基于公平效用函数的多波束卫星通信下行链路波束成形算法

孙士勇; 王薇; 顾晨伟; 赵柏; 林敏

doi:10.11999/JEIT220409

基于公平效用函数的多波束卫星通信下行链路波束成形算法

doi: 10.11999/JEIT220409

孙士勇^1, ,,
王薇¹,
顾晨伟²,
赵柏³,
林敏³

1.
中国电子科技集团公司第五十四研究所石家庄 050086
2.
中国移动通信集团江苏有限公司无锡分公司无锡 214125
3.
南京邮电大学通信与信息工程学院南京 210003

基金项目: 重点国际合作项目(61720106003)，中国电科基金(BBX21104Z003)

详细信息

作者简介:
孙士勇：男，研究员级高级工程师，研究方向为通信网络系统、无线通信、智能网络等

王薇：女，高级工程师，研究方向为卫星通信系统、无线通信、卫星载荷等

顾晨伟：男，工程师，研究方向为卫星通信、物理层安全等

赵柏：男，博士生，研究方向为卫星通信、通信信号处理等

林敏：男，教授，博士生导师，研究方向为卫星通信、无线通信、智能信号处理等

通讯作者:
孙士勇　shiyongsun@sina.com

中图分类号: TN92
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出版历程
- 收稿日期: 2022-04-07
- 修回日期: 2022-05-16
- 网络出版日期: 2022-06-29
- 刊出日期: 2022-09-19

Beamforming Algorithm Based on Fair Utility Function for Multibeam Satellite Communication Downlink Transmission

1.
The 54th Research Institute of China Electronic Technology Corporation, Shijiazhuang 050086, China
2.
China Mobile Group Jiangsu Company Limited, Wuxi 214125, China
3.
College of Telecommunications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China

Funds: The Key International Cooperation Projects (61720106003), The Development Fundation of CETC (BBX21104Z003)

摘要

摘要: 为了更好地平衡多波束卫星通信系统的频谱效率和能量效率，以及保证多用户服务场景下的用户服务公平性，该文提出一种基于公平效用函数的波束成形(BF)方案。具体而言，首先在同时考虑卫星发射功率最小化准则以及系统和速率最大化准则的前提下，建立一个多目标优化问题，并在最大化系统频谱效率的同时利用$\alpha $公平效用函数提升用户间的服务公平性。然后利用加权和方法对复杂的多目标问题进行转换处理，并提出一种联合使用循环坐标上升(CCA)方法以及回溯直线搜索(BLS)方法的波束成形方案，从而求得最优的波束成形权矢量以及最优的帕累托解集。最后计算机仿真结果验证了所提方案的用户服务公平性，以及分析一些典型参数对公平性能的影响。并通过与其他传统方案相比，验证所提方案能够获得更高的系统频谱效率。
- 多波束卫星通信 /
- 多目标优化 /
- $\alpha $公平效用函数 /
- 波束成形
Abstract: To balance the spectrum efficiency and energy efficiency of multi-beam satellite communication system, and guarantee the fairness of user service in multiusers scenarios, a fairness utility function-based BeamForming (BF) scheme is proposed. Specifically, considering the satellite transmit power minimization criteria and the system sum rate maximization criteria, a multi-objective optimization problem is first formulated, which adopts the $\alpha $-fairness function to improve the fairness of user service as maximizing the system spectrum efficiency. Then, the weighted sum method is used to transform the complexity multi-objective optimization problem, and a BF scheme based on the Cyclic Coordinate Ascent (CCA) method and the Backtracking Line Search (BLS) method is proposed to obtain the optimal BF weight vectors and the optimal Pareto set. Finally, the simulation results demonstrate the fairness of user service of the proposed BF scheme, and the influence of some typical parameters on the system fairness performance are analyzed. Besides, in comparison with the conventional schemes, the proposed scheme is capable of enhancing the system spectrum efficiency.
- Multibeam satellite communication /
- Multi-objective optimization /
- $\alpha $-fairness function /
- Beamforming

HTML全文

图 1 多波束卫星下行通信系统模型

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图 2 波束成形权矢量${{\boldsymbol{w}}_3}$的归一化增益方向图

