{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:25:04Z","timestamp":1760243104878,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2015,9,25]],"date-time":"2015-09-25T00:00:00Z","timestamp":1443139200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61471142","61102084"],"award-info":[{"award-number":["61471142","61102084"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Orthogonal frequency division multiple access (OFDMA), which is widely used in the wireless sensor networks, allows different users to obtain different subcarriers according to their subchannel gains. Therefore, how to assign subcarriers and power to different users to achieve a high system sum rate is an important research area in OFDMA systems. In this paper, the focus of study is on the rate adaptive (RA) based resource allocation with proportional fairness constraints. Since the resource allocation is a NP-hard and non-convex optimization problem, a new efficient resource allocation algorithm  ACO-SPA is proposed, which combines ant colony optimization (ACO) and suboptimal power allocation (SPA). To reduce the computational complexity, the optimization problem of resource allocation in OFDMA systems is separated into two steps. For the first one, the ant colony optimization algorithm is performed to solve the subcarrier allocation. Then, the suboptimal power allocation algorithm is developed with strict proportional fairness,  and the algorithm is based on the principle that the sums of power and the reciprocal of  channel-to-noise ratio for each user in different subchannels are equal. To support it, plenty of simulation results are presented. In contrast with root-finding and linear methods, the proposed method provides better performance in solving the proportional resource allocation problem in OFDMA systems.<\/jats:p>","DOI":"10.3390\/s151024996","type":"journal-article","created":{"date-parts":[[2015,9,28]],"date-time":"2015-09-28T03:02:55Z","timestamp":1443409375000},"page":"24996-25014","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Rate Adaptive Based Resource Allocation with Proportional Fairness Constraints in OFDMA Systems"],"prefix":"10.3390","volume":"15","author":[{"given":"Zhendong","family":"Yin","sequence":"first","affiliation":[{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology, 92 Xidazhi Street, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shufeng","family":"Zhuang","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology, 92 Xidazhi Street, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhilu","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology, 92 Xidazhi Street, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology, 92 Xidazhi Street, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,9,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1918","DOI":"10.1109\/TVT.2014.2341712","article-title":"Position-based compressed channel estimation and pilot design for high-mobility OFDM systems","volume":"64","author":"Ren","year":"2015","journal-title":"IEEE Trans. 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