Probabilistic-constrained robust secure transmission for energy harvesting over MISO channels

  • Bin Li
  • Zesong FeiEmail author
Research Paper


In this paper, we consider a system supporting simultaneous wireless information and power transfer (SWIPT), where the transmitter delivers private message to a destination receiver (DR) and powers to multiple energy receivers (ERs) with multiple single-antenna external eavesdroppers (Eves). We study secure robust beamformer and power splitting (PS) design under imperfect channel state information (CSI). The artificial noise (AN) scheme is further utilized at the transmitter to provide strong wireless security. We aim at maximizing the energy harvested by ERs subject to the transmission power constraint, a range of outage constraints concerning the signal-to-interference-plus-noise ratio (SINR) recorded at the DR and the Eves, as well as concerning the energy harvested at the DR. The energy harvesting maximization (EHM) problem is challenging to directly solve, we resort to Bernstein-type inequality restriction technique to reformulate the original problem as a tractable approximated version. Numerical results show that our robust beamforming scheme outperforms the beamforming scheme relying on the worst-case design philosophy.


secure communication wireless power transfer power splitting Bernstein-type inequality robust beamforming 



This work was supported by National Natural Science Foundation of China (Grant Nos. 61371075, 61421001) and 111 Project of China (Grant No. B14010).


