Add Phase Transitions in FAR using CS folder
This commit is contained in:
Ksyer
@@ -0,0 +1,26 @@
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% Expr1.m to draw Fig 2(a)
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max_n = 125;
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max_s = 35;
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trials_time = 50;
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m = 4;
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d = 32;
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eps = 1e-5;
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prob = zeros(max_n, max_s);
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for n = 1:max_n
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parfor s = 1:max_s
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x = 0;
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for t = 1:trials_time
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x = x + Expr1_can_recovery(n, s, m, d, eps);
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end
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prob(n, s) = x / trials_time;
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end
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end
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save("Expr1.mat", "prob");
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Binary file not shown.
@@ -0,0 +1,25 @@
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function flg = Expr1_can_recovery(n, s, m, d, eps)
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theta = randn(n, m * d);
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x = zeros(d, 1);
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random_indices = randperm(d, s);
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x(random_indices) = randn(s, 1);
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x = sign(x);
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y = theta * x;
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cvx_begin
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variable s1(d)
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minimize(norm(s1, 1))
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subject to
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norm(y - theta * s1) <= eps
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cvx_end
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p = norm(x - s1, 2);
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if p < eps
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flg = 1;
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else
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flg = 0;
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end
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end
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@@ -0,0 +1,11 @@
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load 'Expr 1.mat'
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p = rot90(prob, 3);
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imagesc(p)
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set(gca, 'xtick', 1:10:100);
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set(gca, 'xticklabel', {'0', '10', '20', '30', '40', '50', '60', '70', '80', '90', '100'})
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xlabel('Sparsity of signal (s)')
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set(gca, 'ytick', 1:10:100);
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set(gca, 'yticklabel', {'0', '10', '20', '30', '40', '50', '60', '70', '80', '90', '100'})
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ylabel('Number of Mersurements (n)')
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@@ -0,0 +1,25 @@
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% Expr2.m to draw Fig 2(b)
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max_n = 100;
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max_s = 100;
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trials_time = 50;
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d = 100;
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eps = 1e-5;
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prob = zeros(max_n, max_s);
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for n = 1:max_n
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for s = 1:max_s
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x = 0;
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for t = 1:trials_time
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x = x + Expr2_can_recovery(n, s, d, eps);
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end
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prob(n, s) = x / trials_time;
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end
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end
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save("Expr2.mat", "prob");
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@@ -0,0 +1,36 @@
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function flg = Expr2_can_recovery(n, s, d, eps)
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theta_real = randn(n, d);
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theta_imag = randn(n, d);
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theta = theta_real + 1j * theta_imag;
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x = zeros(d, 1);
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random_indices = randperm(d, s);
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x(random_indices) = randn(s, 1);
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for i = 1:d
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if x(i) ~= 0
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t = rand(1);
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x(i) = cos(t) + 1j * sin(t);
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end
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end
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y = theta * x;
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cvx_begin
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variable s1(d)
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minimize(norm(s1, 1))
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subject to
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norm(y - theta * s1) <= eps
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cvx_end
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p = norm(x - s1, 2);
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if p < eps
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flg = 1;
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else
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flg = 0;
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end
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end
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@@ -0,0 +1,72 @@
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% Expr2.m to draw Fig 3(a)
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clc;
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clear;
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M = 4;
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N = 128;
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rate = 0.02; % \Delta f / f_c = 0.02
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beta = 1;
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max_n = 125;
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max_k = 25;
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trials_time = 50;
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prob = zeros(max_n, max_k);
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rng(1)
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Phi_far = zeros(N, N * M);
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C = randi([1, M], 1, N);
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xi = 1 + 0.02 * C;
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% for i = 1:N
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%
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% Phi_x = zeros(N, M);
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%
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% for p = 1:M
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%
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% for q = 1:N
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% range = ((p - 1) * C(i)) / M; % p start from 0 or 1?
