function [ res_MF, res_CS, P_fa, H1_MF_cnt, H0_MF_cnt, H1_CS_cnt, H0_CS_cnt ] = yAxn_MC( A, SNR, Target_index, lambda, rep_time )

    % matrix parameters
    [M, N] = size(A);
    mul = A(:,1)'*A(:,1);
    
    % H0 sample
    L = round(Target_index + N * 0.1);
    R = round(N * 0.9);
    Lambda_C = L: R;
    
    % parameters
    sigma_n = 0.1;
    Target_amplitude = sqrt(10^(SNR/10) * sigma_n^2 / mul);

    
    %% CS setting
    % CS-parameters
%     lambda = 0.0005;
    alpha = 1/4;
    delta = 1e-8*alpha;
    
    % CS-normalization
    J1 = A*A';
    lambda_J=eig(J1);
    A_norm = A / sqrt(lambda_J(end));
    Hp = A_norm'*A_norm;
    [~, D] = eig(Hp);
    d = diag(D);
    sigma_n_norm = sigma_n / sqrt(lambda_J(end));
    
    
    %% generate x
    x = zeros(N, 1);
    x(Target_index) = Target_amplitude;
    
    
    %% MC parameters
    P_fa = [1e-6, 1e-5, 1e-4, 5e-4, 1e-3, 5e-3, 1e-2, 5e-2, 1e-1, 5e-1, 1];
    len_P_fa = length(P_fa);
    
    P_fa_MF_cnt = zeros(len_P_fa, rep_time);
    P_d_MF_cnt = zeros(len_P_fa, rep_time);
    P_fa_CS_cnt = zeros(len_P_fa, rep_time);
    P_d_CS_cnt = zeros(len_P_fa, rep_time);  
    
    H1_index = zeros(N, 1);
    H1_index(Target_index) = 1;
    H0_index = ones(size(x));
    H0_index(Target_index) = 0;
    H1_MF_cnt = zeros(1, rep_time);
    H0_MF_cnt = zeros(N - 1, rep_time);
    H1_CS_cnt = zeros(1, rep_time);
    H0_CS_cnt = zeros(N - 1, rep_time);
    
    %% MC
    parfor rep = 1: rep_time
%     for rep = 1: rep_time
        %% generate y
        noise = random('Normal', 0, sigma_n/sqrt(2), M, 1) + 1j * random('Normal', 0, sigma_n/sqrt(2), M, 1);
        y = A*x + noise;

        %% recover
        % MF
        x_mf = A' * y ./ mul;
        % sigma_MF = sqrt(var(x_mf(Lambda_C)));
        sigma_MF = sigma_n / sqrt(mul);
        x_mf_norm = x_mf ./ sigma_MF;
        stat_MF = abs(x_mf ./ sigma_MF).^2;

        % CS
        y_norm = y / sqrt(lambda_J(end));
        x_FISTA = FISTA_v1(y_norm, A_norm, lambda, delta, Hp);
        [x_d_cal_f, hat_Q1_cal_f, sigma_d_cal_f] = cal_debiased_LASSO_v1(x_FISTA, A_norm, y_norm, lambda, sigma_n_norm, d);
        % sigma_CS = sqrt(var(x_d_cal_f(Lambda_C)));
        sigma_CS = sigma_d_cal_f;
        x_cs_norm = x_d_cal_f ./ sigma_CS;
        stat_CS = abs(x_d_cal_f ./ sigma_CS).^2;

        %% detect
        H1_MF_cnt(rep) = x_mf(Target_index);
        H0_MF_cnt(:,rep) = [x_mf(1:Target_index-1);x_mf(Target_index+1:end)];
        H1_CS_cnt(rep) = x_d_cal_f(Target_index);
        H0_CS_cnt(:,rep) = [x_d_cal_f(1:Target_index-1);x_d_cal_f(Target_index+1:end)];
        
        kd = chi2inv(1 - P_fa, 2) / 2;
        for cnt_h_th = 1: len_P_fa
            P_fa_MF_cnt(cnt_h_th, rep) = sum(stat_MF(H0_index > 0) > kd(cnt_h_th)) / sum(H0_index);
            P_d_MF_cnt(cnt_h_th, rep) = sum(stat_MF(H1_index > 0) > kd(cnt_h_th)) / sum(H1_index);
            P_fa_CS_cnt(cnt_h_th, rep) = sum(stat_CS(H0_index > 0) > kd(cnt_h_th)) / sum(H0_index);
            P_d_CS_cnt(cnt_h_th, rep) = sum(stat_CS(H1_index > 0) > kd(cnt_h_th)) / sum(H1_index);
        end
        
        fprintf('%d\n', rep);
    end
    
    P_fa_MF = mean(P_fa_MF_cnt, 2);
    P_d_MF = mean(P_d_MF_cnt, 2);
    P_fa_CS = mean(P_fa_CS_cnt, 2);
    P_d_CS = mean(P_d_CS_cnt, 2);
    
    res_MF = [P_fa_MF, P_d_MF];
    res_CS = [P_fa_CS, P_d_CS];
    
end