{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:57:25Z","timestamp":1760241445272,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,4,9]],"date-time":"2018-04-09T00:00:00Z","timestamp":1523232000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>In this paper, we investigate secure communication for a dual-hop multiuser relay network, where a source communication with N (    N \u2265 1    ) destinations via an untrusted variable gains relay. To exploit multiuser diversity while protecting source\u2019s confidential message, we first propose a joint destination-based jamming and opportunistic scheduling (DJOS) scheme. Then, we derive closed-form approximated and asymptotic expressions of the secrecy outage probability (SOP) for the considered system with DJOS. Furthermore, we determine an asymptotical optimal power allocation (OPA), which minimizes the asymptotic SOP, to further improve the secrecy performance. Our analytical results show that the achievable secrecy diversity order in terms of SOP with fixed power allocation is     min ( 1 ,  N 2  )    , whereas, with OPA, the achievable secrecy diversity order can be improved up to     min ( 1 ,   2 N   N + 2   )    . This interesting result reveals that OPA can improve the secrecy diversity order of the single-user network. This is intuitive since full diversity order of 1 cannot be achieved when     N = 1    , thus leaving some space for OPA to improve the diversity order. Nevertheless, for     N \u2265 2    , the effect of OPA is to increase the secrecy array gain rather than the secrecy diversity order since full diversity order 1 has been achieved by the OS scheme. Finally, simulation results are presented to validate our analysis.<\/jats:p>","DOI":"10.3390\/info9040084","type":"journal-article","created":{"date-parts":[[2018,4,10]],"date-time":"2018-04-10T13:06:08Z","timestamp":1523365568000},"page":"84","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hybrid Destination-Based Jamming and Opportunistic Scheduling with Optimal Power Allocation to Secure Multiuser Untrusted Relay Networks"],"prefix":"10.3390","volume":"9","author":[{"given":"Fan","family":"Ding","sequence":"first","affiliation":[{"name":"School of Physics and Electromechanical Engineering, Shaoguan University, Shaoguan 512005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongming","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Physics and Electromechanical Engineering, Shaoguan University, Shaoguan 512005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3000","DOI":"10.1109\/TIT.2012.2184692","article-title":"On secrecy capacity scaling in wireless networks","volume":"58","author":"Koyluoglu","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1109\/JSAC.2012.120215","article-title":"On the application of cooperative transmission to secrecy communications","volume":"30","author":"Ding","year":"2012","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3856","DOI":"10.1109\/TWC.2016.2530068","article-title":"Exploiting Direct Links for Physical Layer Security in Multiuser Multirelay Networks","volume":"15","author":"Fan","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5039","DOI":"10.1109\/TCOMM.2015.2494012","article-title":"Cooperative beamforming and user selection for improving the security of relay-aided systems","volume":"63","author":"Hoang","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5003","DOI":"10.1109\/TWC.2009.090323","article-title":"Relay selection for secure cooperative networks with jamming","volume":"8","author":"Krikidis","year":"2009","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4871","DOI":"10.1109\/TSP.2011.2161295","article-title":"Cooperative jamming for secure communications in MIMO relay networks","volume":"59","author":"Huang","year":"2011","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1875","DOI":"10.1109\/TSP.2009.2038412","article-title":"Improving wireless physical layer security via cooperating relays","volume":"58","author":"Dong","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1725","DOI":"10.1109\/TWC.2011.040511.101694","article-title":"Opportunistic relaying for secrecy communications: Cooperative jamming vs. relay chatting","volume":"10","author":"Ding","year":"2011","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"682","DOI":"10.1109\/TIFS.2013.2248730","article-title":"Destination assisted cooperative jamming for wireless physical-layer security","volume":"8","author":"Liu","year":"2013","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1109\/TIFS.2014.2374356","article-title":"Secrecy transmission with a helper: To relay or to jam","volume":"10","author":"Deng","year":"2015","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1109\/LSP.2012.2227725","article-title":"Joint cooperative beamforming and jamming to secure AF relay systems with individual power constraint and no eavesdropper\u2019s CSI","volume":"20","author":"Wang","year":"2013","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1109\/TWC.2014.2354635","article-title":"Hybrid opportunistic relaying and jamming with power allocation for secure cooperative networks","volume":"14","author":"Wang","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1741","DOI":"10.1109\/JSAC.2013.130908","article-title":"On the jamming power allocation for secure amplify-and-forward relaying via cooperative jamming","volume":"31","author":"Park","year":"2013","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1109\/TSP.2011.2172433","article-title":"Joint secure beamforming design at the source and the relay for an amplify-and-forward MIMO untrusted relay system","volume":"60","author":"Jeong","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2185","DOI":"10.1109\/TSP.2014.2307276","article-title":"Secure beamforming for MIMO two-way communications with an untrusted relay","volume":"62","author":"Mo","year":"2014","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3807","DOI":"10.1109\/TIT.2010.2050958","article-title":"Cooperation with an untrusted relay: A secrecy perspective","volume":"56","author":"He","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3801","DOI":"10.1109\/TVT.2012.2207438","article-title":"Performance study of two-hop amplify-and-forward systems with untrustworthy relay