323 lines
8.5 KiB
Matlab
323 lines
8.5 KiB
Matlab
clc
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clear
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close all;
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%% 蜿よ焚隶ｾ鄂ｮ
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B = 5e6; % 菫｡蜿ｷ蟶ｦ�??5MHz
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Tp = 20e-6; % 閼牙??100us
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fs = 2 * B; % 驥��ｷ鬚醍紫
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Ts = 1 / fs; % 驥��ｷ蜻ｨ譛�
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K = B / Tp; % 郤ｿ諤ｧ隹�｢醍紫
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fc = 1.25e9; % 霓ｽ豕｢鬚醍紫1.25GHz
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PRF = 5000; % 閼牙�驥榊?埼?醍紫
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Tr = 1 / PRF; % 閼牙�驥榊?埼龍髫?
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numP = 64; % 閼牙�謨ｰ驥�
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t = 0: 1 / fs: Tr - 1 / fs;
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tP = 0: 1 / fs: Tr * numP - 1 / fs;
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c = 3e8; % 蜈蛾?
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slow_len = 128;
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%%
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sigma_n = 0.1;
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alpha_prop = 0.8;
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% SNR = -30;
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SNR = [-5,0,5,8,10,12,15,20,25];
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len_SNR = length(SNR);
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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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rep_time = 200;
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% rou >= c / 2B = 15(m)
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%%
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delta_VAMP = 1e-6;
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iter_max = 1000;
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lambda_val = 0.05;
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lambda = zeros(slow_len,1) + lambda_val;
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%% 莠ｧ逕溷書蟆�ｿ｡蜿ｷ
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N = Tr * fs;
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N_high = Tp * fs;
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signal_t = zeros(1, N * numP);
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for j = 1: numP
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for i = 1: N_high
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tp = ((j - 1) * N + i) * (1 / fs);
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signal_t(1, i + (j-1)*N) = exp(1j * 2 * pi * (fc * tp + 0.5 * K * tp .^ 2));
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end
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end
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multiple_r = signal_t(1, 1: N) * signal_t(1, 1: N)';
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% figure(1);
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% subplot(311)
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% plot(tP,real(signal_t));
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% xlabel('譌ｶ髣ｴ/t');ylabel('蟷�ｺｦ');
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% title('蜿大ｰ�ｿ｡蜿ｷ');
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%% 隶ｾ鄂ｮ逶?譬? 1
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distance1 = 18000;
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v1 = 187.5;
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tau1 = distance1 * 2 / c;
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n_tau1 = round(tau1 * fs);
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f_d1 = 2 * fc * v1 / c;
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alpha1 = alpha_prop;
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% alpha1 = 0;
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signal_r1 = zeros(1, N * numP);
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for j = 1: numP
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for i = 1: N
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temp = i - n_tau1;
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if temp >= 1 && temp <= N_high
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tp = ((j - 1) * N + i - n_tau1) * (1 / fs);
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signal_r1(1, i + (j-1)*N) = alpha1 * exp(1j*2*pi*((fc - f_d1) * tp + 0.5 * K * tp .^ 2));
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end
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end
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end
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%% 逕滓�蝗樊ｳ｢
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signal_r = signal_r1;
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% figure(1);
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% subplot(312)
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% plot(tP, real(signal_r));
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% xlabel('譌ｶ髣ｴ/t');
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% ylabel('蟷�ｺｦ');
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% title('蝗樊ｳ｢菫｡蜿ｷ');
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%%
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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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F_ori = dftmtx(slow_len);
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F = F_ori(1:numP,:);
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multiple_d = F(:,1)' * F(:,1);
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F_inv = conj(F)/slow_len;
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A = (sqrt(slow_len) * eye(numP)) * F_inv;
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n = slow_len;
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m = numP;
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gamma = numP / slow_len;
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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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%% 蝎?螢ｰ�?�炊
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noise = random('Normal', 0, sigma_n/sqrt(2), 1, N * numP) + 1j * random('Normal', 0, sigma_n/sqrt(2), 1, N * numP);
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alpha_SNR = sqrt(10^(SNR(cnt_SNR)/10) * sigma_n^2 / (multiple_r * multiple_d));
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signal_r_n = signal_r * alpha_SNR + noise;
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% figure(1);
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% subplot(313)
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% plot(tP, real(signal_r_n));
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% xlabel('譌ｶ髣ｴ/t');
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% ylabel('蟷�ｺｦ');
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% title('蝗樊ｳ｢+蝎?螢ｰ菫｡蜿?');
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%% 蛹ｹ驟肴ｻ､豕｢窶披疲潔Tr蛻貞�
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Srange = zeros(N, numP);
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% A = generate_matrix(transpose(signal_t(1, 1: N)), 1);
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count_fa=0;
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for i = 1: numP
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sr = signal_r_n(1, 1 + (i - 1) * N: i * N);
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st = signal_t(1, 1 + (i - 1) * N: i * N);
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% A = generate_matrix(transpose(st), 1);
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% mf = A' * transpose(sr);
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% filterred_rf_r = mf ./ multiple_r;
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% 蛹ｹ驟肴ｻ､豕｢
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rf_r_fft_conj = conj(fft(st));
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filterred_rf_r = ifft(fft(sr) .* rf_r_fft_conj);
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filterred_rf_r = filterred_rf_r ./ multiple_r;
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Srange(:,i) = filterred_rf_r';
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end
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% figure(101)
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% mesh(abs(Srange))
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% title('謖欝r霑幄?悟源驟肴ｻ､豕｢扈捺�?')
