Add lyh-非满秩相变

2024-11-11 16:33:48 +08:00
parent e6a19b477e
commit e0b910b56d
52 changed files with 208020 additions and 0 deletions
@@ -0,0 +1,229 @@
+close all;
+clear all;
+clc;
+M = 4;
+N = 128;
+%block_sparsity = 1;
+tol = 1e-5;
+trial = 50;
+epi = 0.02;
+result = zeros(N,25);
+for col = 4:4:128
+    for block_sparsity = 10:18
+        success_count = 0;
+        for loop = 1:trial
+            FAR_model = zeros(N,M*N);
+            %Cn = randperm(M)-1
+            for n = 0 : N-1
+                Cn = floor(rand()*M);
+                for q = 0 : N-1
+                    for p = 0:M-1
+                        FAR_model(n+1,q*M+p+1) = exp(1i*2*pi*p/M*Cn+1i*2*pi*q/N*n*(1+Cn*epi));
+                    end
+                end
+            end
+            col_choose = randperm(N,col);
+            FAR_model = FAR_model(col_choose,:);
+            sparse_signal = zeros(M,N);
+            block = randperm(N,block_sparsity);
+            sparse_signal(:,block) = exp(1i*2*pi*rand(M,block_sparsity));
+            y = FAR_model * sparse_signal(:);
+            cvx_begin
+            variable x(M,N) complex
+            norm21 = 0;
+            for i = 1:N
+                norm21 = norm21 + norm(x(:,i));
+            end
+            minimize(norm21)
+            subject to
+            FAR_model * x(:) == y
+            cvx_end
+            if norm(x(:)-sparse_signal(:))<tol
+                success_count = success_count+1;
+            end
+        end
+        result(col,block_sparsity) = success_count/trial;
+    end
+end
+%save('FARblockepsilon2.mat');
+
+%%
+close all;
+clear all;
+clc;
+M = 4;
+N = 128;
+%block_sparsity = 1;
+tol = 1e-5;
+trial = 30;
+epi = 0.02;
+result = zeros(1,25);
+col = 128;
+Prob = [1/3,1/3,1/6,1/6];
+for block_sparsity = 4:18
+    success_count = 0;
+    for loop = 1:trial
+        FAR_model = zeros(N,M*N);
+        %Cn = randperm(M)-1
+        for n = 0 : N-1
+            Cn = randsrc(1,1,[[0,1,2,3];Prob]);
+            for q = 0 : N-1
+                for p = 0:M-1
+                    FAR_model(n+1,q*M+p+1) = exp(1i*2*pi*p/M*Cn+1i*2*pi*q/N*n*(1+Cn*epi));
+                end
+            end
+        end
+        %col_choose = randperm(N,col);
+        %FAR_model = FAR_model(col_choose,:);
+        sparse_signal = zeros(M,N);
+        block = randperm(N,block_sparsity);
+        sparse_signal(:,block) = exp(1i*2*pi*rand(M,block_sparsity));
+        y = FAR_model * sparse_signal(:);
+        cvx_begin
+        variable x(M,N) complex
+        norm21 = 0;
+        for i = 1:N
+            norm21 = norm21 + norm(x(:,i));
+        end
+        minimize(norm21)
+        subject to
+        FAR_model * x(:) == y
+        cvx_end
+        if norm(x(:)-sparse_signal(:))<tol
+            success_count = success_count+1;
+        end
+    end
+    result(block_sparsity) = success_count/trial;
+end
+%%
+clc;
+M = 4;
+N = 128;
+%block_sparsity = 1;
+tol = 1e-5;
+trial = 30;
+epi = 0.02;
+result2 = zeros(2,25);
+col = 128;
+Prob = [1/3,1/3,1/6,1/6];
