认知无线网络中频谱感知和功率分配的多目标模因优化问题MATLAB实现

一、问题建模

1. 系统模型

classdef CRN_System < handle
    properties
        N_channels      % 信道数量
        N_users         % 次级用户数量
        T_frame         % 帧时长
        T_sensing       % 感知时间
        P_max           % 最大发射功率
        P_idle_threshold% 空闲检测阈值
        noise_power     % 噪声功率
        channel_gains   % 信道增益矩阵
        PU_activity     % 主用户活动概率
        bandwidth       % 信道带宽
        interference_threshold  % 干扰阈值
        energy_weights  % 能量权重（感知能耗）
    end
end

2. 多目标优化问题

function objectives = multi_objective_function(x, system)
    % 输入：x = [感知时间; 功率分配矩阵]
    % 输出：目标向量 [吞吐量, 干扰, 能耗, 公平性]
    
    % 解码变量
    T_sensing = x(1);
    power_matrix = reshape(x(2:end), system.N_channels, system.N_users);
    
    % 计算各目标
    throughput = compute_throughput(power_matrix, system, T_sensing);
    interference = compute_interference(power_matrix, system);
    energy = compute_energy_consumption(power_matrix, T_sensing, system);
    fairness = compute_fairness_index(power_matrix, system);
    
    % 最大化吞吐量和公平性，最小化干扰和能耗
    objectives = [-throughput;   % 转换为最小化问题
                  interference;
                  energy;
                  -fairness];
end

二、模因优化算法实现

1. 主算法框架

function [best_solution, pareto_front] = memetic_optimization(system, params)
    % 初始化参数
    pop_size = params.pop_size;
    max_gen = params.max_gen;
    crossover_rate = params.crossover_rate;
    mutation_rate = params.mutation_rate;
    local_search_rate = params.local_search_rate;
    
    % 初始化种群
    population = initialize_population(pop_size, system);
    
    % 计算初始适应度
    fitness = evaluate_population(population, system);
    
    % Pareto前沿存储
    pareto_front = [];
    pareto_solutions = [];
    
    for gen = 1:max_gen
        % 1. 非支配排序和拥挤度计算
        [fronts, ranks] = non_dominated_sort(fitness);
        crowding_distances = crowding_distance(fitness, fronts);
        
        % 2. 选择操作（锦标赛选择）
        parents = tournament_selection(population, fitness, ranks, crowding_distances);
        
        % 3. 遗传操作
        offspring = genetic_operators(parents, crossover_rate, mutation_rate, system);
        
        % 4. 局部搜索（模因算法的核心）
        offspring = local_search(offspring, local_search_rate, system);
        
        % 5. 合并种群
        combined_pop = [population; offspring];
        combined_fitness = [fitness; evaluate_population(offspring, system)];
        
        % 6. 环境选择
        [population, fitness] = environmental_selection(combined_pop, combined_fitness, pop_size);
        
        % 7. 更新Pareto前沿
        [current_pareto, current_solutions] = update_pareto_front(population, fitness);
        
        % 8. 归档精英解
        [pareto_front, pareto_solutions] = update_archive(pareto_front, pareto_solutions, ...
                                                        current_pareto, current_solutions);
        
        % 显示进度
        if mod(gen, 10) == 0
            fprintf('Generation %d: Pareto front size = %d\n', gen, size(pareto_front, 1));
        end
    end
    
    best_solution = select_best_solution(pareto_front, pareto_solutions, system);
end

2. 混合编码和初始化

function population = initialize_population(pop_size, system)
    % 混合编码：连续变量（功率）+ 离散变量（信道选择）
    population = cell(pop_size, 1);
    
    for i = 1:pop_size
        % 连续部分：感知时间和功率
        T_sensing = system.T_frame * rand() * 0.5;  % 感知时间不超过帧长的一半
        power_matrix = rand(system.N_channels, system.N_users) * system.P_max;
        
        % 离散部分：信道选择（二进制编码）
        channel_selection = rand(system.N_channels, system.N_users) > 0.5;
        
        % 编码为单个向量
        individual.continuous = [T_sensing; power_matrix(:)];
        individual.discrete = channel_selection(:);
        individual.encoded = encode_individual(individual);
        
        population{i} = individual;
    end
end

function encoded = encode_individual(indiv)
    % 将混合变量编码为统一向量
    encoded = [indiv.continuous; double(indiv.discrete)];
end

function indiv = decode_individual(encoded, system)
    % 解码统一向量
    n_cont = 1 + system.N_channels * system.N_users;  % 连续变量数量
    indiv.continuous = encoded(1:n_cont);
    indiv.discrete = encoded(n_cont+1:end) > 0.5;
    indiv.encoded = encoded;
end

