{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:48:14Z","timestamp":1740149294502,"version":"3.37.3"},"reference-count":57,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,1,12]],"date-time":"2018-01-12T00:00:00Z","timestamp":1515715200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research Foundation of Korea (NRF) funded by the Ministry of Education","award":["2016R1D1A1B03930060"]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"As an intrinsic part of the Internet of Things (IoT) ecosystem, machine-to-machine (M2M) communications are expected to provide ubiquitous connectivity between machines. Millimeter-wave (mmWave) communication is another promising technology for the future communication systems to alleviate the pressure of scarce spectrum resources. For this reason, in this paper, we consider multi-hop M2M communications, where a machine-type communication (MTC) device with the limited transmit power relays to help other devices using mmWave. To be specific, we focus on hop distance statistics and their impacts on system performances in multi-hop wireless networks (MWNs) with directional antenna arrays in mmWave for M2M communications. Different from microwave systems, in mmWave communications, wireless channel suffers from blockage by obstacles that heavily attenuate line-of-sight signals, which may result in limited per-hop progress in MWNs. We consider two routing strategies aiming at different types of applications and derive the probability distributions of their hop distances. Moreover, we provide their baseline statistics assuming the blockage-free scenario to quantify the impact of blockages. Based on the hop distance analysis, we propose a method to estimate the end-to-end performances (e.g., outage probability, hop count, and transmit energy) of the mmWave MWNs, which provides important insights into mmWave MWN design without time-consuming and repetitive end-to-end simulation.<\/jats:p>","DOI":"10.3390\/s18010204","type":"journal-article","created":{"date-parts":[[2018,1,15]],"date-time":"2018-01-15T09:01:55Z","timestamp":1516006915000},"page":"204","source":"Crossref","is-referenced-by-count":10,"title":["Performance Analysis of Millimeter-Wave Multi-hop Machine-to-Machine Networks Based on Hop Distance Statistics"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1901-2784","authenticated-orcid":false,"given":"Haejoon","family":"Jung","sequence":"first","affiliation":[{"name":"Department of Information and Telecommunication Engineering, Incheon National University, Incheon 22012, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2104-9781","authenticated-orcid":false,"given":"In-Ho","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Electrical, Electronic and Control Engineering, Hankyong National University, Anseong 17579, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1172","DOI":"10.1109\/JSYST.2014.2298837","article-title":"Intelligent device-to-device communication in the internet of things","volume":"10","author":"Bello","year":"2016","journal-title":"IEEE Syst. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1109\/MCOM.2015.7158273","article-title":"Cognitive vehicular communication for 5G","volume":"53","author":"Mumtaz","year":"2015","journal-title":"IEEE Commun. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1109\/JSAC.2016.2525418","article-title":"Internet of Things in the 5G era: Enablers, architecture, and business models","volume":"34","author":"Palattella","year":"2016","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/MCOM.2014.6736748","article-title":"Networks and devices for the 5G era","volume":"52","author":"Bangerter","year":"2014","journal-title":"IEEE Commun. Mag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1109\/MCOM.2012.6231296","article-title":"Radio resource allocation in LTE-advanced cellular networks with M2M communications","volume":"50","author":"Zheng","year":"2012","journal-title":"IEEE Commun. Mag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1109\/JIOT.2015.2390775","article-title":"Cognitive Machine-to-Machine Communications for Internet-of-Things: A Protocol Stack Perspective","volume":"2","author":"Aijaz","year":"2015","journal-title":"IEEE Internet Things J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.jnca.2016.02.016","article-title":"Machine-to-Machine (M2M) communications: A survey","volume":"66","author":"Verma","year":"2016","journal-title":"J. Netw. Comput. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.adhoc.2013.03.007","article-title":"Machine-to-machine communicatiofns: Technologies and challenges","volume":"18","author":"Chen","year":"2014","journal-title":"Ad Hoc Netw."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Vullers, R.J.M., Schaihk, R.V., Visser, H.J., Penders, J., and Hoof, C.V. (2010). Energy Harvesting for Autonomous Wireless Sensor Networks. IEEE Solid State Circuits Mag., 29\u201338.","DOI":"10.1109\/MSSC.2010.936667"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1109\/SURV.2013.110113.00249","article-title":"A Survey of Recent Developments in Home M2M Networks","volume":"16","author":"Chen","year":"2014","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"9628565","DOI":"10.1155\/2017\/9628565","article-title":"Performance analysis of three-dimensional clustered device-to-device networks for Internet of things","volume":"2017","author":"Jung","year":"2017","journal-title":"Wirel. Commun. Mob. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1801","DOI":"10.1109\/COMST.2014.2319555","article-title":"A Survey on Device-to-Device Communication in Cellular Networks","volume":"16","author":"Asadi","year":"2014","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.1109\/TWC.2005.850376","article-title":"On routing in random Rayleigh fading networks","volume":"4","author":"Haenggi","year":"2005","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1109\/MCOM.2005.1522131","article-title":"Routing in ad hoc networks: A case for long hops","volume":"43","author":"Haenggi","year":"2005","journal-title":"IEEE Commun. Mag."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1109\/TWC.2013.112613.130093","article-title":"Multi-packet opportunistic large array transmission on strip-shaped cooperative routes or networks","volume":"13","author":"Jung","year":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_16","unstructured":"Jung, H., and Weitnauer, M.A. (2012, January 10\u201315). Analysis of intra-flow interference in opportunistic large array transmission for strip networks. Proceedings of the 2012 IEEE International Conference on Communications (ICC), Ottawa, ON, Canada."},{"key":"ref_17","unstructured":"Bettstetter, C., and Eberspacher, J. (2003, January 22\u201325). Hop distances in homogeneous ad hoc networks. Proceedings of the 2003 Vehicular Technology Conference, Jeju, Korea."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1109\/MNET.2002.1020231","article-title":"Scalable routing protocols for mobile ad hoc networks","volume":"16","author":"Hong","year":"2002","journal-title":"IEEE Netw."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1109\/MCOM.2015.7010536","article-title":"Enabling device-to-device communications in millimeter-wave 5G cellular networks","volume":"53","author":"Qiao","year":"2015","journal-title":"IEEE Commun. Mag."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1997","DOI":"10.1109\/LCOMM.2015.2475428","article-title":"Outage probability for multi-hop d2d communications with shortest path routing","volume":"19","author":"Wang","year":"2015","journal-title":"IEEE Commun. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1109\/JSAC.2014.2328098","article-title":"What will 5G be?","volume":"32","author":"Andrews","year":"2014","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1109\/MVT.2015.2496240","article-title":"Massive MIMO and mmWave for 5G wireless HetNet: Potential benefits and challenges","volume":"11","author":"Bogale","year":"2016","journal-title":"IEEE Veh. Technol. Mag."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1109\/MCOM.2014.6736746","article-title":"Five disruptive technology directions for 5G","volume":"52","author":"Boccardi","year":"2014","journal-title":"IEEE Commun. Mag."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1109\/MCOM.2014.6736752","article-title":"Cellular architecture and key technologies for 5G wireless communication networks","volume":"52","author":"Wang","year":"2014","journal-title":"IEEE Commun. Mag."},{"key":"ref_25","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_26","doi-asserted-by":"crossref","first-page":"4391","DOI":"10.1109\/TCOMM.2013.090513.120848","article-title":"Millimeter wave beamforming for wireless backhaul and access in small cell networks","volume":"61","author":"Hur","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1109\/MCOM.2011.5783993","article-title":"An introduction to millimeter-wave mobile broadband systems","volume":"49","author":"Pi","year":"2011","journal-title":"IEEE Commun. Mag."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/MNET.2014.6963798","article-title":"5G wireless backhaul networks: Challenges and research advances","volume":"28","author":"Ge","year":"2014","journal-title":"IEEE Netw."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"5070","DOI":"10.1109\/TWC.2014.2331971","article-title":"Analysis of blockage effects on urban cellular networks","volume":"13","author":"Bai","year":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1100","DOI":"10.1109\/TWC.2014.2364267","article-title":"Coverage and rate analysis for millimeter-wave cellular networks","volume":"14","author":"Bai","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4065","DOI":"10.1109\/TSP.2016.2551690","article-title":"Performance analysis of outdoor mmwave ad hoc networks","volume":"64","author":"Thornburg","year":"2016","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1109\/JSAC.2009.090902","article-title":"Stochastic geometry and random graphs for the analysis and design of wireless networks","volume":"27","author":"Haenggi","year":"2009","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"762","DOI":"10.1109\/49.56383","article-title":"Optimum transmission range in a direct-sequence spread spectrum multihop packet radio network","volume":"8","author":"Sousa","year":"1990","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"5058","DOI":"10.1109\/T-WC.2008.071047","article-title":"Transmission capacity of ad hoc networks with spatial diversity","volume":"7","author":"Hunter","year":"2008","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1078","DOI":"10.1109\/JSAC.2009.090906","article-title":"On unbounded path-loss models: Effects of singularity on wireless network performance","volume":"27","author":"Inaltekin","year":"2009","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2602","DOI":"10.1109\/TCOMM.2012.071312.110730","article-title":"Random power control in Poisson networks","volume":"60","author":"Zhang","year":"2012","journal-title":"IEEE Trans. Commun."