{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:11:34Z","timestamp":1760235094462,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,7,20]],"date-time":"2021-07-20T00:00:00Z","timestamp":1626739200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["19-07-00933","20-07-01064"],"award-info":[{"award-number":["19-07-00933","20-07-01064"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Future Internet"],"abstract":"<jats:p>The 5G New Radio (NR) technology operating in millimeter wave (mmWave) frequency band is designed for support bandwidth-greedy applications requiring extraordinary rates at the access interface. However, the use of directional antenna radiation patterns, as well as extremely large path losses and blockage phenomenon, requires efficient algorithms to support these services. In this study, we consider the multi-layer virtual reality (VR) service that utilizes multicast capabilities for baseline layer and unicast transmissions for delivering an enhanced experience. By utilizing the tools of stochastic geometry and queuing theory we develop a simple algorithm allowing to estimate the deployment density of mmWave NR base stations (BS) supporting prescribed delivery guarantees. Our numerical results show that the highest gains of utilizing multicast service for distributing base layer is observed for high UE densities. Despite of its simplicity, the proposed multicast group formation scheme operates close to the state-of-the-art algorithms utilizing the widest beams with longest coverage distance in approximately 50\u201370% of cases when UE density is \u03bb\u22650.3. Among other parameters, QoS profile and UE density have a profound impact on the required density of NR BSs while the effect of blockers density is non-linear having the greatest impact on strict QoS profiles. Depending on the system and service parameters the required density of NR BSs may vary in the range of 20\u2013250 BS\/km2.<\/jats:p>","DOI":"10.3390\/fi13070185","type":"journal-article","created":{"date-parts":[[2021,7,20]],"date-time":"2021-07-20T05:10:59Z","timestamp":1626757859000},"page":"185","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Quantifying the Density of mmWave NR Deployments for Provisioning Multi-Layer VR Services"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1373-4014","authenticated-orcid":false,"given":"Vitalii","family":"Beschastnyi","sequence":"first","affiliation":[{"name":"Department of Applied Probability and Informatics, Peoples\u2019 Friendship University of Russia (RUDN University), 117198 Moscow, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2795-6251","authenticated-orcid":false,"given":"Daria","family":"Ostrikova","sequence":"additional","affiliation":[{"name":"Department of Applied Probability and Informatics, Peoples\u2019 Friendship University of Russia (RUDN University), 117198 Moscow, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7542-5228","authenticated-orcid":false,"given":"Roman","family":"Konyukhov","sequence":"additional","affiliation":[{"name":"Department of Applied Probability and Informatics, Peoples\u2019 Friendship University of Russia (RUDN University), 117198 Moscow, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1689-7345","authenticated-orcid":false,"given":"Elizaveta","family":"Golos","sequence":"additional","affiliation":[{"name":"Department of Applied Probability and Informatics, Peoples\u2019 Friendship University of Russia (RUDN University), 117198 Moscow, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0697-5207","authenticated-orcid":false,"given":"Alexander","family":"Chursin","sequence":"additional","affiliation":[{"name":"Department of Applied Economics, Peoples\u2019 Friendship University of Russia (RUDN University), 117198 Moscow, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4007-7187","authenticated-orcid":false,"given":"Dmitri","family":"Moltchanov","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology and Communication Sciences, Tampere University, 33720 Tampere, Finland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2655-4805","authenticated-orcid":false,"given":"Yuliya","family":"Gaidamaka","sequence":"additional","affiliation":[{"name":"Department of Applied Probability and Informatics, Peoples\u2019 Friendship University of Russia (RUDN University), 117198 Moscow, Russia"},{"name":"Federal Research Center \u201cComputer Science and Control\u201d of Russian Academy of Sciences, 119333 Moscow, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Holma, H., Toskala, A., and Nakamura, T. (2020). 