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Abstract

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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Authors and contacts

Corresponding author:Luo Ying,yluo@swust.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 61771410), the Sichuan Science and Technology Program (Grant No. 2021YJ0097), and the SouthWest University of Science and Technology Research Fund (Grant No. 18zx7144).

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Cited By

DownLoad: Full-Size Img PowerPoint

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;λ^k= {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μ^t=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 $, 则算法结束; 反之, 根据求解问题(34)得到μ^; 令t=t+ 1;μ^t=μ^; 返回步骤2; 　　步骤3(b): 若步骤3不可行, 求解松弛问题(35); 令k=k+ 1;λ^k= {$ {\lambda _s} $}; 返回步骤2.

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;λ^k= {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μ^t=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 $, 则算法结束; 反之, 根据求解问题(34)得到μ^*; 令t=t+ 1;μ^t=μ^*; 返回步骤2; 　　步骤3(b): 若步骤3不可行, 求解松弛问题(35); 令k=k+ 1;λ^k= {$ {\lambda _s} $}; 返回步骤2.

DownLoad: CSV

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]
N_j	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

DownLoad: CSV

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Vol. 71, Issue 16 - 2022-08-20

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