ROC curves are formed by plotting Pd against Pfa and first you should decide whether you will use the CFAR approach or the CDR approach. For plotting Pd Vs SNR you should set a target Pfa and then calculate your Pd for each SNR value.

I have tried to plot ROC curve for MME-algorithm using following  code but it gives Pd always equal 1....

clc

close all

clear all

N = 60e3; %# of samples

L=4; %Length of recieved signal vector

snr_dB = -16; % 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=1:1 % Number of Monte Carlo Simulations %Run 1 time or 1000 time your own choice

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

y=y-mean(y);

r = xcorr(y); % Auto-correlation of y

R=abs(toeplitz(y(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=((sqrt(N)+sqrt(L))/(sqrt(N)-sqrt(L)))^2*(1+((sqrt(N)+sqrt(L))^(-2/3)/(N*L)^(1/6))*0.45); %Threshold

test=MN*TH;

if (MX>test)

%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)

title('Final false alarm probability versus Pd')

xlabel('Pf')

ylabel('Pd')

grid on

hold on

I think you should check your Monte Carlo loop

Yes, I checked. I tried to simulate Monte Carlo loop up-to 100 and 1000 time but  its not working same error

@Muhammad Karam Shehzad 

I think there might be problem with your threshold. It is constant and not changing as per your Pf. The MX is always greater than test(m). Therefore you are getting Pd as always 1.

do you want to plot pd vs snr or pd vs pfa?

in your program pd vs pfa is plotted, but pfa u consider is 0.1 that is equal to 0.45. Pfa is varing in your progrom. The value 0.45 is calculated for tracy-widom distribution for pfa=0.1. if pfa=0.2 then the value changes to  other value.

I hope u, where u did mistake?