Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Beck A, Eldar YC, 2006. Strong duality in nonconvex quadratic optimization with two quadratic constraints. SIAM J Optim, 17(3):844–860. https://doi.org/10.1137/050644471
Boyd S, Vandenberghe L, 2004. Convex Optimization. Cambridge University Press, Cambridge, UK.
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. https://doi.org/10.1109/TSP.2010.2077632
Golub G, van Loan CF, 2012. Matrix Computations. Johns Hopkins University Press, Baltimore, Maryland, USA.
Grant M, Boyd S, 2015. CVX: Matlab software for disciplined convex programming (Version 2.1, Build 1110). https://doi.org/cvxr.com/cvx/[Accessed on June 10, 2015].
Grover P, Sahai A, 2010. Shannon meets Tesla: wireless information and power transfer. Proc IEEE Int Symp Information Theory, p.2363–2367. https://doi.org/10.1109/ISIT.2010.5513714
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. https://doi.org/10.1109/TSP.2008.925945
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. https://doi.org/10.1109/LSP.2014.2305737
Khandaker MRA, Rong Y, 2012. Joint transceiver optimization for multiuser MIMO relay communication systems. IEEE Trans Signal Process, 60(11):5977–5986. https://doi.org/10.1109/TSP.2012.2212013
Khandaker MRA, Wong KK, 2014. SWIPT in MISO multicasting systems. IEEE Wirel Commun Lett, 3(3):277–280. https://doi.org/10.1109/WCL.2014.030514.140057
Khandaker MRA, Wong KK, 2015. Robust secrecy beamforming with energy-harvesting eavesdroppers. IEEE Wirel Commun Lett, 4(1):10–13. https://doi.org/10.1109/LWC.2014.2358586
Kramer G, Gastpar M, Gupta P, 2005. Cooperative strategies and capacity theorems for relay networks. IEEE Trans Inform Theory, 51(9):3037–3063. https://doi.org/10.1109/TIT.2005.853304
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. https://doi.org/10.1109/TIT.2004.838089
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. https://doi.org/10.1049/el.2014.2777
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. https://doi.org/10.1109/TWC.2014.2314654
Polik I, Terlaky T, 2010. Interior point methods for nonlinear optimization. In: di Pillo G, Schoen F (Eds.), Nonlinear Optimization. Springer Berlin Heidelberg.
Sendonaris A, Erkip E, Aazhang B, 2003. User cooperation diversity. Part I. system description. IEEE Trans Commun, 51(11):1927–1938. https://doi.org/10.1109/TCOMM.2003.818096
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. https://doi.org/10.1109/TWC.2010.04.080749
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. https://doi.org/10.1109/TSP.2013.2278819
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. https://doi.org/10.1080/002071700219803
Varshney LR, 2008. Transporting information and energy simultaneously. Proc IEEE Int Symp on Information Theory, p.1612–1616. https://doi.org/10.1109/ISIT.2008.4595260
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. https://doi.org/10.1109/LSP.2015.2410833
Xiang ZZ, Tao MX, 2012. Robust beamforming for wireless information and power transmission. IEEE Wirel Commun Lett, 1(4):372–375. https://doi.org/10.1109/WCL.2012.053112.120212
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. https://doi.org/10.1109/LCOMM.2014.2340851
Zhang R, Ho CK, 2013. MIMO broadcasting for simultaneous wireless information and power transfer. IEEE Trans Wirel Commun, 12(5):1989–2001. https://doi.org/10.1109/TWC.2013.031813.120224
Zheng G, Wong KK, Paulraj A, 2008. Robust collaborative-relay beamforming. IEEE Trans Signal Process, 57(8): 3130–3143. https://doi.org/10.1109/TSP.2009.2021456
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. https://doi.org/10.1109/LSP.2008.2010810
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (No. 61601295) and the Zhejiang Provincial Natural Science Foundation of China (No. LY18F030015)
Rights and permissions
About this article
Cite this article
Zhao, Ll., Jiang, Xl., Li, Lm. et al. Optimization of a robust collaborative-relay beamforming design for simultaneous wireless information and power transfer. Frontiers Inf Technol Electronic Eng 19, 1432–1443 (2018). https://doi.org/10.1631/FITEE.1601268
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/FITEE.1601268
Key words
- Simultaneous wireless information and power transfer
- Channel state information
- Robust beamforming
- Semidefinite relaxation
- Iterative sub-gradient