5G Technology: 3GPP New Radio, John Wiley & Sons.","DOI":"10.1002\/9781119236306"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1109\/MCOMSTD.001.1800036","article-title":"5G new radio: Unveiling the essentials of the next generation wireless access technology","volume":"3","author":"Lin","year":"2019","journal-title":"IEEE Commun. Stand. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1109\/ACCESS.2020.3046773","article-title":"An overview of physical layer design for Ultra-Reliable Low-Latency Communications in 3GPP Releases 15, 16, and 17","volume":"9","author":"Le","year":"2020","journal-title":"IEEE Access"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Hoppari, M., Uitto, M., M\u00e4kel\u00e4, J., Harjula, I., and Rantala, S. (2021). Performance of the 5th Generation Indoor Wireless Technologies-Empirical Study. Future Internet, 13.","DOI":"10.3390\/fi13070180"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3421","DOI":"10.1109\/TWC.2020.2973375","article-title":"Characterizing Resource Allocation Trade-Offs in 5G NR Serving Multicast and Unicast Traffic","volume":"19","author":"Samuylov","year":"2020","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Karembai, A.K., Thompson, J., and Seeling, P. (2018). Towards Prediction of Immersive Virtual Reality Image Quality of Experience and Quality of Service. Future Internet, 10.","DOI":"10.3390\/fi10070063"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Nasrabadi, A.T., Mahzari, A., Beshay, J.D., and Prakash, R. (2017, January 18\u201322). Adaptive 360-degree video streaming using layered video coding. Proceedings of the 2017 IEEE Virtual Reality (VR), Los Angeles, CA, USA.","DOI":"10.1109\/VR.2017.7892319"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Long, K., Cui, Y., Ye, C., and Liu, Z. (2019, January 9\u201313). Optimal Transmission of Multi-Quality Tiled 360 VR Video by Exploiting Multicast Opportunities. Proceedings of the 2019 IEEE Global Communications Conference (GLOBECOM), Waikoloa, HI, USA.","DOI":"10.1109\/GLOBECOM38437.2019.9014280"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Park, J., Hwang, J., and Wei, H. (2018, January 9\u201313). Cross-Layer Optimization for VR Video Multicast Systems. Proceedings of the 2018 IEEE Global Communications Conference (GLOBECOM), Abu Dhabi, United Arab Emirates.","DOI":"10.1109\/GLOCOM.2018.8647389"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2491","DOI":"10.1109\/TCOMM.2020.2965527","article-title":"Taming the Latency in Multi-User VR 360\u00b0: A QoE-Aware Deep Learning-Aided Multicast Framework","volume":"68","author":"Perfecto","year":"2020","journal-title":"IEEE Trans. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hosseini, M., and Swaminathan, V. (2016, January 11\u201313). Adaptive 360 VR Video Streaming: Divide and Conquer. Proceedings of the IEEE International Symposium on Multimedia (ISM), San Jose, CA, USA.","DOI":"10.1109\/ISM.2016.0028"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"12239","DOI":"10.1109\/TVT.2019.2945987","article-title":"Toward Optimal Grouping and Resource Allocation for Multicast Streaming in LTE","volume":"68","author":"Zuhra","year":"2019","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Tran, T.X., and Yue, G. (2019, January 9\u201313). GRAB: Joint Adaptive Grouping and Beamforming for Multi-Group Multicast with Massive MIMO Networks. Proceedings of the IEEE Globecom Workshops (GC Wkshps), Waikoloa, HI, USA.","DOI":"10.1109\/GLOBECOM38437.2019.9013133"},{"key":"ref_14","unstructured":"3GPP (2021, May 25). Physical Channels and Modulation (Release 16), Available online: https:\/\/www.3gpp.org\/ftp\/Specs\/archive\/38_series\/38.211\/38211-g50.zip."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1791","DOI":"10.1109\/TWC.2017.2654351","article-title":"Interference and SINR in Millimeter Wave and Terahertz Communication Systems With Blocking and Directional Antennas","volume":"16","author":"Petrov","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1513","DOI":"10.1109\/TNET.2011.2122343","article-title":"Interference Analysis for Highly Directional 60-GHz Mesh Networks: The Case for Rethinking Medium Access Control","volume":"19","author":"Singh","year":"2011","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_17","unstructured":"Constantine, A.B. (2005). Antenna theory: Analysis and design. Microstrip Antennas, John Wiley & Sons."