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);
for i = 1:numNodes
validPosition = false;
while ~validPosition
pos = areaSize * rand(1, 2);
if i == 1
validPosition = true;
else
dists = sqrt(sum((positions(1:i-1,:) - pos).^2, 2));
if all(dists >= minDistance)
validPosition = true;
end
end
end
positions(i,:) = pos;
end
% 计算信道增益
channelGain = zeros(numNodes, numNodes);
distanceMatrix = zeros(numNodes, numNodes);
for i = 1:numNodes
for j = 1:numNodes
if i ~= j
distanceMatrix(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
end
end
end
% 显示网络拓扑
if visualizeResults
figure('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 visualizeResults
figure('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:numIter
prevPower = 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:numNodes
if j ~= i
interference = interference + channelGain(i,j)*currentPower(j);
end
end
% 自干扰
selfInterference = channelGain(i,i)*currentPower(i);
% 计算SINR
sinr = (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:numNodes
interference = 0;
for j = 1:numNodes
if j ~= i
interference = interference + channelGain(i,j)*currentPower(j);
end
end
selfInterference = 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)) < tol
break;
end
end
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:numIter
prevPower = currentPower;
% 领导者 (基站) 先决策
baseInterference = 0;
for u = 1:numUsers
baseInterference = baseInterference + channelGain(1,u+1)*currentPower(u+1);
end
baseSelfInterference = 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:numUsers
userInterference = 0;
for j = 1:numUsers+1
if j ~= u+1 && j ~= 1 % 排除自己和基站
userInterference = userInterference + channelGain(u+1,j)*currentPower(j);
end
end
userSelfInterference = 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+1
interference = 0;
for j = 1:numUsers+1
if j ~= i
interference = interference + channelGain(i,j)*currentPower(j);
end
end
selfInterference = 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)) < tol
break;
end
end
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:numIter
prevPower = coalitionPower;
% 每个联盟更新功率
for c = 1:numCoalitions
coalitionMembers = (c-1)*nodesPerCoalition + (1:nodesPerCoalition);
coalitionMembers = coalitionMembers(coalitionMembers <= numNodes);
numMembers = length(coalitionMembers);
% 计算联盟总效用
coalitionUtility = 0;
for i = 1:numMembers
nodeIdx = coalitionMembers(i);
interference = 0;
for j = 1:numNodes
if j ~= nodeIdx
interference = interference + channelGain(nodeIdx,j)*prevPower(ceil(j/nodesPerCoalition), mod(j-1, nodesPerCoalition)+1);
end
end
selfInterference = 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 > 0
powerRatio = prevPower(c,:) / totalPower;
else
powerRatio = 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:numCoalitions
for m = 1:nodesPerCoalition
if m <= size(coalitionPower, 2)
power(iter,c,m) = coalitionPower(c,m);
convergence(iter,c,m) = coalitionPower(c,m);
end
end
end
% 计算联盟吞吐量
for c = 1:numCoalitions
coalitionMembers = (c-1)*nodesPerCoalition + (1:nodesPerCoalition);
coalitionMembers = coalitionMembers(coalitionMembers <= numNodes);
numMembers = length(coalitionMembers);
coalitionThroughput = 0;
for i = 1:numMembers
nodeIdx = coalitionMembers(i);
interference = 0;
for j = 1:numNodes
if j ~= nodeIdx
otherCoal = ceil(j/nodesPerCoalition);
otherMem = mod(j-1, nodesPerCoalition)+1;
interference = interference + channelGain(nodeIdx,j)*coalitionPower(otherCoal, otherMem);
end
end
selfInterference = 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);
end
throughput(iter,c) = coalitionThroughput;
end
% 检查收敛
if iter > 1 && max(abs(coalitionPower(:) - prevPower(:))) < tol
break;
end
end
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SINR
sinr = 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 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：\(PL(d)=(λ/(4πd))^2\)
- 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);
else
utility = 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
浙公网安备 33010602011771号