J., Panduro,M., ReynaMaldonado,A., Romero,G., & DelR\u00edo, C. (2016). Design of uavs-based 3d antenna arrays for a maximum performance in terms of directivity and sll. International Journal of Antennas and Propagation (Vol. 2016, pp. 1\u20138).","DOI":"10.1155\/2016\/2621862"},{"key":"2954_CR3","doi-asserted-by":"crossref","unstructured":"Nijsure, Y., Ahmed, M. F. A., Kaddoum, G., & Gagnon, G. (2016). F (pp. 1\u20135). Wsn-uav monitoring system with collaborative beamforming and ads-b based multilateration: Gagnon.","DOI":"10.1109\/VTCSpring.2016.7504535"},{"issue":"3","key":"2954_CR4","doi-asserted-by":"publisher","first-page":"2109","DOI":"10.1109\/TWC.2017.2789293","volume":"17","author":"Q Wu","year":"2018","unstructured":"Wu, Q., Zeng, Y., & Zhang, R. (2018). Joint trajectory and communication design for multi-uav enabled wireless networks. IEEE Transactions on Wireless Communications, 17(3), 2109\u20132121.","journal-title":"IEEE Transactions on Wireless Communications"},{"issue":"2","key":"2954_CR5","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1109\/LCOMM.2017.2772254","volume":"22","author":"H He","year":"2018","unstructured":"He, H., Zhang, S., Zeng, Y., & Zhang, R. (2018). Joint altitude and beamwidth optimization for uav-enabled multiuser communications. IEEE Communications Letters, 22(2), 344\u2013347.","journal-title":"IEEE Communications Letters"},{"issue":"6","key":"2954_CR6","doi-asserted-by":"publisher","first-page":"3747","DOI":"10.1109\/TWC.2017.2688328","volume":"16","author":"Y Zeng","year":"2017","unstructured":"Zeng, Y., & Zhang, R. (2017). Energy-efficient uav communication with trajectory optimization. IEEE Transactions on Wireless Communications, 16(6), 3747\u20133760.","journal-title":"IEEE Transactions on Wireless Communications"},{"key":"2954_CR7","doi-asserted-by":"crossref","unstructured":"Mozaffari, M., Saad, W., & Bennis, M. (2016). M (pp. 1\u20136). Optimal transport theory for power-efficient deployment of unmanned aerial vehicles: Debbah.","DOI":"10.1109\/ICC.2016.7510870"},{"issue":"6","key":"2954_CR8","doi-asserted-by":"publisher","first-page":"1377","DOI":"10.1109\/TMC.2015.2467381","volume":"15","author":"K Li","year":"2016","unstructured":"Li, K., Ni, W., Wang, X., Liu, R. P., Kanhere, S. S., & Jha, S. (2016). Energy-efficient cooperative relaying for unmanned aerial vehicles. IEEE Transactions on Mobile Computing, 15(6), 1377\u20131386.","journal-title":"IEEE Transactions on Mobile Computing"},{"key":"2954_CR9","doi-asserted-by":"crossref","unstructured":"Sambo,Y. A., Klaine, P. V., Nadas, J. P. B., & Imran, M. A. (2019). Energy minimization uav trajectory design for delay-tolerant emergency communication (pp. 1\u20136).","DOI":"10.1109\/ICCW.2019.8757127"},{"issue":"11","key":"2954_CR10","doi-asserted-by":"publisher","first-page":"4110","DOI":"10.1109\/TSP.2005.857028","volume":"53","author":"H Ochiai","year":"2005","unstructured":"Ochiai, H., Mitran, P., Poor, H. V., & Tarokh, V. (2005). Collaborative beamforming for distributed wireless ad hoc sensor networks. IEEE Transactions on Signal Processing, 53(11), 4110\u20134124.","journal-title":"IEEE Transactions on Signal Processing"},{"key":"2954_CR11","doi-asserted-by":"crossref","unstructured":"Ahmed, M., & Vorobyov, S. (2003). Collaborative beamforming for wireless sensor networks with gaussian distributed sensor nodes. IEEE Transactions on Wireless Communications, 8, 638\u2013643.","DOI":"10.1109\/TWC.2009.071339"},{"key":"2954_CR12","doi-asserted-by":"crossref","unstructured":"Nijsure, Y., Ahmed, M., Kaddoum, G., Gagnon, G., & Gagnon, F. (2016). Wsn-uav monitoring system with collaborative beamforming and ads-b based multilateration.","DOI":"10.1109\/VTCSpring.2016.7504535"},{"key":"2954_CR13","doi-asserted-by":"crossref","unstructured":"Ahmed, M., & Vorobyov, S. (2011). Power control for collaborative beamforming in wireless sensor networks. 