### Highlights from Phase Noise

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# Phase Noise

### Alex Bar-Guy (view profile)

27 Oct 2005 (Updated )

Oscillator Phase Noise Model

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Description

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 );

MATLAB release MATLAB 6.5.1 (R13SP1)
Other requirements -
21 Jul 2015 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)));

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07 Oct 2013 wei wang

### wei wang (view profile)

26 Sep 2013 Frank Wang

### Frank Wang (view profile)

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

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10 Feb 2013 Mark

### Mark (view profile)

great work Alex, thank you for sharing!

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10 Feb 2013 Mark

12 Jan 2012 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.

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12 Oct 2011 glacier w

### glacier w (view profile)

11 Aug 2011 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

20 Jun 2011 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?

25 Feb 2011 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

18 Mar 2010 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.

12 Dec 2008 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

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03 Dec 2008 xu zhenhua

### xu zhenhua (view profile)

xie xie

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02 Dec 2008 wendy

### wendy (view profile)

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

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06 Oct 2008 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

18 May 2008 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..

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20 Feb 2008 CT Lin

thank you

20 Feb 2008 chuntel Lin

thank you

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01 Aug 2007 john kedziora

Works very well!

19 Dec 2006 thomas hÃ¶hne

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