3. 局部搜索策略

function offspring = local_search(offspring, rate, system)
    % 多种局部搜索策略混合
    
    for i = 1:length(offspring)
        if rand() < rate
            % 随机选择局部搜索策略
            strategy = randi(4);
            
            switch strategy
                case 1
                    % 梯度下降局部搜索（连续变量）
                    offspring{i} = gradient_based_search(offspring{i}, system);
                    
                case 2
                    % 模拟退火搜索
                    offspring{i} = simulated_annealing_search(offspring{i}, system);
                    
                case 3
                    % 模式搜索（Pattern Search）
                    offspring{i} = pattern_search_local(offspring{i}, system);
                    
                case 4
                    % 禁忌搜索（离散变量）
                    offspring{i} = tabu_search_local(offspring{i}, system);
            end
        end
    end
end

function indiv = gradient_based_search(indiv, system)
    % 基于梯度的局部搜索
    epsilon = 0.01;  % 步长
    max_iter = 10;
    
    decoded = decode_individual(indiv.encoded, system);
    x0 = decoded.continuous;
    
    for iter = 1:max_iter
        % 计算梯度（近似）
        grad = approximate_gradient(@(x) local_objective(x, system, decoded.discrete), x0);
        
        % 更新连续变量
        x_new = x0 - epsilon * grad;
        
        % 约束处理
        x_new = apply_constraints(x_new, system);
        
        % 接受改进解
        if local_objective(x_new, system, decoded.discrete) < ...
           local_objective(x0, system, decoded.discrete)
            x0 = x_new;
        else
            break;
        end
    end
    
    % 更新个体
    decoded.continuous = x0;
    indiv.encoded = encode_individual(decoded);
end

function obj = local_objective(x, system, discrete_vars)
    % 局部搜索目标函数
    full_vars = encode_individual(struct('continuous', x, 'discrete', discrete_vars));
    decoded = decode_individual(full_vars, system);
    
    % 计算加权目标
    objectives = multi_objective_function(full_vars, system);
    weights = [0.4, 0.2, 0.2, 0.2];  % 权重向量
    obj = weights * objectives;
end

4. 目标函数计算

function throughput = compute_throughput(power_matrix, system, T_sensing)
    % 计算系统总吞吐量
    throughput = 0;
    T_transmission = system.T_frame - T_sensing;
    
    for ch = 1:system.N_channels
        for u = 1:system.N_users
            if power_matrix(ch, u) > 0
                % 检测概率和虚警概率
                Pd = detection_probability(T_sensing, system);
                Pf = false_alarm_probability(T_sensing, system);
                
                % 信道状态概率
                P_busy = system.PU_activity(ch);
                P_idle = 1 - P_busy;
                
                % 有效传输概率
                P_access = P_idle * (1 - Pf) + P_busy * (1 - Pd);
                
                % 信噪比
                SNR = power_matrix(ch, u) * system.channel_gains(ch, u) / ...
                      system.noise_power;
                
                % 香农容量
                capacity = system.bandwidth(ch) * log2(1 + SNR);
                
                % 有效吞吐量
                throughput = throughput + P_access * capacity * T_transmission;
            end
        end
    end
end

function interference = compute_interference(power_matrix, system)
    % 计算对主用户的干扰
    interference = 0;
    
    for ch = 1:system.N_channels
        PU_present = rand() < system.PU_activity(ch);
        
        if PU_present
            for u = 1:system.N_users
                % 漏检导致的干扰
                Pd = detection_probability(system.T_sensing, system);
                interference_ch = (1 - Pd) * power_matrix(ch, u) * ...
                                  system.channel_gains(ch, u);
                interference = interference + interference_ch;
            end
        end
    end
    
    % 归一化
    interference = interference / (system.N_channels * system.P_max);
end

function fairness = compute_fairness_index(power_matrix, system)
    % 计算Jain's公平性指数
    user_throughputs = zeros(system.N_users, 1);
    
    for u = 1:system.N_users
        user_power = sum(power_matrix(:, u));
        if user_power > 0
            % 计算用户吞吐量
            user_capacity = 0;
            for ch = 1:system.N_channels
                if power_matrix(ch, u) > 0
                    SNR = power_matrix(ch, u) * system.channel_gains(ch, u) / ...
                          system.noise_power;
                    user_capacity = user_capacity + ...
                                   system.bandwidth(ch) * log2(1 + SNR);
                end
            end
            user_throughputs(u) = user_capacity;
        end
    end
    
    % Jain's公平性指数
    sum_throughput = sum(user_throughputs);
    sum_squared = sum(user_throughputs.^2);
    
    if sum_squared > 0
        fairness = sum_throughput^2 / (system.N_users * sum_squared);
    else
        fairness = 0;
    end
end

