A Joint Beamforming Method Based on Cooperative Co-evolutionary in Reconfigurable Intelligent Surface-Assisted Unmanned Aerial Vehicle Communication System
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摘要: 针对传统联合波束成形方法在智能超表面(RIS)辅助无人机(UAV)通信系统优化中存在的局限性,包括针对RIS仅考虑相移矩阵优化、优化方法缺乏应用普适性等问题,该文面向RIS辅助无人机通信服务多用户场景,创新性提出一种基于合作协同进化(CCEA)的联合波束优化方法。该方法利用两个子种群的独立进化将联合波束成形问题分解成RIS反射波波束设计和发射端波束设计两个子问题进行求解,通过进化过程中的信息交互与协作来实现联合波束成形设计。数值仿真结果表明,相较于仅考虑RIS相移矩阵设计的联合波束优化,CCEA通过设计RIS反射波波束形状改变了反射波在3维空间中的能量分布,进而提升了接收端信干噪比(SINR)和频谱效率;此外,基于种群的CCEA算法能够产生更加多样的解,因此在UAV和用户的不同位置设置下均能实现反射波对用户方向的有效覆盖,相对于传统方法能够避免局部最优、具有更强的应用普适性。Abstract: Considering the limitations of traditional joint beamforming methods in optimizing Reconfigurable Intelligent Surface (RIS)-assisted Unmanned Aerial Vehicle (UAV) communication systems, such as solely focusing on the phase shift matrix optimization of RIS and the lack of universality in the optimization approach, a joint beamforming method based on Cooperative Co-Evolutionary Algorithm (CCEA) for the RIS-assisted UAV multi-user communication system is proposed. This method decomposes the joint beamforming problem into subproblems involving RIS reflection beam design and transmitter beam design, which are solved through information exchange and collaboration during the independent evolutionary process of two subpopulations. Simulation results demonstrate that compared to joint beamforming optimization only considering RIS phase shift matrix design, CCEA changes the energy distribution of the reflection wave in three-dimensional space by optimizing the RIS reflection wave shape, leading to improved reception-side Signal-to-Interference-plus-Noise Ratio (SINR) and spectral efficiency. Additionally, CCEA generates more diverse solutions that effectively cover user directions at various UAV and user positions, avoiding local optima and exhibiting greater applicability across different scenarios compared to traditional methods.
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1 基于CCEA的RIS辅助无人机通信联合波束成形优化算法
(1)输入初始位置信息${{\boldsymbol{w}}_{\rm{U}}},{{\boldsymbol{w}}_{\rm{R}}},{{\boldsymbol{w}}_k}$和其他基本系统参数;获得
$ {{\boldsymbol{H}}_{{\mathrm{U}} {\text{-}}{\mathrm{ R}}}} $, $ {{\boldsymbol{h}}_{{\mathrm{R}}{\text{-}} k}} $, ${{\boldsymbol{h}}_{{\mathrm{U}} {\text{-}} k}}$(2)根据式(16)及式(9)生成初始子种群:
${\bf{pop}}_0^{\boldsymbol{\varPhi}} = [{{\boldsymbol{\varPhi}} _1},{{\boldsymbol{\varPhi}} _2},\cdots,{{\boldsymbol{\varPhi}} _{{\text{pop}}}}]$, $ {\bf{pop}}_0^{\mathrm{G}} = [{{\boldsymbol{G}}_1},{{\boldsymbol{G}}_2},\cdots,{{\boldsymbol{G}}_{{\text{pop}}}}] $(3)随机初始化两个子种群的代表解${{\boldsymbol{\varPhi}} _{{\text{best}}}}$, $ {{\boldsymbol{G}}_{{\text{best}}}} $ (4)根据式(17)计算两个子种群组合解的初始综合适应度,并将子种群中的个体根据综合适应度排序,即 $\begin{aligned} {\text{Fitnes}}{{\text{s}}_1}({\bf{pop}}_0^{\boldsymbol{\varPhi}} ;{{\boldsymbol{G}}_{{\text{best}}}}) =\;& [{\text{Fitness}}({{\boldsymbol{\varPhi}} _1},{{\boldsymbol{G}}_{{\text{best}}}}),\cdots,\\& {\text{Fitness}}({{\boldsymbol{\varPhi}} _{{\text{pop}}}},{{\boldsymbol{G}}_{{\text{best}}}})]\end{aligned}$ $\begin{aligned} {\text{Fitnes}}{{\text{s}}_2}({{\boldsymbol{\varPhi}} _{{\text{best}}}};{\bf{pop}}_0^{\boldsymbol{G}}) = \;& [{\text{Fitness}}({{\boldsymbol{\varPhi}} _{{\text{best}}}},{{\boldsymbol{G}}_1}),\cdots,\\& {\text{Fitness}}({{\boldsymbol{\varPhi}} _{{\text{best}}}},{{\boldsymbol{G}}_{{\text{pop}}}})]\end{aligned}$ (5)for i = 1, 2, ···, inter do (6) 从${\bf{pop}}_{i - 1}^{\boldsymbol{\varPhi}} $和$ {\bf{pop}}_{i - 1}^{\boldsymbol{G}} $选择${\text{pop}} \times {\text{Selectrate}}$个体作为父代 (7) if rand< 交叉概率Crossrate (8) 在两个子种群父代中随机选择个体进行染色体交叉; (9) end if (10) if rand< 突变概率Mutationrate (11) 在两个子种群的个体随机选择染色体进行突变; (12) end if (13) 得到两个子种群对应的子代种群${\bf{pop}}_i^{\boldsymbol{\varPhi}} $和$ {\bf{pop}}_i^{\boldsymbol{G}} $ (14) 利用式(17)计算组合解综合适应度:${\text{Fitnes}}{{\text{s}}_1}({\bf{pop}}_i^{\boldsymbol{\varPhi }};{{\boldsymbol{G}}_{{\text{best}}}})$
和${\text{Fitnes}}{{\text{s}}_2}({{\boldsymbol{\varPhi}} _{{\text{best}}}};{\bf{pop}}_i^{\boldsymbol{G}})$,并将得到的解按适应度降序排序;(15) if max(${\text{Fitnes}}{{\text{s}}_1}({\bf{pop}}_i^\varPhi ;{{\boldsymbol{G}}_{{\text{best}}}})$)>${\text{Fitness}}({{\boldsymbol{\varPhi}} _{{\text{best}}}},{{\boldsymbol{G}}_{{\text{best}}}})$ (16) 更新${{\boldsymbol{\varPhi }}_{{\text{best}}}}$; (17) end if (18) if max(${\text{Fitnes}}{{\text{s}}_2}({{\boldsymbol{\varPhi }}_{{\text{best}}}};{\bf{pop}}_i^{\boldsymbol{G}})$)>${\text{Fitness}}({{\boldsymbol{\varPhi}} _{{\text{best}}}},{{\boldsymbol{G}}_{{\text{best}}}})$ (19) 更新$ {{\boldsymbol{G}}_{{\text{best}}}} $; (20) end if (21) 计算并更新代表解的适应度${\text{Fitness}}({{\boldsymbol{\varPhi}} _{{\text{best}}}},{{\boldsymbol{G}}_{{\text{best}}}})$ (22)end for (23)得到$[{{\boldsymbol{\varPhi}} _{{\text{best}}}},{{\boldsymbol{G}}_{{\text{best}}}}]$作为联合波束成形优化解; 表 1 系统参数
参数符号 参数值 参数符号 参数值 参数符号 参数值 参数符号 参数值 ${P_{\max }}$ 30 dBm ${\sigma ^2}$ –114 dBm f 2.4 GHz $\rho $ 0.01 ${\alpha _{{\mathrm{U}} {\text{-}} {\mathrm{R}}}}$ 2.2 ${\alpha _{{\mathrm{U}} {\text{-}} k}}$ 3.5 ${\alpha _{{\mathrm{R}} {\text{-}} k}}$ 2.8 K 2 M 4 ${L_x}$ 4 ${L_y}$ 4 $\phi $ $0.43\pi $ ${A_{\min }}$ 0.2 $\alpha $ 1.6 ${K_1}$ 10 ${K_2}$ 10 表 2 CCEA算法参数
参数名 参数值 参数名 参数值 种群个体数量pop 20 选择率 Selectrate 0.2 交叉概率 Crossrate 0.6 突变率 Mutationrate 0.1 最大迭代次数 inter 1 000 k1 0.5 c1 60 c2 1.0 表 3 图3对应的位置参数及频谱效率对比
UAV和用户位置参数 用户1方位
$[\theta _1^{{\text{azi}}},\theta _1^{{\text{ele}}}]$用户2方位
$[\theta _2^{{\text{azi}}},\theta _2^{{\text{ele}}}]$初始频谱效率
(bit/(s·Hz))优化后的频谱效率
(bit/(s·Hz))图3(a) $ {{\boldsymbol{w}}_{\rm{U}}} = {(25\,{\text{m}},30\,{\text{m}},30\,{\text{m}})^{\mathrm{T}}} $
$ {{\mathbf{w}}_1} = {(47\,m,15\,m,0\,m)^{\mathrm{T}}} $
$ {{\boldsymbol{w}}_2} = {(25\,m,5\,m,0\,m)^{\mathrm{T}}} $[59.04°, 64.99°] [30.96°, 23.21°] 6.511 7 26.868 9 图3(b) $ {{\boldsymbol{w}}_{\rm{U}}} = {(25\,{\text{m}},15\,{\text{m}},30\,{\text{m}})^{\mathrm{T}}} $
$ {{\mathbf{w}}_1} = {(47\,m,15\,m,0\,m)^{\mathrm{T}}} $
$ {{\boldsymbol{w}}_2} = {(25\,m,5\,m,0\,m)^{\mathrm{T}}} $[59.04°, 64.99°] [30.96°, 23.21°] 3.320 4 28.713 6 图3(c) $ {{\mathbf{w}}_{\rm{U}}} = {(25\,{\text{m}},30\,{\text{m}},30\,{\text{m}})^{\mathrm{T}}} $
$ {{\boldsymbol{w}}_1} = {(30\,m,15\,m,0\,m)^{\mathrm{T}}} $
$ {{\boldsymbol{w}}_2} = {(5\,m,5\,m,0\,m)^{\mathrm{T}}} $[36.67°, 26.36°] [6.30°, 15.47°] 6.234 8 27.642 8 -
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