From b48ab07dd0429ae06a7d6aec2343c0aacf6a4684 Mon Sep 17 00:00:00 2001 From: Ksyer <> Date: Sat, 11 May 2024 15:43:25 +0800 Subject: [PATCH] Add "FAR vs PD" --- FAR vs PD/Analyse_of_Psi.m | 42 +++++++++++ FAR vs PD/FAR_simu.m | 72 ++++++++++++++++++ FAR vs PD/Main.m | 27 +++++++ FAR vs PD/PD_simu.m | 73 ++++++++++++++++++ FAR vs PD/README.md | 16 ++++ FAR vs PD/cVAMPro.m | 82 +++++++++++++++++++++ FAR vs PD/config.json | 11 +++ FAR vs PD/get_Psi.m | 11 +++ FAR vs PD/get_sparse_vector.m | 13 ++++ FAR vs PD/recovery.m | 53 +++++++++++++ FAR vs PD/result/0_LASSO.jpg | Bin 0 -> 29480 bytes FAR vs PD/result/0_debiased_LASSO.jpg | Bin 0 -> 33293 bytes FAR vs PD/result/0_debiased_LASSO_T.jpg | Bin 0 -> 30659 bytes FAR vs PD/result/1_LASSO.jpg | Bin 0 -> 33398 bytes FAR vs PD/result/1_debiased_LASSO.jpg | Bin 0 -> 33424 bytes FAR vs PD/result/1_debiased_LASSO_T.jpg | Bin 0 -> 27343 bytes FAR vs PD/result/PD_0_debiased_LASSO.jpg | Bin 0 -> 31738 bytes FAR vs PD/result/PD_0_debiased_LASSO_T.jpg | Bin 0 -> 27395 bytes FAR vs PD/result/PD_1_debiased_LASSO.jpg | Bin 0 -> 31243 bytes FAR vs PD/result/PD_1_debiased_LASSO_T.jpg | Bin 0 -> 32578 bytes FAR vs PD/untitled.m | 12 +++ 21 files changed, 412 insertions(+) create mode 100755 FAR vs PD/Analyse_of_Psi.m create mode 100755 FAR vs PD/FAR_simu.m create mode 100755 FAR vs PD/Main.m create mode 100755 FAR vs PD/PD_simu.m create mode 100755 FAR vs PD/README.md create mode 100755 FAR vs PD/cVAMPro.m create mode 100755 FAR vs PD/config.json create mode 100755 FAR vs PD/get_Psi.m create mode 100755 FAR vs PD/get_sparse_vector.m create mode 100755 FAR vs PD/recovery.m create mode 100755 FAR vs PD/result/0_LASSO.jpg create mode 100755 FAR vs PD/result/0_debiased_LASSO.jpg create mode 100755 FAR vs PD/result/0_debiased_LASSO_T.jpg create mode 100755 FAR vs PD/result/1_LASSO.jpg create mode 100755 FAR vs PD/result/1_debiased_LASSO.jpg create mode 100755 FAR vs PD/result/1_debiased_LASSO_T.jpg create mode 100755 FAR vs PD/result/PD_0_debiased_LASSO.jpg create mode 100755 FAR vs PD/result/PD_0_debiased_LASSO_T.jpg create mode 100755 FAR vs PD/result/PD_1_debiased_LASSO.jpg create mode 100755 FAR vs PD/result/PD_1_debiased_LASSO_T.jpg create mode 100755 FAR vs PD/untitled.m diff --git a/FAR vs PD/Analyse_of_Psi.m b/FAR vs PD/Analyse_of_Psi.m new file mode 100755 index 0000000..b821b74 --- /dev/null +++ b/FAR vs PD/Analyse_of_Psi.m @@ -0,0 +1,42 @@ +%% 参数设置 +N = 16; +M = 4; + +A = get_Psi(N, M, 0); + +%% 检查每一行 / 列的二范数 +col_norms = zeros(N, 1); +for i = 1: N + col_norms(i) = norm(A(i, :), 2); +end + +row_norms = zeros(N * M, 1); +for i = 1: N * M + row_norms(i) = norm(A(:, i), 2); +end + +figure(1); + +subplot(211); +plot(1: N, col_norms); +xlabel("Col"); +ylabel("L2 norm of col"); +title("L2 norm of cols"); + +subplot(212); +plot(1: N * M, row_norms); +xlabel("Row"); +ylabel("L2 norm of row"); +title("L2 norm of rows"); + + +%% +AH = conj(A).'; +figure(2); +result = abs(A * AH); +subplot(211); +plot(diag(result)); +subplot(212); +heatmap(result); +a = sum(result(:)) - sum(diag(result)); +fprintf("%f", a); diff --git a/FAR vs PD/FAR_simu.m b/FAR vs PD/FAR_simu.m new file mode 100755 index 0000000..c62a710 --- /dev/null +++ b/FAR vs PD/FAR_simu.m @@ -0,0 +1,72 @@ +function P_fa = FAR_simu(threshold) + global N M epi trail_times + + % Define measurement matrix + A = get_Psi(N, M, epi); + + % Define sparse vector x + [Lambda, x] = get_sparse_vector(N * M, 1); + Lambda_C = setdiff(1:N*M, Lambda); + + % Try "trail_times" times + NN = N; + results = zeros(trail_times, N * M); + + if exist("FAR_recovery_1_LASSO_5.mat") + load("FAR_recovery_0_debiasedLASSO_500.mat", "results"); + else + for T = 1: trail_times + % y = Ax + n + n = randn(NN, 1) * 0.1; + y_noise = A * x + n; + + % x_hat = CS(A, y) + x_hat = recovery(A, y_noise); + results(T, :) = x_hat; + end + end + + % Distribute of H_0 and H_1 + H_0_distribute = zeros(1, length(Lambda_C)); + H_1_distribute = zeros(1, length(Lambda)); + + i1 = 1; + i2 = 1; + Ts = []; + + for t = 1: trail_times + x_hat = results(t, :); + T = 0; + for i = 1: length(x) + if ismember(i, Lambda_C) + H_0_distribute(i1) = x_hat(i); + i1 = i1 + 1; + elseif ismember(i, Lambda) + T = T + abs(x_hat(i)); + H_1_distribute(i2) = x_hat(i); + i2 = i2 + 1; + end + end + Ts = [Ts T]; + end + + + % Draw + figure(1) + subplot(2, 1, 1); + title("Freq histogram of H_0"); + histfit(real(H_0_distribute)); + + subplot(2, 1, 2); + title("Freq histogram of H_1"); + histfit(real(H_1_distribute)); + + H_0_mean = mean(H_0_distribute); + H_0_std = std(H_0_distribute); + H_1_mean = mean(H_1_distribute); + H_1_std = std(H_1_distribute); + + fprintf("H_0: mu = %f, std = %f\n", H_0_mean, H_0_std); + fprintf("H_1: mu = %f, std = %f\n", H_1_mean, H_1_std); + % P_fa = normcdf(threshold, H_0_mean, H_0_std); +end diff --git a/FAR vs PD/Main.m b/FAR vs PD/Main.m new file mode 100755 index 0000000..c58632e --- /dev/null +++ b/FAR vs PD/Main.m @@ -0,0 +1,27 @@ +clear; clc; + +%% 参数设置 +global N M lambda tau iter_max method trail_times epi extend_target K; + +N = 64; +M = 4; +K = 10; +lambda = zeros(M * N, 1); +lambda(:) = 0.3; +tau = 1e-4; +iter_max = 500; +% method = "debiased_LASSO"; +% method = "LASSO"; +method = "BP"; +% method = "VAMP"; +trail_times = 1e2; +epi = 0; +extend_target = 1; + +%% FAR +P_fa_FAR = FAR_simu(3); +% fprintf("FAR: %f\n", P_fa_FAR); + +%% PD +P_fa_PD = PD_simu(1); +fprintf("PD: %f\n", P_fa_PD); diff --git a/FAR vs PD/PD_simu.m b/FAR vs PD/PD_simu.m new file mode 100755 index 0000000..f2a8206 --- /dev/null +++ b/FAR vs PD/PD_simu.m @@ -0,0 +1,73 @@ +function P_fa = PD_simu(threshold) + global N method trail_times + + % Define measurement matrix + B = dftmtx(N); + + % Define sparse vector z + [Lambda, z] = get_sparse_vector(N, 1); + Lambda_C = setdiff(1:N, Lambda); + results = zeros(trail_times, N); + + % Calcuate test statistics + P2 = []; + + if exist("PD_recovery_0_debiasedLASSO_500.mat") + load("PD_recovery_1_debiasedLASSO_500.mat", "results"); + else + for T = 1: trail_times + % y = Bz + n + n = randn(N, 1) * 0.1; + y_noise = n; + + % z_hat = CS(B, y) + z_hat = recovery(B, y_noise); + + % Calculate test statistic + results(T, :) = z_hat; + end + end + + % Distribute of H_0 and H_1 + H_0_distribute = zeros(1, length(Lambda_C)); + H_1_distribute = zeros(1, length(Lambda)); + + i1 = 1; + i2 = 1; + Ts = []; + + for t = 1: trail_times + z_hat = results(t, :); + T = 0; + for i = 1: length(z) + if ismember(i, Lambda_C) + H_0_distribute(i1) = z_hat(i); + i1 = i1 + 1; + elseif ismember(i, Lambda) + T = T + abs(z_hat(i)); + H_1_distribute(i2) = z_hat(i); + i2 = i2 + 1; + end + end + Ts = [Ts T]; + end + + % Draw + figure(2) + subplot(2, 1, 1); + title("Freq histogram of H_0"); + histfit(real(H_0_distribute)); + + subplot(2, 1, 2); + title("Freq histogram of H_1"); + histfit(real(H_1_distribute)); + + H_0_mean = mean(H_0_distribute); + H_0_std = std(H_0_distribute); + H_1_mean = mean(H_1_distribute); + H_1_std = std(H_1_distribute); + + fprintf("H_0: mu = %f, std = %f\n", H_0_mean, H_0_std); + fprintf("H_1: mu = %f, std = %f\n", H_1_mean, H_1_std); + % P_fa = normcdf(threshold, H_0_mean, H_0_std); +end \ No newline at end of file diff --git a/FAR vs PD/README.md b/FAR vs PD/README.md new file mode 100755 index 0000000..6ef6980 --- /dev/null +++ b/FAR vs PD/README.md @@ -0,0 +1,16 @@ +# 频率捷变雷达和单载频雷达的性能对比分析 + +本项目用于分析频率捷变雷达和单载频雷达的性能。 + +频率捷变雷达的观测矩阵满足行正交性质,利用这一性质,可以使用 cVAMPro 算法作为压缩感知恢复算法,通过观测检测出目标。 + +For simplicity, we denote Psi as the measurement matrix for FAR. + +Code structure: + +- Analyze_of_Psi.m: Verify the row orthonormal properity of Psi +- cVAMPro.m: cVAMPro recovery algorithm +- get_Psi.m: Generate Psi. +- FAR_simu.m: Simulate P_fd in FAR. +- PD_simu.m: Simulate P_fd in PD. +- Main.m: The entry of simulation. \ No newline at end of file diff --git a/FAR vs PD/cVAMPro.m b/FAR vs PD/cVAMPro.m new file mode 100755 index 0000000..ee21f8d --- /dev/null +++ b/FAR vs PD/cVAMPro.m @@ -0,0 +1,82 @@ +% Input: y,A,lambda,tau,Kit +% Output: x_hat_wl,x_hat_d + +% Main structure of cVAMP +function [x_hat_wl, x_hat_d] = 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; + x_hat_d = h_1_next / Q_1_next; + % next + h_1 = h_1_next; + Q_1 = Q_1_next; + end + +end + +% SoftThreshold function +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 diff --git a/FAR vs PD/config.json b/FAR vs PD/config.json new file mode 100755 index 0000000..791a969 --- /dev/null +++ b/FAR vs PD/config.json @@ -0,0 +1,11 @@ +{ + "N": 64, + "M": 4, + "K": 10, + "method": "debiased_LASSO", + "trail_times": 5e2, + "extend_target": true, + "debiased_LASSO_params": { + + } +} diff --git a/FAR vs PD/get_Psi.m b/FAR vs PD/get_Psi.m new file mode 100755 index 0000000..3042b5d --- /dev/null +++ b/FAR vs PD/get_Psi.m @@ -0,0 +1,11 @@ +function Psi = get_Psi(N, M, epi) + Psi = zeros(N,M*N); + for n = 0 : N-1 + Cn = floor(rand()*M); + for q = 0 : N-1 + for p = 0:M-1 + Psi(n+1,q*M+p+1) = exp(1i*2*pi*p/M*Cn+1i*2*pi*q/N*n*(1+Cn*epi)) / sqrt(N); + end + end + end +end diff --git a/FAR vs PD/get_sparse_vector.m b/FAR vs PD/get_sparse_vector.m new file mode 100755 index 0000000..a88b9ef --- /dev/null +++ b/FAR vs PD/get_sparse_vector.m @@ -0,0 +1,13 @@ +function [indices, z] = get_sparse_vector(N, Amp) + global K extend_target; + z = zeros(N, 1); + if extend_target + target_start_idx = fix(0.4 * N); + target_size = K; + indices = target_start_idx: target_start_idx + target_size; + else + indices = randperm(N, K); + end + z(indices) = Amp; +end + diff --git a/FAR vs PD/recovery.m b/FAR vs PD/recovery.m new file mode 100755 index 0000000..3132ca0 --- /dev/null +++ b/FAR vs PD/recovery.m @@ -0,0 +1,53 @@ +function x_hat = recovery(A, y_noise) + global method + if method == "debiased_LASSO" + sz = size(A); + N = sz(2); + LASSO_lambda = 2; + + gamma = sz(1) / sz(2); + + cvx_begin quiet + variable x_LASSO(N) complex + minimize(LASSO_lambda * norm(x_LASSO, 1) + norm(y_noise - A * x_LASSO, 2)) + cvx_end + + 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 - LASSO_lambda./(Q_hat*abs(x_LASSO) + LASSO_lambda))) / 2 / N; + diff = 1; + while(diff > 1e-4) + Rho_pre = Rho; + Rho = sum((abs(x_LASSO) > 1e-3).* (2 - LASSO_lambda./((gamma-Rho)/(1-Rho)*abs(x_LASSO) + LASSO_lambda))) / 2 / N; + diff = abs(Rho - Rho_pre); + end + Q_hat = (gamma-Rho)/(1-Rho); + x_d_CROD = x_LASSO + A'*(y_noise - A*x_LASSO)/Q_hat; + x_hat = x_d_CROD; + + elseif method == "LASSO" + sz = size(A); + N = sz(2); + LASSO_lambda = 1; + cvx_begin quiet + variable x_LASSO(N) complex + minimize(LASSO_lambda * norm(x_LASSO, 1) + norm(y_noise - A * x_LASSO, 2)) + cvx_end + + x_hat = x_LASSO; + + elseif method == "BP" + sz = size(A); + N = sz(2); + cvx_begin quiet + variable x_hat(N) complex + minimize(norm(x_hat, 1)) + subject to + A * x_hat == y_noise + cvx_end + else + global lambda tau iter_max; + [x_hat, z_hat_d] = cVAMPro(y_noise, A, lambda, tau, iter_max); + end +end + diff --git a/FAR vs PD/result/0_LASSO.jpg b/FAR vs PD/result/0_LASSO.jpg new file mode 100755 index 0000000000000000000000000000000000000000..0d4eececf3111cf0bb982bf868d976e77bed29d9 GIT binary patch literal 29480 zcmeFZ2Ut_R^rlq6(aS;MS@H0fG&z?SgmX@59oc3RS;2Quc5`wf-*9i%( z0H>%32&oA0EdVRn!P5l)@c{nzAUFly;~8R-v*$>`Uno5foFX73JViwKl!zYsF=9K z4N0jxcjXlnm6TO9wX}6$x_bI%<`$1Ft*mVvot#}<-P}F=UcT}VcpVrN8TB?gCidO? zxRlhi^o-1pS=mL!C8cHM6_r&@%`L5M?Vmfo^z{!64h@ftj?K=^FDx!Ce_vTeZ}05x z?H^zckAC!v03iI&Zh`;*XUBf(7ZupAQ$$3BM8rS(MR3X$JP4_XPG1%}Lw)-Jv8g@H z72y{ov~q7g6gHk^7tuh`J#y$hN6#TT%ZdKcwg2eZU+b9ff2n8xt7HGWUt<6nAptmf 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result(i, j) = F_inv(i,:) * conj(F_inv(j,:))'; + end +end