Update Expr3

Phase Transitions in FAR using CS/Expr3.asv

@@ -1,72 +0,0 @@
-% Expr2.m to draw Fig 3(a)
-clc;
-clear;
-
-M = 4;
-N = 128;
-rate = 0.02; % \Delta f / f_c = 0.02
-beta = 1;
-
-max_n = 125;
-max_k = 25;
-trials_time = 50;
-
-prob = zeros(max_n, max_k);
-
-rng(1)
-
-Phi_far = zeros(N, N * M);
-C = randi([1, M], 1, N);
-xi = 1 + 0.02 * C;
-
-% for i = 1:N
-% 
-%     Phi_x = zeros(N, M);
-% 
-%     for p = 1:M
-% 
-%         for q = 1:N
-%             range = ((p - 1) * C(i)) / M; % p start from 0 or 1?
-%             doppler = ((q - 1) * (i - 1) * xi(i)) / N; % q start from 0 or 1?
-%             Phi_x(q, p) = exp(1j * 2 * pi * (range + doppler)) / sqrt(N);
-%         end
-% 
-%     end
-% 
-%     % t == ctranspose(Phi_x(:,1)) * Phi_x(:,1) == 1
-%     Phi_far(:, (i - 1) * M + 1:i * M) = Phi_x;
-% 
-% end
-
-for i = 1:n
-    for j = 1:m
-        
-
-n = 60;
-k = 5;
-
-s = beta * k * M;
-x = 0;
-
-for t = 1:trials_time
-    x = x + Expr3_can_recovery(Phi_far, N, M, n, s, eps);
-end
-disp(x);
-
-
-for n = 1:max_n
-
-    parfor k = 1:max_k
-        s = beta * k * M;
-        x = 0;
-
-        for t = 1:trials_time
-            x = x + Expr3_can_recovery(Phi_far, N, M, n, s, eps);
-        end
-
-        prob(n, k) = x / trials_time;
-    end
-
-end
-
-save("Expr3.mat", "prob");

Phase Transitions in FAR using CS/Expr3.m

@@ -4,12 +4,12 @@ clear;
 
 M = 4;
 N = 128;
-rate = 0.02; % \Delta f / f_c = 0.02
+epi = 0.02; % \Delta f / f_c = 0.02
 beta = 1;
 
 max_n = 125;
 max_k = 25;
-trials_time = 10;
+trials_time = 5;
 eps = 1e-5;
 
 prob = zeros(max_n, max_k);
@@ -18,33 +18,19 @@ rng(1)
 
 Phi_far = zeros(N, N * M);
 
-C = randi([0, M-1], 1, N);
+for n = 0:N - 1
-vecn = 0:N-1;
+    Cn = floor(rand() * M);
-xi = 1 + rate .* C;
+
+    for q = 0:N - 1
+
+        for p = 0:M - 1
+            Phi_far(n + 1, q * M + p + 1) = exp(1i * 2 * pi * p / M * Cn + 1i * 2 * pi * q / N * n * (1 + Cn * epi));
+        end
 
-for i = 1:N
-    for j = 1:M
-        t = (i-1)*M+j;
-        temp = 1/sqrt(N) .* exp(1j * 2 * pi + (j-1) / M .* C + 1j * 2 * pi * (i-1)/N .* vecn .* xi);
-        Phi_far(:, t) = temp;
     end
-    disp(ctranspose(Phi_far(:,1)) * Phi_far(:,1))
+
 end
 
-
-% n = 60; 0
-n = 70;
-k = 7;
-
-s = beta * k * M;
-x = 0;
-
-for t = 1:trials_time
-    x = x + Expr3_can_recovery(Phi_far, N, M, n, s, eps);
-end
-disp(x);
-
-
 for n = 1:max_n
 
     parfor k = 1:max_k

Phase Transitions in FAR using CS/Expr3_can_recovery.asv

@@ -1,43 +0,0 @@
-function flg = Expr3_can_recovery(Phi_far, N, M, n, s, eps)
-    Phi = zeros(n, N * M);
-    indices = randperm(N, n);
-
-    for i = 1:n
-        Phi(i, :) = Phi_far(indices(i), :);
-    end
-    d = M*N;
-    x = zeros(d, 1);
-    random_indices = randperm(d, s);
-    x(random_indices) = randn(s, 1);
-    x = sign(x);
-
-    for i = 1:M * N
-
-        if x(i) ~= 0
-            t = rand(1) * 2 * pi;
-            x(i) = cos(t) + 1j * sin(t);
-        end
-
-    end
-
-    y = Phi * x;
-
-    cvx_begin quiet
-        variable s1(d) complex
-        minimize(norm(s1, 1))
-        subject to
-        norm(y - Phi * s1) <= eps
-    cvx_end
-
-    x = sign(real(x));
-    s1 = real(s1);
-    p = norm(x - s1, 2);
-    disp(p);
-
-    if p < eps
-        flg = 1;
-    else
-        flg = 0;
-    end
-
-end

Phase Transitions in FAR using CS/Expr3_can_recovery.m

@@ -1,39 +1,25 @@
 function flg = Expr3_can_recovery(Phi_far, N, M, n, s, eps)
-    Phi = zeros(n, N * M);
-    indices = randperm(N, n);
 
-    for i = 1:n
+    % select random n cols
-        Phi(i, :) = Phi_far(indices(i), :);
+    col_choose = randperm(N, n);
-    end
+    Phi = Phi_far(col_choose, :);
-    d = M*N;
-    x = zeros(d, 1);
-    random_indices = randperm(d, s);
-    x(random_indices) = randn(s, 1);
-    x = sign(x);
 
-    for i = 1:M * N
+    % generate sparse signal
+    sparse_signal = zeros(M, N);
+    block = randperm(N, s);
+    sparse_signal(:, block) = exp(1i * 2 * pi * rand(M, s));
 
-        if x(i) ~= 0
+    % generate y
-            t = rand(1) * 2 * pi;
+    y = Phi * sparse_signal(:);
-            x(i) = cos(t) + 1j * sin(t);
-        end
-
-    end
-
-    y = Phi * x;
 
     cvx_begin quiet
-        variable s1(d) complex
+    variable x(M * N) complex
-        minimize(norm(s1, 1))
+    minimize(norm(x, 1))
-        subject to
+    subject to
-        norm(y - Phi * s1) <= eps
+    Phi * x == y
     cvx_end
 
-    x = sign(real(x));
+    p = norm(x - sparse_signal(:), 2);
-    s1 = real(s1);
-    
-    p = norm(x - s1, 2);
-    disp(p);
 
     if p < eps
         flg = 1;