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Ksyer
2024-11-11 16:32:53 +08:00
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commit 29ae9585f9
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0 - example/20221025_那斯琦_ICASSP2022.zip
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0 - example/CS-Recovery-Algorithms
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Submodule 0 - example/CS-Recovery-Algorithms added at 24ed57443d
0 - example/CompressedSensing.jl
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Submodule 0 - example/CompressedSensing.jl added at addf3f147a
0 - example/nsq - ICASSP2022/Fig. 2/FISTA.m
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function [z] = FISTA(y, A, lambda, delta)
x_pre = A'*y;
t = 1;
z = x_pre;
z_pre = z;
t_pre = t;
N = size(A, 2);
diff = 1;
E = eig(A'*A);
L = E(end);
temp1 = A'*y/L;
temp2 = eye(N) - A'*A/L;
k = 0;
while((diff > delta) && (k < 1000))
temp = temp1 + temp2 * z_pre;
x = sft_thd(temp, lambda/L);
t = 0.5*(1 + sqrt(1+4*t_pre*t_pre));
z = x + (x - x_pre) * (t_pre-1) / t;
diff = mean(abs(z_pre - z));
x_pre = x;
z_pre = z;
t_pre = t;
k = k + 1;
end
end
0 - example/nsq - ICASSP2022/Fig. 2/plot_Pfa_Pd_SNR_PF_CROD_CAMP_SDL_ROD_SNR.m
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clear;
close all;
clc;
load test_Pfa_Pd_SNR_PF_CROD_CAMP_SDL_ROD_SNR.mat;
Fontsize = 18;
plot_width = 800;
plot_height = 600;
Linewidth = 2;
Markersize = 8;
%% plot
figure(1);
plot(SNR, P_fa_CROD, '-o', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
hold on;
grid on;
plot(SNR, P_fa_CAMP, '-d', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
plot(SNR, P_fa_SDL, '-s', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
plot(SNR, P_fa_ROD, '-+', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
legend('CROD', 'CAMP', 'SDL-test', 'ROD');
xlabel('SNR');
ylabel('P_{fa}');
set(gca, 'FontSize', Fontsize);
%set(gca, 'FontSize', Fontsize, 'fontname', 'Times New Roman');
set(gcf, 'position', [200, 300, plot_width, plot_height]);
figure(2);
plot(SNR, P_d_CROD, '-o', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
hold on;
grid on;
plot(SNR, P_d_CAMP, '-d', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
plot(SNR, P_d_SDL, '-s', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
plot(SNR, P_d_ROD, '-+', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
legend('CROD', 'CAMP', 'SDL-test', 'ROD');
xlabel('SNR');
ylabel('P_{d}');
set(gca, 'FontSize', Fontsize);
%set(gca, 'FontSize', Fontsize, 'fontname', 'Times New Roman');
set(gcf, 'position', [200, 300, plot_width, plot_height]);
0 - example/nsq - ICASSP2022/Fig. 2/test_Pfa_Pd_SNR_PF_CROD_CAMP_SDL_ROD_SNR.m
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clc;
clear;
close all;
%% parameter setting
m = 128;
n = 256;
SNR = 0: 1: 15;
len_SNR = length(SNR);
rep_time = 1e4;
P_fa = 1e-2;
p0 = 0.1;
lambda = 0.1;
sigma_0 = 0.1;
sigma_n = sigma_0;
%% experiment
gamma = m/n;
P_fa_CROD_cnt = zeros(len_SNR, rep_time);
P_fa_CAMP_cnt = zeros(len_SNR, rep_time);
P_fa_SDL_cnt = zeros(len_SNR, rep_time);
P_fa_ROD_cnt = zeros(len_SNR, rep_time);
P_fa_LASSO_cnt = zeros(len_SNR, rep_time);
P_d_CROD_cnt = zeros(len_SNR, rep_time);
P_d_CAMP_cnt = zeros(len_SNR, rep_time);
P_d_SDL_cnt = zeros(len_SNR, rep_time);
P_d_ROD_cnt = zeros(len_SNR, rep_time);
P_d_LASSO_cnt = zeros(len_SNR, rep_time);
x_idx = rand(n, 1);
if p0 == 0
thd = -1;
x_l0 = sum(x_idx > thd);
else
thd = sort(x_idx);
thd = thd(round(n*p0));
x_l1 = sum(x_idx <= thd);
x_l0 = sum(x_idx > thd);
end
x = zeros(n, 1);
x_temp = sigma_0 * exp(1j*random('Uniform', 0, 2*pi, n, 1));
x(x_idx <= thd) = x_temp(x_idx <= thd);
x = x * sqrt(n/m);
h_thd = -log(P_fa);
parfor rep = 1: rep_time
A_idx = randperm(n);
A_idx = A_idx(1: m);
A_idx = sort(A_idx);
A = dftmtx(n);
A = A(A_idx, :);
A = A / sqrt(n);
w = random('Normal', 0, sigma_0/sqrt(2), m, 1) + 1j * random('Normal', 0, sigma_0/sqrt(2), m, 1);
% w = w / sqrt(10^(SNR(cnt_SNR)/10));
for cnt_SNR = 1: len_SNR
x1 = x * sqrt(10^(SNR(cnt_SNR)/10));
y = A * x1 + w;
% x_LASSO = LASSO_cvx(y, A, lambda);
x_LASSO = FISTA(y, A, lambda, 1e-5);
% CROD
rho_active = sum(abs(x_LASSO) > 1e-3)/n;
Q_hat = (gamma - rho_active)/(1 - rho_active);
Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./(Q_hat*abs(x_LASSO) + lambda))) / 2 / n;
diff = 1;
while(diff > 1e-4)
Rho_pre = Rho;
Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./((gamma-Rho)/(1-Rho)*abs(x_LASSO) + lambda))) / 2 / n;
diff = abs(Rho - Rho_pre);
end
Q_hat = (gamma-Rho)/(1-Rho);
x_d_CROD = x_LASSO + A'*(y - A*x_LASSO)/Q_hat;
RSS = sum(abs(y - A * x_LASSO).^2)/m;
chi = Rho*(1 - Rho)/(gamma - Rho);
if chi ~= 0
chi_temp = sqrt((chi+1)*(chi+1)-4*gamma*chi);
z = -(1 - chi + chi_temp) / (2*chi);
z_prime = -(1 - 2*gamma*chi + chi + chi_temp) / (2*chi*chi*chi_temp);
G_prime = (z + 1/chi);
G_wprime = (z_prime + 1/chi/chi);
chi_hat = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
else
G_prime = gamma;
G_wprime = gamma*(1-gamma);
chi_hat = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
end
sigma_CROD = sqrt(2*chi_hat) / Q_hat;
stat_CROD = abs(x_d_CROD / sigma_CROD).^2;
P_fa_CROD_cnt(cnt_SNR, rep) = sum(stat_CROD(x_idx > thd) > h_thd) / x_l0;
P_d_CROD_cnt(cnt_SNR, rep) = sum(stat_CROD(x_idx <= thd) > h_thd) / x_l1;
% CAMP
Q_hat1 = gamma - rho_active;
Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./(Q_hat1*abs(x_LASSO) + lambda))) / 2 / n;
diff = 1;
while(diff > 1e-4)
Rho_pre = Rho;
Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./((gamma-Rho)*abs(x_LASSO) + lambda))) / 2 / n;
diff = abs(Rho - Rho_pre);
end
Q_hat1 = (gamma-Rho);
x_d_CAMP = x_LASSO + A'*(y - A*x_LASSO)/Q_hat1;
sigma_CAMP = 1/sqrt(log(2))*median(abs(x_d_CAMP));
stat_CAMP = abs(x_d_CAMP / sigma_CAMP).^2;
P_fa_CAMP_cnt(cnt_SNR, rep) = sum(stat_CAMP(x_idx > thd) > h_thd) / x_l0;
P_d_CAMP_cnt(cnt_SNR, rep) = sum(stat_CAMP(x_idx <= thd) > h_thd) / x_l1;
% SDL
Q_hat2 = (gamma - rho_active);
x_d_SDL = x_LASSO + A'*(y - A*x_LASSO)/Q_hat2;
sigma_SDL = sqrt(gamma)/sqrt(log(2))/(gamma - rho_active)*median(abs(y - A*x_LASSO));
stat_SDL = abs(x_d_SDL / sigma_SDL).^2;
P_fa_SDL_cnt(cnt_SNR, rep) = sum(stat_SDL(x_idx > thd) > h_thd) / x_l0;
P_d_SDL_cnt(cnt_SNR, rep) = sum(stat_SDL(x_idx <= thd) > h_thd) / x_l1;
% ROD
Q_hat3 = (gamma - rho_active)/(1 - rho_active);
x_d_ROD = x_LASSO + A'*(y - A*x_LASSO)/Q_hat3;
chi = rho_active*(1 - rho_active)/(gamma - rho_active);
if chi ~= 0
chi_temp = sqrt((chi+1)*(chi+1)-4*gamma*chi);
z = -(1 - chi + chi_temp) / (2*chi);
z_prime = -(1 - 2*gamma*chi + chi + chi_temp) / (2*chi*chi*chi_temp);
G_prime = (z + 1/chi);
G_wprime = (z_prime + 1/chi/chi);
chi_hat2 = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
else
G_prime = gamma;
G_wprime = gamma*(1-gamma);
chi_hat2 = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
end
sigma_ROD = sqrt(2*chi_hat2) / Q_hat3;
stat_ROD = abs(x_d_ROD / sigma_ROD).^2;
P_fa_ROD_cnt(cnt_SNR, rep) = sum(stat_ROD(x_idx > thd) > h_thd) / x_l0;
P_d_ROD_cnt(cnt_SNR, rep) = sum(stat_ROD(x_idx <= thd) > h_thd) / x_l1;
% LASSO
% stat_LASSO = abs(x_LASSO).^2;
% if p0 ~= 0
% stat_H1_LASSO_cnt(rep, :) = stat_LASSO(x_idx <= thd);
% end
% stat_H0_LASSO_cnt(rep, :) = stat_LASSO(x_idx > thd);
end
fprintf('%d\n', rep);
end
P_fa_CROD = mean(P_fa_CROD_cnt, 2);
P_fa_CAMP = mean(P_fa_CAMP_cnt, 2);
P_fa_SDL = mean(P_fa_SDL_cnt, 2);
P_fa_ROD = mean(P_fa_ROD_cnt, 2);
P_d_CROD = mean(P_d_CROD_cnt, 2);
P_d_CAMP = mean(P_d_CAMP_cnt, 2);
P_d_SDL = mean(P_d_SDL_cnt, 2);
P_d_ROD = mean(P_d_ROD_cnt, 2);
%% plot
figure(1);
plot(SNR, P_fa_CROD, 'linewidth', 2);
hold on;
grid on;
plot(SNR, P_fa_CAMP, 'linewidth', 2);
plot(SNR, P_fa_SDL, 'linewidth', 2);
plot(SNR, P_fa_ROD, 'linewidth', 2);
legend('CROD', 'CAMP', 'SDL-test', 'ROD');
xlabel('SNR');
ylabel('P_{fa}');
figure(2);
plot(SNR, P_d_CROD, 'linewidth', 2);
hold on;
grid on;
plot(SNR, P_d_CAMP, 'linewidth', 2);
plot(SNR, P_d_SDL, 'linewidth', 2);
plot(SNR, P_d_ROD, 'linewidth', 2);
legend('CROD', 'CAMP', 'SDL-test', 'ROD');
xlabel('SNR');
ylabel('P_{d}');
save test_Pfa_Pd_SNR_PF_CROD_CAMP_SDL_ROD_SNR.mat ...
SNR...
P_fa_CROD...
P_fa_CAMP...
P_fa_SDL...
P_fa_ROD...
P_d_CROD...
P_d_CAMP...
P_d_SDL...