+for block_sparsity = 4:18
+    success_count = 0;
+    success_count2 = 0;
+    for loop = 1:trial
+        FAR_model = zeros(N,M*N);
+        %Cn = randperm(M)-1
+        for n = 0 : N-1
+            Cn = randsrc(1,1,[[0,1,2,3];Prob]);
+            for q = 0 : N-1
+                for p = 0:M-1
+                    FAR_model(n+1,q*M+p+1) = exp(1i*2*pi*p/M*Cn+1i*2*pi*q/N*n*(1+Cn*epi));
+                end
+            end
+        end
+        %col_choose = randperm(N,col);
+        %FAR_model = FAR_model(col_choose,:);
+        sparse_signal = zeros(M,N);
+        block = randperm(N,block_sparsity);
+        sparse_signal(:,block) = exp(1i*2*pi*rand(M,block_sparsity));
+        y = FAR_model * sparse_signal(:);
+        cvx_begin
+        variable x(M,N) complex
+        norm21 = 0;
+        for i = 1:N
+            norm21 = norm21 + norm(FAR_model(:,M*i-3:M*i)*x(:,i));
+        end
+        minimize(norm21)
+        subject to
+        FAR_model * x(:) == y
+        cvx_end
+        err1 = 0;
+        for i =1:N
+            err1 = err1 + norm(FAR_model(:,M*i-3:M*i)*(x(:,i)-sparse_signal(:,i)));
+        end
+        if err1<tol
+            success_count2 = success_count2 +1;
+        end
+        if norm(x(:)-sparse_signal(:))<tol
+            success_count = success_count+1;
+        end
+    end
+    result2(1,block_sparsity) = success_count/trial;
+    result2(2,block_sparsity) = success_count2/trial;
+end
+
+
+%%
+
+
+close all;
+clear all;
+clc;
+M = 4;
+N = 64;
+%block_sparsity = 1;
+tol = 1e-5;
+trial = 50;
+epi = 0.02;
+%result = zeros(N,25);
+%for col = 4:4:128
+col = 64;
+block_sparsity = 6;
+err = 0.1;
+sigma = 0.5*sqrt(block_sparsity);
+
+        
+        
+FAR_model = zeros(N,M*N);
+%Cn = randperm(M)-1
+for n = 0 : N-1
+    Cn = floor(rand()*M);
+    for q = 0 : N-1
+        for p = 0:M-1
+            FAR_model(n+1,q*M+p+1) = exp(1i*2*pi*p/M*Cn-1i*2*pi*q/N*n*(1+Cn*epi));
+        end
+    end
+end
+%col_choose = randperm(N,col);
+%FAR_model = FAR_model(col_choose,:);
+sparse_signal = zeros(M,N);
+block = randperm(N,block_sparsity);
+sparse_signal(:,block) = exp(1i*2*pi*rand(M,block_sparsity));
+y = FAR_model * sparse_signal(:) + sigma*(randn(N,1)) + 1i*sigma*(randn(N,1));
+cvx_begin
+variable x(M,N) complex
+norm21 = 0;
+for i = 1:N
+    norm21 = norm21 + norm(x(:,i));
+end
+minimize(norm21)
+subject to
+norm(FAR_model * x(:) - y)<err
+cvx_end
+
+
+x_block_norm = zeros(N,1);
+x_norm = zeros(N,1);
+for i = [1:N]
+    x_block_norm(i) = norm(FAR_model(:,M*i-3:M*i)*x(:,i)); 
+    x_norm(i) = norm(FAR_model(:,M*i-3:M*i)*sparse_signal(:,i));
+end
+
+hold on 
+plot(x_block_norm,'--o');
+plot(x_norm,'-.s');
+lgh = legend("Estimated","Ground Truth", ...
+    "MF");
+set(lgh,'interpreter','latex','FontName','Times New Roman')
+%set(gcf,'interpreter','latex','FontName','Times New Roman')
+xlabel("\fontname{Times New Roman}Velocity Cell Index");
+ylabel("\fontname{Times New Roman}Test Statistics \it{T_i}");
+xlim([0 75]);
+
+
+
+ 
+%end
+
+
+
+