Abstract
Beside of cryptography-the primary traditional methods for ensuring information security and confidentiality, the appearance of the physical layer security approach plays an important role for not only enabling the data transmission confidentially without relying on higher-layer encryption, but also enhancing confidentiality of the secret key distribution in cryptography. Many techniques are employed in physical layers to improve secure transmission including cooperative relaying and beamforming technique. In this paper, we consider the secrecy rate maximization problems using two techniques mentioned above with two different relaying protocols: Amplify-and-Forward and Decode-and-Forward. The optimization problems with the aim of maximizing secrecy rate subject to total and individual relay power constraints are formulated as nonconvex problems, which can be reformulated as DC (difference of two convex functions) programs and thus can be solved by DC Algorithms (DCA). The special structure of feasible set is exploited which results to an efficient DC decomposition in the sense that it leads to convex subproblems that can be explicitly solved. The numerical results show that the proposed DCA schemes are better than the existing methods in terms of both runtime and secrecy rate.
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Al-Shatri, A., Weber, T.: Achieving the maximum sum rate using DC programming in cellular networks. IEEE Trans. Signal Process. 60(3), 1331–1341 (2012)
Cheng, Y., Pesavento, M.: Joint optimization of source power allocation and distributed relay beamforming in multiuser peer-to-peer relay networks. Signal Process. IEEE Trans. 60(6), 2962–2973 (2012)
Csiszár, K.J.: Broadcast channels with confidential messages. IEEE Trans. Inf. Theory 24(3), 339–348 (1978)
Dong, L., Han, Z., Petropulu, A., Poor, H.: Amplify-and-forward based cooperation for secure wireless communications. In: Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. IEEE International Conference on, pp. 2613–2616 (2009)
Dong, L., Han, Z., Petropulu, A., Poor, H.: Improving wireless physical layer security via cooperating relays. IEEE Trans. Signal Process. 58(3), 1875–1888 (2010)
Ekrem, E., Ulukus, S.: Secrecy in cooperative relay broadcast channels. Inf. Theory IEEE Trans. 57(1), 137–155 (2011)
Fazeli-Dehkordy, S., ShahbazPanahi, S., Gazor, S.: Multiple peer-to-peer communications using a network of relays. Signal Process. IEEE Trans. 57(8), 3053–3062 (2009)
Goel, S., Negi, R.: Guaranteeing Secrecy using Artificial Noise. Wireless Commun. IEEE Trans. 7(6), 2180–2189 (2008)
Havary-Nassab, V., ShahbazPanahi, S., Grami, A.: Joint receive-transmit beamforming for multi-antenna relaying schemes. Signal Process. IEEE Trans. 58(9), 4966–4972 (2010)
He, X., Yener, A.: Cooperation with an untrusted relay: A secrecy perspective. IEEE Trans. Inf. Theor. 56(8), 3807–3827 (2010)
Hero, A.: Secure space-time communication. Inf. Theory IEEE Trans. 49(12), 3235–3249 (2003)
Jeong, C., Kim, I.M., Kim, D.I.: Joint Secure Beamforming Design at the Source and the Relay for an Amplify-and-Forward MIMO Untrusted Relay System. Signal Process. IEEE Trans. 60(1), 310–325 (2012)
Jing, Y., Jafarkhani, H.: Network beamforming using relays with perfect channel information. Inf. Theory IEEE Trans. 55(6), 2499–2517 (2009)
Kha, H.H., Tuan, H.D., Nguyen, H.H.: Fast global optimal power allocation in wireless network by local DC programming. IEEE Trans. Wireless Commun. 11(2), 510–512 (2012)
Khisti, A., Tchamkerten, A., Wornell, G.W.: Secure broadcasting over fading channels. Inf. Theory IEEE Trans. 54(6), 2453–2469 (2008)
Le Thi, H.A.: Contribution à l’optimisation non convexe et l’optimisation globale: Théorie. Algorithmes et Applications. Habilitation à Diriger des Recherches. Université de Rouen, France (1997)
Le Thi, H.A.: An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints. Math. Program. 87(3), 401–426 (2000)
Le Thi, H.A., Huynh, V.N., Pham Dinh, T.: DC Programming and DCA for General DC Programs, vol. 282. Springer, Berlin (2014)
Le Thi, H.A., Van Huynh, N., Pham Dinh, T.: Convergence Analysis of Difference-of-Convex Algorithm with Subanalytic Data. Optim. Theory Appl. 179(1), 103–126 (2018)
Le Thi, H.A., Nguyen, M.C., Pham Dinh, T.: A DC Programming Approach for Finding Communities in Networks. Neural Comput. 26(12), 2827–2854 (2014)
Le Thi, H.A., Nguyen, M.C., Pham Dinh, T.: Self-Organizing Maps by Difference of Convex functions optimization. Data Min. Knowl. Disc. 28, 1336–1365 (2014)
Le Thi, H.A., Nguyen, Q.T., Phan, K.T., Pham Dinh, T.: DC Programming and DCA Based Cross-Layer Optimization in Multi-hop TDMA Networks, pp. 398–408. Intelligent Information and Database Systems: 5th Asian Conference, ACIIDS 2013, Kuala Lumpur, Malaysia, March 18-20, 2013, Proceedings, Part II. Springer Berlin Heidelberg, Berlin, Heidelberg (2013)
