281 lines
6.9 KiB
Matlab
281 lines
6.9 KiB
Matlab
clc;
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clear;
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close all;
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%% parameter setting
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% SNR = 5: 1: 6;
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% SNR = 0: 2: 10;
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% SNR = 0: 5: 25;
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SNR = [0,5,8,10,12,15,20,25];
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len_SNR = length(SNR);
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SNR_t2 = 25;
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rep_time = 2000;
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% P_fa = 1e-1;
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P_fa = [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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target_scattering = [0.8,1,0.9];
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win_size = length(target_scattering);
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alpha_prop = 0.8;
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% alpha_prop = [0.6, 0.4, 0.2];
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lambda = 0.1;
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% Sparsity
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sigma_0 = 0.1;
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% noise sigma
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sigma_n = sigma_0;
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%% vamp set
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delta_VAMP = 1e-6;
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iter_max = 500;
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lambda_val = 0.1;
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gamma = 0.5;
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%% 参数设置
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B=5e5; %信号带宽10MHz
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Tp=100e-6; %脉宽100us
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fs=2*B; %采样频率
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Ts= 1 / fs; %采样周期
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K = B / Tp; %线性调频率
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fc = 1e8; %载波频率
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Tr = 1e-3;
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t = 0:1/fs:Tr-1/fs;
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t2 = 0:1/fs/2:Tr-1/fs/2;
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c = 3e8; % 光速
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distance_max = (Tr-Tp) * c / 2;
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n = Tr * fs;
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m = round(n * gamma);
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%% experiment
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P_fa_CROD_cnt = zeros(len_SNR, len_P_fa, rep_time);
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P_d_CROD_cnt = zeros(len_SNR, len_P_fa, rep_time);
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% h_thd = -log(P_fa);
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h_thd = chi2inv(1 - P_fa, 6) / 2;
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%%
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parfor rep = 1: rep_time
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% for rep = 1: rep_time
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for cnt_SNR = 1: len_SNR
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% 设置目标位置
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% target_index = randi([2,n - length(target_scattering)]);
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target_index = 300;
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target2_index = round(n * 0.4);
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% 根据 SNR 设置散射点强度
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alpha = alpha_prop * sqrt(10^(SNR(cnt_SNR)/10) * sigma_n^2);
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alpha2 = alpha_prop * sqrt(10^(SNR_t2/10) * sigma_n^2);
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% 设置 x
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x = zeros(n ,1);
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x(target_index:target_index+2,1) = target_scattering * alpha;
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x(target2_index:target2_index+2,1) = target_scattering * alpha2;
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% plot(x)
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%% 生成矩阵 A
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A_idx = randperm(n);
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A_idx = A_idx(1: m);
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A_idx = sort(A_idx);
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A = dftmtx(n);
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A = A(A_idx, :);
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A = A / sqrt(n);
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% % 匹配滤波放大倍数
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% multiple = A(:,1)' * A(:,1);
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%% 生成 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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%% cVAMPro 求解
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lambda = zeros(n,1) + lambda_val;
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[x_LASSO, x_hat_d_ro] = cVAMPro(y, A, lambda, delta_VAMP, iter_max);
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%%
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% CROD
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rho_active = sum(abs(x_LASSO) > 1e-3)/n;
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Q_hat = (gamma - rho_active)/(1 - rho_active);
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Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./(Q_hat*abs(x_LASSO) + lambda))) / 2 / n;
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diff = 1;
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while(diff > 1e-4)
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Rho_pre = Rho;
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Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./((gamma-Rho)/(1-Rho)*abs(x_LASSO) + lambda))) / 2 / n;
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diff = abs(Rho - Rho_pre);
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end
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Q_hat = (gamma-Rho)/(1-Rho);
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x_d_CROD = x_LASSO + A'*(y - A*x_LASSO)/Q_hat;
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% plot(abs(x_d_CROD))
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%%
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RSS = sum(abs(y - A * x_LASSO).^2)/m;
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chi = Rho*(1 - Rho)/(gamma - Rho);
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if chi ~= 0
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chi_temp = sqrt((chi+1)*(chi+1)-4*gamma*chi);
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z = -(1 - chi + chi_temp) / (2*chi);
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z_prime = -(1 - 2*gamma*chi + chi + chi_temp) / (2*chi*chi*chi_temp);
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G_prime = (z + 1/chi);
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G_wprime = (z_prime + 1/chi/chi);
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chi_hat = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
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+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
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else
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G_prime = gamma;
