176 lines
3.4 KiB
Matlab
176 lines
3.4 KiB
Matlab
clc;
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clear;
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%close all;
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%% 参数设置
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sigma_n = 0.1;
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gamma = 0.5;
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% 信号参数
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B = 5e5; %信号带宽
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Tp = 100e-6; %脉宽100us
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fs = 2 * B; %采样频率
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Ts = 1 / fs; %采样周期
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K = B / Tp; %线性调频率
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fc = 1e8; %载波频率
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Tr = 1e-3;
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t = 0: 1/fs: Tr - 1/fs;
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t2 = 0: 1/fs/2: Tr - 1/fs/2;
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c = 3e8; % 光速
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distance_max = (Tr-Tp) * c / 2;
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target_scattering = [0.8, 1, 0.9]; %扩展目标各点散射强度
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%% 生成矩阵 A
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% 生成发射信号 signal_t 及
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N = Tr * fs;
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N_high = Tp * fs;
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signal_t = zeros(1, N);
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signal_td = 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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tp2 = (i - 0.5) * (1 / fs);
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signal_td(1, i + 1) = exp(1j*2*pi*(fc*tp2+0.5*K*tp2.^2));
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end
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A = generate_matrix_new(signal_t.', signal_td.');
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temp = 0;
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for i = 1: size(A, 1)
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for j = 1: size(A, 2)
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temp = temp + abs(A(mod(i, size(A, 1))+1, mod(j+1, size(A, 2))+1) - A(i, j));
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end
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end
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%% 生成回波 y
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% 设置目标 - 扩展目标，由三个点组成
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distance1 = 52000;
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tau1 = distance1 * 2 / c;
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n_tau1 = round(tau1 * fs);
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alpha1 = 0.6; % 扩展目标整体散射强度
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signal_r1_t1 = zeros(1, N);
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signal_r2_t1 = zeros(1, N);
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signal_r3_t1 = 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_t1(1, i) = alpha1 * target_scattering(1) * signal_t(1, temp);
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if i + 1 <= N
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signal_r2_t1(1, i + 1) = alpha1 * target_scattering(2) * signal_t(1, temp);
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end
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if i + 1 <= N
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signal_r3_t1(1, i + 2) = alpha1 * target_scattering(3) * signal_t(1, temp);
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end
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end
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end
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signal_r1 = signal_r1_t1 + signal_r2_t1 + signal_r3_t1;
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% 回波
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signal_r = signal_r1;
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% 加入噪声
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noise = random('Normal', 0, sigma_n/sqrt(2), 1, length(signal_r)) + 1j * random('Normal', 0, sigma_n/sqrt(2), 1, length(signal_r));
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signal_r_n = signal_r + noise;
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y = signal_r_n.';
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%% 理论 x
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distance_node = round((distance1 * 2 / c) * fs);
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x_t = zeros(1, 2 * N);
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for i = 1: length(target_scattering)
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x_t((distance_node + i) * 2 - 1) = alpha1 * target_scattering(i);
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end
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x = x_t.';
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%% Experiment
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%% Parameters setting
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lambda = 0.002;
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alpha = 1/4;
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delta = 1e-8*alpha;
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iter_max = round(2000/alpha);
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n = size(A, 2);
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% J = A'*A;
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J1 = A*A';
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lambda_J=eig(J1);
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% histogram(lambda_J, 100);
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%% Normalized
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A = A / sqrt(lambda_J(end));
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y = y / sqrt(lambda_J(end));
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sigma_n = sigma_n / sqrt(lambda_J(end));
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%% cVAMP
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tic;
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[x_VAMP, x_d, hat_Q1, sigma_d, ifcvg] = cVAMPa_dampling(y, A, lambda, alpha, delta, iter_max, sigma_n);
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toc;
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%% cvx
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tic;
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cvx_begin quiet
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variable x_cvx(n, 1) complex
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z = lambda*sum(abs(x_cvx)) + 0.5*sum(pow_abs((y - A * x_cvx), 2));
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minimize(z)
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cvx_end
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[x_d_cal, hat_Q1_cal, sigma_d_cal] = cal_debiased_LASSO(x_cvx, A, y, lambda, sigma_n);
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toc;
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sigma_ex = std(x_d_cal - x, 1);
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tmp = (x_d_cal - x)/sigma_ex;
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[h_r, p_r, k_r, c_r] = kstest(real(tmp)*sqrt(2));
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[h_i, p_i, k_i, c_i] = kstest(imag(tmp)*sqrt(2));
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%% results
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% whether cVAMP algorithm converges
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ifcvg
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% whether the output of cVAMP converges to the LASSO solution
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sum(abs(x_cvx - x_VAMP))
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% check the results from cVAMP and "calculation"
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abs(hat_Q1 - hat_Q1_cal)
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abs(sigma_d - sigma_d_cal)
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sum(abs(x_d - x_d_cal))
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% accuracy of estimating the variance
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abs(sigma_d_cal - sigma_ex)/abs(sigma_ex)
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% p-value of KS-test
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% the larger, the higher probability it is drawn from Gaussian distribution
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p_r
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p_i
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