380 lines
9.4 KiB
Matlab
380 lines
9.4 KiB
Matlab
clc
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clear
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% rng(1)
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%% 参数设置
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B = 5e6; % 信号带宽5MHz
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Tp = 20e-6; % 脉宽100us
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fs = 2 * B; % 采样频率
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Ts = 1 / fs; % 采样周期
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K = B / Tp; % 线性调频率
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fc = 1.25e9; % 载波频率1.25GHz
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PRF = 5000; % 脉冲重复频率
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Tr = 1 / PRF; % 脉冲重复间隔
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numP = 64; % 脉冲数量
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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; % 光速
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%%
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sigma_n = 0.1; % 噪声标准差
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alpha_prop = 0.8; % 目标散射点强度
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SNR = 50; % 信噪比（积累后信噪比）
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% rou >= c / 2B = 15(m)
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slow_len = 128; % 多普勒维采样点
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% 是否有目标，0无目标，1有目标
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has_target = 0;
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%% 产生发射信号
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% t=-Tp/2:1/fs:Tp/2-1/fs;
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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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% signal_t = zeros(1, N);
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% for i = 1:N_high
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% tp = (i - 1) * (1 / fs);
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% signal_t(1, i) = exp(1j*2*pi*(fc*tp+0.5*K*tp.^2));
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% end
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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('时间/t');ylabel('幅度');
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title('发射信号');
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%%
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% 距离匹配滤波增益
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multiple_r = signal_t(1, 1: N) * signal_t(1, 1: N)';
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% 多普勒匹配滤波增益
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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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%% 设置目标 1
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distance1 = 18000;
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v1 = 187.5;
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tau1 = distance1 * 2 / c; % 时延
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n_tau1 = round(tau1 * fs); % 对应采样点
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f_d1 = 2 * fc * v1 / c; % 多普勒频率
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% 根据 SNR 设置回波散射强度
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if has_target
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alpha1 = alpha_prop * sqrt(10^(SNR/10) * sigma_n^2 / (multiple_r * multiple_d));
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else
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alpha1 = 0;
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end
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% 生成目标 1 回波
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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 = (temp - 1) * (1 / fs);
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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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% signal_r1 = zeros(1, N);
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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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% signal_r1(1, i) = alpha1 * signal_t(1, temp);
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% end
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% end
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%% 生成回波
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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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% plot(real(signal_r));
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xlabel('时间/t');
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ylabel('幅度');
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title('回波信号');
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%% 噪声处理
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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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signal_r_n = signal_r + 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('时间/t');
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ylabel('幅度');
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title('回波+噪声信号');
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%% 对回波求多普勒频移
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% s_R_slow = zeros(1, slow_len);
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%
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% slow_freqs = ((0:slow_len - 1) .* (1 / Tr)) / slow_len;
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%
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% init_idx = 1;
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% while abs(signal_r_n(init_idx)) == 0
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% init_idx = init_idx + 1;
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% end
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%
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% for i = 0:numP - 1
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% s_R_slow(i + 1) = signal_r_n(init_idx + i * N + 1);
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% end
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%
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% s_R_fft = fftshift(fft(s_R_slow));
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% figure(3)
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% plot(real(s_R_fft))
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% [~, max_index_s_R] = max(s_R_fft);
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% freq_s_R = slow_freqs(max_index_s_R);
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%
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% f_d = 1 / Tr - freq_s_R;
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% v = f_d * c / (2 * (fc - B / 2))
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%% 距离匹配滤波——按Tr划分
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Srange = zeros(N, numP);
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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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% % 匹配滤波
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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;
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% 匹配滤波
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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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% figure(2000)
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% plot(abs(filterred_rf_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('按Tr进行匹配滤波结果')
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%% R匹配滤波——分布验证
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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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%% 多普勒滤波
