On the Performance of the Relay Selection in Multi-hop Cluster-based Wireless Networks with Multiple Eavesdroppers Under Equally Correlated Rayleigh Fading


  • Pham Minh Nam Industrial University of Ho Chi Minh City image/svg+xml
  • Phong Ngo Dinh Posts and Telecommunications Institute of Technology
  • Nguyen Luong Nhat Posts and Telecommunications Institute of Technology
  • Tu Lam-Thanh Ton Duc Thang University image/svg+xml
  • Thuong Le-Tien Ho Chi Minh City University of Technology image/svg+xml




Eavesdroppers, Equally Correlated Rayleigh Fading, Multi-hop Wireless Networks, Power Allocation, Outage Probablity


The performance of multi-hop cluster-based wireless networks under multiple eavesdroppers is investigated in the present work. More precisely, we derive the outage probability (OP) of the considered networks under two relay selection schemes: the channel-gain-based scheme and the random scheme. Although equally correlated Rayleigh fading is taken into consideration, the derived mathematical framework remains tractable. Specifically, we represent the exact expression of the OP under the channel-based scheme in series form, while the OP under the random scheme is computed in a closed-form expression. Additionally, we propose a novel power allocation for each transmitter that strictly satisfies the given intercept probability. Numerical results based on the Monte Carlo method are provided to verify the correctness of the derived framework. These results are also used to identify the influences of various parameters, such as the number of clusters, the number of relays per cluster, and the transmit power.


Download data is not yet available.


Tran, Q.N., Vo, N.S., Nguyen, Q.A., Bui, M.P., Phan, T.M., Lam, V.V. and Masaracchia, A. (2021) D2d multi-hop multi-path communications in b5g networks: A survey on models, techniques, and applications. EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 7(25): 167839. doi:10.4108/eai.7-1-2021.167839, URL http://dx.doi.org/10.4108/eai. 7-1-2021.167839. DOI: https://doi.org/10.4108/eai.7-1-2021.167839

Tu, L.T., Phan, V.D., Nguyen, T.N., Tran, P.T., Duy, T.T., Nguyen, Q.S., Nguyen, N.T. et al. (2023) Performance analysis of multihop full-duplex NOMA systems with imperfect interference cancellation and near-field pathloss. Sensors 23(1): 524. doi:10.3390/s23010524, URL https://doi.org/10.3390/s23010524. DOI: https://doi.org/10.3390/s23010524

Duy, T.T. and Kong, H.Y. (2015) Secrecy performance analysis of multihop transmission protocols in cluster networks. Wireless Personal Communications 82(4): 2505–2518. doi:10.1007/s11277-015-2361-y, URL http://dx.doi.org/10.1007/s11277-015-2361-y. DOI: https://doi.org/10.1007/s11277-015-2361-y

Anh, N.T., Minh, N.C., Duy, T.T., Hanh, T. and Hai, H.D. (2021) Reliability-security analysis for harvest-to-jam based multi-hop cluster mimo networks using cooperative jamming methods under impact of hardware impairments. EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 8(28). doi:10.4108/eai.17-9-2021.170963. DOI: https://doi.org/10.4108/eai.17-9-2021.170963

Phu, T.T., Dang, T.H., Tran, T.D. and Voznak, M. (2017) Security-reliability analysis of noma-based multi-hop relay networks in presence of an active eavesdropper with imperfect eavesdropping csi. Advances in Electrical and Electronic Engineering 15(4). doi:10.15598/aeee.v15i4.2386, URL http://dx.doi.org/10.15598/aeee.v15i4.2386. DOI: https://doi.org/10.15598/aeee.v15i4.2386

Huan, N.T., Duy, T.T., Tu, L.T., Sang, N.Q., Ta, Q.H. and Tuan, P.V. (2022) Incremental cooperation based multi-hop relaying scheme with fountain codes, wirelessly energy harvesting and partial relay selection. In 2022 International Conference on Advanced Technologies for Communications (ATC): 338–343. doi:10.1109/ATC55345.2022.9943044. DOI: https://doi.org/10.1109/ATC55345.2022.9943044

Thi Nguyen, T.T. and Do, D.T. (2021) Exploiting full-duplex and fixed power allocation approaches for dual-hop transmission in downlink noma. Advances in Electrical and Electronic Engineering 19(3). doi:10.15598/aeee.v19i3.4116, URL http://dx.doi.org/10.15598/aeee.v19i3.4116. DOI: https://doi.org/10.15598/aeee.v19i3.4116

Vo, D.T., Van Chien, T., Nguyen, T.N., Tran, D.H., Voznak, M., Kim, B.S. and Tu, L.T. (2023) Swiptenabled cooperative wireless iot networks with friendly jammer and eavesdropper: Outage and intercept probability analysis. IEEE Access 11: 86165–86177. doi:10.1109/ACCESS.2023.3303369. DOI: https://doi.org/10.1109/ACCESS.2023.3303369

