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The cluster heads (CHs) will face the contradiction between the lack of available energy and the demand of high energy consumption in energy harvesting-supported device-to-device multicast communications (EH-D2MD). Wireless power transfer (WPT) technology is a possible way to address the above contradiction. The members of a device-to-device (D2D) multicast cluster can transfer part of their available energy to the CH by WPT and jointly undertake contents unloading. As a result, the transmission robustness of the multicast cluster can be improved. Therefore, a transmission scheme with energy cooperation (EC) is designed on the premise of cellular spectrum reusing. The EC scheme designs elaborately the energy harvesting, energy cooperation and data transmission of the spectrum reusing process. To realize the EC scheme, this work is to maximize the transmission rate of a multicast cluster and give the joint optimal solution of multi-domain resources including spectrum resource allocation, cooperative time factor planning, and power control. The rate maximization problem is a typical non-convex mixed integer non-linear programming (non-convex MINLP) problem. To investigate the performance of EH-D2MD communication scenario, a convex approximate lower-bound algorithm is proposed, which can transfer the non-convex problem into convex MINLP and can give a joint solution. Simulation results show that the proposed algorithm obtains a lower-bound solution of the rate maximization problem in comparison with the exhausted searching method. Furthermore, compared with the scheme without energy cooperation, the established EC transmission scheme can increase the transmission rate of D2MD by more than 45% and enhance the robustness of EH-D2MD.
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Keywords:
- energy harvesting /
- D2D multicast communication /
- energy cooperative communication /
- convex approximation algorithm
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图 1 单簇头的能量协作内容卸载场景
Figure 1. Energy cooperative content offloading scheme for a single cluster head multicast scenario.
图 2 CU和EH-D2MD一对一频谱复用下能量协作传输机制
Figure 2. Energy cooperative transmission schemewhen one CU and one EH-D2MD share a spectrum.
图 3 一个单蜂窝EH-D2MD通信场景示例
Figure 3. A single EH-D2MD communication scenario example.
图 4 3种算法在多播簇半径分别为50 m (a)和150 m (b)场景下的性能
Figure 4. The performance of the above three algorithms in the scenario where the radius of multicast cluster are 50 m (a) and 150 m (b)
图 5 EC和without EC算法在簇半径为50 m, 100 m, 150 m场景下的性能对比 (a)多播簇平均传输速率; (b)复用蜂窝链路下行平均传输速率
Figure 5. Performance comparison of EC and Without EC algorithms in scenarios with cluster radius of 50 m, 100 m, and 150 m: (a) The average transmission rate of multicast cluster; (b) the average transmission rate of downlink of cellular user.
图 6 EC算法在不同多播簇半径场景下参与能量协作的簇员比例分析
Figure 6. The proportion of the cluster members participating in energy cooperation of EC algorithm under scenarios with different multicast cluster radius.
GBD算法执行步骤: 初始化. 定义GBD每一次迭代的计数器为t, 并初始化为1; k为主问题不可行后λ的计数次数, 初始化为0; λk = {0}, 设置使算法停止的上下界阈值$\zeta = 0.001$. 步骤1: 在取值区间内给定一组二值变量$\left\{ {\bar {\boldsymbol{X}}, \bar {\boldsymbol{Y}}, \bar {\boldsymbol{Z}}} \right\}$, 根据问题(33)和(34)分别求得此时的连续变量和拉格朗日乘子最优解$\{ {{{\boldsymbol{\alpha}} ^ * }, {{\boldsymbol{\beta}} ^ * }, {{\boldsymbol{\tau}} ^ * }, \hat {\boldsymbol{P}}^* }\}$, μ*; 将此时的目标方程$F( {\bar {\boldsymbol{X}}, \bar {\boldsymbol{Y}}, \bar {\boldsymbol{Z}}, {\boldsymbol{\alpha}} ^ * }, {{\boldsymbol{\beta}} ^ * }, {{\boldsymbol{\tau}} ^ * }, \hat {\boldsymbol{P}}^* )$设为下界U; 步骤2: 若此时给定二值变量的问题(33)可行, 则将μt = μ*, 并求解松弛的master问题(36); 将问题(36)求得的二值变量定义为新的$ \left\{ {\bar {\boldsymbol{X}}, \bar{\boldsymbol{ Y}}, \bar {\boldsymbol{Z}}} \right\} $, 以及目标方程$F( {\bar {\boldsymbol{X}}, \bar {\boldsymbol{Y}}, \bar {\boldsymbol{Z}}, {\boldsymbol{\alpha}} ^ * }, {{\boldsymbol{\beta}} ^ * }, {{\boldsymbol{\tau}} ^ * }, \hat {\boldsymbol{P}}^* )$的上界f0; 步骤3: 根据步骤2求得的二值变量, 求解问题(33), 并得到此时的目标方程$F( {\bar {\boldsymbol{X}}}, \bar {\boldsymbol{Y}}, \bar {\boldsymbol{Z}}, {\boldsymbol{\alpha}} ^ * , {{\boldsymbol{\beta}} ^ * }, {{\boldsymbol{\tau}} ^ * }, \hat {\boldsymbol{P}}^* )$设为新的下界U; 步骤3(a): 若步骤3可行, 判断|f0U| ≤ $\zeta $, 则算法结束; 反之, 根据求解问题(34)得到μ*; 令t = t + 1; μt = μ*; 返回步骤2; 步骤3(b): 若步骤3不可行, 求解松弛问题(35); 令k = k + 1; λk = {$ {\lambda _s} $}; 返回步骤2. 