P_d_ROD;
0 - example/nsq - ICASSP2022/Fig. 3/FISTA.m
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function [z] = FISTA(y, A, lambda, delta)
x_pre = A'*y;
t = 1;
z = x_pre;
z_pre = z;
t_pre = t;
N = size(A, 2);
diff = 1;
E = eig(A'*A);
L = E(end);
temp1 = A'*y/L;
temp2 = eye(N) - A'*A/L;
k = 0;
while((diff > delta) && (k < 1000))
temp = temp1 + temp2 * z_pre;
x = sft_thd(temp, lambda/L);
t = 0.5*(1 + sqrt(1+4*t_pre*t_pre));
z = x + (x - x_pre) * (t_pre-1) / t;
diff = mean(abs(z_pre - z));
x_pre = x;
z_pre = z;
t_pre = t;
k = k + 1;
end
end
0 - example/nsq - ICASSP2022/Fig. 3/plot_Pfa_Pd_SNR_PF_CROD_CAMP_SDL_ROD_p0.m
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clear;
close all;
clc;
load test_Pfa_Pd_SNR_PF_CROD_CAMP_SDL_ROD_p0.mat;
Fontsize = 18;
plot_width = 800;
plot_height = 600;
Linewidth = 2;
Markersize = 8;
%% plot
figure(1);
plot(p0_total, P_fa_CROD, '-o', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
hold on;
grid on;
plot(p0_total, P_fa_CAMP, '-d', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
plot(p0_total, P_fa_SDL, '-s', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
plot(p0_total, P_fa_ROD, '-+', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
legend('CROD', 'CAMP', 'SDL-test', 'ROD');
xlabel('signal density');
ylabel('P_{fa}');
set(gca, 'FontSize', Fontsize);
%set(gca, 'FontSize', Fontsize, 'fontname', 'Times New Roman');
set(gcf, 'position', [200, 300, plot_width, plot_height]);
figure(2);
plot(p0_total, P_d_CROD, '-o', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
hold on;
grid on;
plot(p0_total, P_d_CAMP, '-d', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
plot(p0_total, P_d_SDL, '-s', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
plot(p0_total, P_d_ROD, '-+', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
legend('CROD', 'CAMP', 'SDL-test', 'ROD');
xlabel('signal density');
ylabel('P_{d}');
set(gca, 'FontSize', Fontsize);
%set(gca, 'FontSize', Fontsize, 'fontname', 'Times New Roman');
set(gcf, 'position', [200, 300, plot_width, plot_height]);
0 - example/nsq - ICASSP2022/Fig. 3/test_Pfa_Pd_SNR_PF_CROD_CAMP_SDL_ROD_p0.m
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clc;
clear;
close all;
%% parameter setting
m = 128;
n = 256;
SNR = 13;
rep_time = 1e4;
P_fa = 1e-2;
p0_total = 0.02: 0.02: 0.2;
len_p0 = length(p0_total);
lambda = 0.1;
sigma_0 = 0.1;
sigma_n = sigma_0;
%% experiment
gamma = m/n;
P_fa_CROD_cnt = zeros(len_p0, rep_time);
P_fa_CAMP_cnt = zeros(len_p0, rep_time);
P_fa_SDL_cnt = zeros(len_p0, rep_time);
P_fa_ROD_cnt = zeros(len_p0, rep_time);
P_fa_LASSO_cnt = zeros(len_p0, rep_time);
P_d_CROD_cnt = zeros(len_p0, rep_time);
P_d_CAMP_cnt = zeros(len_p0, rep_time);
P_d_SDL_cnt = zeros(len_p0, rep_time);
P_d_ROD_cnt = zeros(len_p0, rep_time);
P_d_LASSO_cnt = zeros(len_p0, rep_time);
h_thd = -log(P_fa);
parfor rep = 1: rep_time
A_idx = randperm(n);
A_idx = A_idx(1: m);
A_idx = sort(A_idx);
A = dftmtx(n);
A = A(A_idx, :);
A = A / sqrt(n);
w = random('Normal', 0, sigma_0/sqrt(2), m, 1) + 1j * random('Normal', 0, sigma_0/sqrt(2), m, 1);
% w = w / sqrt(10^(SNR(cnt_SNR)/10));
for cnt_p0 = 1: len_p0
p0 = p0_total(cnt_p0);
x_idx = rand(n, 1);
if p0 == 0
thd = -1;
x_l0 = sum(x_idx > thd);
else
thd = sort(x_idx);
thd = thd(round(n*p0));
x_l1 = sum(x_idx <= thd);
x_l0 = sum(x_idx > thd);
end
x = zeros(n, 1);
x_temp = sigma_0 * exp(1j*random('Uniform', 0, 2*pi, n, 1));
x(x_idx <= thd) = x_temp(x_idx <= thd);
x = x * sqrt(n/m);
x1 = x * sqrt(10^(SNR/10));
y = A * x1 + w;
% x_LASSO = LASSO_cvx(y, A, lambda);
x_LASSO = FISTA(y, A, lambda, 1e-5);
% CROD
rho_active = sum(abs(x_LASSO) > 1e-3)/n;
Q_hat = (gamma - rho_active)/(1 - rho_active);
Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./(Q_hat*abs(x_LASSO) + lambda))) / 2 / n;
diff = 1;
while(diff > 1e-4)
Rho_pre = Rho;
Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./((gamma-Rho)/(1-Rho)*abs(x_LASSO) + lambda))) / 2 / n;
diff = abs(Rho - Rho_pre);
end
Q_hat = (gamma-Rho)/(1-Rho);
x_d_CROD = x_LASSO + A'*(y - A*x_LASSO)/Q_hat;
RSS = sum(abs(y - A * x_LASSO).^2)/m;
chi = Rho*(1 - Rho)/(gamma - Rho);
if chi ~= 0
chi_temp = sqrt((chi+1)*(chi+1)-4*gamma*chi);
z = -(1 - chi + chi_temp) / (2*chi);
z_prime = -(1 - 2*gamma*chi + chi + chi_temp) / (2*chi*chi*chi_temp);
G_prime = (z + 1/chi);
G_wprime = (z_prime + 1/chi/chi);
chi_hat = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
else
G_prime = gamma;
G_wprime = gamma*(1-gamma);
chi_hat = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
end
sigma_CROD = sqrt(2*chi_hat) / Q_hat;
stat_CROD = abs(x_d_CROD / sigma_CROD).^2;
P_fa_CROD_cnt(cnt_p0, rep) = sum(stat_CROD(x_idx > thd) > h_thd) / x_l0;
P_d_CROD_cnt(cnt_p0, rep) = sum(stat_CROD(x_idx <= thd) > h_thd) / x_l1;
% CAMP
Q_hat1 = gamma - rho_active;
Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./(Q_hat1*abs(x_LASSO) + lambda))) / 2 / n;
diff = 1;
while(diff > 1e-4)
Rho_pre = Rho;
Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./((gamma-Rho)*abs(x_LASSO) + lambda))) / 2 / n;
diff = abs(Rho - Rho_pre);
end
Q_hat1 = (gamma-Rho);
x_d_CAMP = x_LASSO + A'*(y - A*x_LASSO)/Q_hat1;
sigma_CAMP = 1/sqrt(log(2))*median(abs(x_d_CAMP));
stat_CAMP = abs(x_d_CAMP / sigma_CAMP).^2;
P_fa_CAMP_cnt(cnt_p0, rep) = sum(stat_CAMP(x_idx > thd) > h_thd) / x_l0;
P_d_CAMP_cnt(cnt_p0, rep) = sum(stat_CAMP(x_idx <= thd) > h_thd) / x_l1;
% SDL
Q_hat2 = (gamma - rho_active);
x_d_SDL = x_LASSO + A'*(y - A*x_LASSO)/Q_hat2;
sigma_SDL = sqrt(gamma)/sqrt(log(2))/(gamma - rho_active)*median(abs(y - A*x_LASSO));
stat_SDL = abs(x_d_SDL / sigma_SDL).^2;
P_fa_SDL_cnt(cnt_p0, rep) = sum(stat_SDL(x_idx > thd) > h_thd) / x_l0;
P_d_SDL_cnt(cnt_p0, rep) = sum(stat_SDL(x_idx <= thd) > h_thd) / x_l1;
% ROD
Q_hat3 = (gamma - rho_active)/(1 - rho_active);
x_d_ROD = x_LASSO + A'*(y - A*x_LASSO)/Q_hat3;
chi = rho_active*(1 - rho_active)/(gamma - rho_active);
if chi ~= 0
chi_temp = sqrt((chi+1)*(chi+1)-4*gamma*chi);
z = -(1 - chi + chi_temp) / (2*chi);
z_prime = -(1 - 2*gamma*chi + chi + chi_temp) / (2*chi*chi*chi_temp);
G_prime = (z + 1/chi);
G_wprime = (z_prime + 1/chi/chi);
chi_hat2 = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
else
G_prime = gamma;
G_wprime = gamma*(1-gamma);
chi_hat2 = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
end
sigma_ROD = sqrt(2*chi_hat2) / Q_hat3;
stat_ROD = abs(x_d_ROD / sigma_ROD).^2;
P_fa_ROD_cnt(cnt_p0, rep) = sum(stat_ROD(x_idx > thd) > h_thd) / x_l0;
P_d_ROD_cnt(cnt_p0, rep) = sum(stat_ROD(x_idx <= thd) > h_thd) / x_l1;
% LASSO
% stat_LASSO = abs(x_LASSO).^2;
% if p0 ~= 0
% stat_H1_LASSO_cnt(rep, :) = stat_LASSO(x_idx <= thd);
% end
% stat_H0_LASSO_cnt(rep, :) = stat_LASSO(x_idx > thd);
end
fprintf('%d\n', rep);
end
P_fa_CROD = mean(P_fa_CROD_cnt, 2);
P_fa_CAMP = mean(P_fa_CAMP_cnt, 2);
P_fa_SDL = mean(P_fa_SDL_cnt, 2);
P_fa_ROD = mean(P_fa_ROD_cnt, 2);
P_d_CROD = mean(P_d_CROD_cnt, 2);
P_d_CAMP = mean(P_d_CAMP_cnt, 2);
P_d_SDL = mean(P_d_SDL_cnt, 2);
P_d_ROD = mean(P_d_ROD_cnt, 2);
%% plot
figure(1);
plot(p0_total, P_fa_CROD, 'linewidth', 2);
hold on;
grid on;
plot(p0_total, P_fa_CAMP, 'linewidth', 2);
plot(p0_total, P_fa_SDL, 'linewidth', 2);
plot(p0_total, P_fa_ROD, 'linewidth', 2);
legend('CROD', 'CAMP', 'SDL-test', 'ROD');
xlabel('signal density');
ylabel('P_{fa}');
figure(2);
plot(p0_total, P_d_CROD, 'linewidth', 2);
hold on;
grid on;
plot(p0_total, P_d_CAMP, 'linewidth', 2);
plot(p0_total, P_d_SDL, 'linewidth', 2);
plot(p0_total, P_d_ROD, 'linewidth', 2);
legend('CROD', 'CAMP', 'SDL-test', 'ROD');
xlabel('signal density');
ylabel('P_{d}');
save test_Pfa_Pd_SNR_PF_CROD_CAMP_SDL_ROD_p0.mat ...
p0_total...
P_fa_CROD...
P_fa_CAMP...
P_fa_SDL...
P_fa_ROD...
P_d_CROD...
P_d_CAMP...
P_d_SDL...
P_d_ROD;
0 - example/nsq - ICASSP2022/Fig. 4/FISTA.m
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function [z] = FISTA(y, A, lambda, delta)
x_pre = A'*y;
t = 1;
z = x_pre;
z_pre = z;
t_pre = t;
N = size(A, 2);
diff = 1;
E = eig(A'*A);
L = E(end);
temp1 = A'*y/L;
temp2 = eye(N) - A'*A/L;
k = 0;
while((diff > delta) && (k < 1000))
temp = temp1 + temp2 * z_pre;
x = sft_thd(temp, lambda/L);
t = 0.5*(1 + sqrt(1+4*t_pre*t_pre));
z = x + (x - x_pre) * (t_pre-1) / t;
diff = mean(abs(z_pre - z));
x_pre = x;
z_pre = z;
t_pre = t;
k = k + 1;
end
end
0 - example/nsq - ICASSP2022/Fig. 4/plot_Pfa_Pd_SNR_PF_CROD_CAMP_SDL_ROD_gamma.m
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clear;
close all;
clc;
load test_Pfa_Pd_SNR_PF_CROD_CAMP_SDL_ROD_gamma.mat;
Fontsize = 18;
plot_width = 800;
plot_height = 600;
Linewidth = 2;
Markersize = 8;
%% plot
figure(1);
plot(gamma_total, P_fa_CROD, '-o', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
hold on;
grid on;
plot(gamma_total, P_fa_CAMP, '-d', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
plot(gamma_total, P_fa_SDL, '-s', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
plot(gamma_total, P_fa_ROD, '-+', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
legend('CROD', 'CAMP', 'SDL-test', 'ROD');
xlabel('compression rate');
ylabel('P_{fa}');
set(gca, 'FontSize', Fontsize);
%set(gca, 'FontSize', Fontsize, 'fontname', 'Times New Roman');
set(gcf, 'position', [200, 300, plot_width, plot_height]);
figure(2);
plot(gamma_total, P_d_CROD, '-o', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
hold on;
grid on;
plot(gamma_total, P_d_CAMP, '-d', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
plot(gamma_total, P_d_SDL, '-s', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
plot(gamma_total, P_d_ROD, '-+', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
legend('CROD', 'CAMP', 'SDL-test', 'ROD');
xlabel('compression rate');
ylabel('P_{d}');
set(gca, 'FontSize', Fontsize);
%set(gca, 'FontSize', Fontsize, 'fontname', 'Times New Roman');
set(gcf, 'position', [200, 300, plot_width, plot_height]);
0 - example/nsq - ICASSP2022/Fig. 4/test_Pfa_Pd_SNR_PF_CROD_CAMP_SDL_ROD_gamma.m
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clc;
clear;
close all;
%% parameter setting
n = 256;
SNR = 13;
rep_time = 1e4;
P_fa = 1e-2;
p0 = 0.1;
gamma_total = (4: 12)/16;
len_gamma = length(gamma_total);
lambda = 0.1;
sigma_0 = 0.1;
sigma_n = sigma_0;
%% experiment
P_fa_CROD_cnt = zeros(len_gamma, rep_time);
P_fa_CAMP_cnt = zeros(len_gamma, rep_time);
P_fa_SDL_cnt = zeros(len_gamma, rep_time);
P_fa_ROD_cnt = zeros(len_gamma, rep_time);
P_fa_LASSO_cnt = zeros(len_gamma, rep_time);
P_d_CROD_cnt = zeros(len_gamma, rep_time);
P_d_CAMP_cnt = zeros(len_gamma, rep_time);
P_d_SDL_cnt = zeros(len_gamma, rep_time);
P_d_ROD_cnt = zeros(len_gamma, rep_time);
P_d_LASSO_cnt = zeros(len_gamma, rep_time);
h_thd = -log(P_fa);
parfor rep = 1: rep_time
for cnt_gamma = 1: len_gamma
gamma = gamma_total(cnt_gamma);
m = round(gamma*n);
A_idx = randperm(n);
A_idx = A_idx(1: m);
A_idx = sort(A_idx);
A = dftmtx(n);
A = A(A_idx, :);
A = A / sqrt(n);
w = random('Normal', 0, sigma_0/sqrt(2), m, 1) + 1j * random('Normal', 0, sigma_0/sqrt(2), m, 1);
x_idx = rand(n, 1);
if p0 == 0
thd = -1;
x_l0 = sum(x_idx > thd);
else
thd = sort(x_idx);
thd = thd(round(n*p0));
x_l1 = sum(x_idx <= thd);
x_l0 = sum(x_idx > thd);
end
x = zeros(n, 1);
x_temp = sigma_0 * exp(1j*random('Uniform', 0, 2*pi, n, 1));
x(x_idx <= thd) = x_temp(x_idx <= thd);
x = x * sqrt(n/m);
x1 = x * sqrt(10^(SNR/10));
y = A * x1 + w;
% x_LASSO = LASSO_cvx(y, A, lambda);
x_LASSO = FISTA(y, A, lambda, 1e-5);
% CROD
rho_active = sum(abs(x_LASSO) > 1e-3)/n;
Q_hat = (gamma - rho_active)/(1 - rho_active);
Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./(Q_hat*abs(x_LASSO) + lambda))) / 2 / n;
diff = 1;
while(diff > 1e-4)
Rho_pre = Rho;
Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./((gamma-Rho)/(1-Rho)*abs(x_LASSO) + lambda))) / 2 / n;
diff = abs(Rho - Rho_pre);
end
Q_hat = (gamma-Rho)/(1-Rho);
x_d_CROD = x_LASSO + A'*(y - A*x_LASSO)/Q_hat;
RSS = sum(abs(y - A * x_LASSO).^2)/m;
chi = Rho*(1 - Rho)/(gamma - Rho);
if chi ~= 0
chi_temp = sqrt((chi+1)*(chi+1)-4*gamma*chi);
z = -(1 - chi + chi_temp) / (2*chi);
z_prime = -(1 - 2*gamma*chi + chi + chi_temp) / (2*chi*chi*chi_temp);
G_prime = (z + 1/chi);
G_wprime = (z_prime + 1/chi/chi);
chi_hat = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
else
G_prime = gamma;
G_wprime = gamma*(1-gamma);
chi_hat = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
end
sigma_CROD = sqrt(2*chi_hat) / Q_hat;
stat_CROD = abs(x_d_CROD / sigma_CROD).^2;
P_fa_CROD_cnt(cnt_gamma, rep) = sum(stat_CROD(x_idx > thd) > h_thd) / x_l0;
P_d_CROD_cnt(cnt_gamma, rep) = sum(stat_CROD(x_idx <= thd) > h_thd) / x_l1;
% CAMP
Q_hat1 = gamma - rho_active;
Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./(Q_hat1*abs(x_LASSO) + lambda))) / 2 / n;
diff = 1;
while(diff > 1e-4)
Rho_pre = Rho;
Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./((gamma-Rho)*abs(x_LASSO) + lambda))) / 2 / n;
diff = abs(Rho - Rho_pre);
end
Q_hat1 = (gamma-Rho);
x_d_CAMP = x_LASSO + A'*(y - A*x_LASSO)/Q_hat1;
sigma_CAMP = 1/sqrt(log(2))*median(abs(x_d_CAMP));
stat_CAMP = abs(x_d_CAMP / sigma_CAMP).^2;
P_fa_CAMP_cnt(cnt_gamma, rep) = sum(stat_CAMP(x_idx > thd) > h_thd) / x_l0;
P_d_CAMP_cnt(cnt_gamma, rep) = sum(stat_CAMP(x_idx <= thd) > h_thd) / x_l1;
% SDL
Q_hat2 = (gamma - rho_active);
x_d_SDL = x_LASSO + A'*(y - A*x_LASSO)/Q_hat2;
sigma_SDL = sqrt(gamma)/sqrt(log(2))/(gamma - rho_active)*median(abs(y - A*x_LASSO));
stat_SDL = abs(x_d_SDL / sigma_SDL).^2;
P_fa_SDL_cnt(cnt_gamma, rep) = sum(stat_SDL(x_idx > thd) > h_thd) / x_l0;
P_d_SDL_cnt(cnt_gamma, rep) = sum(stat_SDL(x_idx <= thd) > h_thd) / x_l1;
% ROD
Q_hat3 = (gamma - rho_active)/(1 - rho_active);
x_d_ROD = x_LASSO + A'*(y - A*x_LASSO)/Q_hat3;
chi = rho_active*(1 - rho_active)/(gamma - rho_active);
if chi ~= 0
chi_temp = sqrt((chi+1)*(chi+1)-4*gamma*chi);
z = -(1 - chi + chi_temp) / (2*chi);
z_prime = -(1 - 2*gamma*chi + chi + chi_temp) / (2*chi*chi*chi_temp);
G_prime = (z + 1/chi);
G_wprime = (z_prime + 1/chi/chi);
chi_hat2 = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
else
G_prime = gamma;
G_wprime = gamma*(1-gamma);
chi_hat2 = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
end
sigma_ROD = sqrt(2*chi_hat2) / Q_hat3;
stat_ROD = abs(x_d_ROD / sigma_ROD).^2;
P_fa_ROD_cnt(cnt_gamma, rep) = sum(stat_ROD(x_idx > thd) > h_thd) / x_l0;
P_d_ROD_cnt(cnt_gamma, rep) = sum(stat_ROD(x_idx <= thd) > h_thd) / x_l1;
% LASSO
% stat_LASSO = abs(x_LASSO).^2;
% if p0 ~= 0
% stat_H1_LASSO_cnt(rep, :) = stat_LASSO(x_idx <= thd);
% end
% stat_H0_LASSO_cnt(rep, :) = stat_LASSO(x_idx > thd);
end
fprintf('%d\n', rep);
end
P_fa_CROD = mean(P_fa_CROD_cnt, 2);
P_fa_CAMP = mean(P_fa_CAMP_cnt, 2);
P_fa_SDL = mean(P_fa_SDL_cnt, 2);
P_fa_ROD = mean(P_fa_ROD_cnt, 2);
P_d_CROD = mean(P_d_CROD_cnt, 2);
P_d_CAMP = mean(P_d_CAMP_cnt, 2);
P_d_SDL = mean(P_d_SDL_cnt, 2);
P_d_ROD = mean(P_d_ROD_cnt, 2);
%% plot
figure(1);
plot(gamma_total, P_fa_CROD, 'linewidth', 2);
hold on;
grid on;
plot(gamma_total, P_fa_CAMP, 'linewidth', 2);
plot(gamma_total, P_fa_SDL, 'linewidth', 2);
plot(gamma_total, P_fa_ROD, 'linewidth', 2);
legend('CROD', 'CAMP', 'SDL-test', 'ROD');
xlabel('compression rate');
ylabel('P_{fa}');
figure(2);
plot(gamma_total, P_d_CROD, 'linewidth', 2);
hold on;
grid on;
plot(gamma_total, P_d_CAMP, 'linewidth', 2);
plot(gamma_total, P_d_SDL, 'linewidth', 2);
plot(gamma_total, P_d_ROD, 'linewidth', 2);
legend('CROD', 'CAMP', 'SDL-test', 'ROD');
xlabel('compression rate');
ylabel('P_{d}');
save test_Pfa_Pd_SNR_PF_CROD_CAMP_SDL_ROD_gamma.mat ...
