{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T11:09:43Z","timestamp":1771844983946,"version":"3.50.1"},"reference-count":56,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,1,12]],"date-time":"2017-01-12T00:00:00Z","timestamp":1484179200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006469","name":"Macao Science and Technology Development Fund","doi-asserted-by":"publisher","award":["096\/2013\/A3"],"award-info":[{"award-number":["096\/2013\/A3"]}],"id":[{"id":"10.13039\/501100006469","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61472338"],"award-info":[{"award-number":["61472338"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program","doi-asserted-by":"publisher","award":["2016YFB1000101"],"award-info":[{"award-number":["2016YFB1000101"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"International Scientific Partnership Program ISPP at King Saud University","award":["ISPP# 0033"],"award-info":[{"award-number":["ISPP# 0033"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we investigate the network connectivity of wireless sensor networks with directional antennas. In particular, we establish a general framework to analyze the network connectivity while considering various antenna models and the channel randomness. Since existing directional antenna models have their pros and cons in the accuracy of reflecting realistic antennas and the computational complexity, we propose a new analytical directional antenna model called the iris model to balance the accuracy against the complexity. We conduct extensive simulations to evaluate the analytical framework. Our results show that our proposed analytical model on the network connectivity is accurate, and our iris antenna model can provide a better approximation to realistic directional antennas than other existing antenna models.<\/jats:p>","DOI":"10.3390\/s17010134","type":"journal-article","created":{"date-parts":[[2017,1,12]],"date-time":"2017-01-12T10:02:08Z","timestamp":1484215328000},"page":"134","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["On Connectivity of Wireless Sensor Networks with Directional Antennas"],"prefix":"10.3390","volume":"17","author":[{"given":"Qiu","family":"Wang","sequence":"first","affiliation":[{"name":"Faculty of Information Technology, Macau University of Science and Technology, Macau, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6165-4196","authenticated-orcid":false,"given":"Hong-Ning","family":"Dai","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, Macau University of Science and Technology, Macau, China"}]},{"given":"Zibin","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Data and Computer Science, Sun Yat-Sen University, Guangzhou 510006, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6946-2591","authenticated-orcid":false,"given":"Muhammad","family":"Imran","sequence":"additional","affiliation":[{"name":"College of Computer and Information Sciences, King Saud University, Riyadh 12372, Saudi Arabia"}]},{"given":"Athanasios","family":"Vasilakos","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Electrical and Space Engineering, Lulea University of Technology, Lule\u00e5 971 87, Sweden"}]}],"member":"1968","published-online":{"date-parts":[[2017,1,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1109\/TNET.2005.845546","article-title":"Impact of interferences on connectivity in ad-hoc networks","volume":"13","author":"Dousse","year":"2005","journal-title":"IEEE\/ACM Trans. Netw. Inf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1093\/comjnl\/47.4.432","article-title":"On the Connectivity of Ad Hoc Networks","volume":"47","author":"Bettstetter","year":"2004","journal-title":"Comput. J."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zhang, J., and Jia, X. (2009, January 19\u201325). Capacity analysis of wireless mesh networks with omni or directional antennas. Proceedings of the IEEE INFOCOM (Mini-Conference), Rio de Janeiro, Brazil.","DOI":"10.1109\/INFCOM.2009.5062251"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Dai, H.N., Ng, K.W., Wong, R.C.W., and Wu, M.Y. (2008, January 13\u201318). On the Capacity of Multi-Channel Wireless Networks Using Directional Antennas. Proceedings of the 27th Conference on Computer Communications INFOCOM 2008, Phoenix, AZ, USA.","DOI":"10.1109\/INFOCOM.2007.112"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Dai, H.N. (2009, January 7\u201310). Throughput