American Institute of Mathematical Sciences

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November  2020, 16(6): 2913-2922. doi: 10.3934/jimo.2019086

A zero-forcing beamforming based time switching protocol for wireless powered internet of things system

Hanyu Cao 1, , Meiying Zhang 1, , Huanxi Cai 1, , Wei Gong 1, , Min Su 1, and  Bin Li 1,2,,

1. 

College of Electrical and Information Technology, Sichuan University, Chengdu, China
2. 

Key Laboratory of Wireless Power Transmission of Ministry of Education, Sichuan University, Chengdu, China

* Corresponding author: Bin Li

Received  November 2018 Revised  March 2019 Published  July 2019

Fund Project: This work was supported by a grant from National Natural Science Foundation of China under number 61701124, a grant from Science and Technology on Space Intelligent Control Laboratory, No.KGJZDSYS-2018-03, a grant from Sichuan Province Government under No.2019YJ0105, and a grant from Fundamental Research Funds for the Central Universities(China)

In this paper, a time switching (TS) protocol for the wireless powered communications system with per-antenna power constraints is considered. To eliminate the multi-user interference, we adopt the zero-forcing beamforming scheme to maximize the sum rate performance. A two-step algorithm is proposed to solve the sum rate maximization problem with per-antenna power constraints. More specifically, golden section search method is used to find optimal time switching factor in the first step. For each given TS factor, the sub-problem in the second step is convex, which can be efficiently solved by standard software package. Numerical results are provided to demonstrate the effectiveness of the proposed methods, and some interesting results are also observed.

Keywords: Energy harvesting, time switching protocol, zero-forcing beamforming, per-antenna power constraints.
Mathematics Subject Classification: Primary: 90C90 Secondary: 49M37.
Citation: Hanyu Cao, Meiying Zhang, Huanxi Cai, Wei Gong, Min Su, Bin Li. A zero-forcing beamforming based time switching protocol for wireless powered internet of things system. Journal of Industrial & Management Optimization, 2020, 16 (6) : 2913-2922. doi: 10.3934/jimo.2019086
References:
[1]

Internet of Things in 2020 - A Road Map in the Future, 2008. Available from: http://www.smart{_}systems{_}integration.org/public/documents/publications/Internet{_}of{_}Things{_}in{_}2020{_}EC-EPoSS{_}Workshop{_}Report{_}2008{_}v3.pdf. Google Scholar

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[3]

B. Clerckx and E. Bayguzina, Waveform design for wireless power transfer, IEEE Trans. Signal Process, 64 (2016), 6313-6328.  doi: 10.1109/TSP.2016.2601284.  Google Scholar

[4]

Z. G. Feng, K. F. C. Yiu and S. E. Nordholm, A two-stage method for the design of near-field broadband beamformer, IEEE Transactions on Signal Processing, 59 (2011), 3647-3656.  doi: 10.1109/TSP.2011.2133490.  Google Scholar

[5]

Z. G. Feng, K. F. C. Yiu and S. E. Nordholm, Placement design of microphone arrays in near-field broadband beamformers, IEEE Transactions on Signal Processing, 60 (2012), 1195-1204.  doi: 10.1109/TSP.2011.2178491.  Google Scholar

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M. Grant, S. Boyd, L. Liberti and N. Maculan, Disciplined convex programming in global optimization: From theory to implementation, Nonconvex Optimization and Its Applications, 84 (2006), 155-210.  doi: 10.1007/0-387-30528-9_7.  Google Scholar

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B. Li, H. H. Dam, A. Cantoni and K. L. Teo, A first-order optimal zero-forcing beamformer design for multiuser MIMO systems via a regularized dual accelerated gradient method, IEEE Commun. Lett., 19 (2015), 195-198.  doi: 10.3934/naco.2016012.  Google Scholar

[8]

B. Li, H. H. Dam, A. Cantoni and K. L. Teo, A global optimal zero-forcing beamformer design with signed power-of-two coefficients, Journal of Industrial and Management Optimization, 12 (2016), 595-607.  doi: 10.3934/jimo.2016.12.595.  Google Scholar

