logo

SCIENTIA SINICA Informationis, Volume 48, Issue 2: 221-232(2018) https://doi.org/10.1360/N112017-00028

Secure beamforming for two-way multiantenna relay systems

More info
  • ReceivedApr 6, 2017
  • AcceptedJun 11, 2017
  • PublishedNov 20, 2017

Abstract

In two-way multiantenna relay systems, confidential information can be easily intercepted by eavesdroppers. To overcome this problem, two secure beamforming schemes are proposed: secrecy sum rate maximization beamforming (SSRMB) and null space beamforming (NSB). For the SSRMB scheme, the nonconvex secrecy sum rate maximization problem is solved using a successive convex approximation strategy, which is convergent. The obtained beamforming solution is locally optimal to the original problem. For the special scenario where the number of antennas at the relay is more than the number of eavesdroppers, the NSB scheme with a low complexity is proposed. The beamforming solution is obtained by solving a generalized Rayleigh quotient problem. Simulation results demonstrate that the proposed schemes can effectively improve the security performance, and the SSRMB scheme has a fast convergence rate.


Funded by

国家高技术研究发展计划 (863)(2015AA01A708)

国家自然科学基金(61601514)

国家自然科学基金(61379006)

国家自然科学基金(61501516)

中国博士后科学基金(2016M592990)


References

[1] Wyner A D. The Wire-Tap Channel. Bell Syst Technical J, 1975, 54: 1355-1387 CrossRef Google Scholar

[2] Tsiligkaridis T. Secure MIMO Communications Under Quantized Channel Feedback in the Presence of Jamming. IEEE Trans Signal Process, 2014, 62: 6265-6275 CrossRef ADS arXiv Google Scholar

[3] Zhang L J, Jin L, Luo W Y, et al. Robust secure transmission for multiusers MIMO systems with probabilistic QoS constraints. Sci China Inf Sci, 2016, 59: 022309. Google Scholar

[4] Chen T, Yu H, Wei G. Study on the physical layer security of cognitive radio networks and its robustness design. J Electron Inf Technol, 2012, 34: 770--775. Google Scholar

[5] Jindal A, Kundu C, Bose R. Secrecy Outage of Dual-Hop AF Relay System With Relay Selection Without Eavesdropper's CSI. IEEE Commun Lett, 2014, 18: 1759-1762 CrossRef Google Scholar

[6] Zhang R, Liang Y C, Chai C C. Optimal beamforming for two-way multi-antenna relay channel with analogue network coding. IEEE J Sel Areas Commun, 2009, 27: 699-712 CrossRef Google Scholar

[7] Wang J, Zhang Y, Long H. Cooperative jamming and power allocation with untrusty two-way relay nodes. IET Commun, 2014, 8: 2290-2297 CrossRef Google Scholar

[8] Mo J, Tao M, Liu Y. Secure Beamforming for MIMO Two-Way Communications With an Untrusted Relay. IEEE Trans Signal Process, 2014, 62: 2185-2199 CrossRef ADS arXiv Google Scholar

[9] 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. IEEE Trans Inf Foren Secur, 2013, 7: 310--320. Google Scholar

[10] Ding Z, Ma Z, Fan P. Asymptotic Studies for the Impact of Antenna Selection on Secure Two-Way Relaying Communications with Artificial Noise. IEEE Trans Wireless Commun, 2014, 13: 2189-2203 CrossRef Google Scholar

[11] Ding Z, Xu M, Lu J. Improving Wireless Security for Bidirectional Communication Scenarios. IEEE Trans Veh Technol, 2012, 61: 2842-2848 CrossRef Google Scholar

[12] Mukherjee A, Swindlehurst A L. Securing multi-antenna two-way relay channels with analog network coding against eavesdroppers. In: Proceedings of IEEE 11th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Marrakech, 2010. 1--5. Google Scholar

[13] Chen J, Zhang R, Song L. Joint Relay and Jammer Selection for Secure Two-Way Relay Networks. IEEE TransInformForensic Secur, 2012, 7: 310-320 CrossRef Google Scholar

[14] Yang Y, Sun C, Zhao H. Algorithms for Secrecy Guarantee With Null Space Beamforming in Two-Way Relay Networks. IEEE Trans Signal Process, 2014, 62: 2111-2126 CrossRef ADS Google Scholar

[15] Wang H M, Yin Q, Xia X G. Distributed Beamforming for Physical-Layer Security of Two-Way Relay Networks. IEEE Trans Signal Process, 2012, 60: 3532-3545 CrossRef ADS Google Scholar

[16] Wang H M, Luo M, Yin Q. Hybrid Cooperative Beamforming and Jamming for Physical-Layer Security of Two-Way Relay Networks. IEEE TransInformForensic Secur, 2013, 8: 2007-2020 CrossRef Google Scholar

[17] Boyd S, Vandenberghe L. Convex Optimization. Cambridge: Cambridge University Press, 2004. Google Scholar

[18] Luo Z Q, Ma W K, So A C, et al. Semidefinite relaxation of quadratic optimization problems. IEEE Signal Proc Mag, 2010, 27: 20--34. Google Scholar

[19] Beck A, Ben-Tal A, Tetruashvili L. A sequential parametric convex approximation method with applications to nonconvex truss topology design problems. J Glob Optim, 2010, 47: 29-51 CrossRef Google Scholar

[20] Boyd S P, Grant M C. CVX: matlab software for disciplined convex programming, version 2.0. 2012. http://cvxr.com/cvx. Google Scholar

[21] Horn R A, Johnson C R. Matrix Analysis. 2nd ed. Cambridge: Cambridge University Press, 2013. Google Scholar

  • Figure 1

    System model

  • Figure 2

    The relationship between the secrecy sum rate and the maximum transmitting power

  • Figure 3

    The security performance VS the eavesdropping nodes number

  • Figure 4

    The relationship between the secrecy sum rate and the iterations number of SSRMB scheme

  •   
    算法1 SCA optimized algorithm for the question (20)
    Initialization: set threshold: $\varepsilon~$, maximum iterations: $L$, $n~=~0$, and initial point in (28): $(t_i^{(n)},x_{i,2}^{(n)},y_{k,1}^{(n)},y_{k,2}^{(n)},t_e^{(n)})$,
    1: while ($|R_s^{(n)}~-~R_s^{(n~-~1)}|~\ge~\varepsilon~$ or $n~\le~L$), do
    2: solve the question of (28), and take $(t_i^~\star,~x_{i,2}^~\star,~y_{k,1}^~\star,~y_{k,2}^~\star,~t_e^~\star~)$ as the optional solution of $({t_i},{x_{i,2}},{y_{k,1}},{y_{k,2}},{t_e})$,
    3: $n~=~n~+~1$,
    4: set $(t_i^{(n)},x_{i,2}^{(n)},y_{k,1}^{(n)},y_{k,2}^{(n)},t_e^{(n)})~=~(t_i^~\star,~x_{i,2}^~\star,~y_{k,1}^~\star,~y_{k,2}^~\star,~t_e^~\star~)$,
    end while

Copyright 2019 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1