{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T14:01:16Z","timestamp":1760709676755,"version":"3.40.5"},"reference-count":35,"publisher":"SAGE Publications","issue":"8","license":[{"start":{"date-parts":[[2018,8,1]],"date-time":"2018-08-01T00:00:00Z","timestamp":1533081600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Distributed Sensor Networks"],"published-print":{"date-parts":[[2018,8]]},"abstract":"<jats:p> In the device-to-device communication network, there is the interference problem when device-to-device users share the same spectrum with cellular users, a distributed beamforming scheme based on non-cooperative game is proposed to maximize weighted sum rate under the rated transmit power and the users\u2019 quality of service. Since the optimization problem is non-concave, we first obtain the solution of the Karush-Kuhn-Tucher (KKT) condition for the downlink beamforming problem of each sender by dual decomposition. Second, a distributed beamforming algorithm based on the non-cooperative game is proposed, which can quickly converge to the Nash equilibrium point with a lower information exchange overhead. Finally, the simulation results show that the proposed algorithm has better performance in terms of system sum rate and fairness than the existing algorithms. <\/jats:p>","DOI":"10.1177\/1550147718786929","type":"journal-article","created":{"date-parts":[[2018,8,7]],"date-time":"2018-08-07T09:01:17Z","timestamp":1533632477000},"page":"155014771878692","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Distributed beamforming algorithm based on game theory in device-to-device communications"],"prefix":"10.1177","volume":"14","author":[{"given":"Xian-zhong","family":"Xie","sequence":"first","affiliation":[{"name":"Institute of Broadband Access Networks, Chongqing University of Posts and Telecommunications, Chongqing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2367-5089","authenticated-orcid":false,"given":"Chuan-wen","family":"Li","sequence":"additional","affiliation":[{"name":"Institute of Broadband 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