{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T23:58:33Z","timestamp":1772063913029,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,4,13]],"date-time":"2017-04-13T00:00:00Z","timestamp":1492041600000},"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, both the spectrum efficiency (SE) and the energy efficiency (EE) are investigated for an uplink massive multiple-input multiple-output (MIMO) system coexisting with an underlay device-to-device (D2D) system. The outage probability and the achievable rates of the cellular user equipments (CUEs) and the D2D link are derived in closed-form, respectively. Constrained by the SE of the D2D link and the CUEs, the EE of the massive MIMO system is maximized by jointly optimizing the transmit power of CUEs and the number of BS antennas. An algorithm with low complexity is proposed to solve the optimization problem. Performance results are provided to validate our derived closed-from results and verify the efficiency of our proposed scheme.<\/jats:p>","DOI":"10.3390\/fi9020012","type":"journal-article","created":{"date-parts":[[2017,4,13]],"date-time":"2017-04-13T10:55:44Z","timestamp":1492080944000},"page":"12","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Spectrum and Energy Efficiency of Uplink Massive MIMO System with D2D Underlay"],"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"}]}],"member":"1968","published-online":{"date-parts":[[2017,4,13]]},"reference":[{"key":"ref_1","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":"2014","journal-title":"IEEE Commun. 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