MATLAB实现：基于博弈论的全双工系统无线资源分配

基于博弈论的全双工(Full-Duplex, FD)系统无线资源分配。该程序实现了非合作博弈、Stackelberg博弈和合作博弈三种模型，并提供了可视化分析功能。

%% 基于博弈论的全双工系统无线资源分配% 功能: 实现三种博弈模型的全双工资源分配仿真% 模型: 非合作博弈、Stackelberg博弈、合作博弈clear;clc;close all;%% 1. 系统参数设置% 网络拓扑参数numNodes=4;% 节点数量areaSize=1000;% 区域大小 (m)minDistance=100;% 节点间最小距离 (m)% 信道参数c=3e8;% 光速 (m/s)fc=2.4e9;% 载波频率 (Hz)lambda=c/fc;% 波长 (m)pathLossExp=3.5;% 路径损耗指数shadowSigma=3;% 阴影衰落标准差 (dB)noisePower=1e-9;% 噪声功率 (W)% 全双工参数selfInterferenceFactor=0.1;% 自干扰因子 (残留干扰比例)maxPower=0.1;% 最大发射功率 (W)minPower=0.001;% 最小发射功率 (W)% 博弈参数numIterations=100;% 最大迭代次数tolerance=1e-3;% 收敛容差learningRate=0.1;% 学习率 (演化博弈)% 仿真参数numRealizations=10;% 蒙特卡洛仿真次数visualizeResults=true;% 是否可视化结果%% 2. 生成网络拓扑% 随机生成节点位置rng(42);% 固定随机种子positions=zeros(numNodes,2);fori=1:numNodes validPosition=false;while~validPosition pos=areaSize*rand(1,2);ifi==1validPosition=true;elsedists=sqrt(sum((positions(1:i-1,:)-pos).^2,2));ifall(dists>=minDistance)validPosition=true;endendendpositions(i,:)=pos;end% 计算信道增益channelGain=zeros(numNodes,numNodes);distanceMatrix=zeros(numNodes,numNodes);fori=1:numNodesforj=1:numNodesifi~=jdistanceMatrix(i,j)=norm(positions(i,:)-positions(j,:));pathLoss=(lambda/(4*pi*distanceMatrix(i,j)))^2;shadowing=10^(shadowSigma*randn()/10);% dB转线性channelGain(i,j)=pathLoss*shadowing;else% 自干扰信道 (残留干扰)channelGain(i,i)=selfInterferenceFactor*(lambda/(4*pi*10))^2;% 假设近距离endendend% 显示网络拓扑ifvisualizeResultsfigure('Name','网络拓扑','Position',[100,100,800,600]);scatter(positions(:,1),positions(:,2),100,'filled');text(positions(:,1)+20,positions(:,2)+20,num2str((1:numNodes)'));title('全双工节点分布');xlabel('x (m)');ylabel('y (m)');grid on;axis equal;end%% 3. 博弈模型实现% 存储性能指标performanceMetrics=struct();% 非合作博弈 (功率分配)[noncoopPower,noncoopThroughput,noncoopConvergence]=noncooperativeGame(...channelGain,noisePower,maxPower,minPower,numIterations,tolerance);% Stackelberg博弈 (基站主导)[stackelbergPower,stackelbergThroughput,stackelbergConvergence]=stackelbergGame(...channelGain,noisePower,maxPower,minPower,numIterations,tolerance);% 合作博弈 (联盟形成)[coopPower,coopThroughput,coopConvergence]=cooperativeGame(...channelGain,noisePower,maxPower,minPower,numIterations,tolerance);% 存储结果performanceMetrics.noncoop.power=noncoopPower;performanceMetrics.noncoop.throughput=noncoopThroughput;performanceMetrics.noncoop.convergence=noncoopConvergence;performanceMetrics.stackelberg.power=stackelbergPower;performanceMetrics.stackelberg.throughput=stackelbergThroughput;performanceMetrics.stackelberg.convergence=stackelbergConvergence;performanceMetrics.coop.power=coopPower;performanceMetrics.coop.throughput=coopThroughput;performanceMetrics.coop.convergence=coopConvergence;%% 4. 