{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:12:53Z","timestamp":1760242373127,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,6,9]],"date-time":"2017-06-09T00:00:00Z","timestamp":1496966400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Future Internet"],"abstract":"<jats:p>In this paper, an energy efficient power allocation scheme is proposed for a distributed massive multiple-input multiple-output (MIMO) system with a circular antenna array. Single-antenna users simultaneously transmit signal to the base station (BS) with a large number of distributed antennas. The tight approximation of the energy efficiency (EE) is derived in closed form expressions. Through jointly optimizing the power allocation and the antenna number of BS, an NP-hard problem is formulated to maximize the EE. The equal power allocation is proved to be optimal given the total transmit power and the number of antennas. Finally, the optimal antenna number is determined by one dimension search. It is noteworthy that the NP-hard problem is solved by one dimension search. Simulation results validate the accuracy and the low-complexity of our proposed scheme.<\/jats:p>","DOI":"10.3390\/fi9020021","type":"journal-article","created":{"date-parts":[[2017,6,9]],"date-time":"2017-06-09T10:29:59Z","timestamp":1497004199000},"page":"21","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Energy Efficient Power Allocation for the Uplink of Distributed Massive MIMO Systems"],"prefix":"10.3390","volume":"9","author":[{"given":"Xinhua","family":"Wang","sequence":"first","affiliation":[{"name":"College of Automation and Electrical Engineering, Qingdao University, Qingdao 266071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Automation and Electrical Engineering, Qingdao University, Qingdao 266071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinlu","family":"Sheng","sequence":"additional","affiliation":[{"name":"College of Traffic and Transportation, Chongqing Jiaotong University, Chongqing 400074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,6,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1206","DOI":"10.1109\/ACCESS.2015.2461602","article-title":"A survey of 5G network: Architecture and emerging technologies","volume":"3","author":"Gupta","year":"2015","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Wong, V., Schober, R., Ng, D.W.K., and Wang, L. (2017). Key Technologies for 5G Wireless Systems, Cambridge University Press.","DOI":"10.1017\/9781316771655"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1109\/MCOM.2014.6736761","article-title":"Massive MIMO for next generation wireless systems","volume":"52","author":"Larsson","year":"2006","journal-title":"IEEE Commun. Mag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1738","DOI":"10.1109\/COMST.2015.2425294","article-title":"Survey of large-scale MIMO systems","volume":"17","author":"Zheng","year":"2015","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2350","DOI":"10.1109\/TCOMM.2013.032713.120408","article-title":"The multicell multiuser MIMO uplink with very large antenna arrays and a finite-dimensional channel","volume":"61","author":"Ngo","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_6","first-page":"4471","article-title":"Uplink performance analysis of multicell MU-SIMO systems with ZF receivers","volume":"62","author":"Ngo","year":"2012","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1219","DOI":"10.1002\/ett.2745","article-title":"Performance analysis for downlink massive MIMO system with ZF precoding","volume":"25","author":"Zhao","year":"2014","journal-title":"Trans. Emerg. Telecommun. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/CC.2015.7386172","article-title":"Spectral efficiency analysis for downlink massive MIMO systems with MRT precoding","volume":"12","author":"Lin","year":"2015","journal-title":"China Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1436","DOI":"10.1109\/TCOMM.2013.020413.110848","article-title":"Energy and spectral efficiency of very large multiuser MIMO systems","volume":"61","author":"Ngo","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_10","unstructured":"Ha, D., Lee, K., and Kang, J. (2013, January 8\u20139). Energy efficiency analysis with circuit power consumption in massive MIMO systems. Proceedings of the 2013 IEEE 24th International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC Workshops), London, UK."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3059","DOI":"10.1109\/TWC.2015.2400437","article-title":"Optimal design of energy-efficient multi-user MIMO systems: Is massive MIMO the answer?","volume":"14","author":"Bjornson","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zhao, L., Zhao, H., Zheng, K., and Zhang, J. (2013, January 2\u20135). Energy efficient power allocation algorithm for downlink massive MIMO with MRT precoding. Proceedings of the 2013 IEEE 78th Vehicular Technology Conference (VTC2013-Fall), Las Vegas, NV, USA.","DOI":"10.1109\/VTCFall.2013.6692185"},{"key":"ref_13","first-page":"3292","article-title":"Energy-efficient resource allocation in OFDMA systems with large numbers of base station antennas","volume":"11","author":"Ng","year":"2012","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2734","DOI":"10.1109\/TCOMM.2009.09.080067","article-title":"Chunk-based resource allocation in OFDMA systems\u2014Part I: Chunk allocation","volume":"57","author":"Zhu","year":"2009","journal-title":"IEEE Trans. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1109\/TCOMM.2011.112811.110036","article-title":"Chunk-based resource allocation in OFDMA systems\u2014Part II: Joint chunk, power and bit allocation","volume":"60","author":"Zhu","year":"2012","journal-title":"IEEE Trans. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3618","DOI":"10.1109\/TWC.2012.083112.111951","article-title":"Energy-efficient resource allocation in multi-cell OFDMA systems with limited backhaul capacity","volume":"11","author":"Ng","year":"2012","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1770","DOI":"10.1109\/LCOMM.2015.2454504","article-title":"Distributed energy efficient fair user association in massive MIMO enabled HetNets","volume":"19","author":"Liu","year":"2015","journal-title":"IEEE Commun. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"7112","DOI":"10.1109\/TIT.2014.2354403","article-title":"Massive MIMO systems with non-ideal hardware: Energy efficiency, estimation, and capacity limits","volume":"60","author":"Bjornson","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"8139","DOI":"10.1109\/TWC.2016.2612636","article-title":"Security-Constrained power allocation in MU-Massive-MIMO with distributed antennas","volume":"15","author":"Guo","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1109\/JSAC.2011.110604","article-title":"Performance comparison between distributed antenna and microcellular systems","volume":"29","author":"Zhu","year":"2011","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1885","DOI":"10.1109\/LCOMM.2015.2474377","article-title":"An SNR approximation for distributed massive MIMO with zero forcing","volume":"19","author":"Senanayake","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1930","DOI":"10.1109\/TCOMM.2016.2519513","article-title":"Spectral-Efficiency analysis of massive MIMO systems in centralized and distributed schemes","volume":"64","author":"Kamga","year":"2016","journal-title":"IEEE Trans. Commun."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1109\/LCOMM.2015.2389803","article-title":"Optimal precoder design maximizing the worst-case average received SNR for massive distributed MIMO systems","volume":"19","author":"Gao","year":"2015","journal-title":"IEEE Commun. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1109\/JCN.2016.000088","article-title":"Energy efficiency of distributed massive MIMO systems","volume":"18","author":"He","year":"2016","journal-title":"J. Commun. Netw."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1642","DOI":"10.1049\/el.2016.2167","article-title":"Energy efficiency maximisation for WPCN with distributed massive MIMO system","volume":"19","author":"Kim","year":"2016","journal-title":"Electron. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"5659","DOI":"10.1109\/TWC.2015.2441057","article-title":"Performance analysis and location optimization for massive MIMO systems with circularly distributed antennas","volume":"14","author":"Yang","year":"2015","journal-title":"IEEE Trans. Wirel. 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