{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T08:35:57Z","timestamp":1777538157341,"version":"3.51.4"},"reference-count":46,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T00:00:00Z","timestamp":1604275200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100014188","name":"Ministry of Science and ICT, South Korea","doi-asserted-by":"publisher","award":["NRF-2019R1C1C1003202"],"award-info":[{"award-number":["NRF-2019R1C1C1003202"]}],"id":[{"id":"10.13039\/501100014188","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we propose a novel statistical beamforming (SBF) method called the partial-nulling-based SBF (PN-SBF) to serve a number of users that are undergoing distinct degrees of spatial channel correlations in massive multiple-input multiple-output (MIMO) systems. We consider a massive MIMO system with two user groups. The first group experiences a low spatial channel correlation, whereas the second group has a high spatial channel correlation, which can happen in massive MIMO systems that are based on fifth-generation networks. By analyzing the statistical signal-to-interference-plus-noise ratio, it can be observed that the statistical beamforming vector for the low-correlation group should be designed as the orthogonal complement for the space spanned by the aggregated channel covariance matrices of the high-correlation group. Meanwhile, the spatial degrees of freedom for the high-correlation group should be preserved without cancelling the interference to the low-correlation group. Accordingly, a group-common pre-beamforming matrix is applied to the low-correlation group to cancel the interference to the high-correlation group. In addition, to deal with the intra-group interference in each group, the post-beamforming vector for each group is designed in the manner of maximizing the signal-to-leakage-and-noise ratio, which yields additional performance improvements for the PN-SBF. The simulation results verify that the proposed PN-SBF outperforms the conventional SBF schemes in terms of the ergodic sum rate for the massive MIMO systems with distinct spatial correlations, without the rate ceiling effect in the high signal-to-noise ratio region unlike conventional SBF schemes.<\/jats:p>","DOI":"10.3390\/s20216255","type":"journal-article","created":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T09:04:46Z","timestamp":1604307886000},"page":"6255","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Statistical Beamforming for Massive MIMO Systems with Distinct Spatial Correlations"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6986-4729","authenticated-orcid":false,"given":"Taehyoung","family":"Kim","sequence":"first","affiliation":[{"name":"Samsung Research, Samsung Electronics Company Ltd., Seoul 06765, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6684-9803","authenticated-orcid":false,"given":"Sangjoon","family":"Park","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Kyonggi University, Suwon 16227, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/MWC.2019.8752473","article-title":"New Radio (NR) and its Evolution toward 5G-Advanced","volume":"3","author":"Kim","year":"2019","journal-title":"IEEE Wirel. Commun."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Guevara, L., and Cheein, F.A. (2020). The Role of 5G Technologies: Challenges in Smart Cities and Intelligent Transportation Systems. Sustainability, 12.","DOI":"10.3390\/su12166469"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1109\/MCOMSTD.001.1800001","article-title":"Advanced Data Transmission Framework for 5G Wireless Communications in the 3GPP New Radio Standard","volume":"3","author":"Yeo","year":"2019","journal-title":"IEEE Commun. Stand. Mag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1109\/MCOM.2018.1700761","article-title":"Modular and High-Resolution Channel State Information and Beam Management for 5G New Radio","volume":"3","author":"Onggosanusi","year":"2018","journal-title":"IEEE Commun. Mag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3590","DOI":"10.1109\/TWC.2010.092810.091092","article-title":"Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas","volume":"11","author":"Marzetta","year":"2010","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1109\/MSP.2011.2178495","article-title":"Scaling up MIMO: Opportunities and Challenges with Very Large Arrays","volume":"1","author":"Rusek","year":"2013","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1109\/MCOM.2014.6736761","article-title":"Massive MIMO for Next Generation Wireless Systems","volume":"2","author":"Larsson","year":"2014","journal-title":"IEEE Commun. Mag."