Abstract
In this paper, we examine the secrecy outage performance of a dual-hop relay network under Nakagami-m fading. Here, we consider a three-terminal wireless communication system, where one node (source) communicates to the other node (destination) via a group of relay nodes. Due to severe fading and heavy shadowing, the direct link between two communicating nodes is not suitable to achieve the desired performance. Therefore, one relay is opportunistically selected amongst K relay nodes to establish their communications. For providing relay cooperation, the best relay is selected based on criteria that maximize the secrecy outage performance. Selected relay applies amplify-and-forward operation to facilitate relay assistance by broadcasting the received signal. Along with the destination node, an eavesdropper also receives the broadcasted signals. For this setup, we derive the closed-form expressions of secrecy outage probability with the assumption that wireless channels experience Nakagami-m fading. Various numerical results are illustrated to highlight the key performance impact of different system and channel parameters. We also verify the accuracy of our derived expressions by comparing the results with similar work done in the literature.
Similar content being viewed by others
References
Wang, H.-M., & Xia, X.-G. (2015). Enhancing wireless secrecy via cooperation: Signal design and optimization. IEEE Communications Magazine, 53(12), 47–53.
Pahuja, S., & Jindal, P. (2019). Cooperative communication in physical layer security: Technologies and challenges. Wireless Personal Communications,. https://doi.org/10.1007/s11277-019-06430-x.
Zhang, Y., Sun, A., Liang, T., & Qiao, X. (2015). Max-ratio relay selection for secure communication in amplify-and-forward buffer-aided cooperative networks. In IEEE international conference on signal processing, communications and computing (ICSPCC) (pp. 1–4). Ningbo.
Yang, N., Wang, L., Geraci, G., Elkashlan, M., Yuan, J., & Renzo, M. D. (2015). Safeguarding 5G wireless communication networks using physical layer security. IEEE Communications Magazine, 53(4), 20–27.
Gurjar, D. S., & Upadhyay, P. K. (2018). Overlay device-to-device communications in asymmetric two-way cellular systems with hybrid relaying. IEEE Systems Journal, 12(4), 3713–3724.
Li, J., Petropulu, A. P., & Weber, S. (2011). On cooperative relaying schemes for wireless physical layer security. IEEE Transactions on Signal Processing, 59(10), 4985–4996.
Gurjar, D. S., Upadhyay, P. K., da Costa, D. B., & de Sousa, R. T. (2017). Beamforming in traffic-aware two-way relay systems with channel estimation error and feedback delay. IEEE Transactions on Vehicular Technology, 66(10), 8807–8820.
Wu, N. E., & Li, H. J. (2013). Effect of feedback delay on secure cooperative networks with joint relay and jammer selection. IEEE Wireless Communications Letters, 2(4), 415–418.
Liu, Y., Wang, L., Duy, T. T., Elkashlan, M., & Duong, T. Q. (2015). Relay selection for security enhancement in cognitive relay networks. IEEE Wireless Communications Letters, 4(1), 46–49.
Hoang, T. M., Duong, T. Q., Vo, N. S., & Kundu, C. (2017). Physical layer security in cooperative energy harvesting networks with a friendly jammer. IEEE Wireless Communications Letters, 6(2), 28–31.
Wang, W., Teh, K. C., & Li, K. H. (2016). Generalized relay selection for improved security in cooperative DF relay networks. IIEEE Wireless Communications Letters, 5(1), 28–31.
Bouallegue, T., & Sethom, K. (2017). Green and secure relay selection algorithm in cooperative networks. In Sixth international conference on communications and networking (ComNet), Hammamet, Tunisia.
Wang, K., Yuan, L., Miyazaki, T., Zeng, D., Guo, S., & Sun, Y. (2017). Strategic antieavesdropping game for physical layer security in wireless cooperative networks. IEEE Transactions on Vehicular Technology, 66(10), 9448–9457.
