{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T18:54:11Z","timestamp":1770490451996,"version":"3.49.0"},"reference-count":51,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,24]],"date-time":"2019-02-24T00:00:00Z","timestamp":1550966400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The research received a financial support from the SGS grant No. SP2018\/59, VSB Technical University of Ostrava, Czech Republic and partially was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 10","award":["No. SP2018\/59 and 102.04-2017.317"],"award-info":[{"award-number":["No. SP2018\/59 and 102.04-2017.317"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we consider a cooperative multi-hop secured transmission protocol to underlay cognitive radio networks. In the proposed protocol, a secondary source attempts to transmit its data to a secondary destination with the assistance of multiple secondary relays. In addition, there exists a secondary eavesdropper who tries to overhear the source data. Under a maximum interference level required by a primary user, the secondary source and relay nodes must adjust their transmit power. We first formulate effective signal-to-interference-plus-noise ratio (SINR) as well as secrecy capacity under the constraints of the maximum transmit power, the interference threshold and the hardware impairment level. Furthermore, when the hardware impairment level is relaxed, we derive exact and asymptotic expressions of end-to-end secrecy outage probability over Rayleigh fading channels by using the recursive method. The derived expressions were verified by simulations, in which the proposed scheme outperformed the conventional multi-hop direct transmission protocol.<\/jats:p>","DOI":"10.3390\/e21020217","type":"journal-article","created":{"date-parts":[[2019,2,25]],"date-time":"2019-02-25T03:06:52Z","timestamp":1551064012000},"page":"217","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Secrecy Performance Enhancement for Underlay Cognitive Radio Networks Employing Cooperative Multi-Hop Transmission with and without Presence of Hardware Impairments"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5793-4627","authenticated-orcid":false,"given":"Phu","family":"Tran Tin","sequence":"first","affiliation":[{"name":"VSB\u2014Technical University of Ostrava, 17. listopadu 15\/2172, 708 33 Ostrava, Poruba, Czech Republic"},{"name":"Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City 71408, Vietnam"}]},{"given":"Dang","family":"The Hung","sequence":"additional","affiliation":[{"name":"Faculty of Radio-Electronics Engineering, Le Quy Don Technical University, Hanoi 11917, Vietnam"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2286-6652","authenticated-orcid":false,"given":"Tan N.","family":"Nguyen","sequence":"additional","affiliation":[{"name":"Wireless Communications Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 72912, Vietnam"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3947-2174","authenticated-orcid":false,"given":"Tran Trung","family":"Duy","sequence":"additional","affiliation":[{"name":"Department of Telecommunications, Posts and Telecommunications Institute of Technology, Ho Chi Minh City 71007, Vietnam"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5135-7980","authenticated-orcid":false,"given":"Miroslav","family":"Voznak","sequence":"additional","affiliation":[{"name":"VSB\u2014Technical University of Ostrava, 17. listopadu 15\/2172, 708 33 Ostrava, Poruba, Czech Republic"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"9303","DOI":"10.1109\/ACCESS.2018.2793301","article-title":"Performance Costs of Software Cryptography in Securing New-Generation Internet of Energy Endpoint Devices","volume":"6","author":"Ledwaba","year":"2018","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1109\/MCOM.2018.1700330","article-title":"Securing Edge Devices in the Post-Quantum Internet of Things Using Lattice-Based Cryptography","volume":"56","author":"Liu","year":"2018","journal-title":"IEEE Commun. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1002\/j.1538-7305.1975.tb02040.x","article-title":"The Wire-tap Channel","volume":"54","author":"Wyner","year":"1975","journal-title":"Bell Syst. Tech. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1109\/TIT.1978.1055892","article-title":"Broadcast Channels With Confidential Messages","volume":"24","author":"Csiszar","year":"1978","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4687","DOI":"10.1109\/TIT.2008.928990","article-title":"On the secrecy capacity of fading channels","volume":"54","author":"Gopala","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Zhang, J., Duong, T.Q., Woods, R., and Marshall, A. (2017). Securing Wireless Communications of the Internet of Things from the Physical Layer, An Overview. Entropy, 19.","DOI":"10.3390\/e19080420"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Chang, S., Li, J., Fu, X., and Zhang, L. (2017). Energy Harvesting for Physical Layer Security in Cooperative Networks Based on Compressed Sensing. Entropy, 19.","DOI":"10.3390\/e19090462"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Sun, L., and Du, Q. (2018). A Review of Physical Layer Security Techniques for Internet of Things: Challenges and Solutions. Entropy, 20.","DOI":"10.3390\/e20100730"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1109\/MCOM.2018.1700439","article-title":"A New Look at Physical Layer Security, Caching, and Wireless