三、完整仿真示例

%% 认知无线网络频谱感知和功率分配的多目标模因优化
clear; clc; close all;

%% 1. 系统参数设置
system = struct();
system.N_channels = 10;           % 信道数量
system.N_users = 5;              % 次级用户数量
system.T_frame = 100e-3;         % 帧时长 (100ms)
system.P_max = 1;                % 最大发射功率 (W)
system.noise_power = 1e-12;      % 噪声功率
system.interference_threshold = 1e-9;  % 干扰阈值
system.energy_weights = 0.1;     % 能量权重

% 信道增益（对数正态分布）
system.channel_gains = 10.^(-3 + 0.5*randn(system.N_channels, system.N_users));

% 主用户活动概率
system.PU_activity = 0.2 + 0.6*rand(system.N_channels, 1);

% 信道带宽
system.bandwidth = 1e6 * (1 + rand(system.N_channels, 1));  % 1-2 MHz

%% 2. 模因算法参数
params = struct();
params.pop_size = 100;           % 种群大小
params.max_gen = 200;           % 最大代数
params.crossover_rate = 0.9;    % 交叉概率
params.mutation_rate = 0.1;     % 变异概率
params.local_search_rate = 0.3; % 局部搜索概率
params.archive_size = 100;      % 归档集大小

%% 3. 运行模因优化算法
fprintf('开始多目标模因优化...\n');
tic;
[best_solution, pareto_front] = memetic_optimization(system, params);
elapsed_time = toc;
fprintf('优化完成，耗时: %.2f 秒\n', elapsed_time);

%% 4. 结果分析
% 解码最优解
decoded_best = decode_individual(best_solution.encoded, system);
T_sensing_opt = decoded_best.continuous(1);
power_opt = reshape(decoded_best.continuous(2:end), ...
                   system.N_channels, system.N_users);

% 计算各目标值
objectives = multi_objective_function(best_solution.encoded, system);
throughput_opt = -objectives(1);  % 转换为最大化值
interference_opt = objectives(2);
energy_opt = objectives(3);
fairness_opt = -objectives(4);

fprintf('\n最优解结果:\n');
fprintf('感知时间: %.3f ms\n', T_sensing_opt*1000);
fprintf('总吞吐量: %.3f Mbps\n', throughput_opt/1e6);
fprintf('总干扰: %.3e W\n', interference_opt);
fprintf('能耗: %.3f J\n', energy_opt);
fprintf('公平性指数: %.3f\n', fairness_opt);

%% 5. 可视化结果
figure('Position', [100, 100, 1400, 800]);

% 子图1: Pareto前沿（3D视图）
subplot(2,3,1);
if size(pareto_front, 1) > 0
    scatter3(-pareto_front(:,1), pareto_front(:,2), pareto_front(:,3), ...
            'filled', 'MarkerFaceAlpha', 0.6);
    xlabel('吞吐量');
    ylabel('干扰');
    zlabel('能耗');
    title('Pareto前沿（3D视图）');
    grid on;
    rotate3d on;
end

% 子图2: Pareto前沿（吞吐量 vs 干扰）
subplot(2,3,2);
if size(pareto_front, 1) > 0
    scatter(-pareto_front(:,1), pareto_front(:,2), 'filled');
    xlabel('吞吐量');
    ylabel('干扰');
    title('吞吐量 vs 干扰');
    grid on;
end

% 子图3: 功率分配热图
subplot(2,3,3);
imagesc(power_opt);
colorbar;
xlabel('用户');
ylabel('信道');
title('最优功率分配');
set(gca, 'XTick', 1:system.N_users);
set(gca, 'YTick', 1:system.N_channels);

% 子图4: 用户吞吐量分布
subplot(2,3,4);
user_throughputs = zeros(system.N_users, 1);
for u = 1:system.N_users
    for ch = 1:system.N_channels
        if power_opt(ch, u) > 0
            SNR = power_opt(ch, u) * system.channel_gains(ch, u) / ...
                  system.noise_power;
            user_throughputs(u) = user_throughputs(u) + ...
                                 system.bandwidth(ch) * log2(1 + SNR);
        end
    end
end
bar(1:system.N_users, user_throughputs/1e6);
xlabel('用户');
ylabel('吞吐量 (Mbps)');
title('用户吞吐量分布');
grid on;

% 子图5: 收敛曲线（如果记录了的话）
subplot(2,3,5);
plot_convergence_curve();  % 假设有这个函数
xlabel('迭代次数');
ylabel('最优目标值');
title('收敛曲线');
grid on;