Le Thi, H.A., Pham Dinh, T.: The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems. Ann. Oper. Res. 133, 23–46 (2005)
Le Thi, H.A., Pham Dinh, T.: Network utility maximisation: A DC programming approach for Sigmoidal utility function. In: 2013 International Conference on Advanced Technologies for Communications (ATC 2013), pp. 50–54 (2013)
Le Thi, H.A., Pham Dinh, T.: DC programming in communication systems: challenging problems and methods. Vietnam J. Comput. Sci. 1(1), 15–28 (2014)
Le Thi, H.A., Pham Dinh, T.: DC programming and DCA: thirty years of developments. Math. Program. 169, 5–68 (2018)
Le Thi, H.A., Ta, A.S., Pham Dinh, T.: An efficient DCA based algorithm for power control in large scale wireless networks. Appl. Math. Comput. 318, 215–226 (2018)
Le Thi, H.A., Vo, X.T., Le, H.M., Pham Dinh, T.: DC approximation approaches for sparse optimization. Eur. J. Oper. Res. 244(1), 26–46 (2015)
Liang, Y., Poor, H., Shamai, S.: Secure communication over fading channels. Inf. Theory IEEE Trans. 54(6), 2470–2492 (2008)
Munoz-Medina, O., Vidal, J., Agustin, A.: Linear transceiver design in nonregenerative relays with channel state information. Signal Process. IEEE Trans. 55(6), 2593–2604 (2007)
Negi, R., Goel, S.: Secret communication using artificial noise. In: Vehicular Technology Conference, 2005. VTC-2005-Fall. 2005 IEEE 62nd, vol. 3, pp. 1906–1910 (2005)
Parada, P., Blahut, R.: Secrecy capacity of SIMO and slow fading channels. In: Information Theory, 2005. ISIT 2005. Proceedings. International Symposium on, pp. 2152–2155 (2005)
Pham Dinh, T., Le Thi, H.A.: Convex analysis approach to DC programming: Theory, algorithms and applications. Acta Math. Vietnamica 22(1), 289–357 (1997)
Pham Dinh, T., Le Thi, H.A.: Optimization algorithms for solving the trust region subproblem. SIAM J. Optim. 8, 476–505 (1998)
Pham Dinh, T., Le Thi, H.A.: Recent Advances in DC Programming and DCA, vol. 8342. Springer, Berlin Heidelberg (2014)
Shafiee, S., Ulukus, S.: Achievable rates in gaussian miso channels with secrecy constraints. In: Information Theory, 2007. ISIT 2007. IEEE International Symposium on, pp. 2466–2470 (2007)
ShahbazPanahi, S., Dong, M.: Achievable rate region under joint distributed beamforming and power allocation for two-way relay networks. Wireless Commun. IEEE Trans. 11(11), 4026–4037 (2012)
Ta, A.S., Le Thi, H.A., Khadraoui, D., Pham Dinh, T.: Solving QoS Routing Problems by DCA, pp. 460–470. Intelligent Information and Database Systems: Second International Conference, ACIIDS, Hue City, Vietnam, March 24-26, 2010. Proceedings, Part II. Springer Berlin Heidelberg, Berlin, Heidelberg (2010)
Tang, X., Liu, R., Spasojevic, P., Poor, H.: Multiple access channels with generalized feedback and confidential messages. In: Information Theory Workshop, 2007. ITW ’07. IEEE, pp. 608–613 (2007)
Tekin, E., Serbetli, S., Yener, A.: On Secure Signaling for the Gaussian Multiple Access Wire-tap Channel. In: Signals, Systems and Computers, 2005. Conference Record of the Thirty-Ninth Asilomar Conference on, pp. 1747–1751 (2005)
Tekin, E., Yener, A.: The general gaussian multiple-access and two-way wiretap channels: Achievable rates and cooperative jamming. Inf. Theory IEEE Trans. 54(6), 2735–2751 (2008)
Tekin, E., Yener, A.: The Gaussian Multiple Access Wire-Tap Channel. Inf. Theory IEEE Trans. 54(12), 5747–5755 (2008)
Vucic, N., Schubert, M.: DC programming approach for resource allocation in wireless networks. IEEE, Proceedings of the 8th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks pp. 380–386 (2010)
Wang, C., Wang, H.M., Ng, D., Xia, X.G., Liu, C.: Joint Beamforming and Power Allocation for Secrecy in Peer-to-Peer Relay Networks. Wireless Commun. IEEE Trans. 14(6), 3280–3293 (2015)
Wyner, A.D.: The wire-tap channel. Bell Syst. Tech. J. 54, 1355–1387 (1975)
Zhang, J., Gursoy, M.: Collaborative relay beamforming for secrecy. In: Communications (ICC), 2010 IEEE International Conference on, pp. 1–5 (2010)
Zhang, J., Gursoy, M.: Relay beamforming strategies for physical-layer security. In: Information Sciences and Systems (CISS), 2010 44th Annual Conference on, pp. 1–6 (2010)
Zheng, G., Arapoglou, P., Ottersten, B.: Physical layer security in multibeam satellite systems. Wireless Commun. IEEE Trans. 11(2), 852–863 (2012)
Zhou, J., Cao, R., Gao, H., Zhang, C., Lv, T.: Secure Beamforming Design in Wiretap MISO Interference Channels. In: Vehicular Technology Conference (VTC Spring), 2015 IEEE 81st, pp. 1–5 (2015)
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Tran, T.T., Pham Thi, H.A., Pham Dinh, T. et al. DC programming and DCA for enhancing physical layer security via relay beamforming strategies. Optim Lett 15, 2377–2405 (2021). https://doi.org/10.1007/s11590-020-01696-8
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DOI: https://doi.org/10.1007/s11590-020-01696-8