gamma_total...
P_fa_CROD...
P_fa_CAMP...
P_fa_SDL...
P_fa_ROD...
P_d_CROD...
P_d_CAMP...
P_d_SDL...
P_d_ROD;
0 - example/nsq - 恢复算法/FISTA.m
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function [z] = FISTA(y, A, lambda, delta)
x_pre = A'*y;
t = 1;
z = x_pre;
z_pre = z;
t_pre = t;
N = size(A, 2);
diff = 1;
E = eig(A'*A);
L = E(end);
temp1 = A'*y/L;
temp2 = eye(N) - A'*A/L;
k = 0;
while((diff > delta) && (k < 1000))
temp = temp1 + temp2 * z_pre;
x = sft_thd(temp, lambda/L);
t = 0.5*(1 + sqrt(1+4*t_pre*t_pre));
z = x + (x - x_pre) * (t_pre-1) / t;
diff = sum(abs(z_pre - z))/sum(abs(z));
x_pre = x;
z_pre = z;
t_pre = t;
k = k + 1;
end
end
0 - example/nsq - 恢复算法/cVAMPa_dampling.m
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function[x, x_d, hat_Q1, sigma_d, ifcvg] = cVAMPa_dampling(y, A, lambda, alpha, delta, iter_max, sigma)
[M, N] = size(A);
gamma = M/N;
p = A'*y;
h1 = p/gamma;
hat_Q1 = gamma;
%Eigenvalue Decomposition
[V, D] = eig(A'*A);
d = diag(D);
t = 0;
diff = 1;
while((diff > delta) && (t < iter_max))
h1_pre = h1;
% Factorized
x1 = sft_thd(h1, lambda/hat_Q1);
chi1 = sum((abs(x1) > 1e-4).* (2 - lambda./((hat_Q1*abs(x1) + lambda)))) / 2 / N / hat_Q1;
% Message F to G
hat_Q2 = 1/chi1 - hat_Q1;
h2 = (x1/chi1 - h1*hat_Q1)/hat_Q2;
% Gaussian
tmp = V'*(p + h2*hat_Q2);
tmp = tmp./(d+hat_Q2);
x2 = V*tmp;
chi2 = sum(1./(d+hat_Q2))/N;
% Message G to F
hat_Q1 = 1/chi2 - hat_Q2;
h1 = alpha*(x2/chi2 - h2*hat_Q2)/hat_Q1+(1-alpha)*h1;
diff = sum(abs(h1_pre - h1))/sum(abs(h1));
t = t+1;
end
ifcvg = diff <= delta;
x = x1;
x_d = h1;
chi = chi1;
t = -hat_Q2;
t_prime = -1/mean((1./(d+hat_Q2)).^2);
G_prime = t + 1/chi;
G_wprime = t_prime + 1/chi/chi;
RSS = sum(abs(y - A*x).^2)/M;
hat_chi = gamma*G_wprime/(2*G_prime-2*chi*G_wprime)*RSS +...
(-G_wprime*gamma+G_prime*G_prime)/(2*G_prime-2*chi*G_wprime)*sigma^2;
sigma_d = sqrt(2*hat_chi)/hat_Q1;
end
0 - example/nsq - 恢复算法/cal_debiased_LASSO.m
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function [x_d, hat_Q1, sigma_d] = cal_debiased_LASSO(x, A, y, lambda, sigma)
[M, N] = size(A);
gamma = M/N;
hat_Q1 = gamma;
[~, D] = eig(A'*A);
d = diag(D);
diff = 1;
T = 1000;
t = 0;
while (t < T) && (diff > 1e-6)
Q1_pre = hat_Q1;
rho = mean((2 - lambda./(hat_Q1*abs(x) + lambda)).*(abs(x) > 1e-4))/2;
hat_Q1 = rho/mean(1./(d + (1-rho)*hat_Q1/rho));
diff = abs(Q1_pre - hat_Q1);
t = t+1;
end
x_d = x + 1/hat_Q1*A'*(y - A*x);
chi = rho/hat_Q1;
hat_Q2 = 1/chi - hat_Q1;
t = -hat_Q2;
t_prime = -1/mean((1./(d+hat_Q2)).^2);
G_prime = t + 1/chi;
G_wprime = t_prime + 1/chi/chi;
RSS = sum(abs(y - A*x).^2)/M;
hat_chi = gamma*G_wprime/(2*G_prime-2*chi*G_wprime)*RSS +...
(-G_wprime*gamma+G_prime*G_prime)/(2*G_prime-2*chi*G_wprime)*sigma^2;
sigma_d = sqrt(2*hat_chi)/hat_Q1;
end
0 - example/nsq - 恢复算法/generate_matrix_new.m
Executable
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function [ A ] = generate_matrix_new(y1, y2)
A = [];
l = length(y1);
temp1 = y1;
temp2 = y2;
for i = 1:l
t1 = circshift(temp1, i-1);
t2 = circshift(temp2, i-1);
if i - 1 > 0
t1(1:i - 1,1) = 0;
end
if i - 1 > 0
t2(1:i - 1,1) = 0;
end
A = [A,t1,t2];
end
end
0 - example/nsq - 恢复算法/model.m
Executable
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clc;
clear;
close all;
%% 参数设置
sigma_n = 0.1;
gamma = 0.5;
% 信号参数
B = 5e5; %信号带宽
Tp = 100e-6; %脉宽100us
fs = 2 * B; %采样频率
Ts = 1 / fs; %采样周期
K = B / Tp; %线性调频率
fc = 1e8; %载波频率
Tr = 1e-3;
t = 0: 1/fs: Tr - 1/fs;
t2 = 0: 1/fs/2: Tr - 1/fs/2;
c = 3e8; % 光速
distance_max = (Tr-Tp) * c / 2;
target_scattering = [0.8, 1, 0.9]; %扩展目标各点散射强度
%% 生成矩阵 A
% 生成发射信号 signal_t 及
N = Tr * fs;
N_high = Tp * fs;
signal_t = zeros(1, N);
signal_td = zeros(1, N);
for i = 1:N_high
tp = (i - 1) * (1 / fs);
signal_t(1, i) = exp(1j*2*pi*(fc*tp+0.5*K*tp.^2));
tp2 = (i - 0.5) * (1 / fs);
signal_td(1, i + 1) = exp(1j*2*pi*(fc*tp2+0.5*K*tp2.^2));
end
A = generate_matrix_new(signal_t.', signal_td.');
J = A'*A;
lambda_J=eig(J);
figure(1)
spy(A)
%% 生成回波 y
% 设置目标 - 扩展目标，由三个点组成
distance1 = 52000;
tau1 = distance1 * 2 / c;
n_tau1 = round(tau1 * fs);
alpha1 = 0.6; % 扩展目标整体散射强度
signal_r1_t1 = zeros(1, N);
signal_r2_t1 = zeros(1, N);
signal_r3_t1 = zeros(1, N);
for i = 1:N
temp = i - n_tau1;
if temp >= 1 && temp <= N_high
signal_r1_t1(1, i) = alpha1 * target_scattering(1) * signal_t(1, temp);
if i + 1 <= N
signal_r2_t1(1, i + 1) = alpha1 * target_scattering(2) * signal_t(1, temp);
end
if i + 1 <= N
signal_r3_t1(1, i + 2) = alpha1 * target_scattering(3) * signal_t(1, temp);
end
end
end
signal_r1 = signal_r1_t1 + signal_r2_t1 + signal_r3_t1;
% 回波
signal_r = signal_r1;
% 加入噪声
noise = random('Normal', 0, sigma_n/sqrt(2), 1, length(signal_r)) + 1j * random('Normal', 0, sigma_n/sqrt(2), 1, length(signal_r));
signal_r_n = signal_r + noise;
y = signal_r_n.';
figure(2)
subplot(211);
plot(t, real(signal_t));
title('发射信号')
xlabel('时间')
ylabel('幅度')
subplot(212);
plot(t, real(y))
title('接收信号(y)')
xlabel('时间')
ylabel('幅度')
%% 理论 x
distance_node = round((distance1 * 2 / c) * fs);
x_t = zeros(1, 2 * N);
for i = 1: length(target_scattering)
x_t((distance_node + i) * 2 - 1) = alpha1 * target_scattering(i);
end
x = x_t.';
figure(3)
plot(t2, x);
title('目标散射点(x)')
xlabel('时间')
ylabel('幅度')
%% 验证
y_t = A * x;
y_r = signal_r.';
figure(4)
subplot(311);
plot(real(y_r))
title('实际回波')
subplot(312);
plot(real(y_t));
title('计算结果')
subplot(313);
plot(abs(y_r - y_t));
title('差异')
0 - example/nsq - 恢复算法/sft_thd.m
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function y = sft_thd(x, thd)
if isequal(size(x), size(thd))
tmp = abs(x);
y = x;
y(tmp <= thd) = 0;
y(tmp > thd) = (tmp(tmp > thd) - thd(tmp > thd)) .* x(tmp > thd) ./ tmp(tmp > thd);
else
tmp = abs(x);
y = x;
y(tmp <= thd) = 0;
y(tmp > thd) = (tmp(tmp > thd) - thd) .* x(tmp > thd) ./ tmp(tmp > thd);
end
end
0 - example/nsq - 恢复算法/test_model.m
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clc;
clear;
%close all;
%% 参数设置
sigma_n = 0.1;
gamma = 0.5;
% 信号参数
B = 5e5; %信号带宽
Tp = 100e-6; %脉宽100us
fs = 2 * B; %采样频率
Ts = 1 / fs; %采样周期
K = B / Tp; %线性调频率
fc = 1e8; %载波频率
Tr = 1e-3;
t = 0: 1/fs: Tr - 1/fs;
t2 = 0: 1/fs/2: Tr - 1/fs/2;
c = 3e8; % 光速
distance_max = (Tr-Tp) * c / 2;
target_scattering = [0.8, 1, 0.9]; %扩展目标各点散射强度
%% 生成矩阵 A
% 生成发射信号 signal_t 及
N = Tr * fs;
N_high = Tp * fs;
signal_t = zeros(1, N);
signal_td = zeros(1, N);
for i = 1:N_high
tp = (i - 1) * (1 / fs);
signal_t(1, i) = exp(1j*2*pi*(fc*tp+0.5*K*tp.^2));
tp2 = (i - 0.5) * (1 / fs);
signal_td(1, i + 1) = exp(1j*2*pi*(fc*tp2+0.5*K*tp2.^2));
end
A = generate_matrix_new(signal_t.', signal_td.');
temp = 0;
for i = 1: size(A, 1)
for j = 1: size(A, 2)
temp = temp + abs(A(mod(i, size(A, 1))+1, mod(j+1, size(A, 2))+1) - A(i, j));
end
end
%% 生成回波 y
% 设置目标 - 扩展目标，由三个点组成
distance1 = 52000;
tau1 = distance1 * 2 / c;
n_tau1 = round(tau1 * fs);
alpha1 = 0.6; % 扩展目标整体散射强度
signal_r1_t1 = zeros(1, N);
signal_r2_t1 = zeros(1, N);
signal_r3_t1 = zeros(1, N);
for i = 1:N
temp = i - n_tau1;
if temp >= 1 && temp <= N_high
signal_r1_t1(1, i) = alpha1 * target_scattering(1) * signal_t(1, temp);
if i + 1 <= N
signal_r2_t1(1, i + 1) = alpha1 * target_scattering(2) * signal_t(1, temp);
end
if i + 1 <= N
signal_r3_t1(1, i + 2) = alpha1 * target_scattering(3) * signal_t(1, temp);
end
end
end
signal_r1 = signal_r1_t1 + signal_r2_t1 + signal_r3_t1;
% 回波
signal_r = signal_r1;
% 加入噪声
noise = random('Normal', 0, sigma_n/sqrt(2), 1, length(signal_r)) + 1j * random('Normal', 0, sigma_n/sqrt(2), 1, length(signal_r));
signal_r_n = signal_r + noise;
y = signal_r_n.';
%% 理论 x
distance_node = round((distance1 * 2 / c) * fs);
x_t = zeros(1, 2 * N);
for i = 1: length(target_scattering)
x_t((distance_node + i) * 2 - 1) = alpha1 * target_scattering(i);
end
x = x_t.';
%% Experiment
%% Parameters setting
lambda = 0.002;
alpha = 1/4;
delta = 1e-8*alpha;
iter_max = round(2000/alpha);
n = size(A, 2);
% J = A'*A;
J1 = A*A';
lambda_J=eig(J1);
% histogram(lambda_J, 100);
%% Normalized
A = A / sqrt(lambda_J(end));
y = y / sqrt(lambda_J(end));
sigma_n = sigma_n / sqrt(lambda_J(end));
%% cVAMP
tic;
[x_VAMP, x_d, hat_Q1, sigma_d, ifcvg] = cVAMPa_dampling(y, A, lambda, alpha, delta, iter_max, sigma_n);
toc;
%% cvx
tic;
cvx_begin quiet
variable x_cvx(n, 1) complex
z = lambda*sum(abs(x_cvx)) + 0.5*sum(pow_abs((y - A * x_cvx), 2));
minimize(z)
cvx_end
[x_d_cal, hat_Q1_cal, sigma_d_cal] = cal_debiased_LASSO(x_cvx, A, y, lambda, sigma_n);
toc;
sigma_ex = std(x_d_cal - x, 1);
tmp = (x_d_cal - x)/sigma_ex;
[h_r, p_r, k_r, c_r] = kstest(real(tmp)*sqrt(2));
[h_i, p_i, k_i, c_i] = kstest(imag(tmp)*sqrt(2));
%% results
% whether cVAMP algorithm converges
ifcvg
% whether the output of cVAMP converges to the LASSO solution
sum(abs(x_cvx - x_VAMP))
% check the results from cVAMP and "calculation"
abs(hat_Q1 - hat_Q1_cal)
abs(sigma_d - sigma_d_cal)
sum(abs(x_d - x_d_cal))
% accuracy of estimating the variance
abs(sigma_d_cal - sigma_ex)/abs(sigma_ex)
% p-value of KS-test
% the larger, the higher probability it is drawn from Gaussian distribution
p_r
p_i
0 - example/wzk - PSK_ROC/test_function.m
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% load st.mat
% [ A ] = generate_matrix_long(transpose(s_T));
N = 512;
A = dftmtx(N) / sqrt(N);
A = A(1: 256, :);
Target_index = 321;
SNR = 10;
lambda = 0.0005;
%%
[ x_mf, x_cs ] = yAxn_recovery( A, SNR, Target_index, lambda );
figure(1111)
subplot(211)
plot(abs(x_mf))
subplot(212)
plot(abs(x_cs))
%%
rep_time = 500;
[ 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 );
P_fa_MF = res_MF(:,1);
P_d_MF = res_MF(:,2);
P_fa_CS = res_CS(:,1);
P_d_CS = res_CS(:,2);
figure;
loglog(P_fa,P_fa_MF, 'linewidth', 2);
hold on;
loglog(P_fa,P_fa_CS, 'linewidth', 2);
legend('MF','CS')
xlabel('P_{fa}');
ylabel('Actual P_{fa}');
figure;
semilogx(P_fa,P_d_MF, 'linewidth', 2);
hold on;
semilogx(P_fa,P_d_CS, 'linewidth', 2);
legend('MF','CS')
xlabel('P_{fa} set');
ylabel('P_{d}');
figure;
semilogx(P_fa_MF,P_d_MF, 'linewidth', 2);
