{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:31:21Z","timestamp":1760239881982,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,1,29]],"date-time":"2019-01-29T00:00:00Z","timestamp":1548720000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF-2015R1A2A2A03004152"],"award-info":[{"award-number":["NRF-2015R1A2A2A03004152"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we study the connectivity of cognitive radio ad-hoc networks (CRAHNs) where primary users (PUs) and secondary users (SUs) are randomly distributed in a given area following a homogeneous Poisson process. Moreover, for the sake of more realistic CRAHNs, contrary to previous works in the literature, we consider the case that primary network is comprised of multiple communication pairs which are spatial-temporal distributed in the network area. We also take into consideration the differences in transmission range and interference range of both PUs and SUs. The connectivity of such CRAHN is studied from three viewpoints. First, we mathematically analyze the probability of isolated secondary transmitter and secondary receiver. Second, we derive the approximation expression of the link probability between two adjacent SUs. Third, we investigate the path connectivity between two arbitrary SUs by using the simulation analysis approach. The correctness of our mathematical expressions is confirmed by comparing analytical results with simulation results. The results in this paper provide insights into how multiple communication pairs in primary network affect the connectivity of secondary network, which can be useful guidelines for the design of CRAHNs.<\/jats:p>","DOI":"10.3390\/s19030565","type":"journal-article","created":{"date-parts":[[2019,1,29]],"date-time":"2019-01-29T11:27:52Z","timestamp":1548761272000},"page":"565","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Connectivity Analysis of Cognitive Radio Ad-Hoc Networks with Multi-Pair Primary Networks"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7297-7705","authenticated-orcid":false,"given":"Le","family":"The Dung","sequence":"first","affiliation":[{"name":"Department of Radio and Communication Engineering, Chungbuk National University, Cheongju City, Chungbuk 28644, Korea"}]},{"given":"Seong-Gon","family":"Choi","sequence":"additional","affiliation":[{"name":"Department of Radio and Communication Engineering, Chungbuk National University, Cheongju City, Chungbuk 28644, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,29]]},"reference":[{"unstructured":"Federal Communications Commission (2019, January 19). Spectrum Policy Task Force, Technical Report, Available online: https:\/\/transition.fcc.gov\/sptf\/files\/SEWGFinalReport_1.pdf.","key":"ref_1"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1109\/98.788210","article-title":"Cognitive radio: Making software radios more personal","volume":"6","author":"Mitola","year":"1999","journal-title":"IEEE Pers. Commun."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"810","DOI":"10.1016\/j.adhoc.2009.01.001","article-title":"Crahns: Cognitive radio ad hoc networks","volume":"7","author":"Akyildiz","year":"2009","journal-title":"Ad Hoc Netw."},{"key":"ref_4","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_5","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":"Wirel. Netw."},{"doi-asserted-by":"crossref","unstructured":"Zhou, X., Durrani, S., and Jones, H.M. (2008, January 15\u201317). Connectivity of ad hoc networks: Is fading good or bad?. Proceedings of the 2nd International Conference on Signal Processing and Communication Systems (ICSPCS 2008), Gold Coast, Australia.","key":"ref_6","DOI":"10.1109\/ICSPCS.2008.4813742"},{"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 (ICC), Seoul, Korea.","key":"ref_7"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5247","DOI":"10.1109\/TVT.2009.2026049","article-title":"Connectivity of wireless ad hoc networks with random beamforming","volume":"58","author":"Zhou","year":"2009","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1109\/LWC.2015.2421903","article-title":"Multihop connectivity of ad hoc networks with randomly oriented directional antennas","volume":"4","author":"Georgious","year":"2015","journal-title":"IEEE Wirel. Commun. Lett."