{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:05:34Z","timestamp":1760231134865,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2022,8,27]],"date-time":"2022-08-27T00:00:00Z","timestamp":1661558400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we considered uplink communication, focusing on the improvement of spectral efficiency (SE) for millimeter wave (mmWave) multiple-input multiple-output non-orthogonal multiple access (MIMO-NOMA) systems. Firstly, we proposed an adaptive cluster head selection algorithm. Then, a channel-aligned analog beamforming scheme was designed based on the selected cluster heads. After that, the user grouping algorithm was designed based on the user-equivalent channel correlation. Subsequently, the power allocation problem was transformed from a nonconvex problem to a convex one using the quadratic transformation (QT) method considering all relevant constraints. Finally, the optimal user power allocation and digital beamforming design was obtained by iteratively optimizing the power and digital beamforming. Simulation results show that our proposed scheme can achieve a higher SE than existing methods.<\/jats:p>","DOI":"10.3390\/s22176466","type":"journal-article","created":{"date-parts":[[2022,8,30]],"date-time":"2022-08-30T01:37:55Z","timestamp":1661823475000},"page":"6466","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Spectral Efficiency Optimization of Uplink Millimeter Wave MIMO-NOMA Systems"],"prefix":"10.3390","volume":"22","author":[{"given":"Yinhao","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Physics and Electronics, Central South University, Changsha 410083, China"}]},{"given":"Honggui","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Changsha 410083, China"}]},{"given":"Jun","family":"He","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, 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, Changsha 410083, China"}]},{"given":"Chengzuo","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Changsha 410083, China"}]},{"given":"Haoqi","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Changsha 410083, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2337","DOI":"10.1109\/TVT.2021.3057648","article-title":"Beam aggregation-based mmWave MIMO-NOMA: An AI-enhanced approach","volume":"70","author":"Ye","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_2","first-page":"1336","article-title":"Decoupling energy efficient approach for hybrid precoding-based mmWave massive MIMO-NOMA with SWIPT","volume":"1","author":"Jawarneh","year":"2020","journal-title":"IEEE Access."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"57726","DOI":"10.1109\/ACCESS.2021.3071992","article-title":"User clustering and optimized power allocation for D2D communications at mmWave underlaying MIMO-NOMA cellular networks","volume":"9","author":"Solaiman","year":"2021","journal-title":"IEEE Access."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"938","DOI":"10.1109\/LWC.2022.3150217","article-title":"Joint Optimal Power Allocation and Beamforming for MIMO-NOMA in mmWave Communications","volume":"11","author":"Aghdam","year":"2022","journal-title":"IEEE Commun. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"101469","DOI":"10.1016\/j.phycom.2021.101469","article-title":"Clustering and power optimization in mmWave massive MIMO\u2013NOMA systems","volume":"49","author":"Wang","year":"2021","journal-title":"Phys. Commun."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2006","DOI":"10.1109\/TWC.2019.2961654","article-title":"Two-side coalitional matching approach for joint MIMO-NOMA clustering and BS selection in multi-cell MIMO-NOMA systems","volume":"19","author":"Ding","year":"2019","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Li, S., Wan, Z., Jin, L., and Du, J. (2019). Energy harvesting maximizing for millimeter-wave massive MIMO-NOMA. Electronics, 9.","DOI":"10.3390\/electronics9010032"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2370","DOI":"10.1109\/JSAC.2017.2725878","article-title":"Spectrum and energy-efficient beamspace MIMO-NOMA for millimeter-wave communications using lens antenna array","volume":"35","author":"Wang","year":"2017","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_9","first-page":"6325","article-title":"Dynamic user clustering and power allocation in non-orthogonal multiple access (NOMA) systems","volume":"4","author":"Ali","year":"2016","journal-title":"IEEE Access."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2961","DOI":"10.1109\/TWC.2018.2804953","article-title":"Joint power allocation and beamforming for non-orthogonal multiple access (NOMA) in 5G millimeter wave communications","volume":"17","author":"Xiao","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"6177","DOI":"10.1109\/TWC.2018.2855151","article-title":"Joint power control and beamforming for uplink non-orthogonal multiple access in 5G millimeter-wave communications","volume":"17","author":"Zhu","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1109\/JSAC.2018.2872364","article-title":"2Hybrid precoding-based millimeter-wave massive MIMO-NOMA with simultaneous wireless information and power transfer","volume":"37","author":"Dai","year":"2019","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5065","DOI":"10.1109\/TWC.2019.2932070","article-title":"Millimeter-wave NOMA with user grouping, power allocation and hybrid beamforming","volume":"18","author":"Zhu","year":"2019","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"139994","DOI":"10.1109\/ACCESS.2020.3013305","article-title":"Spectrum and energy efficiency optimization for hybrid precoding-based SWIPT-enabled mmWave mMIMO-NOMA systems","volume":"8","author":"Uwaechia","year":"2020","journal-title":"IEEE Access."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Zhu, Z., Deng, H., Xu, F., Zhang, W., Liu, G., and Zhang, Y. (2022). Hybrid Precoding-Based Millimeter Wave Massive MIMO-NOMA Systems. Symmetry, 14.","DOI":"10.3390\/sym14020412"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Sun, Y., Guo, Y., Li, S., Wu, D., and Wang, B. (2018). Optimal resource allocation for NOMA-TDMA scheme with \u03b1-fairness in industrial internet of things. Sensors, 18.","DOI":"10.3390\/s18051572"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"152993","DOI":"10.1016\/j.aeue.2019.152993","article-title":"Performance analysis at far and near user in NOMA based system in presence of SIC error","volume":"114","author":"Jain","year":"2020","journal-title":"Int. J. Electron Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"101441","DOI":"10.1016\/j.phycom.2021.101441","article-title":"Modeling and analysis of self-interference impaired two-user cooperative MIMO-NOMA system","volume":"48","author":"Ghous","year":"2021","journal-title":"Phys. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"10553","DOI":"10.1109\/TVT.2021.3109603","article-title":"Power Minimization Precoder Design for Uplink MIMO Systems With Multi-Group NOMA Scheme","volume":"70","author":"Zhang","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"7858","DOI":"10.1109\/TVT.2021.3093716","article-title":"Impact of Max-Min Power Control, Channel Estimation and User Grouping Strategies on Uplink Massive MIMO-NOMA Systems","volume":"70","author":"Pawar","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_21","first-page":"2034","article-title":"Enhanced user grouping and power allocation for hybrid mmWave MIMO-NOMA systems","volume":"21","author":"Zhu","year":"2021","journal-title":"IEEE Trans.Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1502","DOI":"10.1109\/TWC.2017.2779504","article-title":"Optimal user scheduling and power allocation for millimeter wave NOMA systems","volume":"17","author":"Cui","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1109\/COMST.2016.2621116","article-title":"Power do- main non-orthogonal multiple access (NOMA) in 5G systems: Potentials and challenges","volume":"19","author":"Islam","year":"2017","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2616","DOI":"10.1109\/TSP.2018.2812733","article-title":"Fractional programming for communication systems Part I: Power control and beamforming","volume":"66","author":"Shen","year":"2018","journal-title":"IEEE Trans. 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