hold on;
grid on;
semilogx(P_fa_CS,P_d_CS, 'linewidth', 2);
xlim([1e-4,1])
legend('MF','CS')
xlabel('Actual P_{fa}');
ylabel('P_{d}');
title('ROC');
figure
subplot(211)
histogram(real(H0_MF_cnt(5,:)))
hold on;
histogram(real(H1_MF_cnt))
subplot(212)
histogram(real(H0_CS_cnt(5,:)))
hold on;
histogram(real(H1_CS_cnt))
0 - example/wzk - PSK_ROC/test_signal_t.m
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clc
clear
close all
rng(6)
PRF = 5000; % 脉冲重复频率
Tr = 1 / PRF; % 脉冲重复间隔
Tp = 2e-5;
P = 10;
B = P / Tp;
fs = 10 * B;
Ts = 1/fs;
fc = 1.25e9;
t = 0:1/fs:1-1/fs;
tsin = Tp / P * 2;
fsin = 1 / tsin;
N = round(Tr * fs);
N_high = round(Tp * fs / P);
signal_t = zeros(1, N);
signal_td = zeros(1, N);
sign_p = sign(randn(1, P));
for p = 1: P
for i = 1: N_high
tp = (i - 1) * (1 / fs);
signal_t(1, (p-1)*N_high + i) = sign_p(p) * exp(1j * 2 * pi * fsin * tp);
tp2 = (i - 0.5) * (1 / fs);
signal_td(1, (p-1)*N_high + i) = sign_p(p) * exp(1j * 2 * pi * fsin * tp2);
end
end
A = zeros(N, 2 * N);
A(:, 1) = transpose(signal_t);
A(:, 2) = transpose([0, signal_td(1: end-1)]);
for k = 3: 2 * N
A(:, k) = [0; A(1: end - 1, k - 2)];
end
figure(1)
subplot(211)
plot(real(A(1:N_high*P+20, 1)))
hold on;
plot(real(A(1:N_high*P+20, 2)))
plot(real(A(1:N_high*P+20, 3)))
subplot(212)
plot(imag(A(1:N_high*P+20, 1)))
hold on;
plot(imag(A(1:N_high*P+20, 2)))
plot(imag(A(1:N_high*P+20, 3)))
0 - example/wzk - PSK_ROC/yAxn_MC.m
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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
0 - example/wzk - PSK_ROC/yAxn_recovery.m
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function [ x_mf_norm, x_cs_norm ] = yAxn_recovery( A, SNR, Target_index, lambda )
% 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;
%% 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)));
x_mf_norm = x_mf ./ sigma_MF;
% 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)));
x_cs_norm = x_d_cal_f ./ sigma_CS;
end
0 - example/wzk - RDA/angle_estimation.m
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function [ target_list_RDA ] = angle_estimation(target_list_RDA_temp, echo_mtx, A, d, lambda, acc)
% This function estimates all targets angle
%
% Usage:
% [target_list_RDA] = angle_estimation(target_list_RDA_temp, echo_mtx, A, d, lambda, acc)
%
% Inputs:
% target_list_RDA_temp: Temporary list of targets before angle estimation
% echo_mtx: Original echo data matrix
% A: Chirp measurement matrix
% d: Antenna spacing
% lambda: Wave length
% acc: Accuracy for angle estimation
%
% Outputs:
% target_list_RDA: Target list include range, doppler and angle information
% parameters
if nargin < 6
acc = 181;
end
% calculate all targets angle
target_list_RDA = zeros(size(target_list_RDA_temp));
for i = 1: size(target_list_RDA_temp, 1)
t_rda = target_list_RDA_temp(i, :);
target_list_RDA(i, 1:2) = t_rda(1:2);
target_list_RDA(i, 3) = cal_angle(t_rda(1), t_rda(2), echo_mtx, A, d, lambda, acc);
end
end
%% sub-functions
% calculate target actual angle with range and doppler index
function [ angle ] = cal_angle(r_idx, d_idx, echo_mtx, A, d, lambda, acc)
% range doppler processing
echo_r = zeros([size(echo_mtx, 1), 1, size(echo_mtx, 3)]);
for i = 1 : size(echo_mtx, 3)
echo_r(:, 1, i) = sum(bsxfun(@times, echo_mtx(:, :, i), A(:, r_idx)'), 2);
end
echo_r = squeeze(echo_r);
echo_r_ex = [echo_r, zeros(size(echo_r))];
echo_rd = zeros(size(echo_r_ex, 1), 1);
for i = 1 : size(echo_r_ex, 1)
temp_v = fftshift(fft(echo_r_ex(i,:)));
echo_rd(i) = temp_v(d_idx);
end
% CBF
THETA = linspace(-90, 90, round(acc));
fai = exp((0: size(echo_r_ex, 1) - 1)' *...
-1j * 2 * pi / lambda * d * sin(THETA / 180 * pi));
angle_mf = abs(fai'* echo_rd);
[v, idx] = max(angle_mf);
angle = THETA(idx);
end
0 - example/wzk - RDA/doppler_process_CS.m
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function [ echo_rd_mtx, stat_RD, sigma_n_o ] = doppler_process_CS(echo_r_mtx, sigma_n, lambda, gamma, delta)
% Doppler processing for echo data using compressed sensing
%
% Usage:
% [echo_rd_mtx, stat_RD, sigma_n_o] = doppler_process_CS(echo_r_mtx, sigma_n, lambda, gamma, delta)
%
% Inputs:
% echo_r_mtx: Range processing echo data
% sigma_n: Input noise standard deviation
% lambda: LASSO weight
% gamma: Compressed ratio(0.5)
% delta: Convergence normalized difference(1e-6)
%
% Outputs:
% echo_rd_mtx: Range-doppler processing echo data
% stat_RD: Range-doppler statistics
% sigma_n_o: Output noise standard deviation
% parameters
if nargin < 5
delta = 1e-6;
end
if nargin < 4
gamma = 0.5;
end
[lenA, lenR, M] = size(echo_r_mtx);
N = round(M / gamma);
iter_max_VAMP = 1000;
lambda_v = zeros(N, 1) + lambda;
% generate mtx
F_ori = dftmtx(N);
F = F_ori(1:M,:);
F_inv = conj(F) / N;
% normalization
A = (sqrt(N) * eye(M)) * F_inv;
echo_r_mtx = sqrt(N) .* echo_r_mtx;
sigma_n = sqrt(N) * sigma_n;
% doppler processing
echo_rd_mtx = zeros(lenA, lenR, N);
stat_RD = zeros(lenA, lenR, N);
sigma_n_o_cnt = zeros(lenA, lenR);
for numA = 1: lenA
parfor numR = 1: lenR
sample = squeeze(echo_r_mtx(numA, numR, :));
y = sample;
x_LASSO = cVAMPro(y, A, lambda_v, delta, iter_max_VAMP);
[x_d_CROD, sigma_CROD] = CROD(y, A, x_LASSO, lambda, sigma_n);
sigma_n_o_cnt(numA, numR) = abs(sigma_CROD);
stat_RD(numA, numR, :) = abs(fftshift(x_d_CROD) / sigma_CROD).^2;
echo_rd_mtx(numA, numR, :) = fftshift(x_d_CROD);
end
end
% sigma_n_o = mean(sigma_n_o_cnt, 2);
sigma_n_o = mean(mean(sigma_n_o_cnt));
end
%% sub-functions
% algorithm for LASSO
% y: measurements
% A: measurement matrix
% lambda: LASSO weight
% tau: convergence normalized difference
% Kit: maximum number of iterations
% LASSO estimator
function x_hat_wl = cVAMPro(y, A, lambda, tau, Kit)
% Initialization
[M, N] = size(A);
gamma = M / N;
k = 0;
p = ctranspose(A) * y;
h_1 = p;
Q_1 = gamma;
tau_d = 1;
% Iteration
while ((k < Kit) && (tau_d > tau))
% Factorized Part
x_1 = ST(h_1, lambda, Q_1);
chi_1 = F1(x_1, lambda, Q_1);
% Message Passing
h_2 = x_1 / chi_1 - h_1;
Q_2 = 1 / chi_1 - Q_1;
% Gaussian Part
t1 = (p + h_2) / Q_2;
t2 = ctranspose(A) * (A * (p + h_2)) / ((Q_2 + 1) * Q_2);
x_2 = t1 - t2;
chi_2 = gamma / (Q_2 + 1) + (1 - gamma) / Q_2;
% Message Passing
h_1_next = x_2 ./ chi_2 - h_2;
Q_1_next = 1 / chi_2 - Q_2;
tau_d = norm(h_1_next - h_1, Inf) / norm(h_1_next, Inf);
k = k + 1;
% output
x_hat_wl = x_1;
% next
h_1 = h_1_next;
Q_1 = Q_1_next;
end
end
% soft threshold function
% x: processing object
% thd: threshold
% y: result
function x = ST(h_1, lambda, Q_1)
[N, M] = size(h_1);
x = zeros(N, M);
for i = 1:N
sign = h_1(i) ./ abs(h_1(i));
diff = abs(h_1(i)) - lambda(i);
x(i) = sign .* (diff ./ Q_1) .* SF(diff);
end
end
% Heaviside's step function
function v = SF(a)
if a > 0
v = 1;
elseif a == 0
v = 0; % at zero points
else
v = 0;
end
end
% Calculation of chi_1
function chi_1 = F1(x_1, lambda, Q_1)
[N, M] = size(x_1);
count = 0;
for i = 1:N
temp = Q_1 * abs(x_1(i)) + lambda(i);
count = count + (2 - lambda(i) / temp) * SF(abs(x_1(i)));
% count = count + (2-lambda(i)/temp) * (abs(x_1(i)) > 1e-4);
end
chi_1 = count / (2 * N * Q_1);
end
% calculate debiased LASSO estimator
% y: measurements
% A: measurement matrix
% x_LASSO: LASSO estimator
% lambda: LASSO weight
% sigma_n: input noise standard deviation
% x_d_CROD: debiased LASSO estimator
% sigma_CROD: equivalent noise standard deviation estimator
function [ x_d_CROD, sigma_CROD ] = CROD(y, A, x_LASSO, lambda, sigma_n)
[m, n] = size(A);
gamma = m / n;
rho_active = sum(abs(x_LASSO) > 1e-3)/n;
Q_hat = (gamma - rho_active)/(1 - rho_active);
Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./(Q_hat*abs(x_LASSO) + lambda))) / 2 / n;
diff = 1;
while(diff > 1e-4)
Rho_pre = Rho;
Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./((gamma-Rho)/(1-Rho)*abs(x_LASSO) + lambda))) / 2 / n;
diff = abs(Rho - Rho_pre);
end
Q_hat = (gamma-Rho)/(1-Rho);
x_d_CROD = x_LASSO + A'*(y - A*x_LASSO)/Q_hat;
RSS = sum(abs(y - A * x_LASSO).^2)/m;
chi = Rho*(1 - Rho)/(gamma - Rho);
if chi ~= 0
chi_temp = sqrt((chi+1)*(chi+1)-4*gamma*chi);
z = -(1 - chi + chi_temp) / (2*chi);
z_prime = -(1 - 2*gamma*chi + chi + chi_temp) / (2*chi*chi*chi_temp);
G_prime = (z + 1/chi);
G_wprime = (z_prime + 1/chi/chi);
chi_hat = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
else
G_prime = gamma;
G_wprime = gamma*(1-gamma);
chi_hat = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
end
sigma_CROD = sqrt(2*chi_hat) / Q_hat;
end
0 - example/wzk - RDA/doppler_process_MF.m
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function [ echo_rd_mtx, stat_RD, sigma_n_o ] = doppler_process_MF(echo_r_mtx, sigma_n, gamma)
% Doppler processing for echo data using matching filter
%
% Usage:
% [echo_rd_mtx, stat_RD, sigma_n_o] = doppler_process_MF(echo_r_mtx, sigma_n, gamma)
%
% Inputs:
% echo_r_mtx: Range processing echo data
% sigma_n: Input noise standard deviation
% gamma: Compressed ratio(0.5)
%
% Outputs:
% echo_rd_mtx: Range-doppler processing echo data
% stat_RD: Range-doppler statistics
% sigma_n_o: Output noise standard deviation
% parameters
if nargin < 3
gamma = 0.5;
end
[lenA, lenR, M] = size(echo_r_mtx);
N = round(M / gamma);
% generate mtx
F_ori = dftmtx(N);
F = F_ori(1:M,:);
multiple_d = F(:,1)' * F(:,1);
% doppler matched filtering
echo_rd_mtx = zeros(lenA, lenR, N);
for numA = 1: lenA
for numR = 1: lenR
sample = squeeze(echo_r_mtx(numA, numR, :));
dpl_temp = transpose(F) * sample;
dpl_norm = fftshift(dpl_temp ./ multiple_d);
echo_rd_mtx(numA, numR, :) = dpl_norm;
end
end
% calculate output noise
sigma_n_o = sqrt(sigma_n^2 / multiple_d);
stat_RD = abs(echo_rd_mtx ./ sigma_n_o).^2;
end
0 - example/wzk - RDA/echo_processing_CS.m
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function [ echo_rd_mtx, target_list_RDA, sigma_n_rd ] = ...
echo_processing_CS( echo_mtx, PRF, fs, fc, B, D, d, sigma_n, P_fa, lambda_r, lambda_d )
% This function processes echo data using compressed sensing method.