1977 11th Asilomar Conference on Circuits, Systems and Computers, 1977. Conference Record (pp. 99\u2013103).","DOI":"10.1109\/ACSSC.2011.6189963"},{"key":"2954_CR14","unstructured":"Mozaffari, M., Saad, W., Bennis, M., & Debbah, M. (2017). Communications and control for wireless drone-based antenna array. IEEE Transactions on Communications, 12."},{"key":"2954_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.inffus.2018.09.013","volume":"49","author":"K Praveen","year":"2019","unstructured":"Praveen, K., Tarachand, A., & Sekhar, C. (2019). Machine learning algorithms for wireless sensor networks: A survey. Information Fusion, 49, 1\u201325.","journal-title":"Information Fusion"},{"issue":"11","key":"2954_CR16","doi-asserted-by":"publisher","first-page":"3555","DOI":"10.1109\/JSAC.2021.3088720","volume":"39","author":"G Sun","year":"2021","unstructured":"Sun, G., Li, J., Liu, Y., Liang, S., & Kang, H. (2021). Time and energy minimization communications based on collaborative beamforming for uav networks: A multi-objective optimization method. IEEE Journal on Selected Areas in Communications, 39(11), 3555\u20133572.","journal-title":"IEEE Journal on Selected Areas in Communications"},{"key":"2954_CR17","first-page":"1","volume":"99","author":"YH Hsu","year":"2020","unstructured":"Hsu, Y. H., & Gau, R. H. (2020). Reinforcement learning-based collision avoidance and optimal trajectory planning in uav communication networks. IEEE Transactions on Mobile Computing, 99, 1.","journal-title":"IEEE Transactions on Mobile Computing"},{"key":"2954_CR18","unstructured":"Yang, W. U., Yang, W., Zhang, D., & Sun, X. (2019). Throughput maximization of uav-enabled wireless network in the presence of jammers: Joint trajectory and communication design. IEICE Transactions on Communications."},{"key":"2954_CR19","unstructured":"Garg, A. (2020). Machine learning coupled trajectory and communication design for uav-facilitated wireless networks."},{"key":"2954_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TVT.2019.2893675","volume":"99","author":"X Liu","year":"2019","unstructured":"Liu, X., Liu, Y., Chen, Y., & Hanzo, L. (2019). Trajectory design and power control for multi-uav assisted wireless networks: A machine learning approach. IEEE Transactions on Vehicular Technology, 99, 1.","journal-title":"IEEE Transactions on Vehicular Technology"},{"key":"2954_CR21","doi-asserted-by":"crossref","unstructured":"Zhao, N., Cheng, Y., Pei, Y., Liang, Y. C., & Niyato, D. (2020). Deep reinforcement learning for trajectory design and power allocation in uav networks. In ICC 2020 - 2020 IEEE International Conference on Communications (ICC).","DOI":"10.1109\/ICC40277.2020.9149196"},{"key":"2954_CR22","first-page":"1","volume":"99","author":"Z Sun","year":"2020","unstructured":"Sun, Z., Yang, D., Xiao, L., Cuthbert, L., & Zhu, Y. (2020). Joint energy and trajectory optimization for uav-enabled relaying network with multi-pair users. IEEE Transactions on Cognitive Communications and Networking, 99, 1.","journal-title":"IEEE Transactions on Cognitive Communications and Networking"},{"issue":"2","key":"2954_CR23","doi-asserted-by":"publisher","first-page":"102466","DOI":"10.1016\/j.adhoc.2021.102466","volume":"116","author":"C