{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T15:39:13Z","timestamp":1766158753153,"version":"3.37.3"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T00:00:00Z","timestamp":1629244800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T00:00:00Z","timestamp":1629244800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Wireless Netw"],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s11276-021-02735-7","type":"journal-article","created":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T15:03:02Z","timestamp":1629298982000},"page":"4581-4601","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Optimal frequency-hopping anti-jamming strategy based on multi-step prediction Markov decision process"],"prefix":"10.1007","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9145-9201","authenticated-orcid":false,"given":"Peng","family":"Wei","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4132-8750","authenticated-orcid":false,"given":"Shilian","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junshan","family":"Luo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Hu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,8,18]]},"reference":[{"key":"2735_CR1","doi-asserted-by":"crossref","unstructured":"Pelechrinis, K., Koufogiannakis, C., & Krishnamurthy, S. V. (2009). Gaming the jammer: Is frequency hopping effective? In International conference on modeling and optimization in mobile.","DOI":"10.1109\/WIOPT.2009.5291621"},{"issue":"3","key":"2735_CR2","first-page":"236","volume":"44","author":"W Yu","year":"2018","unstructured":"Yu, W. (2018). Research on status and future development of US protected satellite communications system. Radio Communications Technology, 44(3), 236\u2013241.","journal-title":"Radio Communications Technology"},{"key":"2735_CR3","first-page":"25","volume":"4","author":"Y Ji","year":"2012","unstructured":"Ji, Y., Tao, L., & Zhu, Q. (2012). Research on the frequenct hopping communication technology of variable hopping rate and variable interval. Wireless Communication Technology, 4, 25\u201329.","journal-title":"Wireless Communication Technology"},{"issue":"7","key":"2735_CR4","first-page":"107","volume":"41","author":"C Gang","year":"2016","unstructured":"Gang, C., & Fu-hai, L. (2016). Research on anti-follower jamming performance of variable rate frequency hopping communications. Fire Control and Command Control, 41(7), 107\u2013109.","journal-title":"Fire Control and Command Control"},{"key":"2735_CR5","unstructured":"Dan-tong, N., Wei-kang, Z., & Ying, Z. (2016). Design and analysis of the module for variable rate frequency hopping communications. In Presented at the proceedings of the fourth China command and control conference."},{"key":"2735_CR6","doi-asserted-by":"publisher","first-page":"414","DOI":"10.1016\/j.comnet.2014.10.001","volume":"75","author":"D Hlavacek","year":"2014","unstructured":"Hlavacek, D., & Chang, J. M. (2014). A layered approach to cognitive radio network security: A survey. Computer Networks, 75, 414\u2013436.","journal-title":"Computer Networks"},{"key":"2735_CR7","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/j.jnca.2015.03.011","volume":"54","author":"T AlSkaif","year":"2015","unstructured":"AlSkaif, T., Guerrero Zapata, M., & Bellalta, B. (2015). Game theory for energy efficiency in wireless sensor networks: Latest trends. Journal of Network and Computer Applications, 54, 33\u201361.","journal-title":"Journal of Network and Computer Applications"},{"issue":"6","key":"2735_CR8","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1109\/MWC.2017.1700363","volume":"25","author":"L Jia","year":"2018","unstructured":"Jia, L., Xu, Y., Sun, Y., Feng, S., & Anpalagan, A. (2018). Stackelberg game approaches for anti-jamming defence in wireless networks. IEEE Wireless Communications, 25(6), 120\u2013128.","journal-title":"IEEE Wireless Communications"},{"issue":"1","key":"2735_CR9","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1109\/JSAC.2012.120102","volume":"30","author":"Y