{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T20:42:55Z","timestamp":1761597775415,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,1,7]],"date-time":"2017-01-07T00:00:00Z","timestamp":1483747200000},"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":["71272144","61503143"],"award-info":[{"award-number":["71272144","61503143"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In the study of power control and allocation based on pricing, the utility of secondary users is usually studied from the perspective of the signal to noise ratio. The study of secondary user utility from the perspective of communication demand can not only promote the secondary users to meet the maximum communication needs, but also to maximize the utilization of spectrum resources, however, research in this area is lacking, so from the viewpoint of meeting the demand of network communication, this paper designs a two stage model to solve spectrum leasing and allocation problem in cognitive radio sensor networks (CRSNs). In the first stage, the secondary base station collects the secondary network communication requirements, and rents spectrum resources from several primary base stations using the Bertrand game to model the transaction behavior of the primary base station and secondary base station. The second stage, the subcarriers and power allocation problem of secondary base stations is defined as a nonlinear programming problem to be solved based on Nash bargaining. The simulation results show that the proposed model can satisfy the communication requirements of each user in a fair and efficient way compared to other spectrum sharing schemes.<\/jats:p>","DOI":"10.3390\/s17010101","type":"journal-article","created":{"date-parts":[[2017,1,9]],"date-time":"2017-01-09T11:03:23Z","timestamp":1483959803000},"page":"101","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Spectrum Sharing Based on a Bertrand Game in Cognitive Radio Sensor Networks"],"prefix":"10.3390","volume":"17","author":[{"given":"Biqing","family":"Zeng","sequence":"first","affiliation":[{"name":"School of Computing, South China Normal University, Guangzhou 510631, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chi","family":"Zhang","sequence":"additional","affiliation":[{"name":"IFLYTEK Co., Ltd., Hefei 230000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pianpian","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Computing, South China Normal University, Guangzhou 510631, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengyu","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computing, South China Normal University, Guangzhou 510631, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,1,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Estrin, D., Govindan, R., Heidemann, J.S., and Kumar, S. (1999, January 15\u201319). Next Century Challenges: Scalable Coordination in Sensor Networks. Proceedings of the 5th ACM\/IEEE International Conference on Mobile Computing and Networking, Seattle, WA, USA.","DOI":"10.1145\/313451.313556"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1109\/98.878531","article-title":"Querying the Physical World","volume":"7","author":"Bonnet","year":"2007","journal-title":"IEEE Pers. Commun."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Callaway, E.J. (2003). Wirelsess Sensor NetWorks: Architechures and Protocols, CRS Press LLC.","DOI":"10.1201\/9780203500705"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1109\/TPDS.2015.2388482","article-title":"Joint Optimization of Lifetime and Transport Delay under Reliability Constraint Wireless Sensor Networks","volume":"27","author":"Dong","year":"2016","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2010","DOI":"10.1587\/transinf.2015INP0005","article-title":"MDMA: A multi-data and multi-ACK verified Selective Forwarding Attack Detection Scheme in WSNs","volume":"E99-D","author":"Liu","year":"2016","journal-title":"IEICE Trans. Inf. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Liu, A., Liu, X., and Long, J. (2016). A trust-based Adaptive Probability Marking and Storage Traceback Scheme for WSNs. Sensors, 16.","DOI":"10.3390\/s16040451"},{"key":"ref_7","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_8","unstructured":"Mitola, J. (2000). Cognitive Radio: An Integrated Agent Archi- Tecture for Software Defined Radio, KTH Royal Institute of Technology."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1109\/MNET.2009.5191144","article-title":"Cognitive radio sensor networks","volume":"23","author":"Akan","year":"2009","journal-title":"IEEE Netw."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Yau, K.L.A., Komisarczuk, P., and Teal, P.D. (2009, January 20\u201323). Cognitive radio-based wireless sensor networks: Conceptual design and open issues. Proceedings of the IEEE 34th Conference on Local Computer Networks (LCN 2009), Zurich, Switzerland.","DOI":"10.1109\/LCN.2009.5355016"},{"key":"ref_11","unstructured":"Huang, J., Berry, R.A., and Honig, M.L. (2005, January 8\u201311). Spectrum sharing with distributed interference compensation. Proceedings of the 2005 First IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, DySPAN 2005, Baltimore, MD, USA."