Xu","year":"2021","unstructured":"Xu, C., Li, D., Chen, Q., Liu, M., & Meng, K. (2021). Joint trajectory and transmission optimization for energy efficient uav enabled elaa network. Ad Hoc Networks, 116(2), 102466.","journal-title":"Ad Hoc Networks"},{"issue":"7","key":"2954_CR24","doi-asserted-by":"publisher","first-page":"2353","DOI":"10.1109\/LCOMM.2021.3067477","volume":"25","author":"Y Gao","year":"2021","unstructured":"Gao, Y., Tang, H., Li, B., & Yuan, X. (2021). Energy minimization for robust secure transmission in uav networks with multiple colluding eavesdroppers. IEEE Communications Letters, 25(7), 2353\u20132357.","journal-title":"IEEE Communications Letters"},{"key":"2954_CR25","volume-title":"Antenna theory and design","author":"W Stutzman","year":"1981","unstructured":"Stutzman, W., & Thiele, G. (1981). Antenna theory and design (Vol. 1). Wiley."},{"key":"2954_CR26","unstructured":"Zeng, Y., & Zhang, R. (2016). Energy-efficient uav communication with trajectory optimization. IEEE Transactions on Wireless Communications, 08."},{"key":"2954_CR27","unstructured":"Zeng, Y., Xu, J., & Zhang, R. (2018). Energy minimization for wireless communication with rotary-wing uav. IEEE Transactions on Wireless Communications, 04."},{"key":"2954_CR28","doi-asserted-by":"publisher","first-page":"01","DOI":"10.1007\/s10589-009-9295-9","volume":"49","author":"Y Cooren","year":"2011","unstructured":"Cooren, Y., Clerc, M., & Siarry, P. (2011). Mo-tribes, an adaptive multiobjective particle swarm optimization algorithm. Computational Optimization and Applications - COMPUT OPTIM APPL, 49, 01.","journal-title":"Computational Optimization and Applications - COMPUT OPTIM APPL"},{"key":"2954_CR29","doi-asserted-by":"crossref","unstructured":"Kennedy, J., Eberhart, R. (1995). Particle swarm optimization. In Proceedings of ICNN\u201995 - International Conference on Neural Networks (Vol. 4, pp. 1942\u20131948).","DOI":"10.1109\/ICNN.1995.488968"},{"key":"2954_CR30","unstructured":"Kennedy, J., & Eberhart, R. C. (2001). Swarm Intelligence. San Francisco, CA, USA: Morgan Kaufmann Publishers Inc."},{"key":"2954_CR31","doi-asserted-by":"crossref","unstructured":"Eberhart & Yuhui Shi (2001). Particle swarm optimization: developments, applications and resources. In Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546) (Vol. 1, pp. 81\u201386).","DOI":"10.1109\/CEC.2001.934377"},{"issue":"3","key":"2954_CR32","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1109\/TMC.2019.2955948","volume":"20","author":"G Sun","year":"2021","unstructured":"Sun, G., Liu, Y., Chen, Z., Wang, A., Zhang, Y., Tian, D., & Leung, V. C. (2021). Energy efficient collaborative beamforming for reducing sidelobe in wireless sensor networks. IEEE Transactions on Mobile Computing, 20(3), 965\u2013982.","journal-title":"IEEE Transactions on Mobile Computing"},{"key":"2954_CR33","doi-asserted-by":"publisher","first-page":"4563","DOI":"10.1109\/TAP.2018.2846771","volume":"66","author":"G Sun","year":"2018","unstructured":"Sun, G., Liu, Y., Chen, Z., Shuang, L., Wang, A., & Ying, Z. (2018). Radiation beam pattern synthesis of concentric circular antenna arrays using hybrid approach based on cuckoo search. IEEE Transactions on Antennas and Propagation, 66, 4563\u20134576.","journal-title":"IEEE Transactions on Antennas and Propagation"},{"key":"2954_CR34","doi-asserted-by":"publisher","first-page":"116118","DOI":"10.1016\/j.eswa.2021.116118","volume":"189","author":"Q Gu","year":"2022","unstructured":"Gu, Q., Liu, Y., Chen, L., & Xiong, N. (2022). An improved competitive particle swarm optimization