On the Optimal Precoder Design for Energy-Efficient and Secure MIMO Systems

  • Tung T. Vu Ho Chi Minh City University of Technology, VNU-HCM, Vietnam
  • Ha Hoang Kha Ho Chi Minh City University of Technology, VNU-HCM, Vietnam


In this research work, we investigate precoder designs to maximize the energy efficiency (EE) of secure multiple-input multiple-output (MIMO) systems in the presence of an eavesdropper. In general, the secure energy efficiency maximization (SEEM) problem is highly nonlinear and nonconvex and hard to be solved directly. To overcome this difficulty, we employ a branch-and-reduce-and-bound (BRB) approach to obtain the globally optimal solution. Since it is observed that the BRB algorithm suffers from highly computational cost, its globally optimal solution is importantly served as a benchmark for the performance evaluation of the suboptimal algorithms. Additionally, we also develop a low-complexity approach using the well-known zero-forcing (ZF) technique to cancel the wiretapped signal, making the design problem more amenable. Using the ZF based method, we transform the SEEM problem to a concave-convex fractional one which can be solved by applying the combination of the Dinkelbach and bisection search algorithm. Simulation results show that the ZF-based method can converge fast and obtain a sub-optimal EE performance which is closed to the optimal EE performance of the BRB method. The ZF based scheme also shows its advantages in terms of the energy efficiency in comparison with the conventional secrecy rate maximization precoder design.