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3534","DOI":"10.1109\/TVT.2019.2896565","article-title":"Capacity of multiconnectivity mmWave systems with dynamic blockage and directional antennas","volume":"68","author":"Gerasimenko","year":"2019","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"144778","DOI":"10.1109\/ACCESS.2020.3013698","article-title":"A comprehensive survey of \u201cmetamaterial transmission-line based antennas: Design, challenges, and applications\u201d","volume":"8","author":"Alibakhshikenari","year":"2020","journal-title":"IEEE Access"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"192965","DOI":"10.1109\/ACCESS.2020.3032826","article-title":"A comprehensive survey on \u201cVarious decoupling mechanisms with focus on metamaterial and metasurface principles applicable to SAR and MIMO antenna systems\u201d","volume":"8","author":"Alibakhshikenari","year":"2020","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3922","DOI":"10.1002\/mop.32529","article-title":"A new class of wideband microstrip falcate patch antennas with reconfigurable capability at circular-polarization","volume":"62","author":"Shirkolaei","year":"2020","journal-title":"Microw. Opt. Technol. Lett."},{"key":"ref_22","first-page":"e22412","article-title":"Wideband linear microstrip array antenna with high efficiency and low side lobe level","volume":"30","year":"2020","journal-title":"Int. J. RF Microw. Comput. Aided Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"6653095","DOI":"10.1155\/2020\/6653095","article-title":"On-chip antenna design using the concepts of metamaterial and SIW principles applicable to terahertz integrated circuits operating over 0.6\u20130.622 THz","volume":"2020","author":"Althuwayb","year":"2020","journal-title":"Int. J. Antennas Propag."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1146","DOI":"10.1016\/j.adhoc.2012.02.005","article-title":"Distance distributions in random networks","volume":"10","author":"Moltchanov","year":"2012","journal-title":"Ad Hoc Netw."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"12345","DOI":"10.1109\/TVT.2019.2948702","article-title":"Quantifying the impact of guard capacity on session continuity in 3GPP new radio systems","volume":"68","author":"Begishev","year":"2019","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2657","DOI":"10.1109\/TVT.2021.3061906","article-title":"Joint Use of Guard Capacity and Multiconnectivity for Improved Session Continuity in Millimeter-Wave 5G NR Systems","volume":"70","author":"Begishev","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"10124","DOI":"10.1109\/TVT.2017.2754543","article-title":"On the temporal effects of mobile blockers in urban millimeter-wave cellular scenarios","volume":"66","author":"Gapeyenko","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Samuylov, A., Beschastnyi, V., Moltchanov, D., Ostrikova, D., Gaidamaka, Y., and Shorgin, V. (2019, January 8\u201311). Modeling Coexistence of Unicast and Multicast Communications in 5G New Radio Systems. Proceedings of the 2019 IEEE 30th Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), Istanbul, Turkey.","DOI":"10.1109\/PIMRC.2019.8904350"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1109\/LCOMM.2013.011513.122519","article-title":"An incremental multicast grouping scheme for mmWave networks with directional antennas","volume":"17","author":"Park","year":"2013","journal-title":"IEEE Commun. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1049\/el.2011.3429","article-title":"Efficient clustering scheme for OFDMA-based multicast wireless systems using grouping genetic algorithm","volume":"48","author":"Tan","year":"2012","journal-title":"Electron. Lett."},{"key":"ref_31","first-page":"48","article-title":"Resource queuing systems as models of wireless communication systems","volume":"12","author":"Gorbunova","year":"2018","journal-title":"Inform. Primen."},{"key":"ref_32","unstructured":"Khintchine, A.Y. (1960). Mathematical Methods in the Theory of Queueing, Griffin."}],"container-title":["Future Internet"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-5903\/13\/7\/185\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:32:06Z","timestamp":1760164326000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-5903\/13\/7\/185"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,20]]},"references-count":32,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["fi13070185"],"URL":"https:\/\/doi.org\/10.3390\/fi13070185","relation":{},"ISSN":["1999-5903"],"issn-type":[{"type":"electronic","value":"1999-5903"}],"subject":[],"published":{"date-parts":[[2021,7,20]]}}}