and Delay in Wireless Sensor Networks using Directional Antennas. Proceedings of the Fifth International Conference on Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP), Melbourne, Australia.","DOI":"10.1109\/ISSNIP.2009.5416826"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Min, B.C., Matson, E.T., and Khaday, B. (2013, January 21\u201326). Design of a Networked Robotic System Capable of Enhancing Wireless Communication Capabilities. Proceedings of the 2013 IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR), Link\u00f6ping, Sweden.","DOI":"10.1109\/SSRR.2013.6719347"},{"key":"ref_7","unstructured":"Georgiou, O., Wang, S., Bocus, M.Z., Dettmann, C.P., and Coon, J.P. (September, January 30). Directional antennas improve the link-connectivity of interference limited ad hoc networks. Proceedings of the 26th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), Hong Kong, China."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Min, B.C., Matson, E.T., and Jung, J.W. (2015). Active Antenna Tracking System with Directional Antennas for Enhancing Wireless Communication Capabilities of a Networked Robotic System. J. Field Robot.","DOI":"10.1002\/rob.21602"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1109\/JPROC.2014.2299397","article-title":"Millimeter Wave Cellular Wireless Networks: Potentials and Challenges","volume":"102","author":"Rangan","year":"2014","journal-title":"Proc. IEEE"},{"key":"ref_10","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_11","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":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_12","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 Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"6939","DOI":"10.1109\/TWC.2016.2594067","article-title":"Directional Radio Propagation Path Loss Models for Millimeter-Wave Wireless Networks in the 28-, 60-, and 73-GHz Bands","volume":"15","author":"Sulyman","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1109\/MCOM.2014.6979964","article-title":"IEEE 802.11ad: Directional 60 GHz communication for multi-Gigabit-per-second Wi-Fi","volume":"52","author":"Nitsche","year":"2014","journal-title":"IEEE Commun. Mag."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Saha, S.K., Vira, V.V., Garg, A., and Koutsonikolas, D. (2016, January 22\u201327). Multi-Gigabit indoor WLANs: Looking beyond 2.4\/5 GHz. Proceedings of the IEEE International Conference on Communications (ICC), Kuala Lumpur, Malaysia.","DOI":"10.1109\/ICC.2016.7511031"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2252","DOI":"10.1016\/j.adhoc.2013.04.016","article-title":"Heuristic optimization techniques for self-orientation of directional antennas in long-distance point-to-point broadband networks","volume":"11","author":"Min","year":"2013","journal-title":"J. Ad Hoc Netw."},{"key":"ref_17","unstructured":"Min, B.C., and Matson, E.T. (2014). Robot Intelligence Technology and Applications 2, Springer."},{"key":"ref_18","first-page":"496","article-title":"Ad Hoc Networking With Directional Antennas: A Complete System Solution","volume":"23","author":"Ramanathan","year":"2005","journal-title":"IEEE JSAC"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5247","DOI":"10.1109\/TVT.2009.2026049","article-title":"Connectivity Analysis of Wireless Ad Hoc Networks with Beamforming","volume":"58","author":"Zhou","year":"2009","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Kiese, M., Hartmann, C., and Vilzmann, R. (December, January 30). Optimality Bounds of the Connectivity of Adhoc Networks with Beamforming Antennas. Proceedings of the IEEE GLOBECOM 2009\u20142009 IEEE Global Telecommunications Conference, Honolulu, HI, USA.","DOI":"10.1109\/GLOCOM.2009.5425735"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Chau, C.K., Gibbens, R.J., and Towsley, D. (2012, January 25\u201330). Impact of directional transmission in large-scale multi-hop wireless ad hoc networks. Proceedings of the 2012 IEEE INFOCOM, Orlando, FL, USA.","DOI":"10.1109\/INFCOM.2012.6195793"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1007\/s11277-013-1206-9","article-title":"On Busy-Tone Based MAC Protocol for Wireless Networks with Directional Antennas","volume":"73","author":"Dai","year":"2013","journal-title":"Wirel. Pers. Commun."