Tran, Q.N., Vo, N.S., Bui, M.P., Phan, T.M., Nguyen, Q.A. and Duong, T.Q. (2022) Spectrum sharing and power allocation optimised multihop multipath d2d video delivery in beyond 5g networks. IEEE Transactions on Cognitive Communications and Networking 8(2): 919–930. doi:10.1109/TCCN.2021.3133838. DOI: https://doi.org/10.1109/TCCN.2021.3133838

Nguyen, Q., Nguyen, V., Trung Duy, T., Nguyen, L. and Tu, L.T. (2023) On the security and reliability tradeoff of the satellite terrestrial networks with fountain codes and friendly jamming. EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 10: e3. doi:10.4108/eetinis.v10i4.4192. DOI: https://doi.org/10.4108/eetinis.v10i4.4192

Mahey, R. and Malhotra, J. (2015) Upper capacity bounds of mimo wireless systems through fading channels. Advances in Electrical and Electronic Engineering 13. doi:10.15598/aeee.v13i5.1407. DOI: https://doi.org/10.15598/aeee.v13i5.1407

Quyen, N.X., Nguyen, N.P. and Vo, N.S. (2015) An oversampling-correlation receiver for enhancing performance of chaotic ds-cdma systems over flat fading channels. In 2015 International Conference on Communications, Management and Telecommunications (ComManTel): 157–161. doi:10.1109/ComManTel.2015.7394279. DOI: https://doi.org/10.1109/ComManTel.2015.7394279

Nguyen, Toan-Van and Vu, Thai-Hoc and Huynh-The, Thien and da Costa, Daniel Benevides (2024) Secrecy performance of short-packet communications in multihop iot networks with imperfect csi. IEEE Wireless Communications Letters: 1-1 doi:10.1109/LWC.2024.3361379. DOI: https://doi.org/10.1109/LWC.2024.3361379

Lu, Jianzhong and He, Dongxuan and Wang, Zhaocheng (2022) Secure routing in multihop adhoc networks with srr-based reinforcement learning. IEEE Wireless Communications Letters 11(2): 362–366. doi:10.1109/LWC.2021.3128582. DOI: https://doi.org/10.1109/LWC.2021.3128582

Trung Duy, Tran and Duong, Trung and Tu, Lam-Thanh and Bao, Vo Nguyen (2015) Secrecy performance analysis with relay selection methods under impact of co-channel interference. IET Communications 9: . doi:10.1049/iet-com.2014.1128. DOI: https://doi.org/10.1049/iet-com.2014.1128

Miao, Jiansong and Li, Hairui and Zheng, Ziyuan and Wang, Chu (2021) Secrecy energy efficiency maximization for uav swarm assisted multi-hop relay system: Joint trajectory design and power control. IEEE Access 9: 37784–37799. doi:10.1109/ACCESS.2021.3062895. DOI: https://doi.org/10.1109/ACCESS.2021.3062895

Letafati, Mehdi and Kuhestani, Ali and Behroozi, Hamid (2020) Three-hop untrusted relay networks with hardware imperfections and channel estimation errors for internet of things. IEEE Transactions on Information Forensics and Security 15: 2856–2868. doi:10.1109/TIFS.2020.2978627. DOI: https://doi.org/10.1109/TIFS.2020.2978627

Wang, Hui-Ming and Zhang, Yan and Zhang, Xu and Li, Zhetao (2020) Secrecy and covert communications against uav surveillance via multi-hop networks. IEEE Transactions on Communications 68(1): 389–401. doi:10.1109/TCOMM.2019.2950940. DOI: https://doi.org/10.1109/TCOMM.2019.2950940

Ty, Vo Ta and Duy, Tran Trung and Tu, Lam-Thanh and Nguyen, Tien-Tung and Trinh, D. and Hanh, Tan (2023) Security-reliability tradeoff of multihop secure communication networks using fountain codes and ris-aided cooperative communication. In 2023 International Conference on Advanced Technologies for Communications (ATC): 499–504. doi:10.1109/ATC58710.2023.10318517. DOI: https://doi.org/10.1109/ATC58710.2023.10318517

Tran, Duc-Dung and Vo, Nguyen-Son and Vo, Tan-Loc and Ha, Dac-Binh (2015) Physical layer secrecy performance of multi-hop decode-and-forward relay networks with multiple eavesdroppers. In 2015 IEEE 29th International Conference on Advanced Information Networking and Applications Workshops: 430–435. doi:10.1109/WAINA.2015.33. DOI: https://doi.org/10.1109/WAINA.2015.33

Nam-Phong Nguyen and Tu, Lam-Thanh and Trung Q. Duong and A. Nallanathan (2017) Secure communications in cognitive underlay networks over nakagamim channel. Physical Communication 25: 610–618. doi:https://doi.org/10.1016/j.phycom.2016.05.003. DOI: https://doi.org/10.1016/j.phycom.2016.05.003

Ha Duy Hung and Tran Trung Duy and Miroslav Voznak (2020) Secrecy outage performance of multi-hop leach networks using power beacon aided cooperative jamming with jammer selection methods. AEU - International Journal of Electronics and Communications 124: 153357. doi:https://doi.org/10.1016/j.aeue.2020.153357, URL https://www.sciencedirect.com/science/article/pii/S1434841120301898. DOI: https://doi.org/10.1016/j.aeue.2020.153357