[9]

B. Li and Y. Rong, Joint transceiver optimization for wireless information and energy transfer in nonregenerative MIMO relay systems, IEEE Transactions on Vehicular Technology, 67 (2018), 8348-8362.  doi: 10.1109/TVT.2018.2846556.  Google Scholar

[10]

B. Li and Y. Rong, AF MIMO relay systems with wireless powered relay node and direct link, IEEE Transactions on Communications, 66 (2018), 1508-1519.  doi: 10.1109/TCOMM.2017.2788006.  Google Scholar

[11]

B. Li, C. Z. Wu, H. H. Dam, A. Cantoni and K. L. Teo, A parallel low complexity zero-forcing beamformer design for multiuser MIMO systems via a regularized dual decomposition method, IEEE Trans. Signal Process, 63 (2015), 4179-4190.  doi: 10.1109/TSP.2015.2437846.  Google Scholar

[12]

X. Lu, P. Wang, D. Niyato, D. I. Kim and Z. Han, Wireless networks with RF energy harvesting: A contemporary survey, IEEE Communications Surveys & Tutorials, 17 (2015), 757–789. doi: 10.1109/COMST.2014.2368999.  Google Scholar

[13]

X. Lu, P. Wang, D. Niyato, D. I. Kim and Z. Han, Wireless charging technologies: fundamentals, standards, and network applications, IEEE Communications Surveys & Tutorials, 18 (2016), 1413–1452. doi: 10.1109/COMST.2015.2499783.  Google Scholar

[14]

L. Ma, Y. Wang and Y. Xu, Sum rate optimization for SWIPT system based on zero-forcing beamforming and time switching, 2017 13th International Wireless Communications and Mobile Computing Conference (IWCMC), (2017), 351–356. doi: 10.1109/TSP.2015.2489603.  Google Scholar

[15]

A. A. Okandeji and et al., SWIPT in MISO full-duplex systems, Journal of Communications and Networks, 19 (2017), 470-480.  doi: 10.1109/JCN.2017.000079.  Google Scholar

[16]

C. Peng, Q. Shi, W. Xu and M. Hong, Energy efficiency optimization for multi-user MISO swipt systems, 2015 IEEE China Summit and International Conference on Signal and Information Processing (ChinaSIP), (2015), 772–776. doi: 10.1109/TSP.2015.2489603.  Google Scholar

[17]

T. D. Ponnimbaduge Perera, D. N. K. Jayakody, S. K. Sharma, S. Chatzinotas and J. Li, Simultaneous wireless information and power transfer (SWIPT): Recent advances and future challenges, IEEE Communications Surveys & Tutorials, 20 (2018), 264–302. doi: 10.1109/COMST.2017.2783901.  Google Scholar

[18]

Q. Shi, L. Liu, W. Xu and R. Zhang, Joint transmit beamforming and receive power splitting for MISO SWIPT systems, IEEE Transactions on Wireless Communications, 13 (2014), 3269-3280.  doi: 10.1109/TWC.2014.041714.131688.  Google Scholar

[19]

Q. Shi, C. Peng, W. Xu, M. Hong and Y. Cai, Energy efficiency optimization for MISO SWIPT systems with zero-forcing beamforming, IEEE Transactions on Signal Processing, 64 (2016), 842-854.  doi: 10.1109/TSP.2015.2489603.  Google Scholar

[20]

L. R. Varshney, Transporting information and energy simultaneously, IEEE Int. Symp. Inf. Theory (ISIT), 6 (2008), 1612-1616.  doi: 10.1109/ISIT.2008.4595260.  Google Scholar

[21]

A. Wiesel, Y. C. Eldar and S. Shamai, Zero-Forcing precoding and generalized inverses, IEEE Transactions on Signal Processing, 56 (2008), 4409-4418.  doi: 10.1109/TSP.2008.924638.  Google Scholar

[22]

R. Zhang, Cooperative multi-cell block diagonalization with per-base-station power constraints, IEEE Journal on Selected Areas in Communications, 28 (2010), 1435-1445.  doi: 10.1109/WCNC.2010.5506527.  Google Scholar