for many-objective optimization problems. Expert Systems with Applications, 189, 116118.","journal-title":"Expert Systems with Applications"},{"key":"2954_CR35","doi-asserted-by":"crossref","unstructured":"Dru\u017eeta, S. Ivi\u0107, & Stefan. (2016). Examination of benefits of personal fitness improvement dependent inertia for particle swarm optimization. Soft Computing.","DOI":"10.1007\/s00500-015-2016-7"},{"issue":"4","key":"2954_CR36","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1016\/j.ecoinf.2006.07.003","volume":"1","author":"A Mehrabian","year":"2006","unstructured":"Mehrabian, A., & Lucas, C. (2006). A novel numerical optimization algorithm inspired from weed colonization. Ecological Informatics, 1(4), 355\u2013366.","journal-title":"Ecological Informatics"},{"key":"2954_CR37","first-page":"1","volume":"2018","author":"G Sun","year":"2018","unstructured":"Sun, G., Liu, Y., Li, H., Liang, S., Wang, A., & Li, B. (2018). An antenna array sidelobe level reduction approach through invasive weed optimization. International Journal of Antennas and Propagation, 2018, 1\u201316.","journal-title":"International Journal of Antennas and Propagation"},{"key":"2954_CR38","unstructured":"Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization (Vol. 4, pp. 1942\u20131948)."},{"issue":"6","key":"2954_CR39","doi-asserted-by":"publisher","first-page":"702","DOI":"10.1109\/TEVC.2008.919004","volume":"12","author":"D Simon","year":"2008","unstructured":"Simon, D. (2008). Biogeography-based optimization. IEEE Transactions on Evolutionary Computation, 12(6), 702\u2013713.","journal-title":"IEEE Transactions on Evolutionary Computation"},{"key":"2954_CR40","doi-asserted-by":"crossref","unstructured":"Yang, X., & Suash Deb (2009). Cuckoo search via l\u00e9vy flights (pp. 210\u2013214).","DOI":"10.1109\/NABIC.2009.5393690"},{"key":"2954_CR41","doi-asserted-by":"crossref","unstructured":"Singh, U., & Singh, D. (2014). C (pp. 1\u20135). Thinning of planar circular array antennas using firefly algorithm: Kaur.","DOI":"10.1109\/RAECS.2014.6799539"},{"key":"2954_CR42","unstructured":"Liang, J, Qu, B., & Suganthan, P. (2013). Problem definitions and evaluation criteria for the cec 2014 special session and competition on single objective real-parameter numerical optimization."},{"key":"2954_CR43","unstructured":"Liu, L., Wang, A., Sun, G., Zheng, T., & Yu, C. An improved biogeography-based optimization approach for beam pattern optimizations of linear and circular antenna arrays. International Journal of Numerical Modelling Electronic Networks Devices and Fields, 11."}],"container-title":["Wireless Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11276-022-02954-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11276-022-02954-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11276-022-02954-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,4]],"date-time":"2022-06-04T06:16:42Z","timestamp":1654323402000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11276-022-02954-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,6]]},"references-count":43,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2022,7]]}},"alternative-id":["2954"],"URL":"https:\/\/doi.org\/10.1007\/s11276-022-02954-6","relation":{},"ISSN":["1022-0038","1572-8196"],"issn-type":[{"type":"print","value":"1022-0038"},{"type":"electronic","value":"1572-8196"}],"subject":[],"published":{"date-parts":[[2022,4,6]]},"assertion":[{"value":"21 March 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 April 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}