Wu","year":"2012","unstructured":"Wu, Y., Wang, B., Liu, K. J. R., & Clancy, T. C. (2012). Anti-jamming games in multi-channel cognitive radio networks. IEEE Journal on Selected Areas in Communications, 30(1), 4\u201315.","journal-title":"IEEE Journal on Selected Areas in Communications"},{"key":"2735_CR10","doi-asserted-by":"crossref","unstructured":"Khattab, S., Mosse, D., & Melhem, R. (2008). Jamming mitigation in multi-radio wireless networks: Reactive or proactive? In International conference on security and privacy in communication netowrks.","DOI":"10.1145\/1460877.1460912"},{"key":"2735_CR11","doi-asserted-by":"crossref","unstructured":"Anwar, A. H., Kelly, J., Atia, G., & Guirguis, M. (2015). Stealthy edge decoy attacks against dynamic channel assignment in wireless networks. In Military communications conference.","DOI":"10.1109\/MILCOM.2015.7357521"},{"key":"2735_CR12","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.automatica.2018.11.039","volume":"101","author":"Y Li","year":"2019","unstructured":"Li, Y., Mehr, A. S., & Chen, T. (2019). Multi-sensor transmission power control for remote estimation through a SINR-based communication channel. Automatica, 101, 78\u201386.","journal-title":"Automatica"},{"issue":"4","key":"2735_CR13","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1109\/JSAC.2011.110418","volume":"29","author":"B Wang","year":"2011","unstructured":"Wang, B., Yongle, W., Liu, K. J. R., & Clancy, T. C. (2011). An anti-jamming stochastic game for cognitive radio networks. IEEE Journal on Selected Areas in Communications, 29(4), 877\u2013889.","journal-title":"IEEE Journal on Selected Areas in Communications"},{"issue":"1","key":"2735_CR14","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s11276-017-1551-9","volume":"25","author":"F Yao","year":"2017","unstructured":"Yao, F., Jia, L., Sun, Y., Xu, Y., Feng, S., & Zhu, Y. (2017). A hierarchical learning approach to anti-jamming channel selection strategies. Wireless Networks, 25(1), 201\u2013213.","journal-title":"Wireless Networks"},{"key":"2735_CR15","unstructured":"Wu, Y. (2010). Game-theoretic strategies for dynamic behavior in cognitive radio networks. Dissertations Theses\u2014Gradworks."},{"key":"2735_CR16","doi-asserted-by":"crossref","unstructured":"Singh, S., & Trivedi, A. (2012). Anti-jamming in cognitive radio networks using reinforcement learning algorithms. In Ninth international conference on wireless and optical communications networks.","DOI":"10.1109\/WOCN.2012.6331885"},{"issue":"1","key":"2735_CR17","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1109\/TCOMM.2017.2755644","volume":"66","author":"A Zappone","year":"2018","unstructured":"Zappone, A., Sanguinetti, L., & Debbah, M. (2018). Energy-delay efficient power control in wireless networks. IEEE Transactions on Communications, 66(1), 418\u2013431.","journal-title":"IEEE Transactions on Communications"},{"key":"2735_CR18","doi-asserted-by":"crossref","unstructured":"Luo, J., Pan, C., Li, R., & Ge, F. (2012). Power control in distributed wireless sensor networks based on noncooperative game theory. International Journal of Distributed Sensor Networks, 8(12), 544\u2013548.","DOI":"10.1155\/2012\/398460"},{"issue":"15","key":"2735_CR19","doi-asserted-by":"publisher","first-page":"1807","DOI":"10.1049\/iet-com.2014.1109","volume":"9","author":"G Yang","year":"2015","unstructured":"Yang, G., Wang, X., Tan, X., & Li, B. (2015). Adaptive power control algorithm in cognitive radio based on game theory. IET Communications, 9(15), 1807\u20131811.","journal-title":"IET Communications"},{"issue":"5","key":"2735_CR20","doi-asserted-by":"publisher","first-page":"1577","DOI":"10.1007\/s11276-014-0867-y","volume":"21","author":"B Chai","year":"2014","unstructured":"Chai, B., Deng, R., Shi, Z., Cheng, P., & Chen, J. (2014). Energy-efficient power allocation in cognitive sensor networks: A coupled constraint game approach. Wireless Networks, 21(5), 1577\u20131589.","journal-title":"Wireless