%
% Usage:
% [echo_rd_mtx, target_list_RDA, sigma_n_rd] = echo_processing_MF(echo_mtx, PRF, fs, fc, B, D, d, sigma_n, P_fa, lambda_r, lambda_d)
%
% Inputs:
% echo_mtx: Matrix containing the echo data
% PRF: Pulse Repetition Frequency
% fs: Sampling frequency
% fc: Carrier frequency
% B: Bandwidth
% D: Duty ratio
% d: Antenna spacing
% sigma_n: Input noise level of the echo data
% P_fa: False alarm probability threshold
% lambda_r: LASSO weight for range processing
% lambda_d: LASSO weight for doppler processing
%
% Outputs:
% echo_rd_mtx: Echo matrix after range-Doppler processing
% target_list_RDA: List of detected targets
% sigma_n_rd: Estimated noise level after range-Doppler processing
% parameters
c = 3e8;
lambda = c / fc;
[num_antenna, N, num_pluse] = size(echo_mtx);
% data processing
[distance_v, speed_v] = get_range_speed_val(PRF, fs, fc, num_pluse);
[echo_sFFT_mtx, angle_v] = spatial_FFT(echo_mtx, d, lambda);
fprintf(' Spatial_FFT done.\n');
[A, signal_t] = generate_chirp_mtx(PRF, B, fs, D);
fprintf(' Generate_chirp_mtx done.\n');
[echo_r_mtx, sigma_n_o] = range_process_CS(echo_sFFT_mtx, A, sigma_n, lambda_r);
fprintf(' Range_processing done.\n');
[echo_rd_mtx, stat_RD, sigma_n_rd] = doppler_process_CS(echo_r_mtx, sigma_n_o, lambda_d);
fprintf(' Doppler_processing done.\n');
[target_list_RDA_temp, target_map] = rda_detection(stat_RD, P_fa);
fprintf(' Target_detection done.\n');
[target_list_RDA] = angle_estimation(target_list_RDA_temp, echo_mtx, A, d, lambda);
fprintf(' Angle_estimation done.\n');
target_list_RDA(:, 1) = distance_v(target_list_RDA(:, 1));
target_list_RDA(:, 2) = speed_v(target_list_RDA(:, 2));
end
0 - example/wzk - RDA/echo_processing_CS_v0.m
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function [ echo_rd_mtx, target_list_RDA, sigma_n_rd ] = ...
echo_processing_CS_v0( echo_mtx, PRF, fs, fc, B, D, d, sigma_n, P_fa, lambda_r, lambda_d )
% parameters
c = 3e8;
lambda = c / fc;
[num_antenna, N, num_pluse] = size(echo_mtx);
% data processing
[distance_v, speed_v] = get_range_speed_val(PRF, fs, fc, num_pluse);
[echo_sFFT_mtx, angle_v] = spatial_FFT(echo_mtx, d, lambda);
[A, signal_t] = generate_chirp_mtx(PRF, B, fs, D);
[echo_r_mtx, sigma_n_o] = range_process_CS(echo_sFFT_mtx, A, sigma_n, lambda_r);
[echo_rd_mtx, stat_RD, sigma_n_rd] = doppler_process_CS(echo_r_mtx, sigma_n_o, lambda_d); %差个方差
[target_list_RDA_temp, target_map] = rda_detection(stat_RD, P_fa);
target_list_RDA = target_list_RDA_temp;
target_list_RDA(:, 1) = distance_v(target_list_RDA(:, 1));
target_list_RDA(:, 2) = speed_v(target_list_RDA(:, 2));
target_list_RDA(:, 3) = angle_v(target_list_RDA(:, 3));
end
0 - example/wzk - RDA/echo_processing_MF.m
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function [ echo_rd_mtx, target_list_RDA, sigma_n_rd ] =...
echo_processing_MF( echo_mtx, PRF, fs, fc, B, D, d, sigma_n, P_fa )
% This function processes echo data using matching filter method.
%
% Usage:
% [echo_rd_mtx, target_list_RDA, sigma_n_rd] = echo_processing_MF(echo_mtx, PRF, fs, fc, B, D, d, sigma_n, P_fa)
% Inputs:
% echo_mtx: Matrix containing the echo data
% PRF: Pulse Repetition Frequency
% fs: Sampling frequency
% fc: Carrier frequency
% B: Bandwidth
% D: Duty ratio
% d: Antenna spacing
% sigma_n: Input noise level of the echo data
% P_fa: False alarm probability threshold
%
% Outputs:
% echo_rd_mtx: Echo matrix after range-Doppler processing
% target_list_RDA: List of detected targets
% sigma_n_rd: Estimated noise level after range-Doppler processing
% parameters
c = 3e8;
lambda = c / fc;
[num_antenna, N, num_pluse] = size(echo_mtx);
% data processing
[distance_v, speed_v] = get_range_speed_val(PRF, fs, fc, num_pluse);
[echo_sFFT_mtx, angle_v] = spatial_FFT(echo_mtx, d, lambda);
fprintf(' Spatial_FFT done.\n');
[A, signal_t] = generate_chirp_mtx(PRF, B, fs, D);
fprintf(' Generate_chirp_mtx done.\n');
[echo_r_mtx, sigma_n_o] = range_process_MF(echo_sFFT_mtx, A, sigma_n);
fprintf(' Range_processing done.\n');
[echo_rd_mtx, stat_RD, sigma_n_rd] = doppler_process_MF(echo_r_mtx, sigma_n_o);
fprintf(' Doppler_processing done.\n');
[target_list_RDA_temp, target_map] = rda_detection(stat_RD, P_fa);
fprintf(' Target_detection done.\n');
[target_list_RDA] = angle_estimation(target_list_RDA_temp, echo_mtx, A, d, lambda);
fprintf(' Angle_estimation done.\n');
target_list_RDA(:, 1) = distance_v(target_list_RDA(:, 1));
target_list_RDA(:, 2) = speed_v(target_list_RDA(:, 2));
end
0 - example/wzk - RDA/echo_processing_MF_v0.m
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function [ echo_rd_mtx, target_list_RDA, sigma_n_rd ] =...
echo_processing_MF_v0( echo_mtx, PRF, fs, fc, B, D, d, sigma_n, P_fa )
% parameters
c = 3e8;
lambda = c / fc;
[num_antenna, N, num_pluse] = size(echo_mtx);
% data processing
[distance_v, speed_v] = get_range_speed_val(PRF, fs, fc, num_pluse);
[echo_sFFT_mtx, angle_v] = spatial_FFT(echo_mtx, d, lambda);
[A, signal_t] = generate_chirp_mtx(PRF, B, fs, D);
[echo_r_mtx, sigma_n_o] = range_process_MF(echo_sFFT_mtx, A, sigma_n);
[echo_rd_mtx, stat_RD, sigma_n_rd] = doppler_process_MF(echo_r_mtx, sigma_n_o); %差个方差
[target_list_RDA_temp, target_map] = rda_detection(stat_RD, P_fa);
target_list_RDA = target_list_RDA_temp;
target_list_RDA(:, 1) = distance_v(target_list_RDA(:, 1));
target_list_RDA(:, 2) = speed_v(target_list_RDA(:, 2));
target_list_RDA(:, 3) = angle_v(target_list_RDA(:, 3));
end
0 - example/wzk - RDA/generate_chirp_mtx.m
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function [ A, signal_t ] = generate_chirp_mtx(PRF, B, fs, D, gamma, sign_mid)
% Generates a chirp measurement matrix
%
% Usage:
% [A, signal_t] = generate_chirp_mtx(PRF, B, fs, D, gamma, sign_mid)
%
% Inputs:
% PRF: Pulse Repetition Frequency
% B: Bandwidth
% fs: Sampling frequency
% D: Duty ratio
% gamma: Compression ratio
% sign_mid: if sign_mid is 0 means the initial frequency is 0,
% if sign_mid is 1 means the initial frequency is -B/2,
%
% Outputs:
% A: Chirp measurement matrix
% signal_t: Transmitting signal
% parameters
if nargin < 5
gamma = 0.5;
end
if nargin < 6
sign_mid = 0;
end
Tr = 1 / PRF;
Tp = Tr * D;
K = B / Tp;
% generate_signal
N = Tr * fs;
N_high = Tp * fs;
N_mtx = round(N / gamma);
signal_t = zeros(1, N);
for i = 1: N_high
tp = i * (1 / fs) - sign_mid * N_high / fs / 2;
signal_t(1, i) = exp(1j * 2 * pi * 0.5 * K * tp .^ 2);
end
signal_t_2fs = zeros(1, N_mtx);
for i = 1: round(N_high / gamma)
tp = (i+1) * (1 / fs / 2) - sign_mid * N_high / fs / 2;
signal_t_2fs(1, i) = exp(1j * pi * K * tp .^ 2);
end
% generate chirp matrix
A = generate_matrix_by_signal2fs(transpose(signal_t_2fs));
end
%% sub-functions
% generate chirp matrix when gamma=0.5
function [ mtx ] = generate_matrix_by_signal2fs(signal)
mtx = [];
l = round(length(signal) / 2);
temp1 = signal(1:2:end);
temp2 = circshift(signal(2:2:end), 1);
if length(temp2) ~= length(temp1)
temp2 = [temp2; 0];
end
for i = 1:l
t1 = circshift(temp1, i-1);
t2 = circshift(temp2, i-1);
if i - 1 > 0
t1(1:i - 1,1) = 0;
end
if i - 1 > 0
t2(1:i - 1,1) = 0;
end
mtx = [mtx,t1,t2];
end
end
0 - example/wzk - RDA/get_range_speed_val.m
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function [distance_v, speed_v] = get_range_speed_val(PRF, fs, fc, numP, gamma_r, gamma_d)
% Calculates range and speed values for node index
%
% Usage:
% [distance_v, speed_v] = get_range_speed_val(PRF, fs, fc, numP, gamma_r, gamma_d)
%
% Inputs:
% PRF: Pulse Repetition frequency
% fs: Sampling frequency
% fc: Carrier frequency
% numP: Number of pulses
% gamma_r: Range compression ratio(0.5)
% gamma_d: Doppler compression ratio(0.5)
%
% Outputs:
% distance_v: Real distance value
% speed_v: Real speed value
% parameters
if nargin < 6
gamma_d = 0.5;
end
if nargin < 5
gamma_r = 0.5;
end
c = 3e8;
Tr = 1 / PRF;
lambda = c / fc;
% calculate
distance_v = 0: (c / fs / 2 * gamma_r) : (Tr * c / 2 - c / fs / 2 * gamma_r);
speed_v = -(-PRF / 2: PRF / numP * gamma_d: PRF / 2 - PRF / numP * gamma_d) * lambda / 2 ;
end
0 - example/wzk - RDA/main_CS.m
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clc
clear
close all
%% load echo data
filename = 'Raw_Echo_5dB';
load(['./data/', filename, '.mat']);
%% parameters
% ladar
PRF = 5000;
B = 5e6;
D = 0.1;
Tp = 2e-5;
fs = 5e6;
fc = 1.25e9;
% antenna
num_antenna = 18;
d = 0.12;
% echo
num_pulse = 64;
sigma_n = 0.1;
% detect
P_fa = 1e-6;
% algorithm
gamma_r = 0.5;
gamma_d = 0.5;
lambda_r = 0.005;
lambda_d = 0.15;
% accurate angle
sign_AA = 1;
%% data processing
fprintf('Using CS\n');
fprintf(['File: ', filename, '\n']);
tic;
if sign_AA == 0
[ echo_rd_mtx, target_list_RDA, sigma_n_out ] = ...
echo_processing_CS_v0( Raw_Echo, PRF, fs, fc, B, D, d, sigma_n, P_fa, lambda_r, lambda_d );
else
[ echo_rd_mtx, target_list_RDA, sigma_n_out ] = ...
echo_processing_CS( Raw_Echo, PRF, fs, fc, B, D, d, sigma_n, P_fa, lambda_r, lambda_d );
end
toc;
%% plot
Fontsize = 18;
plot_width = 800;
plot_height = 600;
Linewidth = 2;
Markersize = 8;
figure(1)
scatter3(target_list_RDA(:,1), target_list_RDA(:,2),...
target_list_RDA(:,3), 'filled', 'o')
xlabel('Range(m)');
ylabel('Speed(m/s)');
zlabel('Angle(°)');
zlim([-90, 90]);
ylim([80, 150]);
xlim([17000, 19000]);
set(gca, 'FontSize', Fontsize);
title('node')
set(gcf, 'position', [100, 200, plot_width+100, plot_height+50]);
set(gca,'fontsize',18,'fontname','Times');
%% save
save(['./output/', filename, '_CS_Pfa', num2str(P_fa), '.mat'],...