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% doppler = ((q - 1) * (i - 1) * xi(i)) / N; % q start from 0 or 1?
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% Phi_x(q, p) = exp(1j * 2 * pi * (range + doppler)) / sqrt(N);
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% end
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%
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% end
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%
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% % t == ctranspose(Phi_x(:,1)) * Phi_x(:,1) == 1
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% Phi_far(:, (i - 1) * M + 1:i * M) = Phi_x;
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%
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% end
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for i = 1:n
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for j = 1:m
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n = 60;
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k = 5;
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s = beta * k * M;
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x = 0;
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for t = 1:trials_time
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x = x + Expr3_can_recovery(Phi_far, N, M, n, s, eps);
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end
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disp(x);
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for n = 1:max_n
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parfor k = 1:max_k
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s = beta * k * M;
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x = 0;
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for t = 1:trials_time
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x = x + Expr3_can_recovery(Phi_far, N, M, n, s, eps);
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end
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prob(n, k) = x / trials_time;
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end
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end
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save("Expr3.mat", "prob");
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@@ -0,0 +1,63 @@
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% Expr2.m to draw Fig 3(a)
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clc;
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clear;
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M = 4;
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N = 128;
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rate = 0.02; % \Delta f / f_c = 0.02
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beta = 1;
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max_n = 125;
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max_k = 25;
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trials_time = 10;
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eps = 1e-5;
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prob = zeros(max_n, max_k);
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rng(1)
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Phi_far = zeros(N, N * M);
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C = randi([0, M-1], 1, N);
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vecn = 0:N-1;
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xi = 1 + rate .* C;
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for i = 1:N
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for j = 1:M
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t = (i-1)*M+j;
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temp = 1/sqrt(N) .* exp(1j * 2 * pi + (j-1) / M .* C + 1j * 2 * pi * (i-1)/N .* vecn .* xi);
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Phi_far(:, t) = temp;
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end
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disp(ctranspose(Phi_far(:,1)) * Phi_far(:,1))
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end
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% n = 60; 0
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n = 70;
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k = 7;
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s = beta * k * M;
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x = 0;
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for t = 1:trials_time
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x = x + Expr3_can_recovery(Phi_far, N, M, n, s, eps);
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end
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disp(x);
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for n = 1:max_n
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parfor k = 1:max_k
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s = beta * k * M;
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x = 0;
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for t = 1:trials_time
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x = x + Expr3_can_recovery(Phi_far, N, M, n, s, eps);
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end
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prob(n, k) = x / trials_time;
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end
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end
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save("Expr3.mat", "prob");
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Binary file not shown.
@@ -0,0 +1,43 @@
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function flg = Expr3_can_recovery(Phi_far, N, M, n, s, eps)
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Phi = zeros(n, N * M);
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indices = randperm(N, n);
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for i = 1:n
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Phi(i, :) = Phi_far(indices(i), :);
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end
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d = M*N;
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x = zeros(d, 1);
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random_indices = randperm(d, s);
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x(random_indices) = randn(s, 1);
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x = sign(x);
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for i = 1:M * N
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if x(i) ~= 0
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t = rand(1) * 2 * pi;
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x(i) = cos(t) + 1j * sin(t);
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end
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end
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y = Phi * x;
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cvx_begin quiet
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variable s1(d) complex
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minimize(norm(s1, 1))
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subject to
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norm(y - Phi * s1) <= eps
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cvx_end
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x = sign(real(x));
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s1 = real(s1);
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p = norm(x - s1, 2);
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disp(p);
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if p < eps
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flg = 1;
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else
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flg = 0;
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end
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end
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@@ -0,0 +1,44 @@
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function flg = Expr3_can_recovery(Phi_far, N, M, n, s, eps)
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Phi = zeros(n, N * M);
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indices = randperm(N, n);
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for i = 1:n
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Phi(i, :) = Phi_far(indices(i), :);
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end
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d = M*N;
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x = zeros(d, 1);
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random_indices = randperm(d, s);
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x(random_indices) = randn(s, 1);
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||||
x = sign(x);
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||||
|
||||
for i = 1:M * N
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||||
|
||||
if x(i) ~= 0
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||||
t = rand(1) * 2 * pi;
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x(i) = cos(t) + 1j * sin(t);
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end
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||||
|
||||
end
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||||
|
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y = Phi * x;
|
||||
|
||||
cvx_begin quiet
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||||
variable s1(d) complex
|
||||
minimize(norm(s1, 1))
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||||
subject to
|
||||
norm(y - Phi * s1) <= eps
|
||||
cvx_end
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||||
|
||||
x = sign(real(x));
|
||||
s1 = real(s1);
|
||||
|
||||
p = norm(x - s1, 2);
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||||
disp(p);
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||||
|
||||
if p < eps
|
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flg = 1;
|
||||
else
|
||||
flg = 0;
|
||||
end
|
||||
|
||||
end
|
||||
Binary file not shown.