Lee, J. H. (2015). Cooperative relaying protocol for improving physical layer security in wireless decode-and-forward relaying networks. Wireless Personal Communications, 83(4), 3033–3044.
Guo, H., Yang, Z., Zhang, L., Zhu, J., & Zou, Y. (2017). Joint cooperative beamforming and jamming for physical-layer security of decode-and-forward relay networks. IEEE Access, 5, 19620–19630.
Zhang, C., Ge, J., Xia, Z., & Du, H. (2017). Graph theory based cooperative transmission for physical-layer security in 5G large-scale wireless relay networks. IEEE Access, 5, 21640–21649.
Saeidi-Khabisi, F. S., Vakili, V. T., & Abbasi-Moghadam, D. (2017). Improving the physical layer security in cooperative networks with multiple eavesdroppers. Wireless Personal Communications, 95(3), 3295–3320.
Rahmanpour, A., Vakili, V. T., & Razavizadeh, S. M. (2017). Enhancement of physical layer security using destination artificial noise based on outage probability. Wireless Personal Communications, 95(2), 1553–1565.
Qing, L., Guangyao, H., & Xiaomei, F. (2018). Physical layer security in multi-hop AF relay network based on compressed sensing. IEEE Communications Letters, 22(9), 1882–1885.
Nguyen, B. V., & Kim, K. (2015). Secrecy outage probability of optimal relay selection for secure AnF cooperative networks. IEEE Communications Letters, 19(12), 2086–2089.
Zou, Y., Champagne, B., Zhu, W. P., & Hanzo, L. (2015). Relay-selection improves the security-reliability trade-off in cognitive radio systems. IEEE Transactions on Communications, 63(1), 215–228.
Amarasuriya, G., Ardakani, M., & Tellambura, C. (2010). Output-threshold multiple relay selection scheme for cooperative wireless networks. IEEE Transactions on Vehicular Technology, 59(6), 3091–3097.
Ikki, S., & Ahmed, M. H. (2007). Performance analysis of cooperative diversity wireless networks over Nakagami-\(m\) fading channel. IEEE Communications Letters, 11(4), 334–336.
Gradshteyn, I., & Ryzhik, I. (2007). Table of integrals, series, and products (7th ed.). San Diego: Academic Press.
Simon, M. K., & Alouini, M.-S. (2005). Digital communication over fading channels: A unified approach to performance analysis (2nd ed.). New York: Wiley.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendices
Appendix A
Here, we provide the detailed step-by-step solution for (12). Based on (12), the expression of \(I_{11}\) can be given as
After incorporating the respective CDF and PDF in (32) and solving further, we get
On applying [24, eqs. 3.381.1, 3.471.9] and doing some adjustments, one can obtain
Similarly, we derive the expression of \(I_{12}\) as
On invoking the PDFs and CDF in the respective part of (12), we represent \(I_{13}\) as
which can be further expressed as
In the same way
Appendix B
On invoking the expressions of respective CDF in the Integral of (17) and solving further using the similar step as followed for \(I_{1}\), the expression of \(I_{2}\) can be given as
Now, simplifying \(I_{2}\) using equations [24, eqs. 3.381.1, 8.352], we have
On applying the binomial expansion in (41), the required solution can be obtained as given in (18).
Appendix C
The Integral expression of \(I_{42}\) can written from (22) as
After incorporating the respective PDFs, we get
After solving further
On incorporating the PDF \(f_{X}(x)\), we get
On solving the simple integration, one can get the final expression of \(I_{42}\) as in (28).
Rights and permissions
About this article
Cite this article
Datta, R., Gurjar, D.S., Manohar Reddy, T.K. et al. Secrecy Performance of Amplify-and-Forward Relay Networks with Relay Selection under Nakagami-m Fading. Wireless Pers Commun 112, 2233–2251 (2020). https://doi.org/10.1007/s11277-020-07147-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11277-020-07147-y