  1. 1.
    Krikidis I, Timotheou S, Nikolaou S, et al. Simultaneous wireless information and power transfer in modern communication systems. IEEE Commun Mag, 2014, 52: 104–110CrossRefGoogle Scholar
  2. 2.
    Zhang H, Du J, Cheng J, et al. Resource allocation in SWIPT enabled heterogeneous cloud small cell networks with incomplete CSI. In: Proceedings of IEEE Global Communications Conference (GLOBECOM), Washington, 2016. 4–8Google Scholar
  3. 3.
    Bi S, Ho C K, Zhang R. Wireless powered communication: opportunities and challenges. IEEE Commun Mag, 2015, 53: 117–125CrossRefGoogle Scholar
  4. 4.
    Chen X, Ng D W K, Chen H H. Secrecy wireless information and power transfer: challenges and opportunities. IEEE Wirel Commun, 2016, 23: 54–61CrossRefGoogle Scholar
  5. 5.
    Xu J, Liu L, Zhang R. Multiuser MISO beamforming for simultaneous wireless information and power transfer. IEEE Trans Signal Process, 2014, 62: 4798–4810MathSciNetCrossRefGoogle Scholar
  6. 6.
    Shi Q, Liu L, Xu W, et al. Joint transmit beamforming and receive power splitting for MISO SWIPT systems. IEEE Trans Wirel Commun, 2014, 13: 3269–3280CrossRefGoogle Scholar
  7. 7.
    Wang H M, Xia X G. Enhancing wireless secrecy via cooperation: signal design and optimization. IEEE Commun Mag, 2015, 53: 47–53CrossRefGoogle Scholar
  8. 8.
    Chu Z, Xing H, Johnston M, et al. Secrecy rate optimizations for a MISO secrecy channel with multiple multiantenna eavesdroppers, IEEE Trans Wirel Commun, 2016, 15: 283–297Google Scholar
  9. 9.
    Liu L, Zhang R, Chua K C. Secrecy wireless information and power transfer with MISO beamforming. IEEE Trans Signal Process, 2014, 62: 1850–1863MathSciNetCrossRefGoogle Scholar
  10. 10.
    Shi Q, Xu W, Wu J, et al. Secure beamforming for MIMO broadcasting with wireless information and power transfer. IEEE Trans Wirel Commun, 2015, 19: 2841–2853CrossRefGoogle Scholar
  11. 11.
    Wang H M, Liu F, Yang M. Joint cooperative beamforming, jamming, and power allocation to secure AF relay systems. IEEE Trans Veh Tech, 2015, 64: 4893–4898CrossRefGoogle Scholar
  12. 12.
    Li Q, Zhang Q, Qin J. Secure relay beamforming for simultaneous wireless information and power transfer in nonregenerative relay networks. IEEE Trans Veh Tech, 2014, 63: 2462–2467CrossRefGoogle Scholar
  13. 13.
    Fang B, Qian Z, Zhong W, et al. AN-aided secrecy precoding for SWIPT in cognitive MIMO broadcast channels. IEEE Commun Lett, 2015, 19: 1632–1635CrossRefGoogle Scholar
  14. 14.
    Zhang M, Liu Y, Zhang R. Artificial noise aided secrecy information and power transfer in OFDMA systems. IEEE Trans Wirel Commun, 2016, 15: 3085–3096CrossRefGoogle Scholar
  15. 15.
    Zhang L J, Jin L, Luo W Y, et al. Robust secure transmission for multiuser MISO systems with probabilistic QoS constraints. Sci China Inf Sci, 2016, 59: 022309Google Scholar
  16. 16.
    Li B, Fei Z. Robust beamforming and cooperative jamming for secure transmission in DF relay systems. EURASIP J Adv Signal Process, 2016, 68: 1–11Google Scholar
  17. 17.
    Zhang Q, Huang X, Li Q, et al. Cooperative jamming aided robust secure transmission for wireless information and power transfer in MISO channels. IEEE Trans Wirel Commun, 2015, 63: 906–915CrossRefGoogle Scholar
  18. 18.
    Zhang H, Huang Y, Li C, et al. Secure beamforming design for SWIPT in MISO broadcast channel with confidential messages and external eavesdroppers. IEEE Trans Wirel Commun, 2016, 15: 7807–7819CrossRefGoogle Scholar
  19. 19.
    Li B, Fei Z, Chen H. Robust artificial noise-aided secure beamforming in wireless-powered non-regenerative relay networks. IEEE Access, 2016, 4: 7921–7929CrossRefGoogle Scholar
  20. 20.
    Wang F, Peng T, Huan Y, et al. Robust transceiver optimization for power-splitting based downlink MISO SWIPT systems. IEEE Signal Process Lett, 2015, 22: 1492–1496CrossRefGoogle Scholar
  21. 21.
    Wu W, Wang B. Robust downlink beamforming design for multiuser MISO communication system with SWIPT. In: Proceedings of IEEE International Conference on Communications (ICC), London, 2015. 4751–4756Google Scholar
  22. 22.
    Khandaker M R A, Wong K K. Robust secrecy beamforming with energy-harvesting eavesdroppers. IEEE Wirel Commun Lett, 2015, 4: 10–13CrossRefGoogle Scholar
  23. 23.
    Wu W, Wang B. Efficient transmission solutions for MIMO wiretap channels with SWIPT. IEEE Commun Lett, 2015, 19: 1989–2001CrossRefGoogle Scholar
  24. 24.
    Zhu Z, Chu Z, Wang Z, et al. Outage constrained robust beamforming for secure broadcasting systems with energy harvesting. IEEE Trans Wirel Commun, 2016, 15: 7610–7620CrossRefGoogle Scholar
  25. 25.
    Guo C, Liao B, Huang L, et al. Convexity of fairnessaware resource allocation in wireless powered communication networks. IEEE Commun Lett, 2016, 20: 474–477CrossRefGoogle Scholar
  26. 26.
    Ng D W K, Lo E S, Schober R. Robust beamforming for secure communication in systems with wireless information and power transfer. IEEE Trans Wirel Commun, 2014, 13: 4599–4615CrossRefGoogle Scholar
  27. 27.
    Wang K Y, So A M C, Chang T H, et al. Outage constrained robust transmit optimization for multiuser MISO downlinks: Tractable approximations by conic optimization. IEEE Trans Signal Process, 2014, 62: 5690–5705MathSciNetCrossRefGoogle Scholar
  28. 28.
    Yang S, Lv T, Hanzo L. Semidefinite programming relaxation based virtually antipodal detection for MIMO systems using Gray-coded high-order QAM. IEEE Trans Veh Tech, 2013, 62: 1667–1677CrossRefGoogle Scholar
  29. 29.
    Boyd S, Vandenberghe L. Convex Optimization. New York: Cambridge University Press,2004CrossRefzbMATHGoogle Scholar
  30. 30.
    Rashid U, Tuan H D, Kha H H, et al. Joint optimization of source precoding and relay beamforming in wireless MIMO relay networks. IEEE Trans Commun, 2014, 62: 488–499CrossRefGoogle Scholar
  31. 31.
    Cheng Y, Pesavento M. Joint optimization of source power allocation and distributed relay beamforming in multiuser peer-to-peer relay networks. IEEE Trans Signal Process, 2012, 60: 2962–2973MathSciNetCrossRefGoogle Scholar
  32. 32.
    Chu Z, Zhu Z, Hussein J. Robust optimization for AN-aided transmission and power splitting for secure MISO SWIPT system. IEEE Commun Lett, 2016, 20: 1571–1574CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Information and ElectronicsBeijing Institute of TechnologyBeijingChina

Personalised recommendations