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);
for i = 1:numNodesvalidPosition = false;while ~validPositionpos = areaSize * rand(1, 2);if i == 1validPosition = true;elsedists = sqrt(sum((positions(1:i-1,:) - pos).^2, 2));if all(dists >= minDistance)validPosition = true;endendendpositions(i,:) = pos;
end% 计算信道增益
channelGain = zeros(numNodes, numNodes);
distanceMatrix = zeros(numNodes, numNodes);
for i = 1:numNodesfor j = 1:numNodesif i ~= 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endend
end% 显示网络拓扑
if visualizeResultsfigure('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
if visualizeResultsfigure('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);for iter = 1:numIterprevPower = currentPower;% 每个节点更新功率for i = 1:numNodes% 计算其他节点的干扰interference = 0;for j = 1:numNodesif j ~= 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for i = 1:numNodesinterference = 0;for j = 1:numNodesif j ~= 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if iter > 1 && max(abs(currentPower - prevPower)) < tolbreak;endend
end%% 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];for iter = 1:numIterprevPower = currentPower;% 领导者 (基站) 先决策baseInterference = 0;for u = 1:numUsersbaseInterference = 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for u = 1:numUsersuserInterference = 0;for j = 1:numUsers+1if j ~= 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for i = 1:numUsers+1interference = 0;for j = 1:numUsers+1if j ~= 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if iter > 1 && max(abs(currentPower - prevPower)) < tolbreak;endend
end%% 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);for iter = 1:numIterprevPower = coalitionPower;% 每个联盟更新功率for c = 1:numCoalitionscoalitionMembers = (c-1)*nodesPerCoalition + (1:nodesPerCoalition);coalitionMembers = coalitionMembers(coalitionMembers <= numNodes);numMembers = length(coalitionMembers);% 计算联盟总效用coalitionUtility = 0;for i = 1:numMembersnodeIdx = coalitionMembers(i);interference = 0;for j = 1:numNodesif j ~= nodeIdxinterference = 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,:));if totalPower > 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for c = 1:numCoalitionsfor m = 1:nodesPerCoalitionif m <= 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for c = 1:numCoalitionscoalitionMembers = (c-1)*nodesPerCoalition + (1:nodesPerCoalition);coalitionMembers = coalitionMembers(coalitionMembers <= numNodes);numMembers = length(coalitionMembers);coalitionThroughput = 0;for i = 1:numMembersnodeIdx = coalitionMembers(i);interference = 0;for j = 1:numNodesif j ~= nodeIdxotherCoal = 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if iter > 1 && max(abs(coalitionPower(:) - prevPower(:))) < tolbreak;endend
end%% 8. 高级分析：公平性评估
function fairnessIndex = 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
function efficiency = 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
| 要素 | 描述 | 实现方式 |
|---|---|---|
| 参与者 | 网络节点（基站、用户设备） | 节点数组 |
| 策略集 | 可调资源参数（功率、频谱） | 功率分配向量 |
| 效用函数 | 衡量策略收益（吞吐量、能效） | \(U_i=log(1+SINR_i)−c⋅pi\) |
| 均衡 | 策略稳定状态（纳什均衡） | 迭代最佳响应算法 |
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
for i = 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
for each useruserUtility = 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：\(PL(d)=(λ/(4πd))^2\)
- 阴影衰落：对数正态分布 \(10^{N(0,σ2)}/^{10}\)
- 自干扰模型：\(h_{ii}=η⋅(λ/(4πd_{ref}))^2\)
2. 效用函数设计
- 吞吐量项：\(log_2(1+SINR)\)（比例公平）
- 成本项：\(c⋅pi\)（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/contentcnm/83490.html
性能评估指标
1. 系统级指标
| 指标 | 公式 | 意义 |
|---|---|---|
| 吞吐量 | \(∑log_2(1+SINR_i)\) | 系统传输能力 |
| 能效 | 吞吐量/总功耗 | 能源利用效率 |
| 公平性 | \((∑x_i)^2/(n∑x_i^2)\) | 资源分配公平性 |
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
if ismember(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
)
