/
Experiment_Effect_L.m
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Experiment_Effect_L.m
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% Effect of the cluster length L
%
% This code demonstrates the effect of cluster length "L" on the
% performance of the algorithm described in "Structure-Based Bayesian
% Sparse Reconstruction", Ahmed A. Quadeer & Tareq Y. Al-Naffouri.
%
% Coded by: Ahmed Abdul Quadeer
% E-mail: ahmedaq@gmail.com
% Last change: Dec. 12, 2012
% Copyright (c) Ahmed Abdul Quadeer, Tareq Y. Al-Naffouri, 2012
clear all;close all;clc
N = 800; %Length of time vector
M = N/4; %Number of Measurements
F = 1/sqrt(N)*exp(-sqrt(-1)*(2*pi)*(0:1:N-1)'*(0:1:N-1)/N); %DFT Matrix
ITER = 5000; %Number of iterations
s = 1:1:8; %Number of non-zero values
p = s./N; %Sparsity rate
SNR_dB = 30; %SNR in dB
N0 = 1; %Noice variance
sigma_imp = 10^(SNR_dB/10)*N0; %Variance of sparse signal
%Initialization
nmse_ocmg_L4 = zeros(1,length(s));
nmse_ocmg_L8 = zeros(1,length(s));
nmse_ocmg_L16 = zeros(1,length(s));
nmse_ocmg_L32 = zeros(1,length(s));
nmse_ocmg = zeros(1,length(s));
t_ocmg_L4 = zeros(1,length(s));
t_ocmg_L8 = zeros(1,length(s));
t_ocmg_L16 = zeros(1,length(s));
t_ocmg_L32 = zeros(1,length(s));
t_ocmg = zeros(1,length(s));
for ss = 1:1:length(s)
%Intialization
error_ocmg_L4 = zeros(1,ITER);
error_ocmg_L8 = zeros(1,ITER);
error_ocmg_L16 = zeros(1,ITER);
error_ocmg_L32 = zeros(1,ITER);
error_ocmg = zeros(1,ITER);
time_ocmg_L4 = zeros(1,ITER);
time_ocmg_L8 = zeros(1,ITER);
time_ocmg_L16 = zeros(1,ITER);
time_ocmg_L32 = zeros(1,ITER);
time_ocmg = zeros(1,ITER);
for iter = 1:ITER
%% Constructing the sparse signal
x = zeros(N,1);
impulse_place = randi(N,1,s(ss)); %Takes s random values out of N
x(impulse_place) = sqrt(sigma_imp/2)*(randn(size(impulse_place)) + 1i*randn(size(impulse_place)));
%% Measured Signal
AA = eye(N);
index= 1:M;
A = AA(index,:);
Psi = A*F; %Measurement matrix
n = sqrt(N0/2)*randn(M,1)+1i*randn(M,1); %Noise vecror
y = Psi*x + n; %Measurement vector
%% OC Gaussian Fixed Cluster
L = 4;
tic
x_ocmg_L4 = OC_Gaussian_fixed(y,Psi,sigma_imp,N0,p(ss),index,L);
time_ocmg_L4(iter) = toc;
error_ocmg_L4(iter) = norm(x-x_ocmg_L4)^2/norm(x)^2;
%
L = 8;
tic
x_ocmg_L8 = OC_Gaussian_fixed(y,Psi,sigma_imp,N0,p(ss),index,L);
time_ocmg_L8(iter) = toc;
error_ocmg_L8(iter) = norm(x-x_ocmg_L8)^2/norm(x)^2;
%
L = 16;
tic
x_ocmg_L16 = OC_Gaussian_fixed(y,Psi,sigma_imp,N0,p(ss),index,L);
time_ocmg_L16(iter) = toc;
error_ocmg_L16(iter) = norm(x-x_ocmg_L16)^2/norm(x)^2;
%
L = 32;
tic
x_ocmg_L32 = OC_Gaussian_fixed(y,Psi,sigma_imp,N0,p(ss),index,L);
time_ocmg_L32(iter) = toc;
error_ocmg_L32(iter) = norm(x-x_ocmg_L32)^2/norm(x)^2;
%% OC Gaussian
tic
x_ocmg = OC_Gaussian_seq(y,Psi,sigma_imp,N0,p(ss),index);
error_ocmg(iter) = norm(x-x_ocmg)^2/norm(x)^2;
time_ocmg(iter) = toc;
end
nmse_ocmg_L4(ss) = 10*log10(sum(error_ocmg_L4)/ITER)
nmse_ocmg_L8(ss) = 10*log10(sum(error_ocmg_L8)/ITER)
nmse_ocmg_L16(ss) = 10*log10(sum(error_ocmg_L16)/ITER)
nmse_ocmg_L32(ss) = 10*log10(sum(error_ocmg_L32)/ITER)
nmse_ocmg(ss) = 10*log10(sum(error_ocmg)/ITER)
t_ocmg_L4(ss) = sum(time_ocmg_L4)/ITER
t_ocmg_L8(ss) = sum(time_ocmg_L8)/ITER
t_ocmg_L16(ss) = sum(time_ocmg_L16)/ITER
t_ocmg_L32(ss) = sum(time_ocmg_L32)/ITER
t_ocmg(ss) = sum(time_ocmg)/ITER
end
figure
plot(p,nmse_ocmg_L4,'b:<',p,nmse_ocmg_L8,'b:>',...
p,nmse_ocmg_L16,'b:^',p,nmse_ocmg_L32,'b:v',...
p,nmse_ocmg,'b-s','LineWidth',2)
legend('OC, L=4','OC, L=8','OC, L=16','OC, L=32','OC')
xlabel('\bf \it p')
ylabel('\bf NMSE (dB)')
grid on
figure
semilogy(p,t_ocmg_L4,'b:<',p,t_ocmg_L8,'b:>',...
p,t_ocmg_L16,'b:^',p,t_ocmg_L32,'b:v',...
p,t_ocmg,'b-s','LineWidth',2)
legend('OC, L=4','OC, L=8','OC, L=16','OC, L=32','OC')
xlabel('\bf \it p')
ylabel('\bf Mean run-time')
grid on