'target_list_RDA', 'echo_rd_mtx', 'sigma_n_out', 'P_fa');
fprintf(['[', filename, '_CS_Pfa', num2str(P_fa), '.mat]', ' saved.\n\n']);
0 - example/wzk - RDA/main_MF.m
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clc
clear
close all
%% load echo data
filename = 'Raw_Echo_5dB';
load(['./data/', filename, '.mat']);
%% parameters
% ladar
PRF = 5000;
B = 5e6;
D = 0.1;
Tp = 2e-5;
fs = 5e6;
fc = 1.25e9;
% antenna
num_antenna = 18;
d = 0.12;
% echo
num_pulse = 64;
sigma_n = 0.1;
% detect
P_fa = 1e-6;
% algorithm
gamma_r = 0.5;
gamma_d = 0.5;
% accurate angle
sign_AA = 1;
%% data processing
fprintf('Using MF\n');
fprintf(['File: ', filename, '\n']);
tic;
if sign_AA == 0
[ echo_rd_mtx, target_list_RDA, sigma_n_out ] = ...
echo_processing_MF_v0( Raw_Echo, PRF, fs, fc, B, D, d, sigma_n, P_fa );
else
[ echo_rd_mtx, target_list_RDA, sigma_n_out ] = ...
echo_processing_MF( Raw_Echo, PRF, fs, fc, B, D, d, sigma_n, P_fa );
end
toc;
%% plot
Fontsize = 18;
plot_width = 800;
plot_height = 600;
Linewidth = 2;
Markersize = 8;
figure(1)
scatter3(target_list_RDA(:,1), target_list_RDA(:,2),...
target_list_RDA(:,3), 'filled', 'o')
xlabel('Range(m)');
ylabel('Speed(m/s)');
zlabel('Angle(°)');
zlim([-90, 90]);
ylim([80, 150]);
xlim([17000, 19000]);
set(gca, 'FontSize', Fontsize);
title('node')
set(gcf, 'position', [100, 200, plot_width+100, plot_height+50]);
set(gca,'fontsize',18,'fontname','Times');
%% save
save(['./output/', filename, '_MF_Pfa', num2str(P_fa), '.mat'],...
'target_list_RDA', 'echo_rd_mtx', 'sigma_n_out', 'P_fa');
fprintf(['[', filename, '_MF_Pfa', num2str(P_fa), '.mat]', ' saved.\n\n']);
0 - example/wzk - RDA/plot_result.m
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clc
clear
close all
Fontsize = 18;
plot_width = 800;
plot_height = 600;
Linewidth = 2;
Markersize = 8;
Pfa_set = '1e-06';
method = 'CS';
SNR = 5;
filename = ['Raw_Echo_', num2str(SNR), 'dB_', method, '_Pfa', Pfa_set];
load(['./output/', filename, '.mat']);
%%
figure(1)
scatter3(target_list_RDA(:,1), target_list_RDA(:,2),...
target_list_RDA(:,3), 'filled', 'o')
xlabel('Range(m)');
ylabel('Speed(m/s)');
zlabel('Angle(°)');
zlim([-90, 90]);
% ylim([80, 150]);
% xlim([17000, 19000]);
set(gca, 'FontSize', Fontsize);
title('node')
set(gcf, 'position', [100, 200, plot_width+100, plot_height+50]);
set(gca,'fontsize',18,'fontname','Times');
0 - example/wzk - RDA/range_process_CS.m
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function [ echo_r_mtx, sigma_n_o ] = range_process_CS(echo_mtx, A, sigma_n, lambda, delta)
% Range processing for echo data using compressed sensing
%
% Usage:
% [echo_r_mtx, sigma_n_o] = range_process_CS(echo_mtx, A, sigma_n, lambda, delta)
%
% Inputs:
% echo_mtx: Original echo data
% A: Chirp measurement matrix
% sigma_n: Input noise standard deviation
% lambda: LASSO weight
% delta: Convergence normalized difference(2e-7)
%
% Outputs:
% echo_r_mtx: Range processing echo data
% sigma_n_o: Output noise standard deviation
% parameters
if nargin < 5
delta = 2e-7;
end
[M, N] = size(A);
[lenA, M, lenP] = size(echo_mtx);
% normalization
J1 = A*A';
lambda_J=eig(J1);
A = A / sqrt(lambda_J(end));
echo_mtx = echo_mtx ./ sqrt(lambda_J(end));
sigma_n = sigma_n / sqrt(lambda_J(end));
% compressed sensing
echo_r_mtx = zeros(lenA, N, lenP);
sigma_n_o_cnt = zeros(lenA, lenP);
for numA = 1: lenA
parfor numP = 1: lenP
sr = echo_mtx(numA, :, numP);
y = transpose(sr);
% LASSO
x_FISTA = FISTA(y, A, lambda, delta);
% debiased LASSO
[x_d, sigma_w] = cal_debiased_LASSO(x_FISTA, A, y, lambda, sigma_n);
sigma_n_o_cnt(numA, numP) = abs(sigma_w);
echo_r_mtx(numA, :, numP) = x_d;
end
end
% calculate output noise
sigma_n_o = mean(mean(sigma_n_o_cnt));
end
%% sub-functions
% algorithm for LASSO
% y: measurements
% A: measurement matrix
% lambda: LASSO weight
% delta: convergence normalized difference
% z: LASSO estimator
function [z] = FISTA(y, A, lambda, delta)
x_pre = A'*y;
t = 1;
z = x_pre;
z_pre = z;
t_pre = t;
N = size(A, 2);
diff = 1;
E = eig(A'*A);
L = E(end);
temp1 = A'*y/L;
temp2 = eye(N) - A'*A/L;
k = 0;
while((diff > delta) && (k < 1000))
temp = temp1 + temp2 * z_pre;
x = sft_thd(temp, lambda/L);
t = 0.5*(1 + sqrt(1+4*t_pre*t_pre));
z = x + (x - x_pre) * (t_pre-1) / t;
diff = mean(abs(z_pre - z));
x_pre = x;
z_pre = z;
t_pre = t;
k = k + 1;
end
end
% soft threshold function
% x: processing object
% thd: threshold
% y: result
function y = sft_thd(x, thd)
if isequal(size(x), size(thd))
tmp = abs(x);
y = x;
y(tmp <= thd) = 0;
y(tmp > thd) = (tmp(tmp > thd) - thd(tmp > thd)) .* x(tmp > thd) ./ tmp(tmp > thd);
else
tmp = abs(x);
y = x;
y(tmp <= thd) = 0;
y(tmp > thd) = (tmp(tmp > thd) - thd) .* x(tmp > thd) ./ tmp(tmp > thd);
end
end
% calculate debiased LASSO estimator
% x: LASSO estimator
% A: measurement matrix
% y: measurements
% lambda: LASSO weight
% sigma_n: input noise standard deviation
% x_d: debiased LASSO estimator
% sigma_d: equivalent noise standard deviation
function [x_d, sigma_d] = cal_debiased_LASSO(x, A, y, lambda, sigma)
[M, N] = size(A);
gamma = M/N;
hat_Q1 = gamma;
[~, D] = eig(A'*A);
d = diag(D);
diff = 1;
T = 1000;
t = 0;
while (t < T) && (diff > 1e-6)
Q1_pre = hat_Q1;
rho = mean((2 - lambda./(hat_Q1*abs(x) + lambda)).*(abs(x) > 1e-4))/2;
hat_Q1 = rho/mean(1./(d + (1-rho)*hat_Q1/rho));
diff = abs(Q1_pre - hat_Q1);
t = t+1;
end
x_d = x + 1/hat_Q1*A'*(y - A*x);
chi = rho/hat_Q1;
hat_Q2 = 1/chi - hat_Q1;
t = -hat_Q2;
t_prime = -1/mean((1./(d+hat_Q2)).^2);
G_prime = t + 1/chi;
G_wprime = t_prime + 1/chi/chi;
RSS = sum(abs(y - A*x).^2)/M;
hat_chi = gamma*G_wprime/(2*G_prime-2*chi*G_wprime)*RSS +...
(-G_wprime*gamma+G_prime*G_prime)/(2*G_prime-2*chi*G_wprime)*sigma^2;
sigma_d = sqrt(2*hat_chi)/hat_Q1;
end
0 - example/wzk - RDA/range_process_MF.m
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function [ echo_r_mtx, sigma_n_o ] = range_process_MF(echo_mtx, A, sigma_n)
% Range processing for echo data using matching filter
%
% Usage:
% [echo_r_mtx, sigma_n_o] = range_process_MF(echo_mtx, A, sigma_n)
%
% Inputs:
% echo_mtx: Original echo data
% A: Chirp measurement matrix
% sigma_n: Input noise standard deviation
%
% Outputs:
% echo_r_mtx: Range processing echo data
% sigma_n_o: Output noise standard deviation
% parameters
multiple_r = A(:, 1)' * A(:, 1);
[M, N] = size(A);
[lenA, M, lenP] = size(echo_mtx);
% matched filtering
echo_r_mtx = zeros(lenA, N, lenP);
for numA = 1: lenA
for numP = 1: lenP
sr = echo_mtx(numA, :, numP);
mf_res = A' * transpose(sr);
mf_norm = mf_res ./ multiple_r;
echo_r_mtx(numA, :, numP) = mf_norm;
end
end
% calculate output noise
sigma_n_o = sqrt(sigma_n^2 / multiple_r);
end
0 - example/wzk - RDA/rda_detection.m
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function [ target_list_RDA, target_map ] = rda_detection(stat_RD, P_fa)
% Target detection, estimating distance, velocity, and angle intervals
%
% Usage:
% [target_list_RDA, target_map] = rda_detection(stat_RD, P_fa)
%
% Inputs:
% stat_RD: Range-Doppler statistics
% P_fa: Probability of false alarm
%
% Outputs:
% target_list_RDA: Target list include range, doppler and angle information
% target_map: Show targets in RD map
% parameters
[lenA, lenR, lenP] = size(stat_RD);
target_map = zeros(lenR, lenP);
% detection threshold
d_thd = chi2inv(1 - P_fa, 2) / 2;
% find target
target_list_RD = [];
for i = 1: lenA
RD_map = squeeze(stat_RD(i, :, :));
detect_map = zeros(size(RD_map));
detect_map(RD_map > d_thd) = 1;
% target_map(i, :, :) = detect_map;
[r, c] = find(detect_map);
temp_node = [r, c];
target_list_RD = [target_list_RD; temp_node];
end
target_list_RD_new = unique(target_list_RD, 'rows');
% estimate target angle interval
target_list_angle = [];
for i = 1: size(target_list_RD_new, 1)
tgt = target_list_RD_new(i, :);
stat_vct = stat_RD(:, tgt(1), tgt(2));
[v, idx] = max(stat_vct);
target_map(tgt(1), tgt(2)) = idx;
target_list_angle = [target_list_angle; idx];
end
target_list_RDA = [target_list_RD_new, target_list_angle];
end
0 - example/wzk - RDA/spatial_FFT.m
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function [ echo_sFFT_mtx, angle_index ] = spatial_FFT(echo_mtx, d, lambda)
% FFT for echo space domain
%
% Usage:
% [echo_sFFT_mtx, angle_index] = spatial_FFT(echo_mtx, d, lambda)
%
% Inputs:
% echo_mtx: Matrix containing the echo data
% d: Antenna spacing
% lambda: Wave length
%
% Outputs:
% echo_sFFT_mtx: Processed echo matrix
% angle_index: True value of the angle
% parameters
[lenA, lenR, lenP] = size(echo_mtx);
% calculate angle
angle_index = asin(-1 * (-1/2: 1/lenA: 1/2 - 1/lenA) * lambda / d) / pi * 180;
% spatial FFT
echo_mtx = reshape(echo_mtx, [lenA, lenR * lenP]);
echo_sFFT_mtx = zeros(size(echo_mtx));
for i = 1: lenR * lenP
echo_sFFT_mtx(:, i) = fftshift(fft(echo_mtx(:, i))) ./ sqrt(lenA);
end
echo_sFFT_mtx = reshape(echo_sFFT_mtx, [lenA, lenR, lenP]);
end
0 - example/wzk - main_process/angle_est.m
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% echo_r_mtx: range processing echo data
% target_list_RD: target list include range and doppler information
% d: antenna spacing
% fc: carrier frequency
% acc: angle estimation accuracy
% target_list_RDA: target list include range, doppler and angle information
% RA_map: range-angle map
% THETA: scale of angle
function [ target_list_RDA, RA_map, THETA ] = angle_est(echo_r_mtx, target_list_RD, d, fc, acc)
% parameters
if nargin < 5
acc = 181;
end
[lenA, lenR, lenP] = size(echo_r_mtx);
c = 3e8;
lambda = c / fc;
% initialization
echo_mtx = squeeze(echo_r_mtx(:, :, 1));
% CBF
THETA = linspace(-90, 90, round(acc));
RA_map = zeros(length(THETA), lenR);
for i = 1: length(THETA)
a = exp((0: lenA - 1)' * -1j * 2 * pi / lambda * d * sin(THETA(i) / 180 * pi));
RA_map(i, :) = a'* echo_mtx;
end
RA_map = transpose(RA_map);
% calculate angle
range_angle = zeros(1, lenR);
for j = 1: lenR
[v, num] = max(abs(RA_map(j, :)));
range_angle(j) = THETA(num);
end
targets_angle = range_angle(target_list_RD(:, 2));
target_list_RDA = [target_list_RD, transpose(targets_angle)];
end
0 - example/wzk - main_process/doppler_process_CS.m
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% echo_r_mtx: range processing echo data
% sigma_n: input noise standard deviation
% lambda: LASSO weight
% gamma: compressed ratio
% delta: convergence normalized difference
% echo_rd_mtx: range-doppler processing echo data
% stat_RD: range-doppler statistics
function [ echo_rd_mtx, stat_RD ] = doppler_process_CS(echo_r_mtx, sigma_n, lambda, gamma, delta)
% parameters
if nargin < 5
delta = 1e-6;
end
if nargin < 4
gamma = 0.5;
end
[lenA, lenR, M] = size(echo_r_mtx);
N = round(M / gamma);
iter_max_VAMP = 1000;
lambda_v = zeros(N, 1) + lambda;
% generate mtx
F_ori = dftmtx(N);
F = F_ori(1:M,:);
F_inv = conj(F) / N;
% normalization
A = (sqrt(N) * eye(M)) * F_inv;
echo_r_mtx = sqrt(N) .* echo_r_mtx;
sigma_n = sqrt(N) * sigma_n;
% doppler matched filtering
echo_rd_mtx = zeros(lenA, lenR, N);
stat_RD = zeros(lenA, lenR, N);
for numA = 1: lenA
for numR = 1: lenR
sample = squeeze(echo_r_mtx(numA, numR, :));
y = sample;
x_LASSO = cVAMPro(y, A, lambda_v, delta, iter_max_VAMP);
[x_d_CROD, sigma_CROD] = CROD(y, A, x_LASSO, lambda, sigma_n);
stat_RD(numA, numR, :) = abs(fftshift(x_d_CROD) / sigma_CROD).^2;
echo_rd_mtx(numA, numR, :) = fftshift(x_d_CROD);
end
end
end
% algorithm for LASSO
% y: measurements
% A: measurement matrix
% lambda: LASSO weight
% tau: convergence normalized difference
% Kit: maximum number of iterations
% LASSO estimator
function x_hat_wl = cVAMPro(y, A, lambda, tau, Kit)
% Initialization
[M, N] = size(A);
gamma = M / N;
k = 0;
p = ctranspose(A) * y;
h_1 = p;
Q_1 = gamma;
tau_d = 1;
% Iteration
while ((k < Kit) && (tau_d > tau))
% Factorized Part
x_1 = ST(h_1, lambda, Q_1);
chi_1 = F1(x_1, lambda, Q_1);
% Message Passing
h_2 = x_1 / chi_1 - h_1;
Q_2 = 1 / chi_1 - Q_1;
% Gaussian Part
t1 = (p + h_2) / Q_2;
t2 = ctranspose(A) * (A * (p + h_2)) / ((Q_2 + 1) * Q_2);
x_2 = t1 - t2;
chi_2 = gamma / (Q_2 + 1) + (1 - gamma) / Q_2;
% Message Passing
h_1_next = x_2 ./ chi_2 - h_2;
Q_1_next = 1 / chi_2 - Q_2;
tau_d = norm(h_1_next - h_1, Inf) / norm(h_1_next, Inf);
k = k + 1;
% output
x_hat_wl = x_1;
% next
h_1 = h_1_next;
Q_1 = Q_1_next;
end
end
% soft threshold function
% x: processing object
% thd: threshold
% y: result
function x = ST(h_1, lambda, Q_1)
[N, M] = size(h_1);
x = zeros(N, M);
for i = 1:N
sign = h_1(i) ./ abs(h_1(i));
diff = abs(h_1(i)) - lambda(i);
x(i) = sign .* (diff ./ Q_1) .* SF(diff);
end
end
% Heaviside's step function
function v = SF(a)
if a > 0
v = 1;
elseif a == 0
v = 0; % at zero points
else
v = 0;
end
end
% Calculation of chi_1
function chi_1 = F1(x_1, lambda, Q_1)
[N, M] = size(x_1);
count = 0;
for i = 1:N
temp = Q_1 * abs(x_1(i)) + lambda(i);
count = count + (2 - lambda(i) / temp) * SF(abs(x_1(i)));
% count = count + (2-lambda(i)/temp) * (abs(x_1(i)) > 1e-4);
end
chi_1 = count / (2 * N * Q_1);
end
% calculate debiased LASSO estimator
% y: measurements
% A: measurement matrix
% x_LASSO: LASSO estimator
% lambda: LASSO weight
% sigma_n: input noise standard deviation
% x_d_CROD: debiased LASSO estimator
% sigma_CROD: equivalent noise standard deviation estimator
function [ x_d_CROD, sigma_CROD ] = CROD(y, A, x_LASSO, lambda, sigma_n)
[m, n] = size(A);
gamma = m / n;
rho_active = sum(abs(x_LASSO) > 1e-3)/n;
Q_hat = (gamma - rho_active)/(1 - rho_active);
Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./(Q_hat*abs(x_LASSO) + lambda))) / 2 / n;
diff = 1;
while(diff > 1e-4)
Rho_pre = Rho;
Rho = sum((abs(x_LASSO) > 1e-3).* (2 - lambda./((gamma-Rho)/(1-Rho)*abs(x_LASSO) + lambda))) / 2 / n;
diff = abs(Rho - Rho_pre);
end
Q_hat = (gamma-Rho)/(1-Rho);
x_d_CROD = x_LASSO + A'*(y - A*x_LASSO)/Q_hat;
RSS = sum(abs(y - A * x_LASSO).^2)/m;
chi = Rho*(1 - Rho)/(gamma - Rho);
if chi ~= 0
chi_temp = sqrt((chi+1)*(chi+1)-4*gamma*chi);
z = -(1 - chi + chi_temp) / (2*chi);
z_prime = -(1 - 2*gamma*chi + chi + chi_temp) / (2*chi*chi*chi_temp);
G_prime = (z + 1/chi);
G_wprime = (z_prime + 1/chi/chi);
chi_hat = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
else
G_prime = gamma;
G_wprime = gamma*(1-gamma);
chi_hat = gamma/2*G_wprime*RSS/(G_prime - chi*G_wprime)...