性能分析与可视化% 计算平均吞吐量avgThroughput=struct(...'noncoop',mean(noncoopThroughput),...'stackelberg',mean(stackelbergThroughput),...'coop',mean(coopThroughput));% 计算能效energyEfficiency=struct(...'noncoop',avgThroughput.noncoop/mean(sum(noncoopPower,2)),...'stackelberg',avgThroughput.stackelberg/mean(sum(stackelbergPower,2)),...'coop',avgThroughput.coop/mean(sum(coopPower,2)));% 打印结果fprintf('===== 性能评估结果 =====\n');fprintf('模型\t\t平均吞吐量(bps/Hz)\t能效(bps/Hz/W)\n');fprintf('非合作博弈\t%.4f\t\t\t%.4f\n',avgThroughput.noncoop,energyEfficiency.noncoop);fprintf('Stackelberg\t%.4f\t\t\t%.4f\n',avgThroughput.stackelberg,energyEfficiency.stackelberg);fprintf('合作博弈\t%.4f\t\t\t%.4f\n',avgThroughput.coop,energyEfficiency.coop);% 可视化收敛过程ifvisualizeResultsfigure('Name','博弈收敛过程','Position',[100,100,1200,800]);% 非合作博弈收敛subplot(3,1,1);plot(squeeze(noncoopConvergence(:,1,:)),'LineWidth',1.5);hold on;plot(squeeze(noncoopConvergence(:,2,:)),'LineWidth',1.5);title('非合作博弈收敛过程');xlabel('迭代次数');ylabel('功率 (W)');legend('节点1','节点2','节点3','节点4');grid on;% Stackelberg博弈收敛subplot(3,1,2);plot(squeeze(stackelbergConvergence(:,1,:)),'LineWidth',1.5);hold on;plot(squeeze(stackelbergConvergence(:,2,:)),'LineWidth',1.5);title('Stackelberg博弈收敛过程');xlabel('迭代次数');ylabel('功率 (W)');legend('基站','用户1','用户2','用户3');grid on;% 合作博弈收敛subplot(3,1,3);plot(squeeze(coopConvergence(:,1,:)),'LineWidth',1.5);hold on;plot(squeeze(coopConvergence(:,2,:)),'LineWidth',1.5);title('合作博弈收敛过程');xlabel('迭代次数');ylabel('功率 (W)');legend('联盟1','联盟2');grid on;% 吞吐量比较figure('Name','吞吐量比较','Position',[100,100,800,600]);throughputData=[avgThroughput.noncoop,avgThroughput.stackelberg,avgThroughput.coop];bar(throughputData);set(gca,'XTickLabel',{'非合作博弈','Stackelberg','合作博弈'});ylabel('平均吞吐量 (bps/Hz)');title('不同博弈模型的吞吐量比较');grid on;% 能效比较figure('Name','能效比较','Position',[100,100,800,600]);efficiencyData=[energyEfficiency.noncoop,energyEfficiency.stackelberg,energyEfficiency.coop];bar(efficiencyData);set(gca,'XTickLabel',{'非合作博弈','Stackelberg','合作博弈'});ylabel('能效 (bps/Hz/W)');title('不同博弈模型的能效比较');grid on;% 功率分配可视化figure('Name','功率分配','Position',[100,100,1200,800]);% 非合作博弈功率分配subplot(3,1,1);imagesc(noncoopPower);colorbar;title('非合作博弈功率分配');xlabel('迭代次数');ylabel('节点');set(gca,'XTick',1:numIterations,'XTickLabel',[]);set(gca,'YTick',1:numNodes);% Stackelberg博弈功率分配subplot(3,1,2);imagesc(stackelbergPower);colorbar;title('Stackelberg博弈功率分配');xlabel('迭代次数');ylabel('节点');set(gca,'XTick',1:numIterations,'XTickLabel',[]);set(gca,'YTick',1:numNodes);% 合作博弈功率分配subplot(3,1,3);imagesc(coopPower);colorbar;title('合作博弈功率分配');xlabel('迭代次数');ylabel('联盟');set(gca,'XTick',1:numIterations,'XTickLabel',[]);set(gca,'YTick',1:size(coopPower,1));end%% 5. 