},{"key":"ref_12","unstructured":"Zheng, H., and Cao, L. (2005, January 8\u201311). Device-centric spectrum management. Proceedings of the 2005 First IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, DySPAN 2005, Baltimore, MD, USA."},{"key":"ref_13","unstructured":"Zhao, J., Zheng, H., and Yang, G.H. (2005, January 8\u201311). Distributed coordination in dynamic spectrum allocation networks. Proceedings of the 2005 First IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, DySPAN 2005, Baltimore, MD, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1109\/JSAC.2004.839380","article-title":"Cognitive radio: Brain-empowered wireless communications","volume":"23","author":"Haykin","year":"2005","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1769","DOI":"10.1109\/TVT.2010.2040492","article-title":"Pricing for uplink power control in cognitive radio networks","volume":"59","author":"Yu","year":"2010","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1109\/LCOMM.2012.120612.121587","article-title":"A Novel Price-Based Power Control Algorithm in Cognitive Radio Networks","volume":"17","author":"Wang","year":"2013","journal-title":"IEEE Commun. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1109\/JSAC.2008.080117","article-title":"Competitive pricing for spectrum sharing in cognitive radio networks: Dynamic game, inefficiency of nash equilibrium, and collusion","volume":"26","author":"Niyato","year":"2008","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2651","DOI":"10.1109\/TWC.2008.070073","article-title":"Competitive spectrum sharing in cognitive radio networks: A dynamic game approach","volume":"7","author":"Niyato","year":"2008","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1042","DOI":"10.1109\/TMC.2010.207","article-title":"Joint spectrum allocation and power control for multihop cognitive radio networks","volume":"10","author":"Wang","year":"2011","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.phycom.2009.02.010","article-title":"Joint power control and spectrum allocation for cognitive radio networks via pricing","volume":"2","author":"Mwangoka","year":"2009","journal-title":"Phys. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2566","DOI":"10.1109\/JSAC.2013.131134","article-title":"Optimal pricing effect on equilibrium behaviors of delay-sensitive users in cognitive radio networks","volume":"31","author":"Tran","year":"2013","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2051","DOI":"10.1109\/JSAC.2006.881628","article-title":"Fair allocation of subcarrier and power in an OFDMA wireless mesh network","volume":"24","author":"Lee","year":"2006","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"38","DOI":"10.4236\/cn.2010.21005","article-title":"Joint power control and spectrum allocation for cognitive radio with QoS constraint","volume":"2","author":"Zhao","year":"2010","journal-title":"Commun. Netw."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1109\/JSAC.2012.120107","article-title":"Nash bargaining game theoretic scheduling for joint channel and power allocation in cognitive radio systems","volume":"30","author":"Ni","year":"2012","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_25","unstructured":"Osborne, M.J., and Rubinstein, A. (1994). A Course in Game Theory, MIT Press."},{"key":"ref_26","unstructured":"Kim, K., Kim, H., and Han, Y. (2004, January 26\u201329). Subcarrier and power allocation in OFDMA systems. Proceedings of the 2004 IEEE 60th Vehicular Technology Conference, Los Angeles, CA, USA."},{"key":"ref_27","unstructured":"Tassiulas, L., and Sarkar, S. (2002, January 23\u201327). Maxmin fair scheduling in wireless networks. Proceedings of the Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies, New York, NY, USA."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2013","DOI":"10.1109\/TIFS.2016.2570740","article-title":"ActiveTrust: Secure and Trustable Routing in Wireless Sensor Networks","volume":"11","author":"Liu","year":"2016","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"30942","DOI":"10.3390\/s151229835","article-title":"PHACK: An Efficient Scheme for Selective Forwarding Attack Detecting in WSNs","volume":"15","author":"Liu","year":"2015","journal-title":"Sensors"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/1\/101\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:25:41Z","timestamp":1760207141000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/1\/101"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,7]]},"references-count":29,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1]]}},"alternative-id":["s17010101"],"URL":"https:\/\/doi.org\/10.3390\/s17010101","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,1,7]]}}}