中继辅助的寄生反向散射通信网络中断性能分析

宋曦; 韩东升

doi:10.11999/JEIT231057

中继辅助的寄生反向散射通信网络中断性能分析

doi: 10.11999/JEIT231057

宋曦^,,
韩东升

华北电力大学电气与电子工程学院北京 102206

基金项目: 国家自然科学基金(61771195)，河北省省级科技计划(SZX2020034)

详细信息

作者简介:
宋曦：男，博士生，研究方向为反向散射通信、电力通信

韩东升：男，教授，博士生导师，研究方向为无线通信新技术、电力系统通信

通讯作者:
宋曦　120212501020@ncepu.edu.cn

中图分类号: TN926
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- 被引次数: 0
出版历程
- 收稿日期: 2023-10-07
- 修回日期: 2023-12-29
- 网络出版日期: 2024-01-22
- 刊出日期: 2024-06-30

Outage Performance of Relay-assisted Parasitic Backscatter Communication Networks

SONG Xi^,,
HAN Dongsheng

School of Electrical and Electronic Engineering, North China Electric Power University, Beijing 102206, China

Funds: The National Natural Science Foundation of China (61771195), S&T Program of Hebei (SZX2020034)

摘要

摘要: 已有寄生反向散射通信网络依赖于收发机之间存在的直达链路，从而无法应用于直达链路深度衰落或不存在场景。针对上述问题，该文提出一种中继辅助的寄生反向散射通信网络，并分析所提网络的中断性能。具体而言，依据所提网络推导得到主系统和次系统的瞬时信噪比，并在考虑次用户能量因果约束的条件下定义了主次系统中断概率，接着利用数学知识推导得到瑞利衰落模型下的主次系统中断概率表达式，最后通过计算机仿真验证了所推导的主次系统中断概率表达式的准确性，并分析了不同系统参数对主、次系统中断概率的影响。
- 反向散射通信 /
- 能量收集 /
- 中继 /
- 中断概率
Abstract: The existing parasitic backscatter communications rely on the direct links between transceivers and do not work when the direct links are blocked or fade deeply. To solve this problem, a relay-assisted parasitic backscatter communication network is proposed, base on which its outage performance is analyzed. Specifically, according to the proposed network, the instantaneous signal-to-noise ratios to decode the primary and secondary systems are given, and then the outage probabilities of primary and secondary systems on the basis of the energy-causality constraint of the secondary user are defined. Under the Rayleigh channel fading model, the expressions for the outage probability of the primary and secondary systems can be obtained by exploiting mathematical theory. Computer simulations validate the accuracy of the derived primary and secondary system outage probabilities, on which the impacts of different system parameters are analyzed.
- Backscatter communications /
- Energy harvesting /
- Relay /
- Outage probability