Dang The Hung and Tran Trung Duy and Do Quoc Trinh (2019) Security-reliability analysis of multi-hop leach protocol with fountain codes and cooperative jamming. EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 6(18). doi:10.4108/eai.28-3-2019.157120. DOI: https://doi.org/10.4108/eai.28-3-2019.157120

Tin, Phu Tran and Minh Nam, Pham and Trung Duy, Tran and Tran, Phuong T. and Voznak, Miroslav (2019) Secrecy performance of tas/sc-based multihop harvest-to-transmit cognitive wsns under joint constraint of interference and hardware imperfection. Sensors 19(5). doi:10.3390/s19051160, URL https://www.mdpi.com/1424-8220/19/5/1160. DOI: https://doi.org/10.3390/s19051160

Tran, Minh and Tu, Lam-Thanh and Minh, Bui Vu and Nguyen, Quang-Sang and Rejfek, Lubos and Lee, Byung Moo (2024) Security and reliability analysis of the power splitting-based relaying in wireless sensors network. Sensors 24(4). doi:10.3390/s24041300, URL https://www.mdpi.com/1424-8220/24/4/1300. DOI: https://doi.org/10.3390/s24041300

Tu, L.T., Bao, V.N.Q., Ngoc, P.T.D. and Duy, T.T. (2016) On the performance of cognitive underlay SIMO networks over equally correlated rayleigh fading channels. REV Journal on Electronics and Communications 5(1-2). doi:10.21553/rev-jec.96, URL https://doi.org/10.21553/rev-jec.96. DOI: https://doi.org/10.21553/rev-jec.96

Duong, T.Q., Alexandropoulos, G.C., Zepernick, H.J. and Tsiftsis, T.A. (2011) Orthogonal space–time block codes with csi-assisted amplify-and-forward relaying in correlated nakagami-m fading channels. IEEE Transactions on Vehicular Technology 60(3): 882–889. doi:10.1109/TVT.2011.2104379. DOI: https://doi.org/10.1109/TVT.2011.2104379

Di Renzo, M., Zappone, A., Tu, L.T. and Debbah, M. (2019) Spectral-energy efficiency pareto front in cellular networks: A stochastic geometry framework. IEEE Wireless Communications Letters 8(2): 424–427. doi:10.1109/LWC.2018.2874642. DOI: https://doi.org/10.1109/LWC.2018.2874642

Abedini, M. and Al-Anbagi, I. (2024) Enhanced active eavesdroppers detection system for multihop wsns in tactical iot applications. IEEE Internet of Things Journal 11(4): 6748–6760. doi:10.1109/JIOT.2023.3313048. DOI: https://doi.org/10.1109/JIOT.2023.3313048

Nguyen, Tan N. and Tu, Lam-Thanh and Fazio, Peppino and Van Chien, Trinh and V. Le, Cuong and Binh, Huynh Thi Thanh and Voznak, Miroslav (2024) On the dilemma of reliability or security in unmanned aerial vehicle communications assisted by energy harvesting relaying. IEEE Journal on Selected Areas in Communications 42(1): 52–67. doi:10.1109/JSAC.2023.3322756. DOI: https://doi.org/10.1109/JSAC.2023.3322756

Tu, L.T., Nguyen, T.N., Duy, T.T., Tran, P.T., Voznak, M. and Aravanis, A.I. (2022) Broadcasting in cognitive radio networks: A fountain codes approach. IEEE Transactions on Vehicular Technology 71(10): 11289– 11294. doi:10.1109/TVT.2022.3188969. DOI: https://doi.org/10.1109/TVT.2022.3188969

Rostami Ghadi, F., López-Martínez, F.J., Zhu, W.P. and Gorce, J.M. (2022) The impact of side information on physical layer security under correlated fading channels. IEEE Transactions on Information Forensics and Security 17: 3626–3636. doi:10.1109/TIFS.2022.3212198. DOI: https://doi.org/10.1109/TIFS.2022.3212198

Ghadi, F.R. and Hodtani, G.A. (2021) Copula-based analysis of physical layer security performances over correlated rayleigh fading channels. IEEE Transactions on Information Forensics and Security 16: 431–440. doi:10.1109/TIFS.2020.3014553. DOI: https://doi.org/10.1109/TIFS.2020.3014553

Le, K. (2015) Comments on “distribution functions of selection combiner output in equally correlated rayleigh, rician, and nakagami-m fading channels”. Communications, IEEE Transactions on 63: 5283–5287. doi:10.1109/TCOMM.2015.2495211. DOI: https://doi.org/10.1109/TCOMM.2015.2495211




How to Cite

Minh Nam, P., Ngo Dinh, P., Luong Nhat, N., Lam-Thanh, T., & Le-Tien, T. (2024). On the Performance of the Relay Selection in Multi-hop Cluster-based Wireless Networks with Multiple Eavesdroppers Under Equally Correlated Rayleigh Fading. EAI Endorsed Transactions on Industrial Networks and Intelligent Systems, 11(3). https://doi.org/10.4108/eetinis.v11i3.4728