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Toe_Rade_Chirp_Zad_2M_SP.m
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Toe_Rade_Chirp_Zad_2M_SP.m
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%function testgold();
% test gold code (size 32x1024);
% parameters
clear
N = 512; % signal length
M = 64;
m=M/2;
% gaussian measurement matrix
%Gauss_op = randn(M,N);
% normalization of the Gaussian matrix;
% Gauss_op1 = randn(1,N+M-1);
% Gauss_op2 = toeplitz(Gauss_op1(1:M),Gauss_op1(M:(M+N-1)));
% Gauss_op = Gauss_op2;
% Gauss_op=zeros(M,N);
% Gauss_op2=randn(1,N);
% Gauss_op3=randn(1,N);
% Gauss_op_row=complex(Gauss_op2(1:N),Gauss_op3(1:N));
% Gauss_op1 = toeplitz(Gauss_op_row, Gauss_op_row);
% rp00=randperm(N);
% Gauss_op=Gauss_op1(rp00(1:M),:);
Gauss_op2 = randn(1,m+N-1);
Gauss_op3 = randn(1,m+N-1);
Gauss_op_row=complex(Gauss_op2(1:N),Gauss_op3(1:N));
Gauss_op_col=complex(Gauss_op2(N:m+N-1),Gauss_op3(N:m+N-1));
Gauss_op4 = toeplitz(Gauss_op_col(1:m), Gauss_op_row);
Gauss_op=Gau_op4;
Gauss_op=[real(Gauss_op);imag(Gauss_op)];
% for ii=1:N,
% Gauss_op(:,ii)=Gauss_op1(:,ii);%/norm(Gauss_op1(:,i));
% end
% Gauss_op2 = [];
% Gauss_op3 = [];
%Gold_op = Goldcode32x1024/sqrt(M);
% % partial Hadamard with random permuatation
% %%%%%
% %WHT = hadamard(N)/sqrt(N);
% %WHT = hadamard(N);
% %%%%%
% WHT = dftmtx(N);
% for i=1:N,
% WHT(:,i)=WHT(:,i)/norm(WHT(:,i));
% end
% %%%%%
% q2 = randperm(N-1);
% WHT_op=[WHT(1,:);WHT(q2(1:(M-1))+1,:)];
% WHT=[];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% thesize=N; %random convolution
% %
% % [a,b] = generate_golay(log2(thesize)-1);
% aaa=exp(2*rand(1,(thesize/2-1))*pi ); % random phase for random convolution
%
% AA=zeros(1,(thesize/2+1));
% AA(1)=sign(randn(1));
% AA(thesize/2+1)=sign(randn(1));
% AA(2:thesize/2)=aaa;
%
% B=zeros(1,thesize);
% B(1:(thesize/2+1))=AA(1:(thesize/2+1));
% for count=1:(thesize/2-1);
% B(thesize/2+1+count)=conj(AA(thesize/2+1-count));
% end
% para=B;
%
% matr5=conj(func_dctmtx(thesize))*diag(para)*func_dctmtx(thesize);
% % aa225=fft(para);
% %matr5=toeplitz(aa225,aa225)/thesize;
% for ii=1:N,
% matr5(ii,:)=matr5(ii,:)/norm(matr5(ii,:));
% end
%
% rp22=randperm(N);
%
% matr15=matr5(rp22(1:M),:);
%
% matr5=[];
% %matr1=matr(1:1:1*M,:);
% matr15=matr15*sqrt(N/M);
% % Circulant Determinisic Matrix
% WHT_op =matr15;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
thesize=N; % Rauhut's code, convolution based on Rademacher sequence in fourier domain