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1109\/JSTSP.2014.2317671","article-title":"An Overview of Massive MIMO: Benefits and Challenges","volume":"5","author":"Lu","year":"2014","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Chinnadurai, S., Selvaprabhu, P., Jeong, Y., Jiang, X., and Lee, M.H. (2017). Worst-Case Energy Efficiency Maximization in a 5G Massive MIMO-NOMA System. Sensors, 17.","DOI":"10.3390\/s17092139"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Alemaishat, S., Saraereh, O.A., Khan, I., Affes, S.H., Li, X., and Lee, J.W. (2019). An Efficient Precoding Scheme for Millimeter-Wave Massive MIMO Systems. Electronics, 8.","DOI":"10.3390\/electronics8090927"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Chataut, R., and Akl, R. (2020). Massive MIMO Systems for 5G and Beyond Networks\u2013Overview, Recent Trends, Challenges, and Future Research Direction. Sensors, 20.","DOI":"10.3390\/s20102753"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Kim, T., and Park, S. (2020). Scaling Laws of Scheduling Gain for Uplink Massive MIMO Systems: Is User Scheduling Still Beneficial for Massive MIMO?. Electronics, 9.","DOI":"10.3390\/electronics9101650"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1109\/TCOMM.2012.021712.110006","article-title":"On the Power Amplifier Nonlinearity in MIMO Transmit Beamforming Systems","volume":"3","author":"Qi","year":"2012","journal-title":"IEEE Trans. Commun."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Fozooni, M., Matthaiou, M., Bjornson, E., and Duong, T.Q. (2015, January 6\u201310). Performance Limits of MIMO Systems with Nonlinear Power Amplifiers. Proceedings of the IEEE Global Communications Conference (GLOBECOM 2015), San Diego, CA, USA.","DOI":"10.1109\/GLOCOM.2015.7417680"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4038","DOI":"10.1109\/TWC.2017.2691318","article-title":"Throughput Analysis of Massive MIMO Uplink with Low-Resolution ADCs","volume":"6","author":"Jacobsson","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"7208","DOI":"10.1109\/TWC.2018.2865786","article-title":"On the Energy Efficiency of MIMO Hybrid Beamforming for Millimeter-Wave Systems with Nonlinear Power Amplifiers","volume":"17","author":"Moghadam","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"172277","DOI":"10.1109\/ACCESS.2019.2956596","article-title":"Theoretical Analysis of Nonlinear Amplification Effects in Massive MIMO Systems","volume":"7","author":"Teodoro","year":"2019","journal-title":"IEEE Access"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1109\/JSAC.2013.130205","article-title":"Massive MIMO in the UL\/DL of Cellular Networks: How Many Antennas Do We Need?","volume":"2","author":"Hoydis","year":"2013","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"7128","DOI":"10.1109\/TVT.2018.2827935","article-title":"Scaling Laws of Optimal Training Lengths for TDD Massive MIMO Systems","volume":"8","author":"Kim","year":"2018","journal-title":"IEEE Trans. Veh. Tech."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Tse, D., and Viswanath, P. (2005). Fundamentals of Wireless Communication, Cambridge University Press.","DOI":"10.1017\/CBO9780511807213"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2868","DOI":"10.1109\/TWC.2015.2396058","article-title":"Achievable Rates of FDD Massive MIMO Systems with Spatial Channel Correlation","volume":"5","author":"Jiang","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_22","first-page":"3261","article-title":"Distributed Compressive CSIT Estimation and Feedback for FDD Multi-User Massive MIMO Systems","volume":"12","author":"Rao","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"4145","DOI":"10.1109\/TWC.2016.2535310","article-title":"Compressed CSI Acquisition in FDD Massive MIMO: How Much Training is Needed?","volume":"6","author":"Shen","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2852","DOI":"10.1109\/TCOMM.2017.2691700","article-title":"Compressed Sensing-Aided Downlink Channel Training for FDD Massive MIMO Systems","volume":"7","author":"Han","year":"2017","journal-title":"IEEE Trans. Commun."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3813","DOI":"10.1109\/TWC.2019.2917905","article-title":"Structured Turbo Compressed Sensing for Downlink Massive MIMO-OFDM Channel Estimation","volume":"8","author":"Kuai","year":"2019","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"5016","DOI":"10.1109\/TCOMM.2013.111413.130379","article-title":"Noncoherent Trellis Coded Quantization: A Practical Limited Feedback Technique for Massive MIMO Systems","volume":"12","author":"Choi","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5371","DOI":"10.1109\/TSP.2012.2204988","article-title":"Statistical Eigenmode-Based SDMA for Two-User Downlink","volume":"10","author":"Wang","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"6464","DOI":"10.1109\/TIT.2013.2267721","article-title":"Statistical Beamforming on the Grassmann Manifold for the Two-User Broadcast