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1776","DOI":"10.1109\/TVT.2008.2003960","article-title":"Interference analysis in a Poisson field of nodes of finite area","volume":"58","author":"Salbaroli","year":"2009","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1109\/COMST.2016.2624939","article-title":"Modeling and analysis of cellular networks using stochastic geometry: A tutorial","volume":"19","author":"ElSawy","year":"2017","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Mudumbai, R., Singh, S.K., and Madhow, U. (2009, January 19\u201325). Medium access control for 60 GHz outdoor mesh networks with highly directional links. Proceedings of the IEEE INFOCOM 2009, Rio de Janeiro, Brazil.","DOI":"10.1109\/INFCOM.2009.5062249"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Perkins, C.E., Belding-Royer, E.M., and Das, S.R. (2003). Ad Hoc on-Demand Distance Vector (AODV) Routing, The Internet Society. Published Online, Internet Engineering Task Force, RFC Experimental 3561.","DOI":"10.17487\/rfc3561"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1109\/TMC.2007.1068","article-title":"A cross-layer framework for exploiting virtual MISO links in mobile ad hoc networks","volume":"6","author":"Jakllari","year":"2007","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Shokri-Ghadikolaei, H., and Fischione, C. (2015, January 6\u201310). Millimeter wave ad hoc networks: Noise-limited or interference-limited?. Proceedings of the 2015 IEEE Globecom Workshops (GC Wkshps), San Diego, CA, USA.","DOI":"10.1109\/GLOCOMW.2015.7414085"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1109\/TCOM.1986.1096436","article-title":"Transmission Range Control in Multihop Packet Radio Networks","volume":"34","author":"Hou","year":"1986","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1653","DOI":"10.1109\/LCOMM.2014.2337293","article-title":"On the macro diversity with multiple BSs to mitigate blockage in millimeter-wave communications","volume":"18","author":"Choi","year":"2014","journal-title":"IEEE Commun. Lett."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"2268","DOI":"10.1109\/LCOMM.2016.2598143","article-title":"Outage analysis of millimeter-wave wireless backhaul in the presence of blockage","volume":"20","author":"Jung","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"4519365","DOI":"10.1155\/2017\/4519365","article-title":"Outage analysis of multihop wireless backhaul using millimeter wave under blockage effects","volume":"2017","author":"Jung","year":"2017","journal-title":"Int. J. Antennas Propag."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"7939671","DOI":"10.1155\/2016\/7939671","article-title":"Connectivity analysis of millimeter-wave device-to-device networks with blockage","volume":"2016","author":"Jung","year":"2016","journal-title":"Int. J. Antennas Propag."},{"key":"ref_48","unstructured":"Browni, M. (1972). Statistical Analysis of Non-Homogeneous Poisson Processes, Wiley-Interscience Stochastic Point Processes."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1109\/JSAC.2007.070209","article-title":"Joint optimization of relay strategies and resource allocations in cooperative cellular networks","volume":"25","author":"Ng","year":"2007","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Wang, B., Han, Z., and Liu, K.J.R. (2007, January 6\u201312). Distributed Relay Selection and Power Control for Multiuser Cooperative Communication Networks Using Buyer\/Seller Game. Proceedings of the IEEE INFOCOM 2007 26th IEEE International Conference on Computer Communications, Barcelona, Spain.","DOI":"10.1109\/INFCOM.2007.70"},{"key":"ref_51","unstructured":"Crofton, M. (1885). Probability, in Encyclopedia Britannica, Britannica Inc.. [9th ed.]."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"3518","DOI":"10.1109\/TCOMM.2013.053013.130031","article-title":"On the Energy Delay Tradeoff of HARQ-IR in Wireless Multiuser Systems","volume":"61","author":"Choi","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1736","DOI":"10.1109\/SURV.2012.121912.00052","article-title":"Energy-Aware Cooperative Content Distribution over Wireless Networks: Design Alternatives and Implementation Aspects","volume":"15","author":"Dawy","year":"2013","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/j.comnet.2005.05.009","article-title":"Cooperative multi-hop transmission in wireless networks","volume":"49","author":"Herhold","year":"2005","journal-title":"Comput. Netw."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1109\/TVT.2016.2536686","article-title":"Aggregated Packet Transmission in Duty-Cycled WSNs: Modeling and Performance Evaluation","volume":"66","author":"Guntupalli","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"3413","DOI":"10.1109\/TCOMM.2013.052013.120707","article-title":"On Using Cooperative Routing for Lifetime Optimization of Multi-Hop Wireless Sensor Networks: Analysis and Guidelines","volume":"61","author":"Jung","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Owen, A.B. (2004). Empirical Likelihood, John Wiley & Sons.","DOI":"10.1002\/0471667196.ess0629"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/1\/204\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,9]],"date-time":"2024-06-09T13:48:32Z","timestamp":1717940912000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/1\/204"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,12]]},"references-count":57,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1]]}},"alternative-id":["s18010204"],"URL":"https:\/\/doi.org\/10.3390\/s18010204","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2018,1,12]]}}}