Add Example

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
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+p_i
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