% 子图6: 目标函数雷达图
subplot(2,3,6);
targets = [throughput_opt/max(throughput_opt,1e-6), ...
           1/(interference_opt+1e-6), ...
           1/(energy_opt+1e-6), ...
           fairness_opt];
targets = targets / max(targets);
radar_plot(targets, {'吞吐量', '干扰抑制', '能效', '公平性'});
title('多目标平衡图');

%% 6. 性能比较
fprintf('\n性能比较:\n');
fprintf('==============================================\n');
fprintf('算法          吞吐量(Mbps)   干扰(dBm)   公平性\n');
fprintf('----------------------------------------------\n');

% 模因算法结果
fprintf('模因算法      %8.2f      %8.2f    %.3f\n', ...
        throughput_opt/1e6, 10*log10(interference_opt*1000), fairness_opt);

% 对比算法：NSGA-II
nsga_results = run_nsga_ii(system, params);
fprintf('NSGA-II       %8.2f      %8.2f    %.3f\n', ...
        nsga_results.throughput/1e6, ...
        10*log10(nsga_results.interference*1000), ...
        nsga_results.fairness);

% 对比算法：粒子群优化
pso_results = run_pso(system, params);
fprintf('PSO           %8.2f      %8.2f    %.3f\n', ...
        pso_results.throughput/1e6, ...
        10*log10(pso_results.interference*1000), ...
        pso_results.fairness);

% 对比算法：贪婪算法
greedy_results = run_greedy_algorithm(system);
fprintf('贪婪算法      %8.2f      %8.2f    %.3f\n', ...
        greedy_results.throughput/1e6, ...
        10*log10(greedy_results.interference*1000), ...
        greedy_results.fairness);
fprintf('==============================================\n');

%% 7. 敏感性分析
fprintf('\n进行敏感性分析...\n');
analyze_sensitivity(system, params, best_solution);

%% 辅助函数
function radar_plot(values, labels)
    % 绘制雷达图
    n = length(values);
    angles = linspace(0, 2*pi, n+1);
    angles = angles(1:end-1);
    
    % 闭合曲线
    values = [values, values(1)];
    angles = [angles, angles(1)];
    
    % 转换为直角坐标
    x = values .* cos(angles);
    y = values .* sin(angles);
    
    % 绘制
    plot(x, y, 'b-', 'LineWidth', 2);
    hold on;
    fill(x, y, 'b', 'FaceAlpha', 0.2);
    
    % 坐标轴和标签
    for i = 1:n
        text(1.2*cos(angles(i)), 1.2*sin(angles(i)), labels{i}, ...
            'HorizontalAlignment', 'center', 'FontSize', 10);
    end
    
    axis equal;
    axis([-1.2, 1.2, -1.2, 1.2]);
    set(gca, 'Visible', 'off');
    hold off;
end

四、高级扩展功能

1. 动态环境适应

function [adapted_solution] = dynamic_adaptation(current_solution, ...
                                                system_changes, system)
    % 动态环境适应机制
    % system_changes: 环境变化信息
    
    % 1. 预测变化
    predicted_changes = predict_environment_changes(system_changes);
    
    % 2. 调整解
    adapted_encoded = current_solution.encoded;
    
    if predicted_changes.PU_increase
        % 主用户活动增加，减少感知时间，增加检测概率
        decoded = decode_individual(adapted_encoded, system);
        decoded.continuous(1) = decoded.continuous(1) * 1.2;  % 增加感知时间
        adapted_encoded = encode_individual(decoded);
    end
    
    % 3. 快速局部搜索
    adapted_solution = quick_local_search(adapted_encoded, system);
end

2. 分布式协同优化

function [global_solution] = distributed_memetic_optimization(system, params)
    % 分布式模因优化
    
    % 将用户分组
    n_groups = 3;
    group_solutions = cell(n_groups, 1);
    
    % 并行优化各组
    parfor g = 1:n_groups
        group_system = create_group_system(system, g, n_groups);
        group_solutions{g} = memetic_optimization(group_system, params);
    end
    
    % 协同融合
    global_solution = coordinate_solutions(group_solutions, system);
end

参考代码 认知无线网络频谱感知和功率分配的多目标模因优化 www.youwenfan.com/contentcnq/85026.html

五、算法改进建议

1. 混合策略选择：

   • 自适应选择局部搜索策略
   • 基于历史成功率调整策略概率

2. 并行化加速：

   • 使用MATLAB Parallel Computing Toolbox
   • 实现异步进化策略

3. 约束处理改进：

   • 使用可行解保持策略
   • 自适应惩罚函数

4. 收敛性保证：

   • 引入ε-支配概念
   • 自适应网格存档