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[1] Y. W. P. Hong, P. C. Lan, and C. C. J. Kuo, “Enhancing physical-layer secrecy in multiantenna wireless systems: An overview of signal processing approaches,” IEEE Signal Proces. Mag., vol. 30, no. 5, pp. 29–40, Sep. 2013.
[2] A. Mukherjee, S. A. Fakoorian, J. Huang, and A. L. Swindlehurst, “Principles of physical layer security in multiuser wireless networks: A survey,” IEEE Commun. Surveys & Tutorials, vol. 16, no. 3, pp. 1550–1573, 2014.
[3] H. D. Ly, T. Liu, and Y. Liang, “Multiple-input multipleoutput gaussian broadcast channels with common and confidential messages,” IEEE Trans. Inf. Theory, vol. 56, no. 11, pp. 5477–5487, Nov. 2010.
[4] H. Reboredo, J. Xavier, and M. R. D. Rodrigues, “Filter design with secrecy constraints: The MIMO gaussian wiretap channel,” IEEE Trans. Signal Process., vol. 61, no. 15, pp. 3799–3814, Aug. 2013.
[5] G. Geraci, S. Singh, J. G. Andrews, J. Yuan, and I. B. Collings, “Secrecy rates in broadcast channels with confidential messages and external eavesdroppers,” IEEE Trans. Wireless Commun., vol. 13, no. 5, pp. 2931–2943, May 2014.
[6] M. Hanif, L.-N. Tran, M. Juntti, and S. Glisic, “On linear precoding strategies for secrecy rate maximization in multiuser multiantenna wireless networks,” IEEE Trans. Signal Process., vol. 62, no. 14, pp. 3536–3551, July 2014.
[7] Y.Wu, C. Xiao, Z. Ding, X. Gao, and S. Jin, “Linear MIMO precoding in multi-antenna wiretap channels for finite-alphabet data,” in Proc. IEEE Int. Conf. Commun. (ICC), Jun. 2012, pp. 2156–2160.
[8] N. Yang, G. Geraci, J. Yuan, and R. Malaney, “Confidential broadcasting via linear precoding in non-homogeneous MIMO multiuser networks,” IEEE Trans. Commun., vol. 62, no. 7, pp. 2515–2530, Jul. 2014.
[9] I. Krikidis and B. Ottersten, “Secrecy sum-rate for orthogonal random beamforming with opportunistic scheduling,” IEEE Signal Process. Lett, vol. 20, no. 2, pp. 141–144, Feb. 2013.
[10] K. Xie and W. Chen, “Precoding strategy based on SLR for secure communication in MUME wiretap systems,” in Proc. IEEE Global Commun. Conf. (GLOBECOM), Dec. 2012, pp. 783–788.
[11] S. Fakoorian and A. Swindlehurst, “MIMO interference channel with confidential messages: Achievable secrecy rates and precoder design,” IEEE Trans. Inf. Forens. Security, vol. 6, no. 3, pp. 640–649, Sep. 2011.
[12] Q. Li, M. Hong, H.-T. Wai, Y.-F. Liu, W.-K. Ma, and Z.-Q. Luo, “Transmit solutions for MIMO wiretap channels using alternating optimization,” IEEE J. Selected Areas in Commun., vol. 31, no. 9, pp. 1714–1727, Sep. 2013.
[13] S. Fakoorian and A. Swindlehurst, “Solutions for the MIMO gaussian wiretap channel with a cooperative jammer,” IEEE Trans. Signal Process., vol. 59, no. 10, pp. 5013–5022, Oct. 2011.
[14] Z. Chu, K. Cumanan, Z. Ding, M. Johnston, and S. Le Goff, “Secrecy rate optimizations for a MIMO secrecy channel with a cooperative jammer,” IEEE Trans. Veh. Technol., vol. 64, no. 5, pp. 1833–1847, May 2015.
[15] X. Zhang, M. R. McKay, X. Zhou, and R.W. Heath, “Artificialnoise-aided secure multi-antenna transmission with limited feedback,” IEEE Trans. Wireless Commun., vol. 14, no. 5, pp. 2742–2754, May 2015.
[16] X. Chen and L. Lei, “Energy-efficient optimization for physical layer security in multi-antenna downlink networks with QoS guarantee,” IEEE Commun. Lett., vol. 17, no. 4, pp. 637–640, Apr. 2013.
[17] G. Wu, C. Yang, S. Li, and G. Y. Li, “Recent advances in energy-efficient networks and their application in 5g systems,”IEEE Wireless Commun., vol. 22, no. 2, pp. 145–151, Apr. 2015.
[18] B. Zhuang, D. Guo, and M. L. Honig, “Energy-efficient cell activation, user association, and spectrum allocation in heterogeneous networks,” IEEE J. Sel. Areas. Commun., vol. 34, no. 4, pp. 823–831, Apr. 2016.
[19] M. Dehghan, D. Goeckel, M. Ghaderi, and Z. Ding, “Energy efficiency of cooperative jamming strategies in secure wireless networks,” IEEE Trans. Wireless Commun., vol. 11, no. 9, pp. 3025–3029, Sep. 2012.
[20] C. Comaniciu and H. Poor, “On energy-secrecy trade-offs for gaussian wiretap channels,” IEEE Trans. Inf. Forens. Security, vol. 8, no. 2, pp. 314–323, Feb. 2013.
[21] H. Zhang, Y. Huang, S. Li, and L. Yang, “Energy-efficient precoder design for MIMO wiretap channels,” IEEE Commun. Lett., vol. 18, no. 9, pp. 1559–1562, Sep. 2014.
[22] H. Tuy, F. Al-Khayyal, and P. Thach, “Monotonic optimization: Branch and cut methods,” in Essays and Surveys in Global Optimization. Springer US, 2005, pp. 39–78.
[23] T. T. Vu and H. H. Kha, “Optimal precoder designs for energy-efficiency maximization in secure MIMO systems,” in Proc. 3rd Nat. Found. Sci. Technology Develop. Conf. Inf. Comput. Sci. (NICS), Sep. 2016, pp. 50–55.
[24] J. Xu and L. Qiu, “Energy efficiency optimization for MIMO broadcast channels,” IEEE Trans. Wireless Commun., vol. 12, no. 2, pp. 690–701, Feb. 2013.
[25] J. Li and A. P. Petropulu, “Transmitter optimization for achieving secrecy capacity in gaussian MIMO wiretap channels.” [Online]. Available: arXiv:0909.2622v1
[26] W. Dinkelbach, “On nonlinear fractional programming,”Manage. Sci., vol. 13, no. 7, pp. 492–498, 1967.
[27] E. Bj ¨ornson, G. Zheng, M. Bengtsson, and B. Ottersten, “Robust monotonic optimization framework for multicell MISO systems,” IEEE Trans. Signal Process., vol. 60, no. 5, pp. 2508–2523, May 2012.
[28] S. Joshi, P. Weeraddana, M. Codreanu, and M. Latva-aho, “Weighted sum-rate maximization for MISO downlink cellular networks via branch and bound,” IEEE Trans. Signal Process., vol. 60, no. 4, pp. 2090–2095, Apr. 2012.
[29] N. T. H. Phuong and H. Tuy, “A unified monotonic approach to generalized linear fractional programming,” J. Global Optimization, vol. 26, no. 3, pp. 229–259, 2003.
[30] R. Liu, T. Liu, H. Poor, and S. Shamai, “Multiple-input multiple-output gaussian broadcast channels with confidential messages,” IEEE Trans. Inf. Theory, vol. 56, no. 9, pp. 4215–4227, Sep. 2010.
[31] F. Oggier and B. Hassibi, “The secrecy capacity of the MIMO wiretap channel,” IEEE Trans. Inf. Theory, vol. 57, no. 8, pp. 4961–4972, Aug. 2011.
[32] M. Grant and S. Boyd, “CVX: Matlab software for disciplined convex programming, version 2.1,” http://cvxr.com/cvx, Mar. 2014.
[33] K. B. Petersen and M. S. Pedersen, The Matrix Cookbook. Technical University of Denmark, Nov. 2012.
[34] S. Boyd and L. Vandenberghe, Convex Optimization. New York, NY: Cambridge University Press, 2004.

How to Cite
T. VU, Tung; KHA, Ha Hoang. On the Optimal Precoder Design for Energy-Efficient and Secure MIMO Systems. Journal of Science and Technology: Issue on Information and Communications Technology, [S.l.], v. 3, n. 1, p. 1-8, mar. 2017. ISSN 1859-1531. Available at: <http://ict.jst.udn.vn/index.php/jst/article/view/32>. Date accessed: 29 may 2020. doi: https://doi.org/10.31130/jst.2017.32.