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图 3 系统频谱效率与最大发射功率的关系图

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图 4 系统的频谱效率与公平参数$\alpha $的关系图

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图 5 Jain公平指数与参数$\alpha $的关系图

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图 6 能效随系统频谱效率的变化曲线图

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表 1 算法流程

基于循环坐标上升法的波束成形算法
1: 输入：$\left\{ { {g_k},P_{\rm{T}}^{{\rm{max}}},\alpha ,\beta ,\varepsilon ,\delta } \right\}$;
2: 迭代①：求解$ U_\alpha ^{\max } $；
3: 初始化$i = 0$和${ {\boldsymbol{V} }^{\left( 0 \right)} } = \left[ {{\boldsymbol{v}}_1^{\left( 0 \right)},{\boldsymbol{v}}_2^{\left( 0 \right)}, \cdots ,{\boldsymbol{v}}_K^{\left( 0 \right)} } \right]$;
4: 　while $\|{{\boldsymbol{V}}^{\left( i \right)} } - {{\boldsymbol{V}}^{\left( {i - 1} \right)} }\|{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} > {\kern 1pt} {\kern 1pt} {\kern 1pt} \varepsilon$
5: 　　for $k = 1,2, \cdots ,k$
6: 　　　使用CVX方法求解优化问题式(16)得到${\boldsymbol{v}}_k^{(i)}$的上升方向　　　　　 ${\boldsymbol{u}}_k^{(i + 1)}$;
7: 　　　使用BLS方法得到上升步长$ a_k^{(i + 1)} $;
8: 　　　更新${\boldsymbol{v} }_k^{(i + 1)} = {\boldsymbol{v} }_k^{(i)} + a_k^{(i + 1)}{\boldsymbol{u}}_k^{(i + 1)}{(i + 1)}$;
9: 　　end for
10: 　 $i = i + 1$;
11: 　end while
12: 　得到$ U_\alpha ^{\max } $;
13: end
14: 迭代②：求解优化问题式(20)；
15: 　初始化$l = 0$和${ {\boldsymbol{V} }^{\left( 0 \right)} } = \left[ {{\boldsymbol{v}}_1^{\left( 0 \right)},{\boldsymbol{v}}_2^{\left( 0 \right)}, \cdots ,{\boldsymbol{v}}_K^{\left( 0 \right)} } \right]$
16: 　while $\|{{\boldsymbol{V}}^{\left( l \right)} } - {{\boldsymbol{V}}^{\left( {l - 1} \right)} }\|{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} > {\kern 1pt} {\kern 1pt} {\kern 1pt} \delta$
17: 　　for $k = 1,2, \cdots ,K$
18: 　　　使用CVX方法求解优化问题(20)得到${\boldsymbol{v}}_k^{\left( l \right)}$的上升方向　　　　　 $\tilde {\boldsymbol{u}}_k^{(l + 1)}$;
19: 　　　使用BLS方法得到上升步长$ \tilde a_k^{(l + 1)} $;
20: 　　　更新${\boldsymbol{v}}_k^{(l + 1)} = {\boldsymbol{v}}_k^{(l)} + \tilde a_k^{(l + 1)}\tilde {\boldsymbol{u}}_k^{(l + 1)}$;
21: 　　end for
22: 　　$l = l + 1$;
23: 　end while
24: 得到${\boldsymbol{V} } = \left[ {{\boldsymbol{v}}_1^{},{\boldsymbol{v}}_2^{}, \cdots ,{\boldsymbol{v}}_K^{} } \right]$;
25: end
26: 输出：最优波束成形权矢量$\left\{ {{\boldsymbol{v}}_1^,{\boldsymbol{v}}_2^, \cdots ,{\boldsymbol{v}}_K^*} \right\}$

下载: 导出CSV

表 2 主要参数

参数	数值
卫星波束数N (个)	7
用户个数K (个)	5
卫星的载波频率${f_c}$(GHz)	18
半功率波束宽度${\theta _{3{\text{ } }{\rm{dB}}} }$	0.8°
卫星天线增益${b_{\max }}$(dB)	52
地面用户天线增益${G_{\max }}$(dB)	17
电路功耗${P_c}$(dBmW)	10
噪声带宽B (MHz)	50

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