+ (G_prime*G_prime/2 - gamma/2*G_wprime)*sigma_n*sigma_n/(G_prime - chi*G_wprime);
end
sigma_CROD = sqrt(2*chi_hat) / Q_hat;
end
0 - example/wzk - main_process/doppler_process_MF.m
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% echo_r_mtx: range processing echo data
% sigma_n: input noise standard deviation
% gamma: compressed ratio
% echo_rd_mtx: range-doppler processing echo data
% stat_RD: range-doppler statistics
function [ echo_rd_mtx, stat_RD ] = doppler_process_MF(echo_r_mtx, sigma_n, gamma)
% parameters
if nargin < 3
gamma = 0.5;
end
[lenA, lenR, M] = size(echo_r_mtx);
N = round(M / gamma);
% generate mtx
F_ori = dftmtx(N);
F = F_ori(1:M,:);
multiple_d = F(:,1)' * F(:,1);
% doppler matched filtering
echo_rd_mtx = zeros(lenA, lenR, N);
for numA = 1: lenA
for numR = 1: lenR
sample = squeeze(echo_r_mtx(numA, numR, :));
dpl_temp = transpose(F) * sample;
dpl_norm = fftshift(dpl_temp ./ multiple_d);
echo_rd_mtx(numA, numR, :) = dpl_norm;
end
end
% calculate output noise
sigma_n_o = sqrt(sigma_n^2 / multiple_d);
stat_RD = abs(echo_rd_mtx ./ sigma_n_o).^2;
end
0 - example/wzk - main_process/draw_target_map.m
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% target_list_RDA: target list, including range, doppler and angle information
% stat_RD: range-doppler statistics
% target_map: show targets information
function [ target_map ] = draw_target_map(target_list_RDA, stat_RD)
% initialization
target_map = ones(size(stat_RD)) .* -300;
t_map = target_list_RDA(:, 1);
t_R = target_list_RDA(:, 2);
t_D = target_list_RDA(:, 3);
t_A = target_list_RDA(:, 4);
% draw_map
for i = 1: size(target_list_RDA, 1)
target_map(t_map(i), t_R(i), t_D(i)) = t_A(i);
end
end
0 - example/wzk - main_process/generate_chirp_mtx.m
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% PRF: pulse repetition frequency
% B: bandwidth
% fs: sampling rate
% D: duty ratio
% gamma: compression ratio
% A: chirp matrix
% signal_t: transmitting beam
function [ A, signal_t ] = generate_chirp_mtx(PRF, B, fs, D, gamma, sign_mid)
% parameters
if nargin < 5
gamma = 0.5;
end
if nargin < 6
sign_mid = 0;
end
Tr = 1 / PRF;
Tp = Tr * D;
K = B / Tp;
% generate_signal
N = Tr * fs;
N_high = Tp * fs;
N_mtx = round(N / gamma);
signal_t = zeros(1, N);
for i = 1: N_high
tp = i * (1 / fs) - sign_mid * N_high / fs / 2;
signal_t(1, i) = exp(1j * 2 * pi * 0.5 * K * tp .^ 2);
end
signal_t_2fs = zeros(1, N_mtx);
for i = 1: round(N_high / gamma)
tp = (i+1) * (1 / fs / 2) - sign_mid * N_high / fs / 2;
signal_t_2fs(1, i) = exp(1j * pi * K * tp .^ 2);
end
% generate chirp matrix
A = generate_matrix_by_signal2fs(transpose(signal_t_2fs));
end
% generate chirp matrix when gamma=0.5
function [ mtx ] = generate_matrix_by_signal2fs(signal)
mtx = [];
l = round(length(signal) / 2);
temp1 = signal(1:2:end);
temp2 = circshift(signal(2:2:end), 1);
if length(temp2) ~= length(temp1)
temp2 = [temp2; 0];
end
for i = 1:l
t1 = circshift(temp1, i-1);
t2 = circshift(temp2, i-1);
if i - 1 > 0
t1(1:i - 1,1) = 0;
end
if i - 1 > 0
t2(1:i - 1,1) = 0;
end
mtx = [mtx,t1,t2];
end
end
0 - example/wzk - main_process/get_range_speed_val.m
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% PRF: pulse repetition frequency
% fs: sampling rate
% fc: carrier frequency
% numP: number of pulses
% gamma_r: range compression ratio
% gamma_d: doppler compression ratio
% distance_v: real distance value
% speed_v: real speed value
function [distance_v, speed_v] = get_range_speed_val(PRF, fs, fc, numP, gamma_r, gamma_d)
% parameters
if nargin < 6
gamma_d = 0.5;
end
if nargin < 5
gamma_r = 0.5;
end
c = 3e8;
Tr = 1 / PRF;
lambda = c / fc;
% calculate
distance_v = 0: (c / fs / 2 * gamma_r) : (Tr * c / 2 - c / fs / 2 * gamma_r);
speed_v = -(-PRF / 2: PRF / numP * gamma_d: PRF / 2 - PRF / numP * gamma_d) * lambda / 2 ;
end
0 - example/wzk - main_process/main_cs_part.m
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clc
clear
close all
%% load echo data
filename = 'Raw_Echo_60dB';
load(['./data/', filename, '.mat']);
%% parameters
% ladar
PRF = 5000;
B = 5e6;
D = 0.1;
Tp = 2e-5;
fs = 5e6;
fc = 1.25e9;
% antenna
num_antenna = 18;
d = 0.12;
% echo
num_pulse = 64;
sigma_n = 0.1;
% detect
P_fa = 1e-5;
% algorithm
gamma_r = 0.5;
gamma_d = 0.5;
lambda_r = 0.005;
lambda_d = 0.15;
%% data processing
fprintf(['File: ', filename, '\n']);
[distance_v, speed_v] = get_range_speed_val(PRF, fs, fc, num_pulse, gamma_r, gamma_d);
[A, signal_t] = generate_chirp_mtx(PRF, B, fs, D);
fprintf(' 1: generate_chirp_mtx done.\n');
% first antenna
Raw_Echo_antenna1 = Raw_Echo(1, :, :);
[echo_r_mtx_cs_antenna1, sigma_n_o_cs_antenna1] = range_process_CS(Raw_Echo_antenna1, A, sigma_n, lambda_r);
fprintf(' 2: first antenna range_process_CS done.\n');
% first pulse
Raw_Echo_pulse1 = Raw_Echo(:, :, 1);
[echo_r_mtx_cs_pulse1, sigma_n_o_cs_pulse1] = range_process_CS(Raw_Echo_pulse1, A, sigma_n, lambda_r);
fprintf(' 3: first pulse range_process_CS done.\n');
[echo_rd_mtx_cs, stat_RD_cs] = doppler_process_CS(echo_r_mtx_cs_antenna1, sigma_n_o_cs_antenna1, lambda_d, gamma_d);
fprintf(' 4: doppler_process_CS done.\n');
[target_list_RD_cs, target_map_cs] = rd_detection(stat_RD_cs, P_fa);
fprintf(' 5: rd_detection done.\n');
[target_list_RDA, RA_map] = angle_est(echo_r_mtx_cs_pulse1, target_list_RD_cs, d, fc);
fprintf(' 6: angle_est done.\n');
%% show result
element = 1;
list_r_idx = find(target_list_RDA(:, 1) == element);
target_list_RDA(:, 2) = distance_v(target_list_RDA(:, 2));
target_list_RDA(:, 3) = speed_v(target_list_RDA(:, 3));
figure(1)
scatter3(target_list_RDA(list_r_idx,2), target_list_RDA(list_r_idx,3),...
target_list_RDA(list_r_idx,4), 'filled', 'o')
% xlim([17000, 19000])
% ylim([80, 160])
% zlim([-90, 90])
%% save
echo_rd_mtx = echo_rd_mtx_cs;
save(['./output/', filename, '_cs_part.mat'],...
'target_list_RDA', 'echo_rd_mtx', 'RA_map', 'P_fa');
0 - example/wzk - main_process/main_mf.m
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clc
clear
close all
%% load echo data
filename = 'Raw_Echo_60dB';
load(['./data/', filename, '.mat']);
%% parameters
% ladar
PRF = 5000;
B = 5e6;
D = 0.1;
Tp = 2e-5;
fs = 5e6;
fc = 1.25e9;
% antenna
num_antenna = 18;
d = 0.12;
% echo
num_pulse = 64;
sigma_n = 0.1;
% detect
P_fa = 1e-4;
% algorithm
gamma_r = 0.5;
gamma_d = 0.5;
%% data processing
[distance_v, speed_v] = get_range_speed_val(PRF, fs, fc, num_pulse, gamma_r, gamma_d);
[A, signal_t] = generate_chirp_mtx(PRF, B, fs, D);
[echo_r_mtx_mf, sigma_n_o_mf] = range_process_MF(Raw_Echo, A, sigma_n);
[echo_rd_mtx_mf, stat_RD_mf] = doppler_process_MF(echo_r_mtx_mf, sigma_n_o_mf, gamma_d);
[target_list_RD_mf, target_map_mf] = rd_detection(stat_RD_mf, P_fa);
[target_list_RDA, RA_map] = angle_est(echo_r_mtx_mf, target_list_RD_mf, d, fc);
%% show result
element = 1;
list_r_idx = find(target_list_RDA(:, 1) == element);
target_list_RDA(:, 2) = distance_v(target_list_RDA(:, 2));
target_list_RDA(:, 3) = speed_v(target_list_RDA(:, 3));
figure(1)
scatter3(target_list_RDA(list_r_idx,2), target_list_RDA(list_r_idx,3),...
target_list_RDA(list_r_idx,4), 'filled', 'o')
% xlim([17000, 19000])
% ylim([80, 160])
% zlim([-90, 90])
%% save
echo_rd_mtx = echo_rd_mtx_mf;
save(['./output/', filename, '_mf.mat'],...
'target_list_RDA', 'echo_rd_mtx', 'RA_map', 'P_fa');
0 - example/wzk - main_process/main_mf_part.m
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clc
clear
close all
%% load echo data
filename = 'Raw_Echo_60dB';
load(['./data/', filename, '.mat']);
%% parameters
% ladar
PRF = 5000;
B = 5e6;
D = 0.1;
Tp = 2e-5;
fs = 5e6;
fc = 1.25e9;
% antenna
num_antenna = 18;
d = 0.12;
% echo
num_pulse = 64;
sigma_n = 0.1;
% detect
P_fa = 1e-4;
% algorithm
gamma_r = 0.5;
gamma_d = 0.5;
%% data processing
[distance_v, speed_v] = get_range_speed_val(PRF, fs, fc, num_pulse, gamma_r, gamma_d);
[A, signal_t] = generate_chirp_mtx(PRF, B, fs, D);
% first antenna
Raw_Echo_antenna1 = Raw_Echo(1, :, :);
[echo_r_mtx_mf_antenna1, sigma_n_o_mf_antenna1] = range_process_MF(Raw_Echo_antenna1, A, sigma_n);
% first pulse
Raw_Echo_pulse1 = Raw_Echo(:, :, 1);
[echo_r_mtx_mf_pulse1, sigma_n_o_mf_pulse1] = range_process_MF(Raw_Echo_pulse1, A, sigma_n);
[echo_rd_mtx_mf, stat_RD_mf] = doppler_process_MF(echo_r_mtx_mf_antenna1, sigma_n_o_mf_antenna1, gamma_d);
[target_list_RD_mf, target_map_mf] = rd_detection(stat_RD_mf, P_fa);
[target_list_RDA, RA_map] = angle_est(echo_r_mtx_mf_pulse1, target_list_RD_mf, d, fc);
%% show result
element = 1;
list_r_idx = find(target_list_RDA(:, 1) == element);
target_list_RDA(:, 2) = distance_v(target_list_RDA(:, 2));
target_list_RDA(:, 3) = speed_v(target_list_RDA(:, 3));
figure(2)
scatter3(target_list_RDA(list_r_idx,2), target_list_RDA(list_r_idx,3),...
target_list_RDA(list_r_idx,4), 'filled', 'o')
% xlim([17000, 19000])
% ylim([80, 160])
% zlim([-90, 90])
%% save
echo_rd_mtx = echo_rd_mtx_mf;
save(['./output/', filename, '_mf_part.mat'],...