Energy Harvesting for Heterogeneous Ultra-Dense Networks","volume":"56","author":"Wang","year":"2018","journal-title":"IEEE Commun. Mag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"11654","DOI":"10.1109\/TVT.2018.2872884","article-title":"Secrecy Analysis of Random MIMO Wireless Networks Over \u03b1-\u03bc Fading Channels","volume":"67","author":"Kong","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Jameel, F., Wyne, S., Kaddoum, G., and Duong, T.Q. (2018). A Comprehensive Survey on Cooperative Relaying and Jamming Strategies for Physical Layer Security. IEEE Commun. Surv. Tutor.","DOI":"10.1109\/COMST.2018.2865607"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1787","DOI":"10.1049\/iet-com.2009.0634","article-title":"Opportunistic Relay Selection For Cooperative Networks With Secrecy Constraints","volume":"4","author":"Krikidis","year":"2010","journal-title":"IET Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1123","DOI":"10.1109\/LCOMM.2017.2655050","article-title":"Secure Full-Duplex Two-Way Relaying Networks With Optimal Relay Selection","volume":"21","author":"Zhong","year":"2017","journal-title":"IEEE Commun. Lett."},{"key":"ref_14","first-page":"341","article-title":"Joint Relay Selection and Power Allocation in Large-Scale MIMO Systems With Untrusted Relays and Passive Eavesdroppers","volume":"13","author":"Kuhestani","year":"2018","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1109\/JIOT.2017.2778185","article-title":"Cooperative Jamming for Physical Layer Security Enhancement in Internet of Things","volume":"5","author":"Hu","year":"2018","journal-title":"IEEE Int. Things J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1109\/TCOMM.2017.2765637","article-title":"Robust MISO Beamforming With Cooperative Jamming for Secure Transmission From Perspectives of QoS and Secrecy Rate","volume":"66","author":"Ma","year":"2018","journal-title":"IEEE Trans. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1109\/TVT.2017.2756877","article-title":"Wireless Powered Cooperative Jamming for Secure OFDM System","volume":"67","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2108","DOI":"10.1109\/TVT.2017.2744660","article-title":"Cooperative-Jamming-Aided Secrecy Enhancement in Wireless Networks With Passive Eavesdroppers","volume":"67","author":"Hu","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1109\/LWC.2016.2544828","article-title":"Secrecy Outage of a Simultaneous Wireless Information and Power Transfer Cognitive Radio System","volume":"5","author":"Singh","year":"2016","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_20","first-page":"1106","article-title":"Secrecy Outage Analysis for SIMO Underlay Cognitive Radio Networks over Generalized-K Fading Channels","volume":"23","author":"Lei","year":"2016","journal-title":"IEEE Sig. Process. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1109\/TCOMM.2016.2618793","article-title":"Secrecy Performance Analysis of Cognitive Decode-and-Forward Relay Networks in Nakagami-m Fading Channels","volume":"65","author":"Zhao","year":"2017","journal-title":"IEEE Trans. Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1109\/LCOMM.2016.2564380","article-title":"Secrecy Outage Performance of a Cooperative Cognitive Relay Network","volume":"21","author":"Chakraborty","year":"2017","journal-title":"IEEE Commun. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Al-Hraishawi, H., Baduge, G.A.A., and Schaefer, R.F. (2017). Artificial Noise-Aided Physical Layer Security in Underlay Cognitive Massive MIMO Systems with Pilot Contamination. Entropy, 19.","DOI":"10.3390\/e19070349"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.phycom.2016.12.001","article-title":"Cognitive Radio Network with Secrecy and Interference Constraints","volume":"22","author":"Hung","year":"2017","journal-title":"Phys. Commun."},{"key":"ref_25","first-page":"42","article-title":"Cooperative Jammer Selection for Secrecy Improvement in Cognitive Internet of Things","volume":"18","author":"Ping","year":"2018","journal-title":"Sensors"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1109\/TVT.2015.2394370","article-title":"Robust Secure Beamforming in MISO Full-Duplex Two-Way Secure Communications","volume":"65","author":"Feng","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Sun, C., Liu, K., Zheng, D., and Ai, W. (2017). Secure Communication for Two-Way Relay Networks with Imperfect CSI. Entropy, 19.","DOI":"10.20944\/preprints201707.0088.v1"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1109\/LCOMM.2017.2772244","article-title":"Secure Communications in Three-Step Two-Way Energy Harvesting DF Relaying","volume":"22","author":"Jameel","year":"2018","journal-title":"IEEE Commun. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"10508","DOI":"10.1109\/ACCESS.2018.2804903","article-title":"Secure Transmission in SWIPT-Powered Two-Way Untrusted Relay Networks","volume":"6","author":"Zhang","year":"2018","journal-title":"IEEE Access"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Lee, J.-H., Sohn, I., and Kim, Y.-H. (2016). Transmit Power Allocation for Physical Layer Security in Cooperative Multi-Hop Full-Duplex Relay Networks. Sensors, 16.","DOI":"10.3390\/s16101726"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1120","DOI":"10.1109\/LCOMM.2016.2550025","article-title":"Secure Relaying in Multihop Communication Systems","volume":"20","author":"Alotaibi","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1109\/LCOMM.2017.2768513","article-title":"Secrecy Rate Maximization With Outage Constraint in Multihop Relaying Networks","volume":"22","author":"Yao","year":"2018","journal-title":"IEEE Commun. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1953","DOI":"10.3390\/en10121953","article-title":"Energy-Efficient Subcarrier Pairing and Power Allocation for DF Relay Networks with an Eavesdropper","volume":"10","author":"Keshav","year":"2017","journal-title":"Energies"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4512","DOI":"10.1109\/TCOMM.2013.100913.130282","article-title":"A new look at dual-hop relaying: Performance limits with hardware impairments","volume":"61","author":"Matthaiou","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.1109\/LCOMM.2013.042313.130191","article-title":"Two-Way Relaying Under The Presence of Relay Transceiver Hardware Impairments","volume":"17","author":"Matthaiou","year":"2013","journal-title":"IEEE Commun. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"7112","DOI":"10.1109\/TIT.2014.2354403","article-title":"Massive MIMO Systems With Non-Ideal Hardware: Energy Efficiency, Estimation, and Capacity Limits","volume":"60","author":"Hoydis","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"15971","DOI":"10.1109\/ACCESS.2017.2735451","article-title":"Performance Analysis of Two-Way Multi-Antenna Multi-Relay Networks with Hardware Impairments","volume":"5","author":"Guo","year":"2017","journal-title":"IEEE Access"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1110","DOI":"10.1109\/TCOMM.2017.2776261","article-title":"Aggregate Hardware Impairments Over Mixed RF\/FSO Relaying Systems With Outdated CSI","volume":"66","author":"Balti","year":"2018","journal-title":"IEEE Trans. Commun."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"820","DOI":"10.1109\/LCOMM.2016.2533500","article-title":"Cognitive relaying with transceiver hardware impairments under interference constraints","volume":"20","author":"Sharma","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_40","first-page":"1305","article-title":"How Much Does I\/Q Imbalance Affect Secrecy Capacity?","volume":"20","author":"Boulogeorgos","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2001","DOI":"10.1109\/TWC.2017.2659724","article-title":"Analysis and Design of Secure Massive MIMO Systems in the Presence of Hardware Impairments","volume":"16","author":"Zhu","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2642","DOI":"10.1109\/TCOMM.2017.2783628","article-title":"Power-Efficient and Secure WPCNs with Hardware Impairments and Non-Linear EH Circuit","volume":"66","author":"Boshkovska","year":"2018","journal-title":"IEEE Trans. Commun."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"4302","DOI":"10.1109\/TWC.2018.2822286","article-title":"Optimal Power Allocation by Imperfect Hardware Analysis in Untrusted Relaying Networks","volume":"17","author":"Kuhestani","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"774","DOI":"10.13164\/re.2016.0774","article-title":"Analysis of Probability of Non-zero Secrecy Capacity for Multi-hop Networks in Presence of Hardware Impairments over Nakagami-m Fading Channels","volume":"25","author":"Tin","year":"2016","journal-title":"RadioEngineering"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/TIFS.2014.2360437","article-title":"Security Enhancement of Cooperative Single Carrier Systems","volume":"10","author":"Wang","year":"2015","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"3062","DOI":"10.1109\/TIT.2004.838089","article-title":"Cooperative Diversity in Wireless Networks: Efficient Protocols and Outage Behavior","volume":"50","author":"Laneman","year":"2004","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1109\/MWC.2006.1678169","article-title":"Cooperative Wireless Communications: A Cross-layer Approach","volume":"13","author":"Liu","year":"2006","journal-title":"IEEE Wirel. Commun."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1109\/JSAC.2005.862417","article-title":"Simple Cooperative Diversity Method based on Network Path Selection","volume":"24","author":"Bletsas","year":"2006","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1109\/LCOMM.2012.042312.120582","article-title":"Relay Placement for Physical Layer Security: A Secure Connection Perspective","volume":"16","author":"Mo","year":"2012","journal-title":"IEEE Commun. Lett."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1340","DOI":"10.1109\/LCOMM.2013.052013.122902","article-title":"Secure Connectivity Using Randomize-and-Forward Strategy in Cooperative Wireless Networks","volume":"17","author":"Cai","year":"2013","journal-title":"IEEE Commun. Lett."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"4864","DOI":"10.1109\/TCOMM.2013.110413.130167","article-title":"On the Performance of Cognitive Underlay Multihop Networks with Imperfect Channel State Information","volume":"61","author":"Vo","year":"2013","journal-title":"IEEE Trans. Commun."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/2\/217\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:34:28Z","timestamp":1760186068000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/2\/217"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,24]]},"references-count":51,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["e21020217"],"URL":"https:\/\/doi.org\/10.3390\/e21020217","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,24]]}}}