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图 1 系统模型

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图 2 主系统中断概率与$\beta $的关系曲线

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图 3 次系统中断概率与$\beta $的关系曲线

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图 4 主、次系统中断概率与${P_0}$的关系曲线

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图 5 主、次系统中断概率与${a_1}$的关系曲线

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表 1 主系统中断概率表达情况总结

不同参数设置	主系统中断概率表达式$ P_{{\text{out}}}^p $
$ {a_1} - \gamma _{{\text{th}}}^s{a_2} \gt 0 $	$ \begin{gathered} 1 - \exp \left( { - \dfrac{{{A_1}}}{{{\lambda _1}}} - \dfrac{{{A_5}}}{{{\lambda _3}}} - \dfrac{{{A_3}}}{{{\lambda _0}}}} \right)\left( {{P_{111}} - {P_{112}}} \right) - {P_{112}}\exp \left( { - \dfrac{{{A_1}}}{{{\lambda _1}}} - \dfrac{{{A_6}}}{{{\lambda _3}}} - \dfrac{{{A_3}}}{{{\lambda _0}}}} \right) \\ - \exp \left( { - \dfrac{{{A_3}}}{{{\lambda _0}}} - \dfrac{{{A_6}}}{{{\lambda _3}}}} \right)\left( {1 - \exp \left( { - \dfrac{{{A_1}}}{{{\lambda _1}}}} \right)} \right) \\ \end{gathered} $
$ {a}_{1}-{\gamma }_{\text{th}}^{s}{a}_{2}\le 0,且{a}_{2}-{\gamma }_{\text{th}}^{c}{a}_{1} \gt 0 $	$ \begin{gathered} 1 - \exp \left( { - \dfrac{{{A_1}}}{{{\lambda _1}}} - \dfrac{{\max \left( {{A_7},{A_8}} \right)}}{{{\lambda _3}}} - \dfrac{{{A_3}}}{{{\lambda _0}}}} \right)\left( {{P_{111}} - {P_{112}}} \right) - \exp \left( { - \dfrac{{{A_1}}}{{{\lambda _1}}} - \dfrac{{{A_6}}}{{{\lambda _3}}} - \dfrac{{{A_3}}}{{{\lambda _0}}}} \right){P_{112}} \\ - \exp \left( { - \dfrac{{{A_3}}}{{{\lambda _0}}} - \dfrac{{{A_6}}}{{{\lambda _3}}}} \right)\left( {1 - \exp \left( { - \dfrac{{{A_1}}}{{{\lambda _1}}}} \right)} \right) \\ \end{gathered} $
$ {a}_{1}-{\gamma }_{\text{th}}^{s}{a}_{2}\le 0,且{a}_{2}-{\gamma }_{\text{th}}^{c}{a}_{1}\le 0 $	$ 1 - \exp \left( { - \dfrac{{{A_1}}}{{{\lambda _1}}} - \dfrac{{{A_6}}}{{{\lambda _3}}} - \dfrac{{{A_3}}}{{{\lambda _0}}}} \right){P_{112}} - \exp \left( { - \dfrac{{{A_3}}}{{{\lambda _0}}} - \dfrac{{{A_6}}}{{{\lambda _3}}}} \right)\left( {1 - \exp \left( { - \dfrac{{{A_1}}}{{{\lambda _1}}}} \right)} \right) $
$ {P_{111}} = - \dfrac{{{\lambda _0}}}{{{A_2}{\lambda _1}{\lambda _2}}}\exp \left( {\dfrac{{{\lambda _0}}}{{{\lambda _1}{\lambda _2}{A_2}}}} \right){\text{Ei}}\left( { - \dfrac{{{\lambda _0}}}{{{\lambda _1}{\lambda _2}{A_2}}}} \right) $，$ {P_{112}} = \dfrac{{\pi {A_4}}}{{{\lambda _1}{\lambda _2}M}}\displaystyle\sum\limits_{m = 1}^M {\sqrt {1 - v_m^2} {K_0}\left( {2\sqrt {\dfrac{{{\kappa _m}}}{{{\lambda _1}{\lambda _2}}}} } \right)\exp \left( { - \dfrac{{{A_2}{\kappa _m}}}{{{\lambda _0}}}} \right)} $， $ {A_1} = \dfrac{{{P_{\text{c}}}d_1^{{\alpha _1}}}}{{\eta \left( {1 - \beta } \right){P_0}}},{A_2} = \gamma _{{\text{th}}}^sd_0^{{\alpha _0}}\beta d_1^{ - {\alpha _1}}d_2^{ - {\alpha _2}},{A_3} = \dfrac{{\gamma _{{\text{th}}}^sd_0^{{\alpha _0}}{\sigma ^2}}}{{{P_0}}},{A_4} = \dfrac{{\gamma _{{\text{th}}}^c{\sigma ^2}d_1^{{\alpha _1}}d_2^{{\alpha _2}}}}{{{P_0}\beta }},{A_5} = \dfrac{{\gamma _{{\text{th}}}^s{\sigma ^2}d_3^{{\alpha _3}}}}{{{P_{\text{R}}}\left( {{a_1} - \gamma _{{\text{th}}}^s{a_2}} \right)}} $，$ {A_6} = \dfrac{{\gamma _{{\text{th}}}^sd_3^{{\alpha _3}}{\sigma ^2}}}{{{P_{\text{R}}}}} $， $ {A_7} = \dfrac{{\gamma _{{\text{th}}}^c{\sigma ^2}d_3^{{\alpha _3}}}}{{{P_{\text{R}}}\left( {{a_2} - \gamma _{{\text{th}}}^c{a_1}} \right)}},{A_8} = \dfrac{{\gamma _{{\text{th}}}^sd_3^{{\alpha _3}}{\sigma ^2}}}{{{P_{\text{R}}}{a_1}}} $