@@ -0,0 +1,201 @@
|
||||
Apache License
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Version 2.0, January 2004
|
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http://www.apache.org/licenses/
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END OF TERMS AND CONDITIONS
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APPENDIX: How to apply the Apache License to your work.
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limitations under the License.
|
||||
@@ -0,0 +1,8 @@
|
||||
Codes:
|
||||
|
||||
- `calc_int.m`: Calc integral $f(x) = (x-tau)^2 * sqrt(2/pi) * exp(-x^2/2)$, range: $[tau, +inf]$.
|
||||
- `can_recovery.m`: Determine if the signal can be recovered.
|
||||
- `draw.m`: Draw.
|
||||
- `get_recovery_prob.m`: Obtain the probability that the signal can be recovered under T experiments.
|
||||
- `main.m`: Main function entry.
|
||||
- `phase_transition.m`:
|
||||
@@ -0,0 +1,15 @@
|
||||
function I = calc_integral(tau, m)
|
||||
|
||||
if (~exist('m', 'var'))
|
||||
m = 1;
|
||||
end
|
||||
|
||||
if tau < 0
|
||||
I = 0;
|
||||
else
|
||||
syms x f;
|
||||
f = (x - tau) ^ 2 * exp(-x ^ 2/2) * u ^ (m - 1) / (2 ^ (m / 2 - 1) * gamma(m / 2));
|
||||
I = double(int(f, [tau, +inf]));
|
||||
end
|
||||
|
||||
end
|
||||
@@ -0,0 +1,37 @@
|
||||
% Eq 20
|
||||
tau_min = 0;
|
||||
tau_max = 100;
|
||||
tau_interval = 0.1;
|
||||
tau_range = tau_min:tau_interval:tau_max;
|
||||
|
||||
s_b_min = 1;
|
||||
s_b_max = 100;
|
||||
s_b_range = s_b_min:s_b_max;
|
||||
|
||||
result = zeros(32, 1);
|
||||
|
||||
cache_filename = "I.mat";
|
||||
|
||||
if exist(cache_filename, "file")
|
||||
load(cache_filename);
|
||||
else
|
||||
I = zeros(length(tau_range), 0);
|
||||
|
||||
for tau_idx = 1:length(tau_range)
|
||||
tau = tau_range(tau_idx);
|
||||
I(tau_idx) = calc_integral(tau);
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
for s_b_idx = 1:length(s_b_range)
|
||||
s_b = s_b_range(s_b_idx);
|
||||
f_set = zeros(length(tau_range), 1);
|
||||
|
||||
for tau_idx = 1:length(tau_range)
|
||||
tau = tau_range(tau_idx);
|
||||
f_set(tau_idx) = s_b * (1 + tau ^ 2) + (100 - s_b) * I(tau_idx);
|
||||
end
|
||||
|
||||
result(s_b_idx) = min(f_set);
|
||||
end
|
||||
Reference in New Issue
Block a user