nodes","volume":"61","author":"Sun","year":"2012","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2703","DOI":"10.1109\/TVT.2014.2345568","article-title":"Opportunistic transmission of nonregenerative network with untrusted relay","volume":"64","author":"Ju","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Hu, H., Gao, Z., and Liao, X. (2017). Secure Communications in CIoT Networks with a Wireless Energy Harvesting Untrusted Relay. Sensors, 17.","DOI":"10.3390\/s17092023"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2545","DOI":"10.1109\/TIT.2016.2530080","article-title":"Near-optimal modulo-and-forward scheme for the untrusted relay channel","volume":"62","author":"Zhang","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"7274","DOI":"10.1109\/TVT.2015.2490099","article-title":"Destination aided cooperative jamming for dual-hop amplify-and-forward MIMO untrusted relay systems","volume":"65","author":"Xiong","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2536","DOI":"10.1109\/TSP.2013.2247600","article-title":"Secure communication via an untrusted non-regenerative relay in fading channels","volume":"61","author":"Huang","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2466","DOI":"10.1109\/TIFS.2016.2584006","article-title":"Relay Selection for Secure Successive AF Relaying Networks With Untrusted Nodes","volume":"11","author":"Wang","year":"2016","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1925","DOI":"10.1049\/el.2016.3079","article-title":"Multiuser untrusted relay networks with joint cooperative jamming and opportunistic scheduling under perfect and outdated CSI","volume":"52","author":"Ding","year":"2016","journal-title":"Electron. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2199","DOI":"10.1109\/TVT.2016.2572960","article-title":"Secure communication via a wireless energy harvesting untrusted relay","volume":"66","author":"Kalamkar","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3866","DOI":"10.1109\/TWC.2015.2413784","article-title":"Capacity scaling and diversity order for secure cooperative relaying with untrustworthy relays","volume":"14","author":"Kim","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1109\/WCL.2014.031114.140018","article-title":"Secure transmission with optimal power allocation in untrusted relay networks","volume":"3","author":"Wang","year":"2014","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"962","DOI":"10.1049\/iet-com.2015.0876","article-title":"Optimal power allocation to improve secrecy performance of non-regenerative cooperative systems using an untrusted relay","volume":"10","author":"Kuhestani","year":"2016","journal-title":"IET Commun."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1879","DOI":"10.1049\/el.2016.3201","article-title":"Optimised power allocation to maximise secure rate in energy harvesting relay network","volume":"52","author":"Yao","year":"2016","journal-title":"Electron. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3724","DOI":"10.1109\/TWC.2015.2410776","article-title":"Secure transmission for multiuser relay networks","volume":"14","author":"Kim","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1109\/LCOMM.2011.092911.111685","article-title":"A study of optimization problem for amplify-and-forward relaying over Weibull fading channels with multiple antennas","volume":"15","author":"Ikki","year":"2011","journal-title":"IEEE Commun. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Zhang, S., Liew, S., and Lam, P. (2006, January 23\u201329). Hot topic: Physical-layer network coding. Proceedings of the ACM Mobicom, Dresden, Germany.","DOI":"10.1145\/1161089.1161129"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/LCOMM.2007.061436","article-title":"Wireless network coding by amplify-and-forward for bi-directional traffic flows","volume":"11","author":"Popovski","year":"2007","journal-title":"IEEE Commun. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2683","DOI":"10.1109\/TCOMM.2010.080310.090292","article-title":"Performance analysis of bidirectional communication protocols based on decode-and-forward relaying","volume":"58","author":"Liu","year":"2010","journal-title":"IEEE Trans. Commun."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2120","DOI":"10.1109\/TVT.2010.2042828","article-title":"Outage probability of multiuser relay networks in Nakagami-m fading channels","volume":"59","author":"Yang","year":"2010","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"848","DOI":"10.1109\/TWC.2017.2772229","article-title":"A General Approach Toward Green Resource Allocation in Relay-Assisted Multiuser Communication Networks","volume":"17","author":"Singh","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3189","DOI":"10.1109\/TWC.2017.2675983","article-title":"QoS-driven resource allocation and EE-balancing for multiuser two-way amplify-and-forward relay networks","volume":"16","author":"Singh","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_38","unstructured":"Gradshteyn, I.S., and Ryzhik, I.M. (2007). Table of Integrals, Series, and Products, Academic Press. [7th ed.]."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1786","DOI":"10.1109\/TCOMM.2013.031213.120686","article-title":"Outage analysis of opportunistic scheduling in dual-hop multiuser relay networks in the presence of interference","volume":"61","author":"Hemachandra","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_40","unstructured":"Abramowitz, M., and Stegun, I.A. (1972). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover. [7th ed.]."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1109\/LCOMM.2007.070470","article-title":"An improved approximation for the Gaussian Q-function","volume":"11","author":"Karagiannidis","year":"2007","journal-title":"IEEE Commun. Lett."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/9\/4\/84\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:00:00Z","timestamp":1760194800000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/9\/4\/84"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,9]]},"references-count":41,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4]]}},"alternative-id":["info9040084"],"URL":"https:\/\/doi.org\/10.3390\/info9040084","relation":{},"ISSN":["2078-2489"],"issn-type":[{"type":"electronic","value":"2078-2489"}],"subject":[],"published":{"date-parts":[[2018,4,9]]}}}