{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,26]],"date-time":"2025-09-26T00:04:31Z","timestamp":1758845071710,"version":"3.37.3"},"reference-count":14,"publisher":"SAGE Publications","issue":"11","license":[{"start":{"date-parts":[[2015,11,1]],"date-time":"2015-11-01T00:00:00Z","timestamp":1446336000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61271259","61301123","CYS14143"],"award-info":[{"award-number":["61271259","61301123","CYS14143"]}],"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":["61271259","61301123","CYS14143"],"award-info":[{"award-number":["61271259","61301123","CYS14143"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004502","name":"Chongqing University of Posts and Telecommunications","doi-asserted-by":"publisher","award":["61271259","61301123","CYS14143"],"award-info":[{"award-number":["61271259","61301123","CYS14143"]}],"id":[{"id":"10.13039\/501100004502","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Distributed Sensor Networks"],"published-print":{"date-parts":[[2015,11,1]]},"abstract":"<jats:p> This paper firstly investigates the problem of uplink power control in cognitive radio networks (CRNs) with multiple primary users (PUs) and multiple second users (SUs) considering channel outage constraints and interference power constraints, where PUs and SUs compete with each other to maximize their utilities. We formulate a Stackelberg game to model this hierarchical competition, where PUs and SUs are considered to be leaders and followers, respectively. We theoretically prove the existence and uniqueness of robust Stackelberg equilibrium for the noncooperative approach. Then, we apply the Lagrange dual decomposition method to solve this problem, and an efficient iterative algorithm is proposed to search the Stackelberg equilibrium. Simulation results show that the proposed algorithm improves the performance compared with those proportionate game schemes. <\/jats:p>","DOI":"10.1155\/2015\/604915","type":"journal-article","created":{"date-parts":[[2015,11,23]],"date-time":"2015-11-23T21:03:21Z","timestamp":1448312601000},"page":"604915","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Stackelberg Game Based Power Control with Outage Probability Constraints for Cognitive Radio Networks"],"prefix":"10.1177","volume":"11","author":[{"given":"Helin","family":"Yang","sequence":"first","affiliation":[{"name":"Chongqing Key Laboratory of Mobile Communications Technology and Institute of Personal Communication, Chongqing University of Posts & Telecommunications, Chongqing 400065, China"}]},{"given":"Xianzhong","family":"Xie","sequence":"additional","affiliation":[{"name":"Chongqing Key Laboratory of Mobile Communications Technology and Institute of Personal Communication, Chongqing University of Posts & Telecommunications, Chongqing 400065, China"}]},{"given":"Athanasios V.","family":"Vasilakos","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Electrical and Space Engineering, Lule\u00e5 University of Technology, 93187 Skellefte\u00e5, Sweden"}]}],"member":"179","published-online":{"date-parts":[[2015,11,23]]},"reference":[{"key":"B1-2015-604915","doi-asserted-by":"publisher","DOI":"10.1109\/surv.2011.122310.000119"},{"key":"B2-2015-604915","doi-asserted-by":"publisher","DOI":"10.1109\/twc.2010.120310.091430"},{"key":"B3-2015-604915","doi-asserted-by":"publisher","DOI":"10.1109\/jsac.2012.120404"},{"key":"B4-2015-604915","doi-asserted-by":"publisher","DOI":"10.1109\/twc.2012.092112.111510"},{"key":"B5-2015-604915","doi-asserted-by":"publisher","DOI":"10.1109\/TWC.2014.2318708"},{"key":"B6-2015-604915","doi-asserted-by":"publisher","DOI":"10.1109\/tvt.2012.2227858"},{"key":"B7-2015-604915","doi-asserted-by":"publisher","DOI":"10.1109\/JSAC.2012.121119"},{"key":"B8-2015-604915","doi-asserted-by":"publisher","DOI":"10.1109\/jsac.2014.140307"},{"key":"B9-2015-604915","doi-asserted-by":"publisher","DOI":"10.1109\/tmc.2008.157"},{"key":"B10-2015-604915","doi-asserted-by":"publisher","DOI":"10.1109\/7693.975444"},{"volume-title":"Dynamic Noncooperative Game Theory","year":"1999","author":"Ba\u015far T.","key":"B11-2015-604915"},{"key":"B12-2015-604915","doi-asserted-by":"publisher","DOI":"10.1007\/s10288-007-0054-4"},{"key":"B13-2015-604915","doi-asserted-by":"publisher","DOI":"10.1145\/1963405.1963433"},{"volume-title":"Nonlinear Programming","year":"1999","author":"Bertsekas D.","key":"B14-2015-604915"}],"container-title":["International Journal of Distributed Sensor Networks"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/journals.sagepub.com\/doi\/pdf\/10.1155\/2015\/604915","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/journals.sagepub.com\/doi\/full-xml\/10.1155\/2015\/604915","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/journals.sagepub.com\/doi\/pdf\/10.1155\/2015\/604915","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,7]],"date-time":"2021-05-07T17:37:03Z","timestamp":1620409023000},"score":1,"resource":{"primary":{"URL":"http:\/\/journals.sagepub.com\/doi\/10.1155\/2015\/604915"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,1]]},"references-count":14,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2015,11,1]]}},"alternative-id":["10.1155\/2015\/604915"],"URL":"https:\/\/doi.org\/10.1155\/2015\/604915","relation":{},"ISSN":["1550-1477","1550-1477"],"issn-type":[{"type":"print","value":"1550-1477"},{"type":"electronic","value":"1550-1477"}],"subject":[],"published":{"date-parts":[[2015,11,1]]}}}