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We formulate the power control problem as a Stackelberg game, where the macrocell user equipment (MUE) acts as the leader and the small-cell user equipment (SUE) acts as the follower. To reduce the cross-tier and cotier interferences and the power consumption of both the MUE and SUE, we propose optimizing not only the transmit rate but also the transmit power. The corresponding optimization problems are solved through a two-layer iteration. In the inner iteration, the SUE items (SUEs) compete with each other, and their optimal transmit powers are obtained through iterative computations. In the outer iteration, the optimal transmit power of the MUE is obtained in a closed form based on the transmit powers of the SUEs through proper mathematical manipulations. We prove the convergence of the proposed power control scheme, and we also theoretically show the existence and uniqueness of the Stackelberg equilibrium (SE) in the formulated Stackelberg game. The simulation results show that the proposed power control scheme provides considerable improvements, particularly for the MUE.<\/jats:p>","DOI":"10.1155\/2019\/1401469","type":"journal-article","created":{"date-parts":[[2019,3,14]],"date-time":"2019-03-14T19:30:56Z","timestamp":1552591856000},"page":"1-10","source":"Crossref","is-referenced-by-count":6,"title":["Power Control via Stackelberg Game for Small-Cell Networks"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8062-7767","authenticated-orcid":true,"given":"Yanxiang","family":"Jiang","sequence":"first","affiliation":[{"name":"National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China"},{"name":"State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019an 710071, China"},{"name":"Key Laboratory of Wireless Sensor Network & Communication, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Ge","sequence":"additional","affiliation":[{"name":"National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mehdi","family":"Bennis","sequence":"additional","affiliation":[{"name":"Centre for Wireless Communications, University of Oulu, Oulu 90014, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fu-Chun","family":"Zheng","sequence":"additional","affiliation":[{"name":"National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China"},{"name":"School of Electronic and Information Engineering, Harbin Institute of Technology, Shenzhen 518055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaohu","family":"You","sequence":"additional","affiliation":[{"name":"National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1109\/MVT.2010.939904"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1109\/tvt.2015.2472995"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1109\/twc.2014.2334673"},{"issue":"1","key":"5","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1109\/TCOMM.2018.2873344","volume":"67","year":"2019","journal-title":"IEEE Transactions on Wireless Communications"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1109\/TWC.2016.2646346"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1109\/TVT.2017.2673245"},{"key":"8","doi-asserted-by":"crossref","first-page":"12 608","DOI":"10.1109\/ACCESS.2018.2799138","volume":"6","year":"2018","journal-title":"IEEE Access"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1109\/JSAC.2012.120404"},{"year":"1993","key":"12"},{"year":"1992","key":"16"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1109\/TMM.2017.2733338"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1109\/JSAC.2007.070804"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1109\/TMC.2008.153"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.2307\/1911749"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.comnet.2010.04.004"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1109\/TVT.2013.2273503"}],"container-title":["Wireless Communications and Mobile Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/wcmc\/2019\/1401469.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/wcmc\/2019\/1401469.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/wcmc\/2019\/1401469.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,14]],"date-time":"2019-03-14T19:31:02Z","timestamp":1552591862000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/wcmc\/2019\/1401469\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,14]]},"references-count":16,"alternative-id":["1401469","1401469"],"URL":"https:\/\/doi.org\/10.1155\/2019\/1401469","relation":{},"ISSN":["1530-8669","1530-8677"],"issn-type":[{"type":"print","value":"1530-8669"},{"type":"electronic","value":"1530-8677"}],"subject":[],"published":{"date-parts":[[2019,3,14]]}}}