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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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% ttttttt = F_inv * transpose(F);
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% VAMP参数
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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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% 放大到行正交
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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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% 设定虚警率
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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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count_Pfa_d = zeros(size(length(P_fa), N));
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Srd = zeros(N, slow_len);
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for i = 1: N
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% for i = 1201: 1201
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x_slow = Srange(i, :); % 慢时间采样
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y = (sqrt(slow_len) * eye(numP)) * transpose(x_slow); % 进行相应放大
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% LASSO 求解
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% x_LASSO = FISTA(y, A, lambda_val, delta_VAMP);
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[x_LASSO,y_d] = cVAMPro(y,A,lambda,delta_VAMP,iter_max);
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% x_LASSO = x_LASSO ./ multiple_d ./ 2;
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% CROD求去偏
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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求门限和检验统计量
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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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% 【经验分布、待解决】
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sigma_CROD = sigma_CROD*0.895;
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stat_CROD = abs(x_d_CROD / sigma_CROD).^2; % 统计量
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h_thd = chi2inv(1 - P_fa, 2) / 2; % 门限
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% 检测
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% 目标点位
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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 j = 1:length(P_fa)
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if i ~= target_node_r % 非目标点的距离慢采样结果（H0假设）
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count_Pfa_d(j,i) = sum(stat_CROD > h_thd(j)) / slow_len;
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else % 要考虑目标点的距离慢采样结果
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stat_index = ones(size(stat_CROD));
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stat_index(target_node_d) = 0; % 去掉目标点（H0假设不考虑目标点）
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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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end
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end
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% if i ~= target_node_r
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% count_Pfa_d(i) = sum(stat_CROD > h_thd) / 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(i) = sum(stat_CROD(stat_index > 0) > h_thd) / sum(stat_index);
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% end
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% count_Pfa_d(i)
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% figure(444)
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% % 归一化
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% plot(abs(x_d_CROD ./ multiple_d ./ 2))
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% figure(555)
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% % 统计量
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% plot(stat_CROD)
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Srd(i, :) = fftshift(transpose(x_d_CROD ./ multiple_d ./ 2));
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end
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%% DCS——分布验证
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output = mean(count_Pfa_d,2); % 把所有多普勒维检测结果求平均得到总体虚警率
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figure(4000)
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loglog(P_fa,output)
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xlabel('P_fa Set')
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ylabel('Actual P_fa')
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title('P_fa')
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%%
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% Srd_bf_mf = zeros(N, slow_len);
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% for i = 1: N
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% Srd_bf_mf(i, :) = fftshift(fft([Srange_bf_mf(i, :),zeros(1,slow_len-numP)]));
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% end
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% figure(102)
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% mesh(abs(Srd))
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% figure(105)
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% mesh(abs(Srd_bf_mf))
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% figure(1)
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% subplot(414)
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% t2 = 0: (c / fs / 2) : (Tr * numP * c / 2 - c / fs / 2);
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% plot(tP, abs(filterred_rf_r) ./ N_high)
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% % plot(abs(filterred_rf_r))
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% xlabel('距离')
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% title('匹配滤波')
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% distance_temp = (0:N - 1) * fs * c / N / 2 / K;
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%% RD 绘制
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Srd = Srd';
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lambda = c / fc;
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% 40*lambda*PRF/2/128
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distance_temp = 0: (c / fs / 2) : (Tr * c / 2 - c / fs / 2);
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speed_temp = (-PRF / 2: PRF / slow_len: PRF / 2 - PRF / slow_len) * lambda / 2 ;
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% speed_temp = (-numP / 2: numP / slow_len: numP / 2 - numP / slow_len) * lambda / Tr / numP / 2 ;
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figure(5)
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[X, Y] = meshgrid(distance_temp, speed_temp);
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mesh(X, Y, abs(Srd));
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xlabel('距离(m)');
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ylabel('速度(m/s)');
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zlabel('信号幅值');
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title('2维RD图');
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figure(6)
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imagesc(distance_temp, speed_temp, abs(Srd));
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title('Range-Doppler Image');
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xlabel('Range (m)');
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ylabel('Speed (m/s)');
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set(gca, 'FontSize', 18);
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set(gcf, 'position', [200, 300, 800, 600]);
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set(gca,'fontsize',20,'fontname','Times');
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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; |