{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T09:56:20Z","timestamp":1768470980971,"version":"3.49.0"},"reference-count":23,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,8]],"date-time":"2022-04-08T00:00:00Z","timestamp":1649376000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In order to solve the energy efficiency optimization problem in the uplink multi-cell massive MIMO system, this paper constructs the system transmission model, of which the channel is symmetry, based on user and base station, and deduces the expression of data transmission rate of each user. Then, we establish a model of the spectral and energy efficiency of multi-cell massive MIMO system by analyzing the pilot transmission and channel estimation. We also derive the nonconvex function for the energy efficiency optimization, which is difficult to solve directly. Therefore, we propose an improved particle swarm optimization algorithm to obtain the suboptimal solution, under low complexity, by optimizing the distribution of user power. To demonstrate the advantages of our proposed algorithm, we simulate the energy efficiency performance of the algorithm. The results show that the proposed algorithm can effectively improve the energy efficiency of the system.<\/jats:p>","DOI":"10.3390\/sym14040780","type":"journal-article","created":{"date-parts":[[2022,4,10]],"date-time":"2022-04-10T06:02:54Z","timestamp":1649570574000},"page":"780","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Energy Efficiency Optimization of Massive MIMO System with Uplink Multi-Cell Based on Imperfect CSI with Power Control"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4336-5902","authenticated-orcid":false,"given":"Jie","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Physics and Electronics, Central South University, Lushan South Road, Changsha 410083, China"}]},{"given":"Honggui","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Lushan South Road, Changsha 410083, China"}]},{"given":"Youzhen","family":"Li","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Lushan South Road, Changsha 410083, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4239-3749","authenticated-orcid":false,"given":"Zaoxing","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Lushan South Road, Changsha 410083, China"}]},{"given":"Gang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Lushan South Road, Changsha 410083, China"},{"name":"College of Information Science and Engineering, Changsha Normal University, Teli Road, Changsha 410100, China"}]},{"given":"Hongmei","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Lushan South Road, Changsha 410083, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"113131","DOI":"10.1109\/ACCESS.2019.2935146","article-title":"Energy Efficiency Optimization for Wireless Power Transfer Enabled Massive MIMO Systems WITH Hardware Impairments","volume":"7","author":"Wang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1109\/OJCAS.2021.3125894","article-title":"Energy Efficiency of Uplink Cell-Free Massive MIMO With Transmit Power Control in Measured Propagation Channel","volume":"2","author":"Choi","year":"2021","journal-title":"IEEE Open J. 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