Adding phase noise in signal

Question

I want to implement phase noise in matlab. Can anyone tell me why i can not see spreadning of my spectrum in frequency domain. Please help me out.In code, first I have plotted simple signal in frequency domain and after i have defined two noise components, one is syncronous and second is accumulating noise components and added into the signal.

fs = 200;
ts = 1/fs;
t = 0:ts:10000-ts;
fc = 50;
S = cos(2*pi*fc*t);                    %%% equation 7.1 noisless
L = length(S);
nfft = L*100;
res = fft(S,nfft)/nfft; % resize into nfft nr of element % normalize the amplitude
f = fs/2*linspace(0,1,nfft/2+1);
res = res(1:nfft/2+1);
figure, plot(f,abs(res));

sigma = 0.2;
phi_sync =  sigma * randn(1,length(t));   %%%% random variable with gaussian distributed
phi_acc = sigma * randn(1,length(t));   %%%% random variable with gaussian distributed
% h = 0;

for i=1:length(S)
    h = phi_sync + phi_acc(i);
end

S1 = cos(2*pi*fc*t + h);

L = length(S1);
nfft = L*100;
res = fft(S1,nfft)/nfft; % resize into nfft nr of element % normalize the amplitude
f = fs/2*linspace(0,1,nfft/2+1);
res = res(1:nfft/2+1);
figure, plot(f,abs(res))
return

Thanks Jonathon for your comment. now, I have mentioned matlab in my question. — Mayank Lakhani
what do you mean by "spreading of spectrum"? can you provide some desired graphs? I set t = 0:ts:1-ts & plot(f, angle(res)), and then find the phase noise is clear out there. — Gnimuc
Hey Gnimuc Key, thanks for your reply. What i understand from the phase noise definition that if i compare noiseless signal with phase noise signal, in the frequency domain the signal with phase noise shoud be having broader spectrum in comparison with the noiseless siganl. FFT of the noiseless signal is just a narrow spectrum and fft of the signal with noise is having broader spectrum. — Mayank Lakhani
have you tried making the noise bigger, for example, set sigma = 1.2 and you will get a spectrum with noise spreading over the whole frequency range. phase noise is just another "representation" of frequency noise, so it will definitely broaden spectrum. — Gnimuc

Unknown Unknown · Accepted Answer · 2015-08-11T08:57:24

(copied from the comments section)

Make the noise bigger, for example, set sigma = 1.2 and you will get a spectrum with noise spreading over the whole frequency range. Phase noise is just another "representation" of frequency noise, so it will definitely broaden spectrum.

Adding phase noise in signal

1 Answers