para= sign(randn(1,thesize));
aa225=fft(para);
aa226=zeros(1,N);
aa226(1)=aa225(1);
for ii=2:N;
aa226(ii)=aa225(N-ii+2);
end
matr5=toeplitz(aa226,aa225)/thesize;
rp22=randperm(N);
matr15=matr5(rp22(1:m),:);
matr5=[];
%matr1=matr(1:1:1*M,:);
matr15=matr15*sqrt(N/M);
% Circulant Determinisic Matrix
WHT_op =matr15;
WHT_op=[real(WHT_op);imag(WHT_op)];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% para=zeros(1,N); %square phase code
% for pp=1:N;
% para(pp)=exp(-(2*pi*sqrt(-1)/N)*(pp-1)^2);
% end
% aa22=fft(para);
% matr=toeplitz(aa22,aa22)*dftmtx(N); % This is F* diag() but not F* diag() F
%
% rp2=randperm(N);
% matr1=matr(rp2(1:M),:)/norm(matr(1,:));
% %matr1=matr(1:1:1*M,:);
% matr1=matr1*sqrt(N/M);
% % Circulant Determinisic Matrix
% CDM_op=matr1;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% matra=zeros(N,N);
% for ii=1:N
% for jj=1:N
% matra(ii,jj)=exp(-(pi*sqrt(-1)/N)*(ii-jj)^2);
% end
% end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
root=1; % Zadoff code
zadoff_seq=zadoff(root, N);
fistrow_zad2=fft(zadoff_seq);
fistrow_zad1=zeros(1,N);
fistrow_zad1(1)=fistrow_zad2(1);
for ii=2:N;
fistrow_zad1(ii)=fistrow_zad2(N-ii+2);
end
fistrow_zad=toeplitz(fistrow_zad1,fistrow_zad2)/N;
rp3=randperm(N);
Zad_op=fistrow_zad(rp3(1:m),:);
Zad_op=Zad_op*sqrt(N/M);
Zad_op=[real(Zad_op);imag(Zad_op)];
%for i=1:N,
% CDM_op(:,i)=CDM_op(:,i)/norm(CDM_op(:,i));
%end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
w=16; % Generalized Chirp-like sequence
w_s=0:(1/w):(1-1/w);
GCL_seq=zeros(1,N);
zadoff_seq_temp=zadoff(1, N);
ran_phase=exp(2*w_s*pi*i );
for ooo=1:N;
GCL_seq(ooo)= zadoff_seq_temp(ooo)*ran_phase(mod(ooo,w)+1);
end
fistrow_gcl2=fft(GCL_seq);
fistrow_gcl1=zeros(1,N);
fistrow_gcl1(1)=fistrow_gcl2(1);
for i=2:N;
fistrow_gcl1(i)=fistrow_gcl2(N-i+2);
end
gcl_full=toeplitz(fistrow_gcl1,fistrow_gcl2)/N;
rp4=randperm(N);
GCL_op=gcl_full(rp4(1:m),:);
GCL_op=GCL_op*sqrt(N/M);
CDM_op=GCL_op;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
trial_num = 100;
kvec=2:2: (M/2);
knum=length(kvec);
success_Gauss = zeros(knum,1);
success_Zad = zeros(knum,1);
success_WHT = zeros(knum,1);
success_CDM = zeros(knum,1);
disp('Now starts the simulations');
for jj = 1:knum,
k=kvec(jj);
for i=1:trial_num
jj
% create a sparse signal in Psi domain
alp = [randn(k,1); zeros(N-k,1)];
p = randperm(N);
x = alp(p);
alp=x;
% observation
y1 = Gauss_op*x;
y2 = Zad_op*x;
y3 = WHT_op*x;
y4 = CDM_op*x;
% reconstruction using OMP alg.
