This paper proposes a zero-forcing beamforming design for the energy efficiency optimization of the magnetic resonance based wireless power transfer system with multiple transmitter coils, which aims to secure energy transfer control. A scheme based on beamforming technology is proposed to prevent unauthorized users from accessing the system, which builds a beamforming model consisting of multiple transmitter coils, a target receiver, and a non-target receiver to simulate the actual system. Then to optimize the proposed system's energy efficiency while constraining the target receiver's energy, spectral efficiency, and transmitter's power, the proposed beamforming model is constructed as an optimization problem. To solve this non-convex nonlinear fractional programming problem, the Dinkelbach algorithm is used for fractional conversion, and then the zero-forcing constraints are equivalently replaced. Finally, two solutions of the nonlinear solution and closed-form solution are derived. The simulation results show that the energy efficiency optimization strategies of zero-forcing beamforming with the two derived solutions can satisfy the design requirements.
1. Zhang, Z., H. Pang, and A. Georgiadis, "Wireless power transfer: An overview," IEEE Transactions on Industrial Electronics, Vol. 66, No. 2, 1044-1058, Feb. 2019. doi:10.1109/TIE.2018.2835378
2. Sun, H., H. Lin, and F. Zhu, "Magnetic resonant beamforming for secured wireless power transfer," IEEE Signal Processing Letters, Vol. 24, No. 9, 1173-1177, Aug. 2017. doi:10.1109/LSP.2017.2703105
3. Sun, H., F. Gao, and F. Zhu, "Inductor design of magnetic resonance coupled circuits for secured wireless power transfer," IEEE International Conference on Communications, 1-6, 2017.
4. Campi, T., S. Cruciani, and F. Palandrani, "Wireless power transfer charging system for AIMDs and pacemakers," IEEE Transactions on Microwave Theory and Techniques, Vol. 64, No. 2, 633-642, Feb. 2016. doi:10.1109/TMTT.2015.2511011
5. Moghadam, M. R. and R. Zhang, "Multiuser wireless power transfer via magnetic resonant coupling: Performance analysis, charging control, and power region characterization," IEEE Transactions on Signal and Information Processing over Networks, Vol. 2, No. 1, 72-83, Mar. 2016. doi:10.1109/TSIPN.2015.2505904
6. Kisseleff, S., W. Gerstacker, and R. Schober, "Channel capacity of magnetic induction based wireless underground sensor networks under practical constraints," IEEE Wireless Communication and Networking Conference, 2603-2608, 2013.
7. Kisseleff, S., I. F. Akyildiz, and W. H. Gerstacker, "Throughput of the magnetic induction based wireless underground sensor networks: Key optimization techniques," IEEE Transactions on Communications, Vol. 62, No. 12, 4426-4439, Dec. 2014. doi:10.1109/TCOMM.2014.2367030
8. Yang, G., M. R. Moghadam, and R. Zhang, "Magnetic MIMO signal processing and optimization for wireless power transfer," IEEE Transactions on Signal Processing, Vol. 65, No. 11, 2860-2874, Jun. 2017. doi:10.1109/TSP.2017.2673816
9. Jadidian, J. and D. Katabi, "Magnetic MIMO: How to charge your phone in your pocket," 20th ACM Annual International Conference on Mobile Computing and Networking, 495-506, 2014.
10. Peng, C., Q. Shi, and W. Xu, "Energy efficiency optimization for multi-user MISO SWIPT systems," IEEE China Summit and International Conference on Signal and Information Processing, 772-776, 2015.
11. Ng, D. W., E. S. Lo, and R. Schober, "Wireless information and power transfer: Energy efficiency optimization in OFDMA systems," IEEE Transactions on Wireless Communications, Vol. 12, No. 12, 6352-6370, Dec. 2013. doi:10.1109/TWC.2013.103113.130470
12. Timotheou, S., I. Krikidis, and G. Zheng, "Beamforming for MISO interference channels with QoS and RF energy transfer," IEEE Transactions on Wireless Communications, Vol. 13, No. 5, 2646-2658, May 2014. doi:10.1109/TWC.2014.032514.131199
13. Tang, J., J. Luo, and M. Liu, "Energy efficiency optimization for NOMA with SWIPT," IEEE Journal of Selected Topics in Signal Processing, Vol. 13, No. 3, 452-466, Jun. 2019. doi:10.1109/JSTSP.2019.2898114
14. Guimaraes, D. A., G. H. Floriano, and L. S. Chaves, "A tutorial on the CVX system for modeling and solving convex optimization problems," IEEE Latin America Transactions, Vol. 13, No. 5, 1228-1257, May 2015. doi:10.1109/TLA.2015.7111976
15. Chu, Z., Z. Zhu, and M. Johnston, "Simultaneous wireless information power transfer for MISO secrecy channel," IEEE Transactions on Vehicular Technology, Vol. 65, No. 9, 6913-6925, Sept. 2016. doi:10.1109/TVT.2015.2499439
16. Xu, K., et al., "SWIPT in mMIMO system with non-linear energy-harvesting terminals: Protocol design and performance optimization," EURASIP Journal on Wireless Communications and Networking, 72, 2019. doi:10.1186/s13638-019-1378-4
17. Yang, X., Z. Wang, X. Wan, and Z. Fan, "Secure energy-efficient resource allocation algorithm of massive MIMO system with SWIPT. Electronics," Electronics, Vol. 9, No. 1, 20, 2020.