Dear researchers
I'm trying to simulate the maximum-minimum eigenvalue (MME) detector via MATLAB;
L=4; % consecutive samples
y=randn(1,L); % Input signal
r = xcorr(y); % Auto-correlation of y
N=length(r); % number of available samples
R=toeplitz(r); % sample covariance matrix
EG=eig(R);
MX=max(abs(EG)); %Maximum Eigenvalue
MN=min(abs(EG)); % Minimum Eigenvalue
TH=((sqrt(N)+sqrt(L))/(sqrt(N)-sqrt(L)))^2*(1+((sqrt(N)+sqrt(L))^-2/3/(N*L)^1/6)*0.45); % Threshold
Ratio=MX/MN; % Maximum-Minimum Eigenvalue ratio
Now, this "Ratio" will be compared to threshold "TH" to decide the occupancy of a given channel.
Is that the right way to implement the MME using MATLAB?
Best regards
References:
[1] Hamid, M.; Bjorsell, N.; Slimane, B., "Energy and Eigenvalue-Based Combined Fully-Blind Self-Adapted Spectrum Sensing Algorithm," Vehicular Technology, IEEE Transactions on , vol.PP, no.99, pp.1,1
[2] Omar, M.H.; Hassan, S.; Nor, S.A., "Eigenvalue-based signal detectors performance comparison," Communications (APCC), 2011 17th Asia-Pacific Conference on , vol., no., pp.1,6, 2-5 Oct. 2011
there are some issues in this code. First of all, you should remove the mean from your signal. Second, using the toeplitz assumption, you also assume that your signal is stationary. Third, I would use SVD instead of eig for a lot of reason (if you don't want to use the toepliz assumption anymore, your covariance matrix could be not a full rank matrix, and svd gives you the closest subspace approximation for your covariance matrix representation; furthermore, svd return the absolute values of the eigenvalues).
Good luck with your research,
Francesco Onorati
@ Francesco
Thanks for answering my concern, I think I still have some issue in understanding (L) which is the consecutive samples; Could you please highlight if it is implemented in the right way based on the references [1] and [2]?
After your corrections the code becomes as follows:
L=4; % consecutive samples
y=randn(1,L);
y=y-mean(y);
r = xcorr(y);
N=length(r);
R=toeplitz(r);
[EG,S,V] = svd(R);
MX=max(EG(:));
MN=min(EG(:));
TH=((sqrt(N)+sqrt(L))/(sqrt(N)-sqrt(L)))^2*(1+((sqrt(N)+sqrt(L))^-2/3/(N*L)^1/6)*0.45);
Best regards
I have tried to simulate MME algorithm by following the procedure as you guys discussed in the above section. But it gives Pd always 1. Additionally, How to plot ROC curve for Pd Vs SNR. Please help me in this regard, Your help will highly be appreciated. Here is code for MME algorithm:
clc
close all
clear all
N = 60000; %# of samples
L=4; %Length of recieved signal vector
snr_dB = -10; % SNR in decibels
snr = 10.^(snr_dB./10); % Linear Value of SNR
Pf = 0.1:0.1:1; % Pf = Probability of False Alarm
%% Simulation to plot Probability of Detection (Pd) vs. Probability of False Alarm (Pf)
for m = 1:length(Pf)
m
i = 0;
for kk=1:100 % Number of Monte Carlo Simulations
n = randn(1,N); %AWGN noise with mean 0 and variance 1
s = sqrt(snr).*randn(1,N); % Real valued Gaussina Primary User Signal
y = s+n; % Received signal at SU
r = xcorr(y); % Auto-correlation of y
R=abs(toeplitz(r(1:L)))/N; % sample covariance matrix
[EG,S,V] = svd(R); %S computes eigenvalues of R
MX=max(S(:)); %Maximum eigenvalue
MN=min(diag(S)); %Minimum eigenvalue
TH(m)=((sqrt(N)+sqrt(L))/(sqrt(N)-sqrt(L)))^2*(1+((sqrt(N)+sqrt(L))^-2/3/(N*L)^1/6)*0.45);
test(m)=MN*TH(m);
if (MX>test(m))
display('Signal is present (As max_eigenvalue>Threshold*min_eigenvalue)....H1')
% Checks whether the received energy is greater than threshold,
%if so, increment Pd (Probability of detection) counter by 1
i = i+1;
end
end
Pd(m) = i/kk;
end
plot(Pf, Pd,'linewidth',2)
hold on
grid on
Francesco Onorati Please check the code given above, I 'm not geeting correct answer
I am also getting the same problem as discussed in my above post. Can anyone help me out?
Thanks!
I have implemented MAXIMUM EIGENVALUE based detection for white noise signal... this might help. The plot is for comparison of energy detection with MED. reference used is "Maximum Eigen Value Detection: Theory and Application: Theory and Application" by Yonghong Zeng. This code will plot Fig. 4 in this reference. I am facing problem with generating wireless microphone signal which they have used as primary signal. if anyone having any idea please reply.
If you find any error please reply.
clc;
clear;
close all;
tic;
%% SNR vs pd using maximum eigenvalue detection
Ns=100000;
SNR=-25:-16;
snr=10.^(SNR./10);
L=8;
pf=0.1;
F1_inv=0.45;
num_iter=2000;
a=((sqrt(Ns)+sqrt(L))^2)/(Ns);
b=1+((sqrt(Ns)+sqrt(L))^(-2/3)*F1_inv)/((Ns*L)^(1/6));
threshold=a*b;
%
w=waitbar(0,'calculating probability of false alarm');
l=1;
for i=1:length(SNR)
count=0;
for h=1:num_iter
signal=randn(1,Ns);
noise=randn(1,Ns);
noise_power=norm(noise)^2;
signal_power=norm(signal)^2;
mult=sqrt(snr(i)*noise_power/signal_power);
signal=mult*signal;
signal=signal+noise;
%noise=noise/std(noise);
k=0;
Cx=zeros(1,L);
for n=0:L-1
for j=1:1:Ns-L-1
Cx(n+1)=Cx(n+1)+signal(j)*signal(j+k);
end
k=k+1;
end
Cx=Cx/Ns;
Cx_mtx=toeplitz(Cx);
eig_value=eig(Cx_mtx);
max_eig=max(max(eig_value));
if max_eig>threshold
count=count+1;
end
end
pd(i)=count/2000;
waitbar(i/length(SNR));
end
close(w);
plot(SNR,pd,'-^');
toc;
%% SNR vs pd using energy detection
M=Ns/2;
Pfa=0.1;
threshold=gammaincinv(1-Pfa,M)*2;
w=waitbar(0,'SNR vs Pd using energy detection');
for i=1:length(SNR)
count=0;
for h=1:num_iter
signal=randn(1,Ns);
noise=randn(1,Ns);
signal_power=norm(signal)^2;
noise_power=norm(noise)^2;
mult=sqrt(snr(i)*noise_power/signal_power);
signal=mult*signal;
signal=signal+noise;
energy=norm(signal)^2;
if energy>threshold
count=count+1;
end
end
Pd1(i)=count/num_iter;
waitbar(i/length(SNR));
end
close(w);
hold on;
plot(SNR,Pd1,'-s');
legend('MED','ED');
xlabel('SNR');
ylabel('P_d');
@Kamal I am facing same problem for wirless microphone signals. Have you implemented that successfully?
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