Abstract
In this paper, we solve two problems aiming at improving the secure communications in a one-way relay system. The system under consideration consists of one source, one destination, N cooperative relays that use amplify and forward, and one eavesdropper. First, we minimize the relays power under information rate constraints for both the legitimate destination and the eavesdropper. When the source power is given, the problem is formulated as a non-convex quadratically constraint quadratic programming, which can be solved using a semidefinite programming (SDP). However, since SDP suffers from high complexity, we propose a novel approach, using generalized eigenvalue, that provides a closed form of the optimal solution in most cases. Then we prove that the relays power can be further decreased as the source power increases. Second, we solve the problem of maximizing the secrecy rate by looking for the optimal relays beamforming vector. We show that the optimization problem of the beamforming vector is a product of two correlated generalized Rayleigh quotients. For this problem, we show that the optimal beamforming vector can be obtained using a series of SDPs, then we significantly simplify the problem by solving it using a series of eigenvalue problem. Numerical results show that the proposed approaches achieve the optimal solution of the relay beamforming vector and enhance the physical layer security with power allocation.
Similar content being viewed by others
References
Obeed, M. (2016). Physical layer security in one-way and two-way relay systems. Master’s thesis, King Fahd University of Petroleum and Minerals. http://eprints.kfupm.edu.sa/139830/.
Wyner, A. D. (1975). The wire-tap channel. The Bell System Technical Journal, 54(8), 1355–1387.
Leung-Yan-Cheong, S. K., & Hellman, M. E. (1978). The Gaussian wire-tap channel. IEEE Transactions on Information Theory, 24(4), 451–456.
Gopala, P. K., Lai, L., & El Gamal, H. (2008). On the secrecy capacity of fading channels. IEEE Transactions on Information Theory, 54(10), 4687–4698.
Parada, P., & Blahut, R. (2005). Secrecy capacity of simo and slow fading channels. In Proceedings of the international symposium on information theory, 2005. ISIT 2005 (pp. 2152–2155). IEEE.
Khisti, A., & Wornell, G. W. (2010). Secure transmission with multiple antennas I: The misome wiretap channel. IEEE Transactions on Information Theory, 56(7), 3088–3104.
Liao, W.-C., Chang, T.-H., Ma, W.-K., & Chi, C.-Y. (2011). Qos-based transmit beamforming in the presence of eavesdroppers: An optimized artificial-noise-aided approach. IEEE Transactions on Signal Processing, 59(3), 1202–1216.
Khisti, A., & Wornell, G. W. (2010). Secure transmission with multiple antennas part II: The mimome wiretap channel. IEEE Transactions on Information Theory, 56(11), 5515–5532.
Shafiee, S., Liu, N., & Ulukus, S. (2009). Towards the secrecy capacity of the Gaussian mimo wire-tap channel: The 2-2-1 channel. IEEE Transactions on Information Theory, 55(9), 4033–4039.
Abedi, M. R., Mokari, N., Saeedi, H., & Yanikomeroglu, H. (2017). Robust resource allocation to enhance physical layer security in systems with full-duplex receivers: Active adversary. IEEE Transactions on Wireless Communications, 16(2), 885–899.
Simeone, O., & Popovski, P. (2008). Secure communications via cooperating base stations. Communications Letters, IEEE, 12(3), 188–190.
Lai, L., & Gamal, H. E. (2008). The relay-eavesdropper channel: Cooperation for secrecy. IEEE Transactions on Information Theory, 54(9), 4005–4019.
Dong, L., Han, Z., Petropulu, A. P., & Poor, H. V. (2010). Improving wireless physical layer security via cooperating relays. IEEE Transactions on Signal Processing, 58(3), 1875–1888.
Zhang, J., & Gursoy, M. C. (2010). Relay beamforming strategies for physical-layer security. In 2010 44th annual conference on information sciences and systems (CISS) (pp. 1–6). IEEE.
