Add basic code

FAR vs PD/Analyse_of_Psi.m

@@ -1,42 +0,0 @@
-%% 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);

basic/debiased_LASSO.m

@@ -0,0 +1,31 @@
+function [x_hat, threshold] = debiased_LASSO(A, y_noise, P_fa, noise_sigma_2)
+    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;
+
+    RSS = 1/sz(2) * norm(y_noise - A*x_LASSO, 2) ^ 2;
+    sigma_w_2 = (gamma * (1 - gamma)) / ((gamma - Rho)^2) * RSS + noise_sigma_2;
+    threshold = -sigma_w_2 * log(P_fa);
+    
+end
+

basic/get_Psi.m

@@ -1,11 +1,15 @@
 function Psi = get_Psi(N, M, epi)
     Psi = zeros(N,M*N);
     for n = 0 : N-1
+        col = zeros(1, M*N);
         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);
+                f1 = p/M*Cn;
+                f2 = q/N*n*(1+Cn*epi);
+                col(q*M+p+1) = exp(1j*2*pi*(f1 + f2));
             end
         end
+        Psi(n+1, :) = col;
     end
 end

basic/get_Psi_KR_product.m

@@ -0,0 +1,29 @@
+function Psi = get_Psi_KR_product(N, M, epi)
+    d_n = floor(rand(N, 1)*M) / M;
+    zeta_n = 1 + d_n .* epi; % epi = B / f_c
+
+    R = zeros(N, M);
+    D = zeros(N, N);
+    for n = 0: N-1
+        for m = 0: M-1
+            R(n+1, m+1) = exp(-1j * 2 * pi * m * d_n(n+1));
+        end
+    end
+
+    for n = 0: N-1
+        for l = 0: N-1
+            D(n+1, l+1) = exp(-1j * 2 * pi * l * n * zeta_n(n+1) / N);
+        end
+    end
+
+    Psi = KR_product(R', D')';
+end
+
+function kr = KR_product(F, G)
+    nR_F = size(F, 1);
+    nR_G = size(G, 1);
+    mul = ones(nR_G, 1);
+    FF = kron(F, mul);
+    GG = repmat(G, nR_F, 1);
+    kr = FF .* GG;
+end