%sigma = 0;
%tau = 0.5;
nn = N;
tol1=10;
tol2=10;
tol3=10;
tol4=10;
sigma = 1e-10;
step_size =5;
lambda=0.0001;
rel_tol=0.005;
mu=0.0001;
% alp1 = omp(x, Gauss_op, y1, k, sigma);
%[alp1,x_debias,objective,times,debias_start,mses]= GPSR_Basic1(y1,Gauss_op,tau);
alp1 = CSRec_SP(k, Gauss_op, y1);
%[alp1,d1]=cosamp(Gauss_op*dct(N),y1,k,tol1);
% [alp1 iter_num1] = SAMP(y1, Gauss_op*dct(N), step_size, sigma);
%alp1 = l1dantzig_pd(Gauss_op'*y1, Gauss_op, [], y1, 4e-3, 5e-3); % l1 minimization
%alp1 =l1_ls(Gauss_op,y1,lambda,rel_tol);
%[alp1,Out1] = fpc_AS(N,Gauss_op*idct(eye(N)),y1,mu,[]);
% alp2 = omp(x, Zad_op, y2, k, sigma);
%[alp2,x_debias,objective,times,debias_start,mses]= GPSR_Basic1(y2,Gold_op,tau);
alp2 = CSRec_SP(k, Zad_op, y2);
%[alp2,d2]=cosamp(Zad_op*dct(N),y2,k,tol1);
% [alp2 iter_num1] = SAMP(y2, Zad_op*dct(N), step_size, sigma);
%alp2 = l1dantzig_pd(Zad_op'*y1, Zad_op, [], y2, 4e-3, 5e-3); % l1 minimization
%alp2 =l1_ls(Zad_op,y2,lambda,rel_tol);
%[alp2,Out2] = fpc_AS(N,Zad_op*idct(eye(N)),y2,mu,[]);
% alp3 = omp(x, WHT_op, y3, k, sigma);
%[alp3,x_debias,objective,times,debias_start,mses]= GPSR_Basic1(y3,WHT_op,tau);
alp3 = CSRec_SP(k, WHT_op, y3);
%[alp3,d3]=cosamp(WHT_op*dct(N),y3,k,tol1);
% [alp3 iter_num3] = SAMP(y3, WHT_op*dct(N), step_size, sigma);
%alp3 = l1dantzig_pd(WHT_op'*y3, WHT_op, [], y3, 4e-3, 5e-3); % l1 minimization
%alp3 = l1_ls(WHT_op,y3,lambda,rel_tol);
%[alp3,Out3] = fpc_AS(N,WHT_op*idct(eye(N)),y3,mu,[]);
% alp4 = omp(x, CDM_op, y4, k, sigma);
%[alp4,x_debias,objective,times,debias_start,mses]= GPSR_Basic1(y4,CDM_op,tau);
alp4 = CSRec_SP(k, CDM_op, y4);
%[alp4,d4]=cosamp(CDM_op*dct(N),y4,k,tol1);
% [alp4 iter_num4] = SAMP(y4, CDM_op*dct(N), step_size, sigma);
%alp4 = l1dantzig_pd(CDM_op'*y4, CDM_op, [], y4, 4e-3, 5e-3); % l1 minimization
%alp4 = l1_ls(CDM_op,y4,lambda,rel_tol);
%[alp4,Out4] = fpc_AS(N,CDM_op*idct(eye(N)),y4,mu,[]);
%figure;
%plot(1:N,alp-alp1);
% if snr >50, it is considered as perfect reconstruction
if snr(alp,alp1)>50
success_Gauss(jj) = success_Gauss(jj)+1;
end
if snr(alp,real(alp2))>50
success_Zad(jj) = success_Zad(jj)+1;
end
if snr(alp,real(alp3))>50
success_WHT(jj) = success_WHT(jj)+1;
end
if snr(alp,alp4)>50
success_CDM(jj) = success_CDM(jj)+1;
end
end
success_Gauss(jj) = success_Gauss(jj)/trial_num;
success_Zad(jj) = success_Zad(jj)/trial_num;
success_WHT(jj)=success_WHT(jj)/trial_num;
success_CDM(jj)=success_CDM(jj)/trial_num;
end
figure;hold on;
plot([kvec], [success_Gauss'],'-b+');
plot([kvec], [success_WHT'], '-k*');
plot([kvec], [success_Zad'], '-rs');
plot([kvec], [success_CDM'], '-mo');
grid
%success_Gauss
legend('Complex Gaussian Toeplitz','Rademacher sequence' ,'Zadoff-Chu Code', 'Chirp-Like Code');
%legend('i.i.d Gaussian Operator','Partial DFT','CDM Matrix','Zadoff-Chu Code');
%legend('i.i.d Gaussian Operator','Partial WHT ','OSTM');
xlabel('No. of Non-zero coefiicients K');
ylabel('Frequency of Exact Reconstruction');
%function snr_val=snr(x0,x1)
%err=norm(x0-x1);
%sig=norm(x0);|
%snr_val=-20*log10(err/sig);