Hu, L., Wen, H., Wu, B., Tang, J., & Pan, F. (2017). Adaptive secure transmission for physical layer security in cooperative wireless networks. IEEE Communications Letters, 21(3), 524–527.
Ouyang, N., Jiang, X.-Q., Bai, E., & Wang, H.-M. (2017). Destination assisted jamming and beamforming for improving the security of af relay systems. IEEE Access, 5, 4125–4131.
Nikookar-Hamedani, P., & Soleimani-Nasab, E. (2016). Physical layer security in the presence of the eavesdroppers in cooperative networks. In Smart grids conference (SGC), 2016 (pp. 1–8). IEEE.
Li, W., Ghogho, M., Chen, B., & Xiong, C. (2012). Secure communication via sending artificial noise by the receiver: Outage secrecy capacity/region analysis. IEEE Communications Letters, 16(10), 1628–1631.
Wang, C., Wang, H.-M., Ng, D. W. K., Xia, X.-G., & Liu, C. (2015). Joint beamforming and power allocation for secrecy in peer-to-peer relay networks. IEEE Transactions on Wireless Communications, 14(6), 3280–3293.
Wang, H.-M., Yin, Q., & Xia, X.-G. (2011). Improving the physical-layer security of wireless two-way relaying via analog network coding. In 2011 IEEE Global telecommunications conference (GLOBECOM 2011) (pp. 1–6). IEEE.
Wang, H.-M., Yin, Q., & Xia, X.-G. (2012). Distributed beamforming for physical-layer security of two-way relay networks. IEEE Transactions on Signal Processing, 60(7), 3532–3545.
Yang, Y., Sun, C., Zhao, H., Long, H., & Wang, W. (2014). Algorithms for secrecy guarantee with null space beamforming in two-way relay networks. IEEE Transactions on Signal Processing, 62(8), 2111–2126.
Wang, H.-M., Luo, M., Yin, Q., & Xia, X.-G. (2013). Hybrid cooperative beamforming and jamming for physical-layer security of two-way relay networks. IEEE Transactions on Information Forensics and Security, 8(12), 2007–2020.
Zhang, R., Song, L., Han, Z., Jiao, B., & Debbah, M. (2010). Physical layer security for two way relay communications with friendly jammers. In 2010 IEEE Global telecommunications conference (GLOBECOM 2010) (pp. 1–6). IEEE.
Obeed, M., & Mesbah, W. (2016). An efficient physical layer security algorithm for two-way relay systems. In 2016 IEEE Wireless communications and networking conference (WCNC) (pp. 1–6). IEEE.
Chen, J., Zhang, R., Song, L., Han, Z., & Jiao, B. (2012). Joint relay and jammer selection for secure two-way relay networks. IEEE Transactions on Information Forensics and Security, 7(1), 310–320.
Huang, Y., & Palomar, D. P. (2010). Rank-constrained separable semidefinite programming with applications to optimal beamforming. IEEE Transactions on Signal Processing, 58(2), 664–678.
Boyd, S., & Vandenberghe, L. (2004). Convex optimization. Cambridge: Cambridge University Press.
Solis, F. J., & Wets, R. J.-B. (1981). Minimization by random search techniques. Mathematics of Operations Research, 6(1), 19–30.
Grant, M., & Boyd, S. (2013). Cvx: Matlab software for disciplined convex programming. http://cvxr.com/cvx.
Acknowledgements
The authors would like to acknowledge the support provided by the Deanship of Scientific Research at King Fahd University of Petroleum and Minerals (KFUPM) under Research Grant RG1416.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work is a part of the M.Sc. thesis of the first author [1].
Rights and permissions
About this article
Cite this article
Obeed, M., Mesbah, W. Efficient algorithms for physical layer security in one-way relay systems. Wireless Netw 25, 1327–1339 (2019). https://doi.org/10.1007/s11276-018-1749-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11276-018-1749-5