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变量 物理含义 参数设置 I 蜂窝用户个数 [2–6] J D2MD簇个数 [2—6] Nj 第j个D2MD簇中簇员个数 [2—10] T 传输时隙 1 s γ 路径衰落指数 蜂窝链路: [3—5], D2 D链路: [1.6—1.8] BW 信道带宽 150 kHz ρ 噪声功率密度 –174 dBm/Hz h 瑞利信道衰落因子 正太高斯分布 η 能量转换效率 [0.6—0.9] $p_B^{{\text{th}}}$ 基站传输功率阈值 43 dBm $p_I^{{\text{th}}}$ 蜂窝用户传输功率阈值 24 dBm $p_D^{{\text{th}}}$ D2D用户传输功率阈值 17 dBm $R_B^{{\text{th}}}$ 蜂窝下行传输速率阈值 1 bps/Hz $R_I^{{\text{th}}}$ 蜂窝上行传输速率阈值 2 bps/Hz $R_J^{{\text{th}}}$ D2MD多播传输速率阈值 4 bps/Hz
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[1] Perera T D P, Jayakody D N K, Sharma S K, Symeon C, Jun L 2018 IEEE Commun. Surv. Tutor. 20 264
Google Scholar
[2] Kusaladharma S, Tellambura C 2017 IEEE Trans. Green Commun. Netw. 2 87
Google Scholar
[3] Lim D W, Kang J, Kim H M 2019 IEEE Wireless Commun. Lett. 8 1333
Google Scholar
[4] Ying L, Peilin H, Runzhou L 2018 IEEE Commun. Lett. 22 1704
Google Scholar
[5] Bhardwaj A, Agnihotri S 2018 IEEE Wireless Commun. Lett. 7 546
Google Scholar
[6] Zhang G, Yang K, Chen H H 2016 IEEE Wireless Commun. Lett. 23 68
Google Scholar
[7] Gurakan B, Ozel O, Yang J, Sennur U 2013 IEEE Trans. Commun. 61 4884
Google Scholar
[8] 胡瑾瑜 2018 博士学位论文 (长沙: 湖南大学)
Hu J Y 2018 Ph. D. Dissertation (Changsha: Hunan University) (in Chinese)
[9] Hu F, Liu X, Shao M, Dan S. Liheng W 2017 IEEE Netw. 31 90
Google Scholar
[10] Xu J, Zhang R 2015 IEEE Trans. Veh. Technol. 64 2476
Google Scholar
[11] 谢振威, 朱琦 2017 通信学报 38 176
Google Scholar
Xie Z W, Zhu Q 2017 J. on Commun. 38 176
Google Scholar
[12] Ercan A Ö, Sunay O, Akyildiz I. F 2018 IEEE Trans. Mobile Comput. 17 1680
Google Scholar
[13] Ni W, Dong X 2015 IEEE Trans. Commun. 63 1457
Google Scholar
[14] Shin D K, Choi W, Kim D I 2015 IEEE Trans. Commun. 63 4551
Google Scholar
[15] Ammar A, Reynolds D 2018 IEEE Commun. Lett. 22 2128
Google Scholar
[16] Zhao D, Cui Y, Tian H, Zhang P 2019 IEEE Access 7 72316
Google Scholar
[17] Gyawali S, Xu S, Ye F, Hu, Rose Q , Qian Y 2018 Proceedings of IEEE 87th Vehicular Technology Conference Porto, Portugal, July 3–6, 2018 p1
[18] Zeng M, Luo Y, Jiang H, Wang Y J 2022 Early Access by IEEE Trans. Wireless Commun.
[19] Mukherjee M, Shu L, Prasad R V, Wang D, Hancke G P 2019 IEEE Commun. Mag. 57 108
Google Scholar
[20] Papandriopoulos J, Evans J S 2009 IEEE Trans. Inf. Theory 55 3711
Google Scholar
[21] Shahbazian A, Fereidunian A, Manshadi S D 2020 IEEE Trans. Smart Grid 11 5009
Google Scholar
[22] Girão-Silva R, Martins L, Gomes T, Tipper D, Alashaikh A 2019 Proceedings of IEEE 15th International Conference on the Design of Reliable Communication Networks Coimbra, Portugal, March 19–21, 2019 p29
[23] Boyd S, Boyd S P, Vandenberghe L 2004 Convex Optimization (Cambridgeshire: Cambridge University Press)
[24] Yuille A L, Rangarajan A 2003 Neural Comput. 15 915
Google Scholar
[25] Kronqvist J, Bernal D E, Lundell A, Grossmann I E 2019 Optim. Eng. 20 397
Google Scholar
[26] Fletcher R, Leyffer S 1994 Math. Program. 66 327
Google Scholar
[27] Shin D K, Choi W, Kim D I 2015 IEEE Trans. Commun. 63 4551
[28] Chen W, Zhao S, Zhang R, Yang, L 2020 IEEE Internet Things J. 8 501
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