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表 2 次系统中断概率表达情况总结

不同参数设置	次系统中断概率表达式$ P_{{\text{out}}}^b $
$ {a_1} - \gamma _{{\text{th}}}^s{a_2} \gt 0 $	$ 1 - \exp \left( { - \dfrac{{{A_1}}}{{{\lambda _1}}} - \dfrac{{\max \left( {{A_5},{A_9}} \right)}}{{{\lambda _3}}} - \dfrac{{{A_3}}}{{{\lambda _0}}}} \right)\left( {{P_{111}} - {P_{112}}} \right) $
$ {a}_{1}-{\gamma }_{\text{th}}^{s}{a}_{2}\le 0,且{a}_{2}-{\gamma }_{\text{th}}^{c}{a}_{1} \gt 0 $	$ 1 - \exp \left( { - \dfrac{{{A_1}}}{{{\lambda _1}}} - \dfrac{{{A_7}}}{{{\lambda _3}}} - \dfrac{{{A_3}}}{{{\lambda _0}}}} \right)\left( {{P_{111}} - {P_{112}}} \right) $
$ {a}_{1}-{\gamma }_{\text{th}}^{s}{a}_{2}\le 0,且{a}_{2}-{\gamma }_{\text{th}}^{c}{a}_{1}\le 0 $	$ 1 $
$ {P_{111}} = - \dfrac{{{\lambda _0}}}{{{A_2}{\lambda _1}{\lambda _2}}}\exp \left( {\dfrac{{{\lambda _0}}}{{{\lambda _1}{\lambda _2}{A_2}}}} \right){\text{Ei}}\left( { - \dfrac{{{\lambda _0}}}{{{\lambda _1}{\lambda _2}{A_2}}}} \right) $，$ {P_{112}} = \dfrac{{\pi {A_4}}}{{{\lambda _1}{\lambda _2}M}}\displaystyle\sum\limits_{m = 1}^M {\sqrt {1 - v_m^2} {K_0}\left( {2\sqrt {\dfrac{{{\kappa _m}}}{{{\lambda _1}{\lambda _2}}}} } \right)\exp \left( { - \dfrac{{{A_2}{\kappa _m}}}{{{\lambda _0}}}} \right)} $， $ {A_1} = \dfrac{{{P_{\text{c}}}d_1^{{\alpha _1}}}}{{\eta \left( {1 - \beta } \right){P_0}}},{A_2} = \gamma _{{\text{th}}}^sd_0^{{\alpha _0}}\beta d_1^{ - {\alpha _1}}d_2^{ - {\alpha _2}},{A_3} = \dfrac{{\gamma _{{\text{th}}}^sd_0^{{\alpha _0}}{\sigma ^2}}}{{{P_0}}},{A_4} = \dfrac{{\gamma _{{\text{th}}}^c{\sigma ^2}d_1^{{\alpha _1}}d_2^{{\alpha _2}}}}{{{P_0}\beta }},{A_5} = \dfrac{{\gamma _{{\text{th}}}^s{\sigma ^2}d_3^{{\alpha _3}}}}{{{P_{\text{R}}}\left( {{a_1} - \gamma _{{\text{th}}}^s{a_2}} \right)}} $，$ {A_7} = \dfrac{{\gamma _{{\text{th}}}^c{\sigma ^2}d_3^{{\alpha _3}}}}{{{P_{\text{R}}}\left( {{a_2} - \gamma _{{\text{th}}}^c{a_1}} \right)}} $， $ {A_9} = \dfrac{{\gamma _{{\text{th}}}^cd_3^{{\alpha _3}}{\sigma ^2}}}{{{P_{\text{R}}}{a_2}}} $

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表 3 仿真参数设置

参数名称	参数符号	数值
路径损耗	${\alpha _0},{\alpha _1},{\alpha _2},{\alpha _3}$	2.7
噪声功率 (W)	${\sigma ^2}$	10^－9
PT到R的距离(m)	${d_{\text{0}}}$	50
PT到BN的距离(m)	${d_{\text{1}}}$	5
BN到R的距离(m)	${d_{\text{2}}}$	48
R到D的距离(m)	${d_{\text{3}}}$	100
PT、R的发射功率(dBm)	${P_0},{P_{\text{R}}}$	30
BN反向散射系数	$\beta $	0.8
BN反向散射通信功耗(μW)	${P_c}$	8.9
BN能量转换效率	$\eta $	0.8
PT的目标速率(bit/Hz)	$R_{{\text{th}}}^s$	1
BN的目标速率(bit/Hz)	$R_{{\text{th}}}^c$	0.1
R处功率分配因子	${a_1},{a_2}$	0.8，0.2
高斯-切比雪夫分段总数	$M$	10

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