[23]

R. Zhang, R. G. Maunder and L. Hanzo, Wireless information and power transfer: From scientific hypothesis to engineering practice, IEEE Communications Magazine, 53 (2015), 99-105.  doi: 10.1109/MCOM.2015.7180515.  Google Scholar

[24]

R. Zhang and C. K. Ho, MIMO broadcasting for simultaneous wireless information and power transfer, IEEE Trans. Wireless Commun., 12 (2013), 1989-2001.  doi: 10.1109/TWC.2013.031813.120224.  Google Scholar

[25]

Y. Zeng, B. Clerckx and and R. Zhang, Communications and signals design for wireless power transmission, IEEE Trans. Commun., 65 (2017), 2264-2290.  doi: 10.1109/TCOMM.2017.2676103.  Google Scholar

show all references

References:
[1]

Internet of Things in 2020 - A Road Map in the Future, 2008. Available from: http://www.smart{_}systems{_}integration.org/public/documents/publications/Internet{_}of{_}Things{_}in{_}2020{_}EC-EPoSS{_}Workshop{_}Report{_}2008{_}v3.pdf. Google Scholar

[2]

G. Caire and S. Shamai, On the achievable throughput of multiantenna Gaussian broadcast channel, IEEE Trans. Inf. Theory, 49 (2003), 1691-1706.  doi: 10.1109/TIT.2003.813523.  Google Scholar

[3]

B. Clerckx and E. Bayguzina, Waveform design for wireless power transfer, IEEE Trans. Signal Process, 64 (2016), 6313-6328.  doi: 10.1109/TSP.2016.2601284.  Google Scholar

[4]

Z. G. Feng, K. F. C. Yiu and S. E. Nordholm, A two-stage method for the design of near-field broadband beamformer, IEEE Transactions on Signal Processing, 59 (2011), 3647-3656.  doi: 10.1109/TSP.2011.2133490.  Google Scholar

[5]

Z. G. Feng, K. F. C. Yiu and S. E. Nordholm, Placement design of microphone arrays in near-field broadband beamformers, IEEE Transactions on Signal Processing, 60 (2012), 1195-1204.  doi: 10.1109/TSP.2011.2178491.  Google Scholar

[6]

M. Grant, S. Boyd, L. Liberti and N. Maculan, Disciplined convex programming in global optimization: From theory to implementation, Nonconvex Optimization and Its Applications, 84 (2006), 155-210.  doi: 10.1007/0-387-30528-9_7.  Google Scholar

[7]

B. Li, H. H. Dam, A. Cantoni and K. L. Teo, A first-order optimal zero-forcing beamformer design for multiuser MIMO systems via a regularized dual accelerated gradient method, IEEE Commun. Lett., 19 (2015), 195-198.  doi: 10.3934/naco.2016012.  Google Scholar

[8]

B. Li, H. H. Dam, A. Cantoni and K. L. Teo, A global optimal zero-forcing beamformer design with signed power-of-two coefficients, Journal of Industrial and Management Optimization, 12 (2016), 595-607.  doi: 10.3934/jimo.2016.12.595.  Google Scholar

[9]

B. Li and Y. Rong, Joint transceiver optimization for wireless information and energy transfer in nonregenerative MIMO relay systems, IEEE Transactions on Vehicular Technology, 67 (2018), 8348-8362.  doi: 10.1109/TVT.2018.2846556.  Google Scholar

[10]

B. Li and Y. Rong, AF MIMO relay systems with wireless powered relay node and direct link, IEEE Transactions on Communications, 66 (2018), 1508-1519.  doi: 10.1109/TCOMM.2017.2788006.  Google Scholar

[11]

B. Li, C. Z. Wu, H. H. Dam, A. Cantoni and K. L. Teo, A parallel low complexity zero-forcing beamformer design for multiuser MIMO systems via a regularized dual decomposition method, IEEE Trans. Signal Process, 63 (2015), 4179-4190.  doi: 10.1109/TSP.2015.2437846.  Google Scholar

[12]

