Optimization of a robust collaborative-relay beamforming design for simultaneous wireless information and power transfer

  • Lu-lu Zhao
  • Xing-long Jiang
  • Li-min LiEmail author
  • Guo-qiang Zeng
  • Hui-jie Liu


We investigate a collaborative-relay beamforming design for simultaneous wireless information and power transfer. A non-robust beamforming design that assumes availability of perfect channel state information (CSI) in the relay nodes is addressed. In practical scenarios, CSI errors are usually inevitable; therefore, a robust collaborative-relay beamforming design is proposed. By applying the bisection method and the semidefinite relaxation (SDR) technique, the non-convex optimization problems of both non-robust and robust beamforming designs can be solved. Moreover, the solution returned by the SDR technique may not always be rank-one; thus, an iterative sub-gradient method is presented to acquire the rank-one solution. Simulation results show that under an imperfect CSI case, the proposed robust beamforming design can obtain a better performance than the non-robust one.

Key words

Simultaneous wireless information and power transfer Channel state information Robust beamforming Semidefinite relaxation Iterative sub-gradient 

CLC number



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Beck A, Eldar YC, 2006. Strong duality in nonconvex quadratic optimization with two quadratic constraints. SIAM J Optim, 17(3):844–860. MathSciNetCrossRefzbMATHGoogle Scholar
  2. Boyd S, Vandenberghe L, 2004. Convex Optimization. Cambridge University Press, Cambridge, UK.CrossRefzbMATHGoogle Scholar
  3. Chalise BK, Vandendorpe L, 2010. Optimization of MIMO relays for multipoint-to-multipoint communications: nonrobust and robust designs. IEEE Trans Signal Process, 58(12):6355–6368. MathSciNetCrossRefzbMATHGoogle Scholar
  4. Golub G, van Loan CF, 2012. Matrix Computations. Johns Hopkins University Press, Baltimore, Maryland, USA.zbMATHGoogle Scholar
  5. Grant M, Boyd S, 2015. CVX: Matlab software for disciplined convex programming (Version 2.1, Build 1110).[Accessed on June 10, 2015].Google Scholar
  6. Grover P, Sahai A, 2010. Shannon meets Tesla: wireless information and power transfer. Proc IEEE Int Symp Information Theory, p.2363–2367. Google Scholar
  7. Havary-Nassab V, Shahbazpanahi S, Grami A, et al., 2008. Distributed beamforming for relay networks based on second-order statistics of the channel state information. IEEE Trans Signal Process, 56(9):4306–4316. MathSciNetCrossRefzbMATHGoogle Scholar
  8. Huang JL, Li QZ, Zhang Q, et al., 2014. Relay beamforming for amplify-and-forward multi-antenna relay networks with energy harvesting constraint. IEEE Signal Process Lett, 21(4):454–458. CrossRefGoogle Scholar
  9. Khandaker MRA, Rong Y, 2012. Joint transceiver optimization for multiuser MIMO relay communication systems. IEEE Trans Signal Process, 60(11):5977–5986. MathSciNetCrossRefzbMATHGoogle Scholar
  10. Khandaker MRA, Wong KK, 2014. SWIPT in MISO multicasting systems. IEEE Wirel Commun Lett, 3(3):277–280. CrossRefGoogle Scholar
  11. Khandaker MRA, Wong KK, 2015. Robust secrecy beamforming with energy-harvesting eavesdroppers. IEEE Wirel Commun Lett, 4(1):10–13. CrossRefGoogle Scholar
  12. Kramer G, Gastpar M, Gupta P, 2005. Cooperative strategies and capacity theorems for relay networks. IEEE Trans Inform Theory, 51(9):3037–3063. MathSciNetCrossRefzbMATHGoogle Scholar
  13. Laneman JN, Tse DNC, Wornell GW, 2004. Cooperative diversity in wireless networks: efficient protocols and outage behavior. IEEE Trans Inform Theory, 50(12):3062–3080. MathSciNetCrossRefzbMATHGoogle Scholar
  14. Li GY, Ren PM, Lv GB, et al., 2014. High-rate relay beamforming for simultaneous wireless information and power transfer. Electron Lett, 50(23):1759–1761. CrossRefGoogle Scholar
  15. Ng DWK, Lo ES, Schober R, 2014. Robust beamforming for secure communication in systems with wireless information and power transfer. IEEE Trans Wirel Commun, 13(8):4599–4615. CrossRefGoogle Scholar
  16. Polik I, Terlaky T, 2010. Interior point methods for nonlinear optimization. In: di Pillo G, Schoen F (Eds.), Nonlinear Optimization. Springer Berlin Heidelberg.Google Scholar
  17. Sendonaris A, Erkip E, Aazhang B, 2003. User cooperation diversity. Part I. system description. IEEE Trans Commun, 51(11):1927–1938. CrossRefGoogle Scholar
  18. Sharma V, Mukherji U, Joseph V, et al., 2010. Optimal energy management policies for energy harvesting sensor nodes. IEEE Trans Wirel Commun, 9(4):1326–1336. CrossRefGoogle Scholar
  19. Shen H, Wang JH, Levy BC, et al., 2013. Robust optimization for amplify-and-forward MIMO relaying from a worst-case perspective. IEEE Trans Signal Process, 61(21):5458–5471. CrossRefGoogle Scholar
  20. Tuan HD, Apkarian P, Hosoe S, et al., 2000. D.C. optimization approach to robust control: feasibility problems. Int J Contr, 73(2):89–104. MathSciNetCrossRefzbMATHGoogle Scholar
  21. Varshney LR, 2008. Transporting information and energy simultaneously. Proc IEEE Int Symp on Information Theory, p.1612–1616. Google Scholar
  22. Wang F, Peng T, Huang YW, et al., 2015. Robust transceiver optimization for power-splitting based downlink MISO SWIPT systems. IEEE Signal Process Lett, 22(9):1492–1496. CrossRefGoogle Scholar
  23. Xiang ZZ, Tao MX, 2012. Robust beamforming for wireless information and power transmission. IEEE Wirel Commun Lett, 1(4):372–375. CrossRefGoogle Scholar
  24. Xu CH, Zhang Q, Li QZ, et al., 2014. Robust transceiver design for wireless information and power transmission in underlay MIMO cognitive radio networks. IEEE Commun Lett, 18(9):1665–1668. CrossRefGoogle Scholar
  25. Zhang R, Ho CK, 2013. MIMO broadcasting for simultaneous wireless information and power transfer. IEEE Trans Wirel Commun, 12(5):1989–2001. CrossRefGoogle Scholar
  26. Zheng G, Wong KK, Paulraj A, 2008. Robust collaborative-relay beamforming. IEEE Trans Signal Process, 57(8): 3130–3143. MathSciNetCrossRefzbMATHGoogle Scholar
  27. Zheng G, Wong KK, Paulraj A, et al., 2009. Collaborative-relay beamforming with perfect CSI: optimum and distributed implementation. IEEE Signal Process Lett, 16(4):257–260. CrossRefGoogle Scholar

Copyright information

© Editorial Office of Journal of Zhejiang University Science and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Shanghai Institute of Microsystem and Information TechnologyChinese Academy of SciencesShanghaiChina
  2. 2.Shanghai Engineering Center for MicrosatellitesShanghaiChina
  3. 3.College of Mathematics, Physics and Electronic Information EngineeringWenzhou UniversityWenzhouChina

Personalised recommendations