Networks"},{"key":"2735_CR21","doi-asserted-by":"crossref","unstructured":"Slimeni, F., Scheers, B., Nir, V. L., Chtourou, Z., & Attia, R. (2016). Learning multi-channel power allocation against smart jammer in cognitive radio networks. In International conference on military communications and information systems.","DOI":"10.1109\/ICMCIS.2016.7496544"},{"key":"2735_CR22","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1016\/j.automatica.2018.11.034","volume":"100","author":"H Liu","year":"2019","unstructured":"Liu, H. (2019). SINR-based multi-channel power schedule under DoS attacks: A Stackelberg game approach with incomplete information. Automatica, 100, 274\u2013280.","journal-title":"Automatica"},{"issue":"8","key":"2735_CR23","doi-asserted-by":"publisher","first-page":"4038","DOI":"10.1109\/TWC.2013.071913121570","volume":"12","author":"D Yang","year":"2013","unstructured":"Yang, D., Xue, G., Zhang, J., Richa, A., & Fang, X. (2013). Coping with a smart jammer in wireless networks: A Stackelberg game approach. IEEE Transactions on Wireless Communications, 12(8), 4038\u20134047.","journal-title":"IEEE Transactions on Wireless Communications"},{"issue":"4","key":"2735_CR24","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1109\/MSP.2015.2406338","volume":"32","author":"G Bacci","year":"2015","unstructured":"Bacci, G., Sanguinetti, L., & Luise, M. J. S. P. M. I. (2015). Understanding game theory via wireless power control. IEEE Signal Processing Magazine, 32(4), 132\u2013137.","journal-title":"IEEE Signal Processing Magazine"},{"key":"2735_CR25","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/j.phycom.2019.03.005","volume":"34","author":"S Najeh","year":"2019","unstructured":"Najeh, S., & Bouallegue, A. (2019). Game theory for SINR-based power control in device-to-device communications. Physical Communication, 34, 135\u2013143.","journal-title":"Physical Communication"},{"issue":"10","key":"2735_CR26","doi-asserted-by":"publisher","first-page":"6503","DOI":"10.1109\/TWC.2017.2724036","volume":"16","author":"R Hu","year":"2017","unstructured":"Hu, R., & Lok, T.-M. (2017). Pareto optimality for the single-stream transmission in multiuser relay networks. IEEE Transactions on Wireless Communications, 16(10), 6503\u20136513.","journal-title":"IEEE Transactions on Wireless Communications"},{"issue":"17","key":"2735_CR27","doi-asserted-by":"publisher","first-page":"3004","DOI":"10.1002\/wcm.2745","volume":"16","author":"N Adem","year":"2016","unstructured":"Adem, N., Hamdaoui, B., & Yavuz, A. (2016). Mitigating jamming attacks in mobile cognitive networks through time hopping. Wireless Communications and Mobile Computing, 16(17), 3004\u20133014.","journal-title":"Wireless Communications and Mobile Computing"},{"key":"2735_CR28","first-page":"1","volume":"99","author":"L Xin","year":"2017","unstructured":"Xin, L., Xu, Y., Jia, L., Wu, Q., & Anpalagan, A. J. I. C. L. (2017). Anti-jamming communications using spectrum waterfall: A deep reinforcement learning approach. IEEE Communications Letters, 99, 1\u20134.","journal-title":"IEEE Communications Letters"},{"issue":"3","key":"2735_CR29","doi-asserted-by":"publisher","first-page":"1239","DOI":"10.1109\/COMST.2015.2420686","volume":"17","author":"M Abu Alsheikh","year":"2015","unstructured":"Abu Alsheikh, M., Hoang, D. T., Niyato, D., Tan, H.-P., & Lin, S. (2015). Markov decision processes with applications in wireless sensor networks: A survey. IEEE Communications Surveys and Tutorials, 17(3), 1239\u20131267.","journal-title":"IEEE Communications Surveys and Tutorials"},{"issue":"4","key":"2735_CR30","doi-asserted-by":"publisher","first-page":"1299","DOI":"10.1007\/s11277-015-3054-2","volume":"87","author":"X-C Hao","year":"2015","unstructured":"Hao, X.-C., Yao, N., Li, X.-D., & Liu, W.