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In this paper, we propose a beamforming design based on energy harvesting proportional fairness to overcome the unbalance of energy harvesting in a simultaneous wireless information and power transfer system. We aim at achieving the energy harvesting proportional fairness while guaranteeing the signal to interference plus noise ratio constraints at the information receivers and total power constraint at the transmitter by optimizing the beamforming vectors. This optimization problem is of non-convex and hence difficult to solve. In order to solve it, in this paper, we first use the semi-definite relaxation technique as a tool to transform it into a semi-definite program problem, and then propose an iterative algorithm based on bisection method to obtain the optimal beamforming vectors. Besides, we also extend our result to a robust case where the transmitter only knows a part of the channel state information and the bound of channel errors, and propose an iterative algorithm based on worst-case method to obtain the corresponding beamforming vectors. Finally, the simulation results show that the proposed algorithms can achieve both the energy harvesting proportional fairness and global optimum.
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Keywords:
- simultaneous wireless information and power transfer /
- beamforming /
- energy harvesting /
- semi-definite relaxation
[1] Han L, Liu B, Li Y Q, Zhao L J 2014 Acta Phys. Sin. 63 150504 (in Chinese) [韩丽, 刘彬, 李雅倩, 赵磊静 2014 物理学报 63 150504]
[2] Liu H R, Yin W X, Han T, Dong M R 2013 Acta Phys. Sin. 62 040509 (in Chinese) [刘浩然, 尹文晓, 韩涛, 董明如 2013 物理学报 62 040509]
[3] Tong X J, Wang Z, Zuo K 2012 Chin. Phys. B 21 020506
[4] Wang Y Q, Yang X Y 2013 Chin. Phys. B 22 010509
[5] Varshney L R 2008 IEEE International Symposium on Information Theory Ontario, Canada, July 7-11, 2008 p1612
[6] Grover P, Sahai A 2010 IEEE International Symposium on Information Theory Austin, USA, June 13-18, 2010 p2363
[7] Zhang R, Ho C 2013 IEEE Trans. Wireless Commun. 12 1989
[8] Xiang Z Z, Tao M X 2012 IEEE Wireless Commun. Lett. 1 372
[9] Park J, Clerckx B 2013 IEEE Trans. Wireless Commun. 12 4210
[10] Xing C W, Wang N W, Ni J Q, Fei Z S, Kuang J M 2013 IEEE Signal Proce. Lett. 12 363
[11] Xu J, Liu L, Zhang R 2013 IEEE International Conference on Acoustics, Speech and Signal Processing Vancouver, Canada, May 26-30, 2013 p4754
[12] Luo Z Q, Ma W K, So A M C, Ye Y Y, Zhang S Z 2010 IEEE Signal Proc. Magazine 27 20
[13] Wang Y, Wu W F, Fan Z, Liang G L 2013 Acta Phys. Sin. 62 184302 (in Chinese) [王燕, 吴文峰, 范展, 梁国龙 2013 物理学报 62 184302]
[14] Sidiropoulos N D, Davidson T N, Luo Z Q 2006 IEEE Trans. Signal Proc. 54 2239
[15] Boyd S, Vandenberghe L 2004 Convex Optimization (New York: Cambridge University Press) p226
[16] Wang J H, Bengtsson M 2011 IEEE Signal Proc. Lett. 10 295
[17] Kwon O M, Kwon J W, Kim S H 2011 Chin. Phys. B 20 050505
[18] Shi Q J, Liu L, Xu W Q, Zhang R 2014 IEEE Trans. Wireless Commun. 13 3269
[19] Hai L, Zhang Y R 2012 Acta Phys. Sin. 61 180101 (in Chinese) [海凛, 张业荣 2012 物理学报 61 180101]
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[1] Han L, Liu B, Li Y Q, Zhao L J 2014 Acta Phys. Sin. 63 150504 (in Chinese) [韩丽, 刘彬, 李雅倩, 赵磊静 2014 物理学报 63 150504]
[2] Liu H R, Yin W X, Han T, Dong M R 2013 Acta Phys. Sin. 62 040509 (in Chinese) [刘浩然, 尹文晓, 韩涛, 董明如 2013 物理学报 62 040509]
[3] Tong X J, Wang Z, Zuo K 2012 Chin. Phys. B 21 020506
[4] Wang Y Q, Yang X Y 2013 Chin. Phys. B 22 010509
[5] Varshney L R 2008 IEEE International Symposium on Information Theory Ontario, Canada, July 7-11, 2008 p1612
[6] Grover P, Sahai A 2010 IEEE International Symposium on Information Theory Austin, USA, June 13-18, 2010 p2363
[7] Zhang R, Ho C 2013 IEEE Trans. Wireless Commun. 12 1989
[8] Xiang Z Z, Tao M X 2012 IEEE Wireless Commun. Lett. 1 372
[9] Park J, Clerckx B 2013 IEEE Trans. Wireless Commun. 12 4210
[10] Xing C W, Wang N W, Ni J Q, Fei Z S, Kuang J M 2013 IEEE Signal Proce. Lett. 12 363
[11] Xu J, Liu L, Zhang R 2013 IEEE International Conference on Acoustics, Speech and Signal Processing Vancouver, Canada, May 26-30, 2013 p4754
[12] Luo Z Q, Ma W K, So A M C, Ye Y Y, Zhang S Z 2010 IEEE Signal Proc. Magazine 27 20
[13] Wang Y, Wu W F, Fan Z, Liang G L 2013 Acta Phys. Sin. 62 184302 (in Chinese) [王燕, 吴文峰, 范展, 梁国龙 2013 物理学报 62 184302]
[14] Sidiropoulos N D, Davidson T N, Luo Z Q 2006 IEEE Trans. Signal Proc. 54 2239
[15] Boyd S, Vandenberghe L 2004 Convex Optimization (New York: Cambridge University Press) p226
[16] Wang J H, Bengtsson M 2011 IEEE Signal Proc. Lett. 10 295
[17] Kwon O M, Kwon J W, Kim S H 2011 Chin. Phys. B 20 050505
[18] Shi Q J, Liu L, Xu W Q, Zhang R 2014 IEEE Trans. Wireless Commun. 13 3269
[19] Hai L, Zhang Y R 2012 Acta Phys. Sin. 61 180101 (in Chinese) [海凛, 张业荣 2012 物理学报 61 180101]
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