},{"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 2013 International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT), Taipei, Taiwan.","key":"ref_10","DOI":"10.1109\/PDCAT.2013.53"},{"doi-asserted-by":"crossref","unstructured":"Cuomo, F., Abbagnale, A., and Gregorini, A. (2010, January 23\u201325). Impact of primary users on the connectivity of a cognitive radio network. Proceedings of the 9th IFIP Annual Mediterranean Ad Hoc Networking Workshop (Med-Hoc-Net), Juna-les-Pins, France.","key":"ref_11","DOI":"10.1109\/MEDHOCNET.2010.5546879"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4315","DOI":"10.1109\/TIT.2011.2145650","article-title":"Connectivity of heterogeneous wireless networks","volume":"57","author":"Ren","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_13","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 wireless networks","volume":"27","author":"Haenggi","year":"2009","journal-title":"IEEE J. Sel. Areas Commun."},{"unstructured":"Liu, J., Zhang, Q., Zhang, Y., Wei, Z., and Ma, S. (2013, January 7\u201310). Connectivity of two nodes in cognitive radio ad hoc networks. Proceedings of the 2013 IEEE Wireless Communications and Networking Conference (WCNC): Networks, Shanghai, China.","key":"ref_14"},{"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 2014 IEEE Global Communication Conference (GLOBECOM), Austin, TX, USA.","key":"ref_15","DOI":"10.1109\/GLOCOM.2014.7036952"},{"key":"ref_16","first-page":"3335","article-title":"Connectivity analysis of cognitive radio ad-hoc networks with shadowing","volume":"9","author":"Dung","year":"2015","journal-title":"KSII Trans. Internet Inf. Syst."},{"doi-asserted-by":"crossref","unstructured":"Wang, Y., Wang, Q., Dai, H.N., Wang, H., Zheng, Z., and Li, J. (2016, January 14\u201316). On Local Connectivity of Cognitive Radio Ad Hoc Networks with Directional Antennas. Proceedings of the 2016 IEEE Internal Conference on Communication System (ICCS), Shenzhen, China.","key":"ref_17","DOI":"10.1109\/ICCS.2016.7833577"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1743","DOI":"10.1007\/s11276-016-1252-9","article-title":"A modeling framework for supporting and evaluating connectivity in cognitive radio ad-hoc networks with beamforming","volume":"23","author":"Dung","year":"2017","journal-title":"Wirel. Netw."},{"doi-asserted-by":"crossref","unstructured":"Do, N.T., Dung, L.T., An, B., and Nam, S.-Y. (2016, January 27\u201330). Connectivity of hybrid overlay\/underlay cognitive radio ad hoc networks. Proceedings of the 2016 International Conference on Electronics, Information, and Communications (ICEIC),  Da Nang, Vietnam.","key":"ref_19","DOI":"10.1109\/ELINFOCOM.2016.7562945"},{"doi-asserted-by":"crossref","unstructured":"Kingman, J.F.C. (1993). Poisson Processes, Clarendon Press. [1st ed.].","key":"ref_20","DOI":"10.1093\/oso\/9780198536932.001.0001"},{"doi-asserted-by":"crossref","unstructured":"Karp, B., and Kung, H.T. (2000, January 6\u201311). GPSR: Greed Perimeter Stateless Routing for Wireless Networks. Proceedings of the 6th Annual International Conference on Mobile Computing and Networking (MobiCom \u201900), Boston, MA, USA.","key":"ref_21","DOI":"10.1145\/345910.345953"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.simpat.2016.09.003","article-title":"Simulation modeling and analysis of the hop count distribution in cognitive radio ad-hoc networks with shadow fading","volume":"69","author":"Dung","year":"2016","journal-title":"Simul. Model. Pract. Theory"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.simpat.2018.01.003","article-title":"Simulation modeling and analysis of the hop count distribution in cognitive radio ad-hoc networks with beamforming","volume":"84","author":"Dung","year":"2018","journal-title":"Simul. Model. Pract. Theory"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/3\/565\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:29:33Z","timestamp":1760185773000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/3\/565"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,29]]},"references-count":23,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["s19030565"],"URL":"https:\/\/doi.org\/10.3390\/s19030565","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,1,29]]}}}