{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T20:06:18Z","timestamp":1778789178493,"version":"3.51.4"},"reference-count":39,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T00:00:00Z","timestamp":1681171200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this study, we consider the combination of clustering and resource allocation based on game theory in ultra-dense networks that consist of multiple macrocells using massive multiple-input multiple-output and a vast number of randomly distributed drones serving as small-cell base stations. In particular, to mitigate the intercell interference, we propose a coalition game for clustering small cells, with the utility function being the ratio of signal to interference. Then, the optimization problem of resource allocation is divided into two subproblems: subchannel allocation and power allocation. We use the Hungarian method, which is efficient for solving binary optimization problems, to assign the subchannels to users in each cluster of small cells. Additionally, a centralized algorithm with low computational complexity and a distributed algorithm based on the Stackelberg game are provided to maximize the network energy efficiency (EE). The numerical results demonstrate that the game-based method outperforms the centralized method in terms of execution time in small cells and is better than traditional clustering in terms of EE.<\/jats:p>","DOI":"10.3390\/s23083899","type":"journal-article","created":{"date-parts":[[2023,4,12]],"date-time":"2023-04-12T02:08:11Z","timestamp":1681265291000},"page":"3899","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Joint Clustering and Resource Allocation Optimization in Ultra-Dense Networks with Multiple Drones as Small Cells Using Game Theory"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8551-4198","authenticated-orcid":false,"given":"Tinh T.","family":"Bui","sequence":"first","affiliation":[{"name":"Faculty of Electrical and Electronics Engineering, Ho Chi Minh City University of Technology (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City 700000, Vietnam"},{"name":"Vietnam National University Ho Chi Minh City, Linh Trung Ward, Thu Duc District, Ho Chi Minh City 700000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1044-257X","authenticated-orcid":false,"given":"Long D.","family":"Nguyen","sequence":"additional","affiliation":[{"name":"Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam"},{"name":"School of Engineering and Technology, Duy Tan University, Da Nang 550000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2569-4152","authenticated-orcid":false,"given":"Ha Hoang","family":"Kha","sequence":"additional","affiliation":[{"name":"Faculty of Electrical and Electronics Engineering, Ho Chi Minh City University of Technology (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City 700000, Vietnam"},{"name":"Vietnam National University Ho Chi Minh City, Linh Trung Ward, Thu Duc District, Ho Chi Minh City 700000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5818-7109","authenticated-orcid":false,"given":"Nguyen-Son","family":"Vo","sequence":"additional","affiliation":[{"name":"Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam"},{"name":"School of Engineering and Technology, Duy Tan University, Da Nang 550000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4703-4836","authenticated-orcid":false,"given":"Trung Q.","family":"Duong","sequence":"additional","affiliation":[{"name":"School of Electronics, Electrical Engineering and Computer Science, Queen\u2019s University Belfast, Belfast BT3 9DT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,11]]},"reference":[{"key":"ref_1","unstructured":"Cisco, V. 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