'target_list_RDA', 'echo_rd_mtx', 'RA_map', 'P_fa');
0 - example/wzk - main_process/plot_result.m
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clc
clear
close all
Fontsize = 18;
plot_width = 800;
plot_height = 600;
Linewidth = 2;
Markersize = 8;
Pfa_set = '1e-4';
method = 'cs';
if_part = 1;
SNR = 10;
if if_part == 1
filename = ['Raw_Echo_', num2str(SNR), 'dB_', method, '_part'];
else
filename = ['Raw_Echo_', num2str(SNR), 'dB_', method];
end
load(['./output/Pfa', Pfa_set, '/', filename, '.mat']);
%%
element = 1;
list_r_idx = find(target_list_RDA(:, 1) == element);
figure(1)
scatter3(target_list_RDA(list_r_idx,2), target_list_RDA(list_r_idx,3),...
target_list_RDA(list_r_idx,4), 'filled', 'o')
xlabel('Range(m)');
ylabel('Speed(m/s)');
zlabel('Angle(°)');
zlim([-90, 90]);
ylim([80, 160]);
xlim([17000, 21000]);
set(gca, 'FontSize', Fontsize);
title(['Target detected by ', upper(method), ' under Pfa=', Pfa_set])
set(gcf, 'position', [100, 200, plot_width+100, plot_height+50]);
set(gca,'fontsize',18,'fontname','Times');
0 - example/wzk - main_process/range_process_CS.m
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% echo_mtx: echo data
% A: chirp matrix
% sigma_n: input noise standard deviation
% lambda: LASSO weight
% delta: convergence normalized difference
% echo_r_mtx: range processing echo data
% signal_n_o: output noise standard deviation
function [ echo_r_mtx, sigma_n_o ] = range_process_CS(echo_mtx, A, sigma_n, lambda, delta)
% parameters
if nargin < 5
delta = 2e-7;
end
[M, N] = size(A);
[lenA, M, lenP] = size(echo_mtx);
% normalization
J1 = A*A';
lambda_J=eig(J1);
A = A / sqrt(lambda_J(end));
echo_mtx = echo_mtx ./ sqrt(lambda_J(end));
sigma_n = sigma_n / sqrt(lambda_J(end));
% compressed sensing
echo_r_mtx = zeros(lenA, N, lenP);
for numA = 1: lenA
for numP = 1: lenP
sr = echo_mtx(numA, :, numP);
y = transpose(sr);
% LASSO
x_FISTA = FISTA(y, A, lambda, delta);
% debiased LASSO
[x_d, sigma_w] = cal_debiased_LASSO(x_FISTA, A, y, lambda, sigma_n);
echo_r_mtx(numA, :, numP) = x_d;
end
end
% calculate output noise
sigma_n_o = sigma_w;
end
% algorithm for LASSO
% y: measurements
% A: measurement matrix
% lambda: LASSO weight
% delta: convergence normalized difference
% z: LASSO estimator
function [z] = FISTA(y, A, lambda, delta)
x_pre = A'*y;
t = 1;
z = x_pre;
z_pre = z;
t_pre = t;
N = size(A, 2);
diff = 1;
E = eig(A'*A);
L = E(end);
temp1 = A'*y/L;
temp2 = eye(N) - A'*A/L;
k = 0;
while((diff > delta) && (k < 1000))
temp = temp1 + temp2 * z_pre;
x = sft_thd(temp, lambda/L);
t = 0.5*(1 + sqrt(1+4*t_pre*t_pre));
z = x + (x - x_pre) * (t_pre-1) / t;
diff = mean(abs(z_pre - z));
x_pre = x;
z_pre = z;
t_pre = t;
k = k + 1;
end
end
% soft threshold function
% x: processing object
% thd: threshold
% y: result
function y = sft_thd(x, thd)
if isequal(size(x), size(thd))
tmp = abs(x);
y = x;
y(tmp <= thd) = 0;
y(tmp > thd) = (tmp(tmp > thd) - thd(tmp > thd)) .* x(tmp > thd) ./ tmp(tmp > thd);
else
tmp = abs(x);
y = x;
y(tmp <= thd) = 0;
y(tmp > thd) = (tmp(tmp > thd) - thd) .* x(tmp > thd) ./ tmp(tmp > thd);
end
end
% calculate debiased LASSO estimator
% x: LASSO estimator
% A: measurement matrix
% y: measurements
% lambda: LASSO weight
% sigma_n: input noise standard deviation
% x_d: debiased LASSO estimator
% sigma_d: equivalent noise standard deviation
function [x_d, sigma_d] = cal_debiased_LASSO(x, A, y, lambda, sigma)
[M, N] = size(A);
gamma = M/N;
hat_Q1 = gamma;
[~, D] = eig(A'*A);
d = diag(D);
diff = 1;
T = 1000;
t = 0;
while (t < T) && (diff > 1e-6)
Q1_pre = hat_Q1;
rho = mean((2 - lambda./(hat_Q1*abs(x) + lambda)).*(abs(x) > 1e-4))/2;
hat_Q1 = rho/mean(1./(d + (1-rho)*hat_Q1/rho));
diff = abs(Q1_pre - hat_Q1);
t = t+1;
end
x_d = x + 1/hat_Q1*A'*(y - A*x);
chi = rho/hat_Q1;
hat_Q2 = 1/chi - hat_Q1;
t = -hat_Q2;
t_prime = -1/mean((1./(d+hat_Q2)).^2);
G_prime = t + 1/chi;
G_wprime = t_prime + 1/chi/chi;
RSS = sum(abs(y - A*x).^2)/M;
hat_chi = gamma*G_wprime/(2*G_prime-2*chi*G_wprime)*RSS +...
(-G_wprime*gamma+G_prime*G_prime)/(2*G_prime-2*chi*G_wprime)*sigma^2;
sigma_d = sqrt(2*hat_chi)/hat_Q1;
end
0 - example/wzk - main_process/range_process_MF.m
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% echo_mtx: echo data
% A: chirp matrix
% sigma_n: input noise standard deviation
% echo_r_mtx: range processing echo data
% signal_n_o: output noise standard deviation
function [ echo_r_mtx, sigma_n_o ] = range_process_MF(echo_mtx, A, sigma_n)
% parameters
multiple_r = A(:, 1)' * A(:, 1);
[M, N] = size(A);
[lenA, M, lenP] = size(echo_mtx);
% matched filtering
echo_r_mtx = zeros(lenA, N, lenP);
for numA = 1: lenA
for numP = 1: lenP
sr = echo_mtx(numA, :, numP);
mf_res = A' * transpose(sr);
mf_norm = mf_res ./ multiple_r;
echo_r_mtx(numA, :, numP) = mf_norm;
end
end
% calculate output noise
sigma_n_o = sqrt(sigma_n^2 / multiple_r);
end
0 - example/wzk - main_process/rd_detection.m
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% stat_RD: range-doppler statistics
% P_fa: false alarm rate
% target_map: show targets in RD map
% target list include range and doppler information
function [ target_list_RD, target_map ] = rd_detection(stat_RD, P_fa)
% parameters
target_map = zeros(size(stat_RD));
[lenA, lenR, lenP] = size(stat_RD);
% detection threshold
d_thd = chi2inv(1 - P_fa, 2) / 2;
% find target
target_list_RD = [];
for i = 1: lenA
RD_map = squeeze(stat_RD(i, :, :));
detect_map = zeros(size(RD_map));
detect_map(RD_map > d_thd) = 1;
target_map(i, :, :) = detect_map;
[r, c] = find(detect_map);
temp_list = zeros(length(r), 3);
temp_list(:, 1) = i;
temp_list(:, 2) = r;
temp_list(:, 3) = c;
target_list_RD = [target_list_RD; temp_list];
end
end
0 - example/wzk - 目标检测/generate_chirp_mtx.m
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% PRF: pulse repetition frequency
% B: bandwidth
% fs: sampling rate
% D: duty ratio
% gamma: compression ratio
% A: chirp matrix
% signal_t: transmitting beam
function [ A, signal_t ] = generate_chirp_mtx(PRF, B, fs, D, gamma, sign_mid)
% parameters
if nargin < 5
gamma = 0.5;
end
if nargin < 6
sign_mid = 0;
end
Tr = 1 / PRF;
Tp = Tr * D;
K = B / Tp;
% generate_signal
N = Tr * fs;
N_high = Tp * fs;
N_mtx = round(N / gamma);
signal_t = zeros(1, N);
for i = 1: N_high
tp = i * (1 / fs) - sign_mid * N_high / fs / 2;
signal_t(1, i) = exp(1j * 2 * pi * 0.5 * K * tp .^ 2);
end
signal_t_2fs = zeros(1, N_mtx);
for i = 1: round(N_high / gamma)
tp = (i+1) * (1 / fs / 2) - sign_mid * N_high / fs / 2;
signal_t_2fs(1, i) = exp(1j * pi * K * tp .^ 2);
end
% generate chirp matrix
A = generate_matrix_by_signal2fs(transpose(signal_t_2fs));
end
function [ mtx ] = generate_matrix_by_signal2fs(signal)
mtx = [];
l = round(length(signal) / 2);
temp1 = signal(1:2:end);
temp2 = circshift(signal(2:2:end), 1);
if length(temp2) ~= length(temp1)
temp2 = [temp2; 0];
end
for i = 1:l
t1 = circshift(temp1, i-1);
t2 = circshift(temp2, i-1);
if i - 1 > 0
t1(1:i - 1,1) = 0;
end
if i - 1 > 0
t2(1:i - 1,1) = 0;
end
mtx = [mtx,t1,t2];
end
end
0 - example/wzk - 目标检测/node_detect.m
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clc
clear
close all;
SNR = 10;
sigma_n = 0.1;
P_fa = [1e-5, 5e-5, 1e-4, 5e-4, 1e-3, 5e-3, 1e-2, 5e-2, 1e-1, 5e-1, 1];
len_P_fa = length(P_fa);
h0_rep_time = 99 * 1e4;
h1_rep_time = 1e5;
% h0_rep_time = 1000;
% h1_rep_time = 1000;
a = sqrt(10^(SNR/10) * sigma_n^2);
P_fa_node_cnt = zeros(len_P_fa, h0_rep_time);
parfor rep = 1: h0_rep_time
% for rep = 1: h0_rep_time
%% 噪声处理
noise = random('Normal', 0, sigma_n/sqrt(2), 1, 1) + 1j * random('Normal', 0, sigma_n/sqrt(2), 1, 1);
y = noise;
stat = abs(y)^2;
kd = sigma_n^2 * chi2inv(1 - P_fa, 2) / 2;
for cnt_h_th = 1: len_P_fa
P_fa_node_cnt(cnt_h_th, rep) = stat > kd(cnt_h_th);
end
fprintf('Pfa-%d\n', rep);
end
P_fa_node = mean(P_fa_node_cnt, 2);
figure(1)
loglog(P_fa,P_fa_node)
title('Pfa')
P_d_node_cnt = zeros(len_P_fa, h1_rep_time);
parfor rep = 1: h1_rep_time
% for rep = 1: h1_rep_time
%% 噪声处理
noise = random('Normal', 0, sigma_n/sqrt(2), 1, 1) + 1j * random('Normal', 0, sigma_n/sqrt(2), 1, 1);
y = a + noise;
stat = abs(y)^2;
kd = sigma_n^2 * chi2inv(1 - P_fa, 2) / 2;
for cnt_h_th = 1: len_P_fa
P_d_node_cnt(cnt_h_th, rep) = stat > kd(cnt_h_th);
end
fprintf('Pd-%d\n', rep);
end
P_d_node = mean(P_d_node_cnt, 2);
figure(2)
loglog(P_fa,P_d_node)
title('Pd')
figure(3)
loglog(P_fa_node,P_d_node)
title('ROC')
save node_detect.mat ...
SNR...
P_fa...
P_fa_node...
P_d_node...
sigma_n...
h0_rep_time...
h1_rep_time...
a;
0 - example/wzk - 目标检测/node_detect_norm.m
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clc
clear
close all;
SNR = 10;
sigma_n = 0.1;
P_fa = [1e-5, 5e-5, 1e-4, 5e-4, 1e-3, 5e-3, 1e-2, 5e-2, 1e-1, 5e-1, 1];
len_P_fa = length(P_fa);
h0_rep_time = 99 * 1e4;
h1_rep_time = 1e5;
% h0_rep_time = 1000;
% h1_rep_time = 1000;
a = sqrt(10^(SNR/10) * sigma_n^2);
P_fa_node_cnt = zeros(len_P_fa, h0_rep_time);
parfor rep = 1: h0_rep_time
% for rep = 1: h0_rep_time
%% 噪声处理
noise = random('Normal', 0, sigma_n/sqrt(2), 1, 1) + 1j * random('Normal', 0, sigma_n/sqrt(2), 1, 1);
y = noise;
stat = abs(y)^2;
kd = sigma_n^2 * chi2inv(1 - P_fa, 2) / 2;
for cnt_h_th = 1: len_P_fa
P_fa_node_cnt(cnt_h_th, rep) = stat > kd(cnt_h_th);
end
fprintf('Pfa-%d\n', rep);
end
P_fa_node = mean(P_fa_node_cnt, 2);
figure(1)
loglog(P_fa,P_fa_node)
title('Pfa')
P_d_node_cnt = zeros(len_P_fa, h1_rep_time);
parfor rep = 1: h1_rep_time
% for rep = 1: h1_rep_time
%% 噪声处理
noise = random('Normal', 0, sigma_n/sqrt(2), 1, 1) + 1j * random('Normal', 0, sigma_n/sqrt(2), 1, 1);
y = a + noise;
stat = abs(y)^2;
kd = sigma_n^2 * chi2inv(1 - P_fa, 2) / 2;
for cnt_h_th = 1: len_P_fa
P_d_node_cnt(cnt_h_th, rep) = stat > kd(cnt_h_th);
end
fprintf('Pd-%d\n', rep);
end
P_d_node = mean(P_d_node_cnt, 2);
figure(2)
loglog(P_fa,P_d_node)
title('Pd')
figure(3)
loglog(P_fa_node,P_d_node)
title('ROC')
save node_detect.mat ...
SNR...
P_fa...
P_fa_node...
P_d_node...
sigma_n...
h0_rep_time...
h1_rep_time...
a;
0 - example/wzk - 目标检测/plot_node_detect.m
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clear;
close all;
clc;
load node_detect.mat;
Fontsize = 18;
plot_width = 850;
plot_height = 600;
Linewidth = 2;
Markersize = 8;
%% plot
figure(1);
loglog(P_fa, P_fa_node, '-o', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
grid on;
legend('SNR = 10dB');
xlabel('P_{fa} Set');
ylabel('Actual P_{fa}');
ylim([1e-5,1]);
set(gca, 'FontSize', Fontsize);
title('P_{fa}')
set(gcf, 'position', [200, 300, plot_width, plot_height]);
set(gca,'fontsize',20,'fontname','Times');
figure(3);
semilogx(P_fa_node, P_d_node, '-o', ...
'Linewidth', Linewidth, ...
'MarkerSize', Markersize);
grid on;
legend('SNR = 10dB');
xlabel('Actual P_{fa}');
ylabel('P_{d}');
xlim([9.99e-6,1]);
set(gca, 'FontSize', Fontsize);
title('ROC')
set(gcf, 'position', [200, 300, plot_width, plot_height]);
set(gca,'fontsize',20,'fontname','Times');