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1109\/LCOMM.2013.020513.121529","article-title":"SPARM: Spatially Pipelined ACK Aggregation for Reliable Multicast in Directional MAC","volume":"17","author":"Park","year":"2013","journal-title":"IEEE Commun. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Yuan, X., Li, C., Song, Y., Yang, L., and Ullah, S. (2015, January 6\u201310). On Energy-Saving in E-Healthcare: A Directional MAC Protocol for WBAN. Proceedings of the 2015 IEEE Globecom Workshops (GC Wkshps), San Diego, CA, USA.","DOI":"10.1109\/GLOCOMW.2015.7414214"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wang, P., and Petrova, M. (2016, January 23\u201327). Cross Talk MAC: A Directional MAC Scheme for Enhancing Frame Aggregation in mm-Wave Wireless Personal Area Networks. Proceedings of the 2016 IEEE International Conference on Communications Workshops (ICC), Kuala Lumpur, Malaysia.","DOI":"10.1109\/ICCW.2016.7503853"},{"key":"ref_26","first-page":"1","article-title":"On the delay reduction of wireless ad hoc networks with directional antennas","volume":"2015","author":"Dai","year":"2015","journal-title":"EURASIP J. Wirel. Commun. Network."},{"key":"ref_27","unstructured":"Renzo, M.D. (2015, January 8\u201312). Stochastic Geometry Modeling and Performance Evaluation of mmWave Cellular Communications. Proceedings of the 2015 IEEE International Conference on Communications (ICC), London, UK."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1374","DOI":"10.1109\/TMC.2010.243","article-title":"The Capacity of Wireless Ad Hoc Networks Using Directional Antennas","volume":"10","author":"Li","year":"2011","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_29","unstructured":"Gupta, P., and Kumar, P.R. (1998). Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W. H. Fleming, Birkh\u00e4user."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1007\/s11276-005-3513-x","article-title":"Connectivity of Wireless Multihop Networks in a Shadow Fading Environment","volume":"11","author":"Bettstetter","year":"2005","journal-title":"ACM Wirel. Netw."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1062","DOI":"10.1109\/TWC.2007.060842","article-title":"The Impact of Channel Randomness on Coverage and Connectivity of Ad Hoc and Sensor Networks","volume":"7","author":"Miorandi","year":"2008","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1016\/j.jnca.2011.11.016","article-title":"A survey on coverage and connectivity issues in wireless sensor networks","volume":"35","author":"Zhu","year":"2012","journal-title":"J. Netw. Comput. Appl."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Zhai, D., Sheng, M., Wang, X., and Zhang, Y. (2014, January 8\u201312). Local Connectivity of Cognitive Radio Ad Hoc Networks. Proceedings of the IEEE Global Communications Conference (GLOBECOM), Austin, TX, USA.","DOI":"10.1109\/GLOCOM.2014.7036952"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1002\/dac.1348","article-title":"An Overview of Using Directional Antennas in Wireless Networks","volume":"26","author":"Dai","year":"2013","journal-title":"Int. J. Commun. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Dai, H.N., Wang, Q., Li, D., and Wong, R.C.W. (2013). On Eavesdropping Attacks in Wireless Sensor Networks with Directional Antennas. Int. J. Distrib. Sens. Netw., 2013.","DOI":"10.1155\/2013\/760834"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.jocs.2014.10.006","article-title":"On Modeling Eavesdropping Attacks in Wireless Networks","volume":"11","author":"Li","year":"2015","journal-title":"J. Comput. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"4415","DOI":"10.1109\/TAP.2016.2593738","article-title":"APRD-MUSIC Algorithm DOA Estimation for Reactance Based Uniform Circular Array","volume":"64","author":"Basikolo","year":"2016","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_38","unstructured":"Bettstetter, C., Hartmann, C., and Moser, C. (2005, January 16\u201320). How does randomized beamforming improve the connectivity of ad hoc networks. Proceedings of the 2005 IEEE International Conference on Communications, Seoul, Korea."},{"key":"ref_39","unstructured":"Zhou, X., Jones, H.M., Durrani, S., and Scott, A. (2007, January 5\u20137). Effect of Beamforming on the Connectivity of Ad Hoc Networks. Proceedings of the Australian Communications Theory Workshop (AusCTW), Adelaide, Australia."