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G_wprime = gamma*(1-gamma);
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chi_hat = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
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+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
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end
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sigma_CROD = sqrt(2*chi_hat) / Q_hat;
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stat_CROD = abs(x_d_CROD / sigma_CROD).^2;
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% window
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stat_extend = stat_window(stat_CROD, win_size);
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figure(100)
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plot(stat_CROD);hold on;
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plot(stat_extend);hold off;
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n_index = ones(size(stat_extend));
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t_index = zeros(size(stat_extend));
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% distance_node = [target_index, target_index + 1, target_index + 2];
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distance_node = target_index;
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distance_area = target_index-2: 1: target_index+2;
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distance_area2 = target2_index-2: 1: target2_index+2;
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n_index(distance_area) = 0;
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n_index(distance_area2) = 0;
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t_index(distance_node) = 1;
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for cnt_h_th = 1: len_P_fa
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figure(12);
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plot(stat_extend)
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hold on;
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kdline = zeros(size(stat_extend)) + h_thd(cnt_h_th);
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plot(kdline)
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hold off;
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P_fa_CROD_cnt(cnt_SNR, cnt_h_th, rep) = sum(stat_extend(n_index>0) > h_thd(cnt_h_th)) / sum(n_index);
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P_d_CROD_cnt(cnt_SNR, cnt_h_th, rep) = sum(stat_extend(t_index>0) > h_thd(cnt_h_th)) / sum(t_index);
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end
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end
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fprintf('%d\n', rep);
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end
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P_fa_CROD = mean(P_fa_CROD_cnt, 3);
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P_d_CROD = mean(P_d_CROD_cnt, 3);
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display(['设定虚警率',num2str(P_fa(1))])
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display(['实验虚警率',num2str(P_fa_CROD(1,1))])
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display(['实验检测率',num2str(P_d_CROD(1,1))])
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%% plot
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figure(1);
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loglog(P_fa,P_fa_CROD(1,:), 'linewidth', 2);
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hold on;
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grid on;
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loglog(P_fa,P_fa_CROD(2,:), 'linewidth', 2);
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loglog(P_fa,P_fa_CROD(3,:), 'linewidth', 2);
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loglog(P_fa,P_fa_CROD(4,:), 'linewidth', 2);
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loglog(P_fa,P_fa_CROD(5,:), 'linewidth', 2);
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loglog(P_fa,P_fa_CROD(6,:), 'linewidth', 2);
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legend('SNR = 0','SNR = 2','SNR = 4','SNR = 6','SNR = 8','SNR = 10');
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xlabel('P_fa');
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ylabel('P_fa_CROD');
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% figure(2);
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% loglog(P_fa_CROD_thry(1,:), P_d_CROD_thry(1,:), 'linewidth', 2);
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% hold on;
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% grid on;
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% loglog(P_fa_CROD_thry(2,:), P_d_CROD_thry(2,:), 'linewidth', 2);
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% loglog(P_fa_CROD_thry(3,:), P_d_CROD_thry(3,:), 'linewidth', 2);
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% legend('SNR = 0', 'SNR = 10', 'SNR = 20');
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% xlabel('P_{fa}');
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% ylabel('P_{d}');
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%
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% % figure(4);
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% % loglog(P_fa_CROD_thry(1,:), P_d_CROD_thry2(1,:), 'linewidth', 2);
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% % hold on;
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% % grid on;
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% % loglog(P_fa_CROD_thry(2,:), P_d_CROD_thry2(2,:), 'linewidth', 2);
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% % loglog(P_fa_CROD_thry(3,:), P_d_CROD_thry2(3,:), 'linewidth', 2);
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% % legend('SNR = 0', 'SNR = 10', 'SNR = 20');
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% % xlabel('P_{fa}');
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% % ylabel('P_{d}');
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%
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%
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% figure(3);
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% loglog(P_fa_CROD(1,:), P_d_CROD(1,:), 'linewidth', 2);
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% hold on;
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% grid on;
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% loglog(P_fa_CROD(2,:), P_d_CROD(2,:), 'linewidth', 2);
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% loglog(P_fa_CROD(3,:), P_d_CROD(3,:), 'linewidth', 2);
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% loglog(P_fa_CROD_thry(1,:), P_d_CROD_thry(1,:), 'linewidth', 2);
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% loglog(P_fa_CROD_thry(2,:), P_d_CROD_thry(2,:), 'linewidth', 2);
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% loglog(P_fa_CROD_thry(3,:), P_d_CROD_thry(3,:), 'linewidth', 2);
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% legend('rSNR = 0', 'rSNR = 10', 'rSNR = 20', ...
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% 'tSNR = 0', 'tSNR = 10', 'tSNR = 20');
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% xlabel('P_{fa}');
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% ylabel('P_{d}');
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save test_Pd_Pfa_vamp_cal_stat.mat ...
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SNR...
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P_fa...
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P_fa_CROD...
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P_d_CROD...
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lambda...
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m...
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n...
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h_thd...
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sigma_n...
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target_scattering;
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