comm.PhaseNoise
Apply phase noise to baseband signal
Description
The comm.PhaseNoise
System object™ adds phase noise to a complex signal. This object emulates impairments
introduced by the local oscillator of a wireless communication transmitter or receiver. The
object generates filtered phase noise according to the specified spectral mask and adds it to
the input signal. For a description of the phase noise modeling, see Algorithms.
To add phase noise using a comm.PhaseNoise object:
Create the
comm.PhaseNoiseobject and set its properties.Call the object with arguments, as if it were a function.
To learn more about how System objects work, see What Are System Objects?.
Creation
Syntax
Description
phznoise = comm.PhaseNoise
phznoise = comm.PhaseNoise(Name,Value)Name set to
the specified Value. You can specify additional name-value pair
arguments in any order as
(Name1,Value1,...,NameN,ValueN).
phznoise = comm.PhaseNoise(level,offset,samplerate)
Properties
Usage
Syntax
Description
Input Arguments
Output Arguments
Object Functions
To use an object function, specify the
System object as the first input argument. For
example, to release system resources of a System object named obj, use
this syntax:
release(obj)
Examples
Phase Noise Effects on 16-QAM Signal
Add a phase noise vector and frequency offset vector to a 16-QAM signal. Then plot the signal.
Create a phase noise System object.
pnoise = comm.PhaseNoise('Level',-50,'FrequencyOffset',20);
Generate modulated symbols.
M = 16; % From 16-QAM
data = randi([0 M-1],1000,1);
modData = qammod(data,M);Use pnoise to apply phase noise. Plot the impaired data.
y = pnoise(modData); scatterplot(y)
View Phase Noise Effects on Signal Spectrum
View the effects of phase noise on a 10 MHz sine wave by using a spectrum analyzer. Adjust the resolution bandwidth of the spectrum analyzer to see its impact on the visualized spectral noise.
Initialize variables for the simulation.
fc = 1e6; % Carrier frequency in Hz fs = 4e6; % Sample rate in Hz. phNzLevel = [-85 -118 -125 -145]; % Phase noise level in dBc/Hz phNzFreqOff = [1e3 9.5e3 19.5e3 195e3]; % Phase noise frequency offset in Hz Nspf = 6e6; % Number of Samples per frame freqSpan = 400e3; % Frequency span in Hz for spectrum computation
Create sine wave, phase noise, and spectrum analyzer objects.
sinewave = dsp.SineWave('Amplitude',1,'Frequency',fc,'SampleRate',fs, ... 'SamplesPerFrame',Nspf,'ComplexOutput',true); pnoise = comm.PhaseNoise('Level',phNzLevel, ... 'FrequencyOffset',phNzFreqOff,'SampleRate',fs); spectrumscopeRBW1 = dsp.SpectrumAnalyzer('NumInputPorts',2, ... 'SampleRate',fs,'FrequencySpan','Span and center frequency', ... 'CenterFrequency',fc,'Span',freqSpan,'RBWSource','Property', ... 'RBW',1,'SpectrumType','Power density','SpectralAverages',10, ... 'SpectrumUnits','dBW','YLimits',[-150 10], ... 'Title','Resolution Bandwidth 1 Hz','Position',[79 147 605 374]); spectrumscopeRBW10 = dsp.SpectrumAnalyzer('NumInputPorts',2, ... 'SampleRate',fs,'FrequencySpan','Span and center frequency', ... 'CenterFrequency',fc,'Span',freqSpan,'RBWSource','Property', ... 'RBW',10,'SpectrumType','Power density','SpectralAverages',10, ... 'SpectrumUnits','dBW','YLimits',[-150 10], ... 'Title','Resolution Bandwidth 10 Hz','Position',[685 146 605 376]);
To analyze the spectrum and phase noise, the example includes two spectrum analyzer objects, with 1 Hz and 10 Hz resolution bandwidths, respectively. The spectrum analyzer objects use the default Hann windowing setting, the units are set to dBW/Hz, and the number of spectral averages is set to 10.
x = sinewave(); y = pnoise(x);
When the resolution bandwidth is 1 Hz, the dBW/Hz view for the spectrum analyzer shows the tone at 0 dBW/Hz. The spectrum analyzer object corrects for the power spreading effect of the Hann windowing. Results show the visual average of the phase noise match the specified phase noise spectrum.
spectrumscopeRBW1(x,y)
When the resolution bandwidth is 10 Hz, the dBW/Hz view for the spectrum analyzer shows the tone at -10 dBW/Hz. The tone energy of the sine wave is now spread across 10 Hz instead of 1 Hz, so the sine wave PSD level reduces by 10 dB. With the resolution bandwidth at 10 Hz, the visual average of the phase noise still achieves the phase noise defined by the phase noise object.
With the resolution bandwidth increased from 1 Hz to 10 Hz, the spectrum analyzer object still corrects for the power spreading effect of the Hann window, and it achieves better spectral averaging with the wider resolution bandwidth. For more information, see Why Use Windows?.
spectrumscopeRBW10(x,y)
Calculate the RMS phase noise in degrees between the pure and noisy sine waves. In the general case, the pure signal must be time aligned with the noisy signal to accurately determine the phase error. However, in this case, the periodicity of the sine wave makes this step unnecessary.
ph_err = unwrap(angle(y) - angle(x));
rms_ph_nz_deg = rms(ph_err)*180/pi();
sprintf('The computed RMS phase noise is %3.2f degrees.\n',rms_ph_nz_deg)ans =
'The computed RMS phase noise is 0.18 degrees.
'
Algorithms
The output signal, yk, is related to input sequence xk by yk=xkejφk, where φk is the phase noise. The phase noise is filtered Gaussian noise such that φk=f(nk), where nk is the noise sequence and f represents a filtering operation.
To model the phase noise, define the power spectrum density (PSD) mask characteristic by specifying scalar or vector values for the frequency offset and phase noise level.
For a scalar frequency offset and phase noise