-J. (2015). Multi-channel allocation algorithm for anti-interference and extending connected lifetime in wireless sensor network. Wireless Personal Communications, 87(4), 1299\u20131318.","journal-title":"Wireless Personal Communications"},{"key":"2735_CR31","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1016\/j.jnca.2018.06.008","volume":"121","author":"AH Anwar","year":"2018","unstructured":"Anwar, A. H., Atia, G., & Guirguis, M. (2018). Adaptive topologies against jamming attacks in wireless networks: A game-theoretic approach. Journal of Network and Computer Applications, 121, 44\u201358.","journal-title":"Journal of Network and Computer Applications"},{"issue":"6","key":"2735_CR32","doi-asserted-by":"publisher","first-page":"2588","DOI":"10.1109\/TCOMM.2018.2799616","volume":"66","author":"W Wang","year":"2018","unstructured":"Wang, W., Kwasinski, A., Niyato, D., & Han, Z. (2018). Learning for robust routing based on stochastic game in cognitive radio networks. IEEE Transactions on Communications, 66(6), 2588\u20132602.","journal-title":"IEEE Transactions on Communications"},{"key":"2735_CR33","doi-asserted-by":"crossref","unstructured":"Han, G., Liang, X., & Poor, H. V. (2017). Two-dimensional anti-jamming communication based on deep reinforcement learning. In IEEE international conference on acoustics.","DOI":"10.1109\/ICASSP.2017.7952524"},{"key":"2735_CR34","doi-asserted-by":"publisher","first-page":"1986","DOI":"10.1109\/JSAC.2019.2929380","volume":"37","author":"J Luo","year":"2019","unstructured":"Luo, J., Wang, S., & Wang, F. (2019). Joint transmitter\u2013receiver spatial modulation design via minimum Euclidean distance maximization. IEEE Journal on Selected Areas in Communications, 37, 1986\u20132000.","journal-title":"IEEE Journal on Selected Areas in Communications"},{"key":"2735_CR35","doi-asserted-by":"publisher","first-page":"12087","DOI":"10.1109\/ACCESS.2019.2892869","volume":"7","author":"L Zhu","year":"2019","unstructured":"Zhu, L., Zhu, J., Wang, S., et al. (2019). Adaptive transmit antenna selection based on PCA for millimeter wave LOS MIMO channel. IEEE Access, 7, 12087\u201312096.","journal-title":"IEEE Access"},{"key":"2735_CR36","doi-asserted-by":"crossref","unstructured":"Li, T., Song, T., & Liang, Y. (2018). Wireless communications under hostile jamming security and efficiency.","DOI":"10.1007\/978-981-13-0821-5"},{"key":"2735_CR37","doi-asserted-by":"crossref","unstructured":"Wu, Y., Wang, B., & Liu, K. J. R. (2009). Optimal power allocation strategy against jamming attacks using the Colonel Blotto game. In Global telecommunications conference.","DOI":"10.1109\/GLOCOM.2009.5425760"},{"issue":"1","key":"2735_CR38","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1186\/1687-1499-2011-53","volume":"2011","author":"CK Tan","year":"2011","unstructured":"Tan, C. K., Sim, M. L., Chuah, T. C., & Su, W. T. (2011). Blotto game-based low-complexity fair multiuser subcarrier allocation for uplink OFDMA networks. EURASIP Journal on Wireless Communications and Networking, 2011(1), 53.","journal-title":"EURASIP Journal on Wireless Communications and Networking"},{"key":"2735_CR39","doi-asserted-by":"crossref","unstructured":"Kim, S. (2015). Cognitive radio anti-jamming scheme for security provisioning IoT communications. KSII Transactions on Internet and Information Systems, 9(10), 4177\u20134190.","DOI":"10.3837\/tiis.2015.10.023"},{"issue":"3","key":"2735_CR40","doi-asserted-by":"publisher","first-page":"1882","DOI":"10.1109\/TWC.2017.2786255","volume":"17","author":"H Zhang","year":"2018","unstructured":"Zhang, H., Du, J., Cheng, J., Long, K., & Leung, V. C. M. (2018). Incomplete CSI based resource optimization in SWIPT enabled heterogeneous networks: A non-cooperative game theoretic approach. IEEE Transactions on Wireless Communications, 17(3), 1882\u20131892.","journal-title":"IEEE Transactions on Wireless Communications"},{"issue":"4","key":"2735_CR41","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1002\/sat.1235","volume":"36","author":"I Aykin","year":"2018","unstructured":"Aykin, I., Krunz, M., & Xiao, Y. (2018). Adaptive frequency-hopping schemes for CR-based multi-link satellite networks. International Journal of Satellite Communications and Networking, 36(4), 315\u2013331.","journal-title":"International Journal of Satellite Communications and