辅助函数：非合作博弈function[power,throughput,convergence]=noncooperativeGame(...channelGain,noisePower,maxPower,minPower,numIter,tol)numNodes=size(channelGain,1);power=zeros(numIter,numNodes);% 记录每次迭代的功率throughput=zeros(numIter,numNodes);% 记录吞吐量convergence=zeros(numIter,numNodes);% 记录收敛过程% 初始化功率 (随机)currentPower=minPower+(maxPower-minPower)*rand(1,numNodes);foriter=1:numIter prevPower=currentPower;% 每个节点更新功率fori=1:numNodes% 计算其他节点的干扰interference=0;forj=1:numNodesifj~=iinterference=interference+channelGain(i,j)*currentPower(j);endend% 自干扰selfInterference=channelGain(i,i)*currentPower(i);% 计算SINRsinr=(channelGain(i,mod(i,numNodes)+1)*currentPower(mod(i,numNodes)+1))/...(interference+selfInterference+noisePower);% 效用函数: 吞吐量 - 功率成本utility=log2(1+sinr)-0.01*currentPower(i);% 最佳响应更新 (梯度上升)newPower=currentPower(i)+0.1*(utility-0.5*currentPower(i));newPower=min(max(newPower,minPower),maxPower);currentPower(i)=newPower;end% 记录当前状态power(iter,:)=currentPower;convergence(iter,:)=currentPower;% 计算吞吐量fori=1:numNodes interference=0;forj=1:numNodesifj~=iinterference=interference+channelGain(i,j)*currentPower(j);endendselfInterference=channelGain(i,i)*currentPower(i);sinr=(channelGain(i,mod(i,numNodes)+1)*currentPower(mod(i,numNodes)+1))/...(interference+selfInterference+noisePower);throughput(iter,i)=log2(1+sinr);end% 检查收敛ifiter>1&&max(abs(currentPower-prevPower))<tolbreak;endendend%% 6. 辅助函数：Stackelberg博弈function[power,throughput,convergence]=stackelbergGame(...channelGain,noisePower,maxPower,minPower,numIter,tol)numUsers=size(channelGain,1)-1;% 假设节点1是基站power=zeros(numIter,numUsers+1);% 记录功率throughput=zeros(numIter,numUsers+1);% 记录吞吐量convergence=zeros(numIter,numUsers+1);% 记录收敛过程% 初始化功率baseStationPower=minPower+(maxPower-minPower)*rand(1);userPowers=minPower+(maxPower-minPower)*rand(1,numUsers);currentPower=[baseStationPower,userPowers];foriter=1:numIter prevPower=currentPower;% 领导者 (基站) 先决策baseInterference=0;foru=1:numUsers baseInterference=baseInterference+channelGain(1,u+1)*currentPower(u+1);endbaseSelfInterference=channelGain(1,1)*currentPower(1);baseSinr=(channelGain(1,2)*currentPower(2))/...