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## Phase Noise

version 1.0 (9.67 KB) by

Oscillator Phase Noise Model

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function Sout = add_phase_noise( Sin, Fs, phase_noise_freq, phase_noise_power )

Oscillator Phase Noise Model

INPUT:
Sin - input COMPLEX signal
Fs - sampling frequency ( in Hz ) of Sin
phase_noise_freq - frequencies at which SSB Phase Noise is defined (offset from carrier in Hz)
phase_noise_power - SSB Phase Noise power ( in dBc/Hz )

OUTPUT:
Sout - output COMPLEX phase noised signal

NOTE:
Input signal should be complex

EXAMPLE ( How to use add_phase_noise ):
Assume SSB Phase Noise is specified as follows:
-------------------------------------------------------
| Offset From Carrier | Phase Noise |
-------------------------------------------------------
| 1 kHz | -84 dBc/Hz |
| 10 kHz | -100 dBc/Hz |
| 100 kHz | -96 dBc/Hz |
| 1 MHz | -109 dBc/Hz |
| 10 MHz | -122 dBc/Hz |
-------------------------------------------------------

Assume that we have 10000 samples of complex sinusoid of frequency 3 KHz
sampled at frequency 40MHz:

Fc = 3e3; % carrier frequency
Fs = 40e6; % sampling frequency
t = 0:9999;
S = exp(j*2*pi*Fc/Fs*t); % complex sinusoid

Then, to produse phase noised signal S1 from the original signal S run follows:

Fs = 40e6;
phase_noise_freq = [ 1e3, 10e3, 100e3, 1e6, 10e6 ]; % Offset From Carrier
phase_noise_power = [ -84, -100, -96, -109, -122 ]; % Phase Noise power
S1 = add_phase_noise( S, Fs, phase_noise_freq, phase_noise_power );

Andy

### Andy (view profile)

Does anybody know how to create a phase noise plot, given a signal such as S1 in this example? It's not clear how to achieve a plot with units of dBc/Hz.

Mayank Lakhani

### Mayank Lakhani (view profile)

Can anybody tell me, Why i cannot see the spreading of spectrum in frequency domain.

Fc = 3e3; % carrier frequency
fs = 40e6; % sampling frequency
t = 0:9999;
S = exp(j*2*pi*Fc/Fs*t); % complex sinusoi

Fs = 40e6;
phase_noise_freq = [ 1e3, 10e3, 100e3, 1e6, 10e6 ]; % Offset From Carrier
phase_noise_power = [ -84, -100, -96, -109, -122 ]; % Phase Noise power
S1 = add_phase_noise( S, fs, phase_noise_freq, phase_noise_power );

%%% first signal S
nfft = length(S);
res = fft(S,nfft)/nfft; % normalizing the fft
f = fs/2*linspace(0,1,nfft/2+1);% choosing correct frequency axes
res = res(1:nfft/2+1); % amplitude of fft(taking the half length of nfft)
figure, plot(f,abs(fftshift(res)));

%%% second signal S1
nfft = length(S1);
res = fft(S1,nfft)/nfft; % normalizing the fft
f = fs/2*linspace(0,1,nfft/2+1);% choosing correct frequency axes
res = res(1:nfft/2+1); % amplitude of fft(taking the half length of nfft)
figure, plot(f,abs(fftshift(res)));

wei wang

Frank Wang

### Frank Wang (view profile)

I think the phase noise = 0dBc/Hz at freq offset of 0 Hz is not correct.

Mark

### Mark (view profile)

great work Alex, thank you for sharing!

Mark

Ping

### Ping (view profile)

I am eager to know, if the Fc is very high (e.g. 300MHz), does this code still work? I found a very strange waveform when I set Fc to a high frequency.

glacier w

### glacier w (view profile)

thank you,it's my first time download codes here.thanks again.

Kei Obara

### Kei Obara (view profile)

I have below OFDM model;
FFT size = 64
Subcarrier spacing = 1e5(Hz)
Symbol duration = 1/subcarrier space = 1e-5(s)
duration of 1 data sample = 1e-5/64 (s) (IFFT data is coverted to serial and become1/64)

in this case, "Fs" in this program should be 1e-5/64 (s) ? or any other values should be used ?

Cheers,
K

Pedram

### Pedram (view profile)

Very good. Thank you. Is there anyway to increase the precision of the approximation? This method is valid only for low phase noise values. How can one produce higher phase noise values?

Michal Eitan

### Michal Eitan (view profile)

i did tried the code- and tried to plot the single side phase noise in [dBc/Hz] units, but i got inncorrect values from what i wrote to the function.

Michael what did u mean by "M vs. (2*M-2)"?

Thanx
Michal

Michael

### Michael (view profile)

I like Alex's work!

However, I need to point out a minor bug in the code. I noticed that the phase noise I received from the code was higher than anticipated. Then I noticed on line 219 that the normalization is incorrect. Alex is correct in that (2*M-2) is needed to compensate for the inverse DFT; however this normalization (line 219) should be M vs. (2*M-2) since on line 222 he creates the two-sided spectrum by adding the negative frequency spectrum. In essence line 222 adds the rest of the normalization (M-2). Once I corrected this the phase noise I get is within 1 dB of anticipation vs. 6 dB.

Finally, there is a little mistake, which makes no difference in the result since the phase noise is generated via a random variable. However, to be numerically correct line 231 should have a -j vs. +j in the exponential.

sia yousef

### sia yousef (view profile)

Hi I wonder how this model can satisfy the real shape of the oscillator that firs we have a 1/f^3 and then 1/f^2 and then noise floor.
and it doesn't have close to carrier phase noise.
I don't know how based on which model you generate phase noise?
thanks

xu zhenhua

xie xie

wendy

### wendy (view profile)

how come i run this program but it says Not enough input arguments. ?

Nick A

This approach is very elegant. However, it limits the amount of low frequency phase noise extracted from the PSD by the original sampling frequency. Any ideas about circumventing this limitation?
Thanks
Nick

Agus Suhendar

i have problem, hope u can help me..
after qam mapping and ifft the signal is in time domain and complex form, with BW=7 MHz the problem is how to sampling the complex time domain signal with sampling factor=8/7 or Fs=8MHz
thanxs b4..

CT Lin

thank you

chuntel Lin

thank you

john kedziora

Works very well!

thomas höhne

Great work. Easy to adapt to own needs. The plot of the generated PSD could be done better.

Madhukar Ramamurthy

Ming-Yu Hsieh

This model is very adequate for ofdm system.

##### MATLAB Release
MATLAB 6.5.1 (R13SP1)
##### Acknowledgements

Inspired: microwae engineering

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