{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:40:43Z","timestamp":1760240443565,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,6,13]],"date-time":"2019-06-13T00:00:00Z","timestamp":1560384000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (no. NRF-2017R1C1B1006607). This research was supported by the Gachon University Research Fund","award":["GCU-2018-0323 of 2018"],"award-info":[{"award-number":["GCU-2018-0323 of 2018"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Efficient and Symmetry based precoding plays a key role in wireless communications. In order to improve the transmission performance of multi-user millimeter wave Multiple-Input Multiple-Output (MIMO) (MU-mmWave MIMO) systems, this paper proposes an analog precoding scheme for the receiver of mmWave MIMO with split sub-array hybrid analog and digital architecture. Then, we propose a hybrid analog and digital precoding algorithm based on channel reciprocity (APoCR) to maximize the spectral efficiency by utilizing the triple joint optimization problem, which can be divided into the analog and digital part. The analog combination vectors (ACVs) are obtained by the signal-to-interference-and-noise ratio (SINR) reception maximization of each downlink user and the analog precoding vectors (APVs) are obtained by the SINR reception maximization of each uplink antenna array. The digital precoder of the transmitter is designed after the analog part optimization to alleviate the interference between multiple data streams of the users. The simulation results show that the proposed precoding algorithm has a better sum rate, fast convergence, and improved SINR than the other state-of-the-art algorithms.<\/jats:p>","DOI":"10.3390\/sym11060786","type":"journal-article","created":{"date-parts":[[2019,6,13]],"date-time":"2019-06-13T11:15:58Z","timestamp":1560424558000},"page":"786","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["An Efficient Algorithm for mmWave MIMO Systems"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3821-8024","authenticated-orcid":false,"given":"Imran","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, University of Engineering &amp; Technology, Peshawar 814, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8579-5444","authenticated-orcid":false,"given":"Mohammed H.","family":"Alsharif","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, College of Electronics and Information Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5637-4798","authenticated-orcid":false,"given":"Mohammad Haseeb","family":"Zafar","sequence":"additional","affiliation":[{"name":"Department of Information Technology, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Madini O.","family":"Alassafi","sequence":"additional","affiliation":[{"name":"Department of Information Technology, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1249-3618","authenticated-orcid":false,"given":"Majid","family":"Ashraf","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, University of Engineering &amp; Technology, Peshawar 814, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongming","family":"Huang","sequence":"additional","affiliation":[{"name":"Department of Communications Engineering, Jilin University, Changchun 130012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jeong","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, College of Electronics and Information Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jin Hong","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, College of Electronics and Information Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1109\/MWC.2019.1800039","article-title":"Integrated millimeter-wave and Sub-6 GHz wireless networks: A roadmap for joint mobile broadband and ultra-reliable low-latency communications","volume":"26","author":"Semiari","year":"2019","journal-title":"IEEE Wirel. Commun."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1109\/TWC.2018.2879109","article-title":"Modeling and analysis of point-to-multipoint millimeter wave backhaul networks","volume":"18","author":"Shi","year":"2019","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1109\/MCOM.2015.7158266","article-title":"5G Spectrum: Is China ready?","volume":"53","author":"Wang","year":"2015","journal-title":"IEEE Commun. Mag."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Saraereh, O.A., Khan, I., Alsafasfeh, Q., Alemaishat, S., and Kim, S. (2019). Low-Complexity Channel Estimation in 5G Massive MIMO-OFDM Systems. Symmetry, 11.","DOI":"10.3390\/sym11050713"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1109\/MCOM.2015.7010530","article-title":"Millimeter-wave communications for 5G-Part 2: Applications","volume":"53","author":"Elkhashlan","year":"2015","journal-title":"IEEE Commun. Mag."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Yu, H., Yang, G., Meng, F., and Li, Y. (2017). Performance analysis of MIMO system with single RF Link based on switched parasitic antenna. Symmetry, 9.","DOI":"10.3390\/sym9120304"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Al-Sharif, M.H., Kelechi, A.H., Kim, J., and Kim, J.H. (2019). Energy efficiency and coverage trade-off in 5G for eco-friendly and sustainable cellular networks. Symmetry, 11.","DOI":"10.3390\/sym11030408"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Yu, H., Yang, G., Li, Y., and Meng, F. (2018). Design and analysis of multiple-input multiple-output radar system based on RF single-link technology. Symmetry, 10.","DOI":"10.3390\/sym10050130"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1849","DOI":"10.1109\/JSAC.2017.2710678","article-title":"Introduction on IMT-2020 5G Trials in China","volume":"35","author":"Deong","year":"2017","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_10","unstructured":"IEEE Std 802.15.3c-2009 (2009). Wireless MEDIUM ACCESS CONTROL (MAC) and Physical Layer (PHY) Specifications for High Rate Wireless Personal Area Networks (WPANs), IEEE Standards Association Press."