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1106","DOI":"10.1109\/TNET.2008.2006224","article-title":"Asymptotic Connectivity in Wireless Ad Hoc Networks Using Directional Antenna","volume":"17","author":"Li","year":"2009","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Xu, H., Dai, H.N., and Zhao, Q. (2012, January 12\u201314). On the Connectivity of Wireless Networks with Multiple Directional Antennas. Proceedings of the 18th IEEE International Conference on Networks (ICON), Singapore.","DOI":"10.1109\/ICON.2012.6506551"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1109\/LCOMM.2014.2332334","article-title":"Millimeter Wave Communications With Symmetric Uniform Circular Antenna Arrays","volume":"18","author":"Wang","year":"2014","journal-title":"IEEE Commun. Lett."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Wang, Q., Dai, H.N., and Zhao, Q. (2013, January 16\u201318). Connectivity of Wireless Ad Hoc Networks: Impacts of Antenna Models. Proceedings of the 14th International Conference on Parallel and Distributed Computing, Applications and Technologies, Taipei, Taiwan.","DOI":"10.1109\/PDCAT.2013.53"},{"key":"ref_44","unstructured":"Balanis, C.A. (2005). Antenna Theory: Analysis and Design, John Wiley & Sons. [3rd ed.]."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1109\/TAP.2014.2384044","article-title":"Direction of Arrival Estimation Using Directive Antennas in Uniform Circular Arrays","volume":"63","author":"Jackson","year":"2015","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"3899","DOI":"10.1109\/TWC.2015.2414413","article-title":"Massive MIMO Performance Evaluation Based on Measured Propagation Data","volume":"14","author":"Gao","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1109\/LCOMM.2015.2401570","article-title":"Deployment Optimization of Uniform Linear Antenna Arrays for a Two-Path Millimeter Wave Communication System","volume":"19","author":"Cai","year":"2015","journal-title":"IEEE Commun. Lett."},{"key":"ref_48","unstructured":"Goldsmith, A. (2005). Wireless Communication, Cambridge University Press."},{"key":"ref_49","unstructured":"Rappaport, T.S. (2002). Wireless Communications: Principles and Practice, Prentice Hall PTR. [2nd ed.]."},{"key":"ref_50","unstructured":"Wackerly, D.D., Mendenhall, W., and Scheaffer, R.L. (2007). Mathematical Statistics With Applications, Cengage Learning."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1016\/j.inffus.2016.09.005","article-title":"Multi-Sensor Fusion in Body Sensor Networks: State-of-the-art and research challenges","volume":"35","author":"Gravina","year":"2016","journal-title":"Inf. Fusion"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1109\/TSMCC.2012.2215852","article-title":"Enabling Effective Programming and Flexible Management of Efficient Body Sensor Network Applications","volume":"43","author":"Fortino","year":"2013","journal-title":"IEEE Trans. Hum.-Mach. Syst."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"8538","DOI":"10.1109\/TVT.2015.2509861","article-title":"Decentralized Time-Synchronized Channel Swapping for Ad Hoc Wireless Networks","volume":"65","author":"Smart","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.inffus.2014.03.005","article-title":"A framework for collaborative computing and multi-sensor data fusion in body sensor networks","volume":"22","author":"Fortino","year":"2014","journal-title":"Inf. Fusion"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Dong, J., and Smith, D. (2014, January 10\u201314). Joint relay selection and transmit power control for wireless body area networks coexistence. Proceedings of the 2014 IEEE International Conference on Communications (ICC), Sydney, Australia.","DOI":"10.1109\/ICC.2014.6884226"},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Ding, J., Dutkiewicz, E., Huang, X., and Fang, G. (2015, January 11\u201314). Energy-Efficient Distributed Beamforming in UWB Based Implant Body Area Networks. Proceedings of the 2015 IEEE 81st Vehicular Technology Conference (VTC Spring), Glasgow, UK.","DOI":"10.1109\/VTCSpring.2015.7145813"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/1\/134\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:26:01Z","timestamp":1760207161000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/1\/134"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,12]]},"references-count":56,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1]]}},"alternative-id":["s17010134"],"URL":"https:\/\/doi.org\/10.3390\/s17010134","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1,12]]}}}