% 假设基站服务用户2(baseInterference+baseSelfInterference+noisePower);baseUtility=log2(1+baseSinr)-0.005*currentPower(1);% 更新基站功率newBasePower=currentPower(1)+0.1*(baseUtility-0.5*currentPower(1));newBasePower=min(max(newBasePower,minPower),maxPower);currentPower(1)=newBasePower;% 跟随者 (用户) 更新功率foru=1:numUsers userInterference=0;forj=1:numUsers+1ifj~=u+1&&j~=1% 排除自己和基站userInterference=userInterference+channelGain(u+1,j)*currentPower(j);endenduserSelfInterference=channelGain(u+1,u+1)*currentPower(u+1);userSinr=(channelGain(u+1,1)*currentPower(1))/...% 用户接收基站信号(userInterference+userSelfInterference+noisePower);userUtility=log2(1+userSinr)-0.01*currentPower(u+1);% 更新用户功率newUserPower=currentPower(u+1)+0.1*(userUtility-0.5*currentPower(u+1));newUserPower=min(max(newUserPower,minPower),maxPower);currentPower(u+1)=newUserPower;end% 记录当前状态power(iter,:)=currentPower;convergence(iter,:)=currentPower;% 计算吞吐量fori=1:numUsers+1interference=0;forj=1:numUsers+1ifj~=iinterference=interference+channelGain(i,j)*currentPower(j);endendselfInterference=channelGain(i,i)*currentPower(i);sinr=(channelGain(i,mod(i,numUsers+1)+1)*currentPower(mod(i,numUsers+1)+1))/...(interference+selfInterference+noisePower);throughput(iter,i)=log2(1+sinr);end% 检查收敛ifiter>1&&max(abs(currentPower-prevPower))<tolbreak;endendend%% 7. 辅助函数：合作博弈function[power,throughput,convergence]=cooperativeGame(...channelGain,noisePower,maxPower,minPower,numIter,tol)numNodes=size(channelGain,1);numCoalitions=2;% 分成两个联盟nodesPerCoalition=ceil(numNodes/numCoalitions);power=zeros(numIter,numCoalitions,nodesPerCoalition);% 记录功率throughput=zeros(numIter,numCoalitions);% 记录吞吐量convergence=zeros(numIter,numCoalitions,nodesPerCoalition);% 记录收敛过程% 初始化联盟功率coalitionPower=minPower+(maxPower-minPower)*rand(numCoalitions,nodesPerCoalition);foriter=1:numIter prevPower=coalitionPower;% 每个联盟更新功率forc=1:numCoalitions coalitionMembers=(c-1)*nodesPerCoalition+(1:nodesPerCoalition);coalitionMembers=coalitionMembers(coalitionMembers<=numNodes);numMembers=length(coalitionMembers);% 计算联盟总效用coalitionUtility=0;fori=1:numMembers nodeIdx=coalitionMembers(i);interference=0;forj=1:numNodesifj~=nodeIdx interference=interference+channelGain(nodeIdx,j)*prevPower(ceil(j/nodesPerCoalition),mod(j-1,nodesPerCoalition)+1);endendselfInterference=channelGain(nodeIdx,nodeIdx)*prevPower(c,i);sinr=(channelGain(nodeIdx,mod(nodeIdx,numNodes)+1)*prevPower(ceil(mod(nodeIdx,numNodes)+1/nodesPerCoalition),mod(mod(nodeIdx,numNodes),nodesPerCoalition)+1))/...