{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:48:48Z","timestamp":1760240928401,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2019,10,16]],"date-time":"2019-10-16T00:00:00Z","timestamp":1571184000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61771410;61601383"],"award-info":[{"award-number":["61771410;61601383"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Sichuan Science and Technology Program","award":["2018GZ0095"],"award-info":[{"award-number":["2018GZ0095"]}]},{"name":"SoutWest University of Science and Technology research fund","award":["18zx7144"],"award-info":[{"award-number":["18zx7144"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The multi-hop cognitive radio network (CRN) has attracted much attention in industry and academia because of its seamless wireless coverage by forming multi-hop links and high spectrum utilization of cognitive radio (CR) technology. Using multi-slot statistical spectrum status information (SSI), this work investigates the average spectrum efficiency (SE) of a multi-radio multi-hop (MRMH) CRN where each hop is permitted to use different spectra and long-distance hops can reuse the same idle primary user (PU) spectrum. Faced with the modeled SE problem, which is a complex non-convex fractional mixed integer nonlinear programming (MINLP) problem, the optimal spectrum and power allocation for multi-hop links in multi-slot and multi-channel scenarios can be obtained with the proposed successive multi-step convex approximation scheme (SMCA). As shown through computational complexity and simulation analysis, SMCA can obtain an approximate lower bound of the optimal solution for the modeled SE problem with a lower computational cost. Furthermore, some potential relationships between network performance and spectrum idle rate can be easily discussed with SMCA, which can provide some sensible deployment strategies for the MRMH CRN in future multi-slot scenarios.<\/jats:p>","DOI":"10.3390\/s19204493","type":"journal-article","created":{"date-parts":[[2019,10,17]],"date-time":"2019-10-17T04:46:06Z","timestamp":1571287566000},"page":"4493","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Spectrum-Efficient Resource Allocation in Multi-Radio Multi-Hop Cognitive Radio Networks"],"prefix":"10.3390","volume":"19","author":[{"given":"Bin","family":"Han","sequence":"first","affiliation":[{"name":"Network and Communication Research Institute, College of Information Engineering, SouthWest University of Science and Technology, Mianyang 621010, Sichuan Province, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Luo","sequence":"additional","affiliation":[{"name":"Network and Communication Research Institute, College of Information Engineering, SouthWest University of Science and Technology, Mianyang 621010, Sichuan Province, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Min","family":"Zeng","sequence":"additional","affiliation":[{"name":"Network and Communication Research Institute, College of Information Engineering, SouthWest University of Science and Technology, Mianyang 621010, Sichuan Province, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hong","family":"Jiang","sequence":"additional","affiliation":[{"name":"Network and Communication Research Institute, College of Information Engineering, SouthWest University of Science and Technology, Mianyang 621010, Sichuan Province, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"11627","DOI":"10.1109\/TVT.2018.2872877","article-title":"Performance analysis of collaborative beamforming with outdated CSI for multi-relay spectrum sharing networks","volume":"67","author":"Hu","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_2","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_3","doi-asserted-by":"crossref","unstructured":"Chen, Y., Lin, L., Cao, G., Chen, Z., and Li, B. (2018, January 16\u201319). Stable Combinatorial Spectrum Matching. Proceedings of the IEEE Conference on Computer Communications (IEEE INFOCOM 2018), Honolulu, HI, USA.","DOI":"10.1109\/INFOCOM.2018.8486258"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1109\/TVT.2016.2565585","article-title":"Suppressing the effects of aliasing and IQ imbalance on multiband spectrum sensing","volume":"66","author":"Imana","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_5","unstructured":"Marcus, M., Burtle, J., Franca, B., Lahjouji, A., and McNeil, N. (2019, September 23). Federal Communications Commission Spectrum Policy Task Force, Available online: https:\/\/www.fcc.gov\/sptf\/files\/EUWGFinalReport.doc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1109\/TMM.2015.2394385","article-title":"Utility-based H.264\/SVC video streaming over multi-channel cognitive radio networks","volume":"17","author":"Yao","year":"2015","journal-title":"IEEE Trans. Multimed."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1109\/MCOM.2018.1700767","article-title":"Clustering in multi-channel cognitive radio ad hoc and sensor networks","volume":"56","author":"Ozger","year":"2018","journal-title":"IEEE Commun. Mag."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1014","DOI":"10.1109\/COMST.2018.2796101","article-title":"Joint inter-flow network coding and opportunistic routing in multi-hop wireless mesh networks: A comprehensive survey","volume":"20","author":"Kafaie","year":"2018","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1002\/wcm.2557","article-title":"A cross-layer study for application-aware multi-hop cognitive radio network","volume":"16","author":"Shu","year":"2016","journal-title":"Wirel. Commun. Mob. Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2634","DOI":"10.1109\/TMC.2014.2312715","article-title":"Robust topology control in multi-hop cognitive radio networks","volume":"13","author":"Zhao","year":"2014","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1176","DOI":"10.1109\/TMC.2016.2582173","article-title":"Spectrum-aware anypath routing in multi-hop cognitive radio networks","volume":"16","author":"Wang","year":"2017","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6304","DOI":"10.1109\/ACCESS.2016.2613122","article-title":"Route selection for multi-hop cognitive radio networks using reinforcement learning: An experimental study","volume":"4","author":"Syed","year":"2016","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1109\/MCOM.2013.6495776","article-title":"Open research issues in multi-hop cognitive radio networks","volume":"51","author":"Sengupta","year":"2013","journal-title":"IEEE Commun. Mag."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3561","DOI":"10.1109\/TWC.2017.2684125","article-title":"End-to-end throughput maximization for underlay multi-hop cognitive radio networks with RF energy harvesting","volume":"16","author":"Xu","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1390","DOI":"10.1109\/TNET.2018.2830122","article-title":"Statistical admission control in multi-hop cognitive radio networks","volume":"26","author":"Gallardo","year":"2018","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.comnet.2016.02.015","article-title":"Per-user throughput analysis for secondary users in multi-hop cognitive radio networks","volume":"106","author":"Zheng","year":"2016","journal-title":"Comput. Netw."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2097","DOI":"10.1109\/TWC.2016.2633527","article-title":"Joint rate adaptation, channel assignment and routing to maximize social welfare in multi-hop cognitive radio networks","volume":"16","author":"Tang","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1109\/TMC.2014.2314107","article-title":"Optimal scheduling for multi-radio multi-channel multi-hop cognitive cellular networks","volume":"14","author":"Li","year":"2015","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1962","DOI":"10.1049\/iet-com.2018.5166","article-title":"Resource allocation strategy against selfishness in cognitive radio ad-hoc network based on Stackelberg game","volume":"13","author":"Liu","year":"2019","journal-title":"IET Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2854","DOI":"10.1109\/JSYST.2016.2638203","article-title":"Power control and relay selection in cognitive radio ad hoc networks using game theory","volume":"12","author":"Mafra","year":"2018","journal-title":"IEEE Syst. J."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1109\/ACCESS.2017.2761910","article-title":"Multi-modal cooperative spectrum sensing based on dempster-shafer fusion in 5G-based cognitive radio","volume":"6","author":"Liu","year":"2017","journal-title":"IEEE Access"},{"key":"ref_22","unstructured":"Rardin, R.L. (1998). Optimization in Operations Research, Prentice Hall."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1287\/mnsc.13.7.492","article-title":"On nonlinear fractional programming","volume":"13","author":"Dinkelbach","year":"1967","journal-title":"Manag. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3711","DOI":"10.1109\/TIT.2009.2023751","article-title":"SCALE: A low-complexity distributed protocol for spectrum balancing in multiuser DSL networks","volume":"55","author":"Papandriopoulos","year":"2009","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Boyd, S., and Vandenberghe, L. (2004). Convex Optimization, Cambridge University Press.","DOI":"10.1017\/CBO9780511804441"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1109\/LSP.2014.2360234","article-title":"Statistical modeling of spectrum sensing energy in multi-hop cognitive radio networks","volume":"22","author":"Arienzo","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"8525","DOI":"10.1109\/TVT.2018.2850799","article-title":"Optimal resource allocation using support vector machine for wireless power transfer in cognitive radio networks","volume":"67","author":"Shrestha","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1109\/TEVC.2004.831258","article-title":"A robust stochastic genetic algorithm (StGA) for global numerical optimization","volume":"8","author":"Tu","year":"2004","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_29","unstructured":"Ilie, D. (2007). Optimization Algorithms with Applications to Unicast QoS Routing in Overlay Networks, Blekinge Institute of Technology."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/4235.996017","article-title":"A fast and elitist multiobjective genetic algorithm: NSGA-II","volume":"6","author":"Deb","year":"2002","journal-title":"IEEE Trans. Evol. Comput."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/20\/4493\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:27:00Z","timestamp":1760189220000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/20\/4493"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,16]]},"references-count":30,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2019,10]]}},"alternative-id":["s19204493"],"URL":"https:\/\/doi.org\/10.3390\/s19204493","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,10,16]]}}}