i need to understand the code for Pd vs SNR(dB). please help guys.
it is given in Detection theory by Steven M. Kay.
Have a look at https://au.mathworks.com/matlabcentral/answers/840-how-to-plot-a-simple-curve
https://au.mathworks.com/matlabcentral/answers/475415-how-to-plot-the-curve
https://www.capterra.com/statistical-analysis-software/
If independent variable : X = [x1, x2, ..., xn], dependent variable Y = [y1, y2, ..., yn], then plot(X,Y). To create a plot with a linear scale on the x-axis and a log (base 10) scale on the y-axis you can use the function semilogy. To create a plot with a linear scale on the x-axis and a log (base 10) scale on the x-axis you can use the function semilogx.
Try this:
https://in.mathworks.com/help/phased/examples/detector-performance-analysis-using-roc-curves.html
Hi Anil Keshari, elaborate what exactly you are seeking.
If you want to understand how MATLAB code is written/working, write that particular code for Pd vs SNR (dB) here. I can include line by line comment to it for the sake of your understanding. Or if it is related to the theoretical derivation of the probability of detection, we can discuss the same.
I hope it will help you.
Cheers!
Hi, Prasanna Raut I have mentioned below. please look into the problem. The theoretical code is working perfectly fine.
clc; close all;
clear all;
SNRdB=-10:.2:20;
r = 2:1:8;
Pfa = 10.^(1-r);
for i=1:length(Pfa)
inv_q=qfuncinv(Pfa(i));
for k=1:length(SNRdB)
SNR=10^(SNRdB(k)/10);
sigma=1/sqrt(SNR);
gama=sigma*inv_q;
Pd(k)=qfunc((gama-1)/sigma);
end
plot(SNRdB,Pd)
hold on
axis tight
grid on
end
xlabel('SNR(dB)');
ylabel('Pd');
title('Pd VS SNR(dB)');
legend('Pfa = 10^-1','Pfa = 10^-2','Pfa = 10^-3','Pfa = 10^-4','Pfa = 10^-5','Pfa = 10^-6','Pfa = 10^-7','location', 'northwest' )
hold off
----------------------------------------------------------------------------------
above code is Pd vs SNRdB. but this is theoreticaly simulated i want to add lets say i transmitted the bits and recieved and then i want to make binary hypothesis to test that the recieved signal lies in which one of the hypothesis by considering threshold as deciding factor. then from there i can calculate ROC also by deciding PD vs PFAand plot Pd vs SNRdb also.
This code is valid when you are using Energy Detection
%% Probability of detection
clear % Clear all data stored in variables
Am = 1; % 1V Amplitude
SR = 48000; % 48 KHz Smapling Rate
f0 = 20e+3; % 20 KHz
duration = (127/SR); % ~ 2.6 ms
t = 0:1/SR:duration; % Time Vector
%%
sinusPulse = Am*sin(2*pi*f0*t);
mySNR = -30:1:30; % SNR buffer
threshold = 150;
detectProbability(sinusPulse,mySNR,threshold)
%%
function detectProbability(yourSignal,snr,threshold)
N = length(yourSignal);
for i = 1:length(snr)
Pd_buff(100) = 0;
for j = 1:100
a(N) = 100;
yourSignal = awgn(yourSignal,snr(i));
a(1) = abs(yourSignal(1)).^2;
for k = 2:N
a(k) = a(k-1) + abs(yourSignal(k)).^2;
end
Pd_buff(j) = sum(a > threshold)/N;
end
Pd = sum(Pd_buff)/100;
plot(snr(i),Pd_ED,'b+');
hold on
title('Energy Detection')
xlabel('SNR (db)')
ylabel('Probaility of Detection')
end
hold off
end
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