(interference+selfInterference+noisePower);coalitionUtility=coalitionUtility+log2(1+sinr)-0.01*sum(prevPower(c,:));end% 联盟内功率分配 (按比例)totalPower=sum(prevPower(c,:));iftotalPower>0powerRatio=prevPower(c,:)/totalPower;elsepowerRatio=ones(1,numMembers)/numMembers;end% 更新联盟功率newPower=prevPower(c,:)+0.1*(coalitionUtility*powerRatio-0.5*prevPower(c,:));newPower=min(max(newPower,minPower),maxPower);coalitionPower(c,:)=newPower;end% 记录当前状态forc=1:numCoalitionsform=1:nodesPerCoalitionifm<=size(coalitionPower,2)power(iter,c,m)=coalitionPower(c,m);convergence(iter,c,m)=coalitionPower(c,m);endendend% 计算联盟吞吐量forc=1:numCoalitions coalitionMembers=(c-1)*nodesPerCoalition+(1:nodesPerCoalition);coalitionMembers=coalitionMembers(coalitionMembers<=numNodes);numMembers=length(coalitionMembers);coalitionThroughput=0;fori=1:numMembers nodeIdx=coalitionMembers(i);interference=0;forj=1:numNodesifj~=nodeIdx otherCoal=ceil(j/nodesPerCoalition);otherMem=mod(j-1,nodesPerCoalition)+1;interference=interference+channelGain(nodeIdx,j)*coalitionPower(otherCoal,otherMem);endendselfInterference=channelGain(nodeIdx,nodeIdx)*coalitionPower(c,i);sinr=(channelGain(nodeIdx,mod(nodeIdx,numNodes)+1)*coalitionPower(ceil(mod(nodeIdx,numNodes)+1/nodesPerCoalition),mod(mod(nodeIdx,numNodes),nodesPerCoalition)+1))/...(interference+selfInterference+noisePower);coalitionThroughput=coalitionThroughput+log2(1+sinr);endthroughput(iter,c)=coalitionThroughput;end% 检查收敛ifiter>1&&max(abs(coalitionPower(:)-prevPower(:)))<tolbreak;endendend%% 8. 高级分析：公平性评估functionfairnessIndex=calculateFairness(throughput)% Jain公平性指数numerator=(sum(throughput))^2;denominator=length(throughput)*sum(throughput.^2);fairnessIndex=numerator/denominator;end% 计算各模型的公平性noncoopFairness=calculateFairness(noncoopThroughput(end,:));stackelbergFairness=calculateFairness(stackelbergThroughput(end,:));coopFairness=calculateFairness(coopThroughput(end,:));fprintf('\n===== 公平性评估 =====\n');fprintf('模型\t\tJain公平性指数\n');fprintf('非合作博弈\t%.4f\n',noncoopFairness);fprintf('Stackelberg\t%.4f\n',stackelbergFairness);fprintf('合作博弈\t%.4f\n',coopFairness);%% 9. 高级分析：能量效率functionefficiency=calculateEfficiency(throughput,power)% 计算系统总吞吐量和总功耗totalThroughput=sum(throughput);totalPower=sum(power(:));efficiency=totalThroughput/totalPower;end% 计算各模型的能量效率noncoopEfficiency=calculateEfficiency(noncoopThroughput(end,:),noncoopPower(end,:));stackelbergEfficiency=calculateEfficiency(stackelbergThroughput(end,:),stackelbergPower(end,:));coopEfficiency=calculateEfficiency(coopThroughput(end,:),coopPower(end,:));fprintf('\n===== 能量效率评估 =====\n');fprintf('模型\t\t能量效率(bps/Hz/W)\n');fprintf('非合作博弈\t%.4f\n',noncoopEfficiency);fprintf('Stackelberg\t%.4f\n',stackelbergEfficiency);fprintf('合作博弈\t%.4f\n',coopEfficiency);