},{"key":"ref_11","unstructured":"IEEE P802.11ad (2012). Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications-Amendment 3: Enhancements for Very High Throughput in the 60 GHz Band, IEEE Standards Association Press."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6213","DOI":"10.1109\/TAP.2017.2734243","article-title":"Overview of millimeter wave communications for fifth-generation (5G) wireless networks-with a focus on propagation models","volume":"65","author":"Rappaport","year":"2017","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1654","DOI":"10.1109\/COMST.2018.2816920","article-title":"IEEE 802.11ay-based mmwave wlans: Design challenges and solutions","volume":"20","author":"Zhou","year":"2018","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1390","DOI":"10.1109\/JSAC.2009.091009","article-title":"Beam codebook-based beamforming protocol for multi-Gbps millimeter-wave WPAN systems","volume":"27","author":"Wang","year":"2009","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1109\/JSTSP.2014.2334278","article-title":"Channel estimation and hybrid precoding for millimeter wave cellular systems","volume":"8","author":"Alkhateeb","year":"2014","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1499","DOI":"10.1109\/TWC.2014.011714.130846","article-title":"Spatially sparse precoding in millimeter-wave MIMO systems","volume":"13","author":"Ayach","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1109\/MCOM.2015.7010533","article-title":"Large-scale antenna systems with hybrid analog and digital beamforming for millimeter wave 5G","volume":"53","author":"Han","year":"2015","journal-title":"IEEE Commun. Mag."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"6411","DOI":"10.1109\/TWC.2015.2455980","article-title":"Limited feedback hybrid precoding for multi-user millimeter wave systems","volume":"14","author":"Alkhateeb","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Li, N., Wei, Z., Geng, J., Sang, L., and Yang, D. (2014, January 2\u20135). Multiuser hybrid beamforming for max-min SINR problem under 60 GHz wireless channel. Proceedings of the IEEE 24th Annual International Symposium on Personal, Indoor, and Mobile Radio Communication (PIMRC), Washington, DC, USA,.","DOI":"10.1109\/PIMRC.2014.7136145"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2714","DOI":"10.1109\/TVT.2014.2346400","article-title":"MSE-based Hybrid RF\/Baseband processing for millimeter wave communication systems in mimo interference channels","volume":"64","author":"Kim","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1617","DOI":"10.1109\/COMST.2016.2532458","article-title":"Next generation 5G wireless networks: A comprehensive survey","volume":"18","author":"Agiwal","year":"2016","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1109\/JSAC.2016.2549418","article-title":"Energy-efficient hybrid analog and digital precoding for mmwave MIMO systems with large antenna arrays","volume":"34","author":"Gao","year":"2016","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_23","unstructured":"Capar, C., Hang, S., and Hui, D. (2015). Efficient Beam Selection for Hybrid Beamforming, IEEE Standards Association Press. IEEE 802.11-15\/1131r0."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1109\/MCOM.2014.6979963","article-title":"Millimeter wave MIMO precoding\/combining: Challenges and potential solutions","volume":"52","author":"Heath","year":"2014","journal-title":"IEEE Commun. Mag."},{"key":"ref_25","unstructured":"Chang, S.H., Taori, R., and Kim, T.Y. (2015). A view on IEEE 802.11ay. IEEE 802.11-15\/0636r0, IEEE Standards Association Press."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1109\/ACCESS.2013.2260813","article-title":"Millimeter wave mobile communications for 5G cellular: It will work!","volume":"1","author":"Rappaport","year":"2013","journal-title":"IEEE Access"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1109\/MCOM.2014.6894456","article-title":"Radio propagation path loss models for 5G cellular networks in the 28 GHz millimeter-wave bands","volume":"52","author":"Sulyman","year":"2014","journal-title":"IEEE Commun. Mag."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1924","DOI":"10.1109\/TVT.2007.897212","article-title":"Simplified spatial correlation models for clustered MIMO channels with different array configurations","volume":"56","author":"Forezna","year":"2007","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Perahia, E., and Stacey, R. (2013). Next Generation Wireless LANs, Cambridge University Press.","DOI":"10.1017\/CBO9781139061407"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Guo, Y., Li, L., Wen, X., Chen, W., and Han, Z. (2017, January 11\u201313). Sub-array based hybrid precoding design for downlink millimeter-wave multi-user massive MIMO systems. Proceedings of the IEEE International Conference on Wireless Communications and Signal Processing (WCSP), Nanjing, China.","DOI":"10.1109\/WCSP.2017.8171159"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/6\/786\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:58:08Z","timestamp":1760187488000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/6\/786"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,13]]},"references-count":30,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2019,6]]}},"alternative-id":["sym11060786"],"URL":"https:\/\/doi.org\/10.3390\/sym11060786","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,6,13]]}}}