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%% R蛹ｹ驟肴ｻ､豕｢窶披泌�蟶�ｪ瑚ｯ?
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% Before MF
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% a+bi
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% a~N(0,sigma_n^2 / 2)
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% b~N(0,sigma_n^2 / 2)
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% After MF
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% a+bi
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% a~N(0,sigma_n^2 / 2 / multiple_r)
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% b~N(0,sigma_n^2 / 2 / multiple_r)
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% a^2 + b^2 ~ chi^2(2) * sigma_n^2 / 2 / multiple_r
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% stat_R = abs(Srange).^2;
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% P_fa = 0.1;
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% kd = sigma_n^2 * chi2inv(1 - P_fa, 2) / 2 / multiple;
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% sum(sum(stat_R>kd))/numel(stat_R)
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%% 螟壽勸蜍呈ｻ､豕?
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Srd = zeros(N, slow_len);
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count_Pfa_d = zeros(length(P_fa), N);
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count_Pd_d = zeros(length(P_fa), 1);
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target_node_d = round(v1 / (c / fc * PRF / 2 / slow_len)) + 1;
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target_node_r = n_tau1 + 1;
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% for i = 1: N
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for i = target_node_r-N_high: target_node_r+N_high
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x_slow = Srange(i, :);
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y = (sqrt(slow_len) * eye(numP)) * transpose(x_slow);
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[x_LASSO,y_d] = cVAMPro(y,A,lambda,delta_VAMP,iter_max);
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% CROD豎ょ悉蛛?
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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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% CROD豎る葎髯仙柱譽鬪檎ｻ溯ｮ｡驥�
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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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sigma_CROD = sigma_CROD*0.895;
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stat_CROD = abs(x_d_CROD / sigma_CROD).^2;
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h_thd = chi2inv(1 - P_fa, 2) / 2;
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% 譽豬?
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for j = 1:length(P_fa)
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if i ~= target_node_r
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count_Pfa_d(j,i) = sum(stat_CROD > h_thd(j)) / slow_len;
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else
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stat_index = ones(size(stat_CROD));
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stat_index(target_node_d) = 0;
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count_Pfa_d(j,i) = sum(stat_CROD(stat_index > 0) > h_thd(j)) / sum(stat_index);
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count_Pd_d(j) = stat_CROD(target_node_d) > h_thd(j);
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end
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end
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Srd(i, :) = fftshift(transpose(x_d_CROD ./ multiple_d ./ 2));
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end
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target_near_count = count_Pfa_d(:,target_node_r-N_high: target_node_r+N_high);
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% P_fa_actual = mean(count_Pfa_d,2);
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P_fa_actual = mean(target_near_count,2);
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for cnt_h_th = 1: len_P_fa
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P_fa_CROD_cnt(cnt_SNR, cnt_h_th, rep) = P_fa_actual(cnt_h_th);
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P_d_CROD_cnt(cnt_SNR, cnt_h_th, rep) = count_Pd_d(cnt_h_th);
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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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%% 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_MF(2,:), 'linewidth', 2);
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% loglog(P_fa,P_fa_MF(3,:), 'linewidth', 2);
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% loglog(P_fa,P_fa_MF(4,:), 'linewidth', 2);
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% loglog(P_fa,P_fa_MF(5,:), 'linewidth', 2);
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% loglog(P_fa,P_fa_MF(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('Actual P_fa');
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figure(2);
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semilogx(P_fa,P_d_CROD(1,:), 'linewidth', 2);
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% hold on;
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% grid on;
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% semilogx(P_fa,P_d_MF(2,:), 'linewidth', 2);
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% semilogx(P_fa,P_d_MF(3,:), 'linewidth', 2);
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% semilogx(P_fa,P_d_MF(4,:), 'linewidth', 2);
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% semilogx(P_fa,P_d_MF(5,:), 'linewidth', 2);
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% semilogx(P_fa,P_d_MF(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_d');
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% save test_Rmf_Dmf.mat ...
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% distance_temp...
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% speed_temp...
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% Srd...
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% Srange...
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% tP...
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% signal_t...
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% signal_r...
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% signal_r_n...
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% F...
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% slow_len;
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save test_MC_Pfa_Rmf_Dcs.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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sigma_n...
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B...
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Tp...
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fs...
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Ts...
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K...
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fc...
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PRF...
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Tr...
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numP...
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t...
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tP...
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slow_len; |