Networking"},{"issue":"9","key":"2735_CR42","doi-asserted-by":"publisher","first-page":"2247","DOI":"10.1109\/TMC.2015.2492556","volume":"15","author":"MK Hanawal","year":"2016","unstructured":"Hanawal, M. K., Abdel-Rahman, M. J., & Krunz, M. (2016). Joint adaptation of frequency hopping and transmission rate for anti-jamming wireless systems. IEEE Transactions on Mobile Computing, 15(9), 2247\u20132259.","journal-title":"IEEE Transactions on Mobile Computing"},{"issue":"8","key":"2735_CR43","doi-asserted-by":"publisher","first-page":"5314","DOI":"10.1109\/TWC.2018.2841921","volume":"17","author":"Y Gao","year":"2018","unstructured":"Gao, Y., Xiao, Y., Wu, M., Xiao, M., & Shao, J. (2018). Game theory-based anti-jamming strategies for frequency hopping wireless communications. IEEE Transactions on Wireless Communications, 17(8), 5314\u20135326.","journal-title":"IEEE Transactions on Wireless Communications"},{"issue":"4","key":"2735_CR44","doi-asserted-by":"publisher","first-page":"1777","DOI":"10.1007\/s11276-017-1629-4","volume":"25","author":"S Arunthavanathan","year":"2017","unstructured":"Arunthavanathan, S., Goratti, L., Maggi, L., de Pellegrini, F., Kandeepan, S., & Reisenfield, S. (2017). An optimal transmission strategy in zero-sum matrix games under intelligent jamming attacks. Wireless Networks, 25(4), 1777\u20131789.","journal-title":"Wireless Networks"},{"issue":"1","key":"2735_CR45","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1186\/1687-6180-2014-171","volume":"2014","author":"K Dabcevic","year":"2014","unstructured":"Dabcevic, K., Betancourt, A., Marcenaro, L., & Regazzoni, C. S. (2014). Intelligent cognitive radio jamming\u2014a game-theoretical approach. EURASIP Journal on Advances in Signal Processing, 2014(1), 171.","journal-title":"EURASIP Journal on Advances in Signal Processing"},{"key":"2735_CR46","first-page":"2019","volume":"1","author":"H Lv","year":"2019","unstructured":"Lv, H., Li, P., Yan, Q., & Zhang, H. (2019). Energy-efficient multi-cell resource allocation in cognitive radio-enabled 5G systems. EURASIP Journal on Advances in Signal Processing, 1, 2019.","journal-title":"EURASIP Journal on Advances in Signal Processing"},{"issue":"4","key":"2735_CR47","doi-asserted-by":"publisher","first-page":"569","DOI":"10.1109\/49.17721","volume":"7","author":"DJ Torrieri","year":"1989","unstructured":"Torrieri, D. J. (1989). Fundamental limitations on repeater jamming of frequency-hopping communications. IEEE Journal on Selected Areas in Communications, 7(4), 569\u2013575.","journal-title":"IEEE Journal on Selected Areas in Communications"},{"key":"2735_CR48","unstructured":"Yao, F. Q., & Zhang, Y. (2005). Analysis and application of jamming ellipse. Journal of Pla University of Science, 6(1), 7\u201310."},{"issue":"2","key":"2735_CR49","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/BF01753236","volume":"7","author":"RB Myerson","year":"1978","unstructured":"Myerson, R. B. (1978). Refinements of the Nash equilibrium concept. International Journal of Game Theory, 7(2), 73\u201380.","journal-title":"International Journal of Game Theory"}],"container-title":["Wireless Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11276-021-02735-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11276-021-02735-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11276-021-02735-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T08:29:11Z","timestamp":1632731351000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11276-021-02735-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,18]]},"references-count":49,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["2735"],"URL":"https:\/\/doi.org\/10.1007\/s11276-021-02735-7","relation":{},"ISSN":["1022-0038","1572-8196"],"issn-type":[{"type":"print","value":"1022-0038"},{"type":"electronic","value":"1572-8196"}],"subject":[],"published":{"date-parts":[[2021,8,18]]},"assertion":[{"value":"20 July 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 August 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}