N = 32;
M =4;
R =2;
epi = 0.02;
noise = [0.1,0.1^(0.5)];
%contri1 = zeros(M,N);
%contri2 = zeros(M,N);
con1 = zeros(20,2);
con2 = zeros(20,2);
re1 = zeros(20,2);
re2 = zeros(20,2);

for noise_k = 1:2
for k = 1:20
    for loop = 1:50

    
        FAR_model = zeros(N,M*N);
        order = randperm(M)-1;
        for n = 0 : N-1
            Cn = order(ceil(rand()*R));
            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
        
        x = zeros(M,N);
        col = randperm(N,k);
        x(:,col) = randn(M,k) + 1i*randn(M,k);
        y = FAR_model * x(:) + (randn(N,1)+1i*randn(N,1))*noise(noise_k);
        
        cvx_begin
        variable x_e(M,N) complex
        norm21 = 0;
        for i = 1:N
            norm21 = norm21 + norm(FAR_model(:,(i-1)*M+1:i*M)*x_e(:,i));
        end
        minimize(norm21)
        subject to
        norm(FAR_model*x_e(:) - y) <= sqrt(N)*noise(noise_k);
        cvx_end
        contri2 = zeros(N,1);
        re_err = zeros(N,1);
        for i = 1:N
            if ismember(i,col)
                re_err = re_err+FAR_model(:,(i-1)*M+1:i*M)*(x_e(:,i));
            end
            contri2(i) = norm(FAR_model(:,(i-1)*M+1:i*M)*(x_e(:,i)));
       	end
		re1(k,noise_k) = re1(k,noise_k) +norm(FAR_model*x(:)-re_err)/norm(FAR_model*x(:));
        con1(k,noise_k) = con1(k,noise_k) + 1-sum(contri2(col))/sum(contri2);      


        cvx_begin
        variable x_e(M,N) complex
        norm21 = 0;
        for i = 1:N
            norm21 = norm21 + norm(x_e(:,i));
        end
        minimize(norm21)
        subject to
        norm(FAR_model*x_e(:) - y) <= sqrt(N)*noise(noise_k);
        cvx_end
        re_err = zeros(N,1);
        contri2 = zeros(N,1);
        for i = 1:N
            if ismember(i,col)
                re_err = re_err+FAR_model(:,(i-1)*M+1:i*M)*(x_e(:,i));
            end
            contri2(i) = norm(FAR_model(:,(i-1)*M+1:i*M)*(x_e(:,i)));
       	end
		re2(k,noise_k) = re2(k,noise_k) +norm(FAR_model*x(:)-re_err)/norm(FAR_model*x(:));
        con2(k,noise_k) = con2(k,noise_k) + 1-sum(contri2(col))/sum(contri2);   
    end
end
end

save("FAR_noise_0206.mat")