X. Lu, P. Wang, D. Niyato, D. I. Kim and Z. Han, Wireless networks with RF energy harvesting: A contemporary survey, IEEE Communications Surveys & Tutorials, 17 (2015), 757–789. doi: 10.1109/COMST.2014.2368999.  Google Scholar

[13]

X. Lu, P. Wang, D. Niyato, D. I. Kim and Z. Han, Wireless charging technologies: fundamentals, standards, and network applications, IEEE Communications Surveys & Tutorials, 18 (2016), 1413–1452. doi: 10.1109/COMST.2015.2499783.  Google Scholar

[14]

L. Ma, Y. Wang and Y. Xu, Sum rate optimization for SWIPT system based on zero-forcing beamforming and time switching, 2017 13th International Wireless Communications and Mobile Computing Conference (IWCMC), (2017), 351–356. doi: 10.1109/TSP.2015.2489603.  Google Scholar

[15]

A. A. Okandeji and et al., SWIPT in MISO full-duplex systems, Journal of Communications and Networks, 19 (2017), 470-480.  doi: 10.1109/JCN.2017.000079.  Google Scholar

[16]

C. Peng, Q. Shi, W. Xu and M. Hong, Energy efficiency optimization for multi-user MISO swipt systems, 2015 IEEE China Summit and International Conference on Signal and Information Processing (ChinaSIP), (2015), 772–776. doi: 10.1109/TSP.2015.2489603.  Google Scholar

[17]

T. D. Ponnimbaduge Perera, D. N. K. Jayakody, S. K. Sharma, S. Chatzinotas and J. Li, Simultaneous wireless information and power transfer (SWIPT): Recent advances and future challenges, IEEE Communications Surveys & Tutorials, 20 (2018), 264–302. doi: 10.1109/COMST.2017.2783901.  Google Scholar

[18]

Q. Shi, L. Liu, W. Xu and R. Zhang, Joint transmit beamforming and receive power splitting for MISO SWIPT systems, IEEE Transactions on Wireless Communications, 13 (2014), 3269-3280.  doi: 10.1109/TWC.2014.041714.131688.  Google Scholar

[19]

Q. Shi, C. Peng, W. Xu, M. Hong and Y. Cai, Energy efficiency optimization for MISO SWIPT systems with zero-forcing beamforming, IEEE Transactions on Signal Processing, 64 (2016), 842-854.  doi: 10.1109/TSP.2015.2489603.  Google Scholar

[20]

L. R. Varshney, Transporting information and energy simultaneously, IEEE Int. Symp. Inf. Theory (ISIT), 6 (2008), 1612-1616.  doi: 10.1109/ISIT.2008.4595260.  Google Scholar

[21]

A. Wiesel, Y. C. Eldar and S. Shamai, Zero-Forcing precoding and generalized inverses, IEEE Transactions on Signal Processing, 56 (2008), 4409-4418.  doi: 10.1109/TSP.2008.924638.  Google Scholar

[22]

R. Zhang, Cooperative multi-cell block diagonalization with per-base-station power constraints, IEEE Journal on Selected Areas in Communications, 28 (2010), 1435-1445.  doi: 10.1109/WCNC.2010.5506527.  Google Scholar

[23]

R. Zhang, R. G. Maunder and L. Hanzo, Wireless information and power transfer: From scientific hypothesis to engineering practice, IEEE Communications Magazine, 53 (2015), 99-105.  doi: 10.1109/MCOM.2015.7180515.  Google Scholar

[24]

R. Zhang and C. K. Ho, MIMO broadcasting for simultaneous wireless information and power transfer, IEEE Trans. Wireless Commun., 12 (2013), 1989-2001.  doi: 10.1109/TWC.2013.031813.120224.  Google Scholar

[25]

Y. Zeng, B. Clerckx and and R. Zhang, Communications and signals design for wireless power transmission, IEEE Trans. Commun., 65 (2017), 2264-2290.  doi: 10.1109/TCOMM.2017.2676103.  Google Scholar

Figure 1.  Sum Rate versus $ P $
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Figure 2.  Sum Rate versus $ P $
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Figure 3.  Sum Rate versus $ P $
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