基于GA-MUSIC的matlab算法代码实现

以下是基于GA-MUSIC的 Matlab 算法代码实现的示例：

% GA-MUSIC 算法实现

% 输入数据
N = 200; % 阵元数
M = 5; % 信源数
theta = [-30 -10 0 10 30]; % 信源方向角
SNR = 10; % 信噪比
P = diag([1 1 1 1 1]); % 信源功率矩阵
R = zeros(N,N); % 传感器阵列的协方差矩阵
for i=1:M
    a = exp(-1i*2*pi*(i-1)*sin(theta(i)*pi/180)*(1:N)');
    R = R + (a*a')*P(i,i);
end
sigma2 = trace(R)/N/SNR/10^(0.1); % 噪声方差

% GA-MUSIC 算法
POP_SIZE = 50; % 种群大小
MAX_GEN = 100; % 最大迭代次数
ELITE_RATE = 0.1; % 精英保留率
MUTATION_RATE = 0.01; % 变异率
CROSSOVER_RATE = 0.9; % 交叉率
N_CHROMOSOMES = N*(N-1)/2; % 染色体长度

pop = rand(POP_SIZE,N_CHROMOSOMES)>0.5; % 随机初始化种群
for gen=1:MAX_GEN
    % 适应度评价
    fitness = zeros(POP_SIZE,1);
    for i=1:POP_SIZE
        theta = zeros(1,N);
        idx = find(pop(i,:));
        [p,q] = meshgrid(1:N);
        p = p(idx);
        q = q(idx);
        theta(q<p) = atan2(imag(R(p,q)),real(R(p,q)));
        [S,f] = musicdoa(theta,1);
        fitness(i) = max(S);
    end
    % 精英保留
    [sorted,idx] = sort(fitness,'descend');
    elite = pop(idx(1:round(ELITE_RATE*POP_SIZE)),:);
    % 选择、交叉、变异
    p1 = randperm(POP_SIZE);
    p2 = randperm(POP_SIZE);
    for i=1:POP_SIZE/2
        % 选择
        if fitness(p1(i))>fitness(p2(i))
            parent1 = pop(p1(i),:);
        else
            parent1 = pop(p2(i),:);
        end
        p1(i) = randperm(POP_SIZE,1);
        p2(i) = randperm(POP_SIZE,1);
        if fitness(p1(i))>fitness(p2(i))
            parent2 = pop(p1(i),:);
        else
            parent2 = pop(p2(i),:);
        end
        % 交叉
        if rand()<CROSSOVER_RATE
            idx = randperm(N_CHROMOSOMES,round(N_CHROMOSOMES/2));
            child1 = [parent1(1,idx),parent2(1,setdiff(1:N_CHROMOSOMES,idx))];
            child2 = [parent2(1,idx),parent1(1,setdiff(1:N_CHROMOSOMES,idx))];
        else
            child1 = parent1;
            child2 = parent2;
        end
        % 变异
        for j=1:N_CHROMOSOMES
            if rand()<MUTATION_RATE
                child1(j) = ~child1(j);
            end
            if rand()<MUTATION_RATE
                child2(j) = ~child2(j);
            end
        end
        % 新种群
        newpop(i*2-1,:) = child1;
        newpop(i*2,:) = child2;
    end
    pop = [elite;newpop];
end

% 最优解
theta = zeros(1,N);
idx = find(elite(1,:));
[p,q] = meshgrid(1:N);
p = p(idx);
q = q(idx);
theta(q<p) = atan2(imag(R(p,q)),real(R(p,q)));
[S,f] = musicdoa(theta,1);
[maxS,idx] = max(S);
doa = theta(idx)*180/pi;
fprintf('GA-MUSIC 估计方向角：%f\n',doa);

% MUSIC 算法
[S,f] = musicdoa(theta,1);
[maxS,idx] = max(S);
doa = theta(idx)*180/pi;
fprintf('MUSIC 估计方向角：%f\n',doa);

其中，`musicdoa` 是 MUSIC 算法函数，`POP_SIZE`、`MAX_GEN`、`ELITE_RATE`、`MUTATION_RATE` 和 `CROSSOVER_RATE` 分别为种群大小、最大迭代次数、精英保留率、变异率和交叉率。代码中先随机初始化种群，然后进行遗传算法迭代，同时利用 MUSIC 算法进行估计。最终输出 GA-MUSIC 估计的方向角和 MUSIC 估计的方向角。