博弈论在全双工资源分配中的应用原理

1. 全双工系统挑战

全双工(FD)系统允许节点同时同频发送和接收，理论上可倍增频谱效率，但面临两大挑战：

• 自干扰(SI)：发射信号对自身接收机的强干扰（比目标信号高60-100dB）
• 双向干扰：多FD节点共存时的相互干扰

2. 博弈论建模要素

3. 三种博弈模型实现

(1) 非合作博弈

• 场景：节点独立决策，追求自身利益最大化
• 策略更新：梯度上升法优化效用函数
• 收敛条件：功率变化小于容差

% 节点策略更新fori=1:numNodes% 计算干扰和SINRsinr=calculateSINR(i,currentPower,channelGain);% 效用函数: 吞吐量 - 功率成本utility=log2(1+sinr)-costCoeff*currentPower(i);% 梯度上升更新newPower=currentPower(i)+learningRate*(utility-penalty*currentPower(i));currentPower(i)=min(max(newPower,minPower),maxPower);end

(2) Stackelberg博弈

• 场景：层级结构（基站主导，用户跟随）
• 策略更新： 领导者（基站）先决策 跟随者（用户）根据领导策略响应
• 均衡：子博弈完美均衡

% 基站(领导者)决策baseUtility=calculateBaseUtility(basePower,userPowers);newBasePower=basePower+lr*(baseUtility-penalty*basePower);% 用户(跟随者)响应foreach user userUtility=calculateUserUtility(userPower,basePower);newUserPower=userPower+lr*(userUtility-penalty*userPower);end

(3) 合作博弈

• 场景：节点形成联盟共享资源
• 策略更新：联盟内联合优化
• 效用分配：Shapley值或比例分配

% 联盟形成coalition1=nodes(1:2);coalition2=nodes(3:4);% 联盟内功率分配totalUtility=calculateCoalitionUtility(coalitionPower);powerRatio=coalitionPower/sum(coalitionPower);newPower=coalitionPower+lr*(totalUtility*powerRatio-penalty*coalitionPower);

关键技术与创新点

1. 信道建模

• 路径损耗：PL(d)=(λ/(4πd))2PL(d)=(λ/(4πd))^2PL(d)=(λ/(4πd))2
• 阴影衰落：对数正态分布10N(0,σ2)/1010^{N(0,σ2)}/^{10}10N(0,σ2)/10
• 自干扰模型：hii=η⋅(λ/(4πdref))2h_{ii}=η⋅(λ/(4πd_{ref}))^2hii​=η⋅(λ/(4πdref​))2

2. 效用函数设计

• 吞吐量项：log2(1+SINR)log_2(1+SINR)log2​(1+SINR)（比例公平）
• 成本项：c⋅pic⋅pic⋅pi（功率消耗）
• 干扰处理：包含所有节点干扰和自干扰

3. 收敛性保障

• 迭代算法：最佳响应动态
• 终止条件：功率变化小于容差或达最大迭代次数
• 学习率调整：自适应学习率加速收敛

参考代码 基于博弈论的全双工系统无线资源分配www.youwenfan.com/contentcsn/83490.html

性能评估指标

1. 系统级指标

2. 可视化分析

• 收敛过程：展示功率迭代变化
• 吞吐量比较：柱状图对比模型性能
• 功率分配：热力图展示资源分布
• 网络拓扑：节点位置与信道关系

扩展功能与应用

1. 多小区扩展

% 多小区拓扑生成numCells=3;cellRadius=200;cellPositions=generateCellPositions(numCells,cellRadius);% 跨小区干扰处理interCellInterference=calculateInterCellInterference(...);

2. 动态场景适应

% 移动节点更新位置positions=updateNodePositions(positions,velocities,timeStep);% 信道状态更新channelGain=updateChannelState(positions,shadowing);

3. 混合博弈模型

% 部分节点合作，部分竞争cooperativeNodes=[1,2];noncooperativeNodes=[3,4];% 差异化效用函数ifismember(i,cooperativeNodes)utility=coalitionUtility(i);elseutility=individualUtility(i);end

4. 机器学习增强

% 强化学习策略优化policyNetwork=trainPolicyNetwork(experienceBuffer);% 预测信道状态channelPredictor=trainChannelPredictor(historicalData);

实际应用场景

1. 5G/6G网络

• 密集小区全双工通信
• D2D通信资源分配
• 超可靠低延迟通信(URLLC)

2. 物联网(IoT)

• 传感器网络数据采集
• 低功耗广域网(LPWAN)
• 工业物联网(IIoT)

3. 车联网(V2X)

• 车辆间通信(V2V)
• 车路协同(V2I)
• 自动驾驶协同感知

4. 应急通信

• 灾区临时网络部署
• 无人机基站中继
• 军事战术通信