Add Phase Transitions in FAR using CS folder

Phase Transitions in FAR using CS/Expr3.m

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+% 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 = 10;
+eps = 1e-5;
+
+prob = zeros(max_n, max_k);
+
+rng(1)
+
+Phi_far = zeros(N, N * M);
+
+C = randi([0, M-1], 1, N);
+vecn = 0:N-1;
+xi = 1 + rate .* C;
+
+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
+        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");