107 lines
3.3 KiB
Matlab
107 lines
3.3 KiB
Matlab
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 )
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% matrix parameters
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[M, N] = size(A);
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mul = A(:,1)'*A(:,1);
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% H0 sample
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L = round(Target_index + N * 0.1);
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R = round(N * 0.9);
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Lambda_C = L: R;
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% parameters
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sigma_n = 0.1;
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Target_amplitude = sqrt(10^(SNR/10) * sigma_n^2 / mul);
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%% CS setting
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% CS-parameters
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% lambda = 0.0005;
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alpha = 1/4;
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delta = 1e-8*alpha;
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% CS-normalization
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J1 = A*A';
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lambda_J=eig(J1);
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A_norm = A / sqrt(lambda_J(end));
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Hp = A_norm'*A_norm;
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[~, D] = eig(Hp);
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d = diag(D);
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sigma_n_norm = sigma_n / sqrt(lambda_J(end));
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%% generate x
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x = zeros(N, 1);
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x(Target_index) = Target_amplitude;
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%% MC parameters
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P_fa = [1e-6, 1e-5, 1e-4, 5e-4, 1e-3, 5e-3, 1e-2, 5e-2, 1e-1, 5e-1, 1];
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len_P_fa = length(P_fa);
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P_fa_MF_cnt = zeros(len_P_fa, rep_time);
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P_d_MF_cnt = zeros(len_P_fa, rep_time);
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P_fa_CS_cnt = zeros(len_P_fa, rep_time);
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P_d_CS_cnt = zeros(len_P_fa, rep_time);
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H1_index = zeros(N, 1);
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H1_index(Target_index) = 1;
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H0_index = ones(size(x));
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H0_index(Target_index) = 0;
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H1_MF_cnt = zeros(1, rep_time);
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H0_MF_cnt = zeros(N - 1, rep_time);
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H1_CS_cnt = zeros(1, rep_time);
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H0_CS_cnt = zeros(N - 1, rep_time);
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%% MC
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parfor rep = 1: rep_time
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% for rep = 1: rep_time
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%% generate y
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noise = random('Normal', 0, sigma_n/sqrt(2), M, 1) + 1j * random('Normal', 0, sigma_n/sqrt(2), M, 1);
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y = A*x + noise;
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%% recover
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% MF
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x_mf = A' * y ./ mul;
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% sigma_MF = sqrt(var(x_mf(Lambda_C)));
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sigma_MF = sigma_n / sqrt(mul);
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x_mf_norm = x_mf ./ sigma_MF;
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stat_MF = abs(x_mf ./ sigma_MF).^2;
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% CS
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y_norm = y / sqrt(lambda_J(end));
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x_FISTA = FISTA_v1(y_norm, A_norm, lambda, delta, Hp);
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[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);
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% sigma_CS = sqrt(var(x_d_cal_f(Lambda_C)));
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sigma_CS = sigma_d_cal_f;
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x_cs_norm = x_d_cal_f ./ sigma_CS;
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stat_CS = abs(x_d_cal_f ./ sigma_CS).^2;
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%% detect
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H1_MF_cnt(rep) = x_mf(Target_index);
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H0_MF_cnt(:,rep) = [x_mf(1:Target_index-1);x_mf(Target_index+1:end)];
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H1_CS_cnt(rep) = x_d_cal_f(Target_index);
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H0_CS_cnt(:,rep) = [x_d_cal_f(1:Target_index-1);x_d_cal_f(Target_index+1:end)];
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kd = chi2inv(1 - P_fa, 2) / 2;
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for cnt_h_th = 1: len_P_fa
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P_fa_MF_cnt(cnt_h_th, rep) = sum(stat_MF(H0_index > 0) > kd(cnt_h_th)) / sum(H0_index);
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P_d_MF_cnt(cnt_h_th, rep) = sum(stat_MF(H1_index > 0) > kd(cnt_h_th)) / sum(H1_index);
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P_fa_CS_cnt(cnt_h_th, rep) = sum(stat_CS(H0_index > 0) > kd(cnt_h_th)) / sum(H0_index);
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P_d_CS_cnt(cnt_h_th, rep) = sum(stat_CS(H1_index > 0) > kd(cnt_h_th)) / sum(H1_index);
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end
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fprintf('%d\n', rep);
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end
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P_fa_MF = mean(P_fa_MF_cnt, 2);
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P_d_MF = mean(P_d_MF_cnt, 2);
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P_fa_CS = mean(P_fa_CS_cnt, 2);
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P_d_CS = mean(P_d_CS_cnt, 2);
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res_MF = [P_fa_MF, P_d_MF];
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res_CS = [P_fa_CS, P_d_CS];
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end
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