Channel","volume":"10","author":"Raghavan","year":"2013","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"6441","DOI":"10.1109\/TIT.2013.2269476","article-title":"Joint Spatial Division and Multiplexing: The Large-Scale Array Regime","volume":"10","author":"Adhikary","year":"2013","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4617","DOI":"10.1109\/TWC.2020.2985686","article-title":"Statistical Beamforming for FDD Downlink Massive MIMO via Spatial Information Extraction and Beam Selection","volume":"7","author":"Liu","year":"2020","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1109\/LCOMM.2017.2740919","article-title":"Statistical Beamforming Based on Effective Channel Gain in Spatially Correlated Massive MIMO Systems","volume":"1","author":"Jang","year":"2018","journal-title":"IEEE Commun. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Wang, W., Huang, Y., You, L., Xiong, J., Li, J., and Gao, X. (2019). Energy Efficiency Optimization for Massive MIMO Non-Orthogonal Unicast and Multicast Transmission with Statistical CSI. Electronics, 8.","DOI":"10.3390\/electronics8080857"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2181","DOI":"10.1109\/TWC.2017.2657745","article-title":"Sum-Rate Analysis for Massive MIMO Downlink with Joint Statistical Beamforming and User Scheduling","volume":"4","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Magueta, R., Castanheira, D., Pedrosa, P., Silva, A., Dinis, R., and Gameiro, A. (2020). Iterative Analog-Digital Multi-User Equalizer for Wideband Millimeter Wave Massive MIMO Systems. Sensors, 20.","DOI":"10.3390\/s20020575"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1109\/MCOMSTD.001.1900048","article-title":"Understanding the Heart of the 5G Air Interface: An Overview of Physical Downlink Control Channel for 5G New Radio","volume":"3","author":"Takeda","year":"2020","journal-title":"IEEE Commun. Standards Mag."},{"key":"ref_36","unstructured":"(2020, July 20). 3GPP Technical Specification TS 38.214. Available online: https:\/\/www.3gpp.org\/dynareport\/38214.htm."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2669","DOI":"10.1109\/JSAC.2019.2947997","article-title":"Millimeter Wave Integrated Access and Backhaul in 5G: Performance Analysis and Design Insights","volume":"12","author":"Saha","year":"2019","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"8195","DOI":"10.1109\/TWC.2018.2874655","article-title":"Bandwidth Partitioning and Downlink Analysis in Millimeter Wave Integrated Access and Backhaul for 5G","volume":"12","author":"Saha","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1549","DOI":"10.1109\/TVT.2018.2888496","article-title":"Beamforming Design for Low-Power In-Band Wireless Backhaul Systems: Centralized and Distributed Approaches","volume":"2","author":"Kwon","year":"2019","journal-title":"IEEE Trans. Veh. Tech."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1109\/JSAC.2015.2416986","article-title":"Massive-MIMO Meets HetNet: Interference Coordination through Spatial Blanking","volume":"6","author":"Adhikary","year":"2015","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1711","DOI":"10.1109\/TWC.2007.360373","article-title":"A Leakage-Based Precoding Scheme for Downlink Multi-User MIMO Channels","volume":"5","author":"Sadek","year":"2007","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1109\/JSTSP.2017.2678108","article-title":"Coordinated SLNR Based Precoding in Large-Scale Heterogeneous Networks","volume":"11","author":"Boukhedimi","year":"2017","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Jung, G.-W., and Lee, Y.-H. (2020). Low-Complexity Multi-User Parameterized Beamforming in Massive MIMO Systems. Electronics, 9.","DOI":"10.3390\/electronics9060882"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1109\/TCOMM.2011.121410.100144","article-title":"Multi-Mode Transmission for the MIMO Broadcast Channel with Imperfect Channel State Information","volume":"3","author":"Zhang","year":"2011","journal-title":"IEEE Trans. Commun."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1109\/JCN.2013.000067","article-title":"Optimal Number of Users in Zero-Forcing Based Multiuser MIMO Systems with Large Number of Antennas","volume":"4","author":"Jung","year":"2013","journal-title":"J. Commun. Netw."},{"key":"ref_46","unstructured":"John, M.E. (1987). Multivariate Statistical Simulation, John Wiley & Sons. [1st ed.]."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/21\/6255\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:28:14Z","timestamp":1760178494000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/21\/6255"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,2]]},"references-count":46,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["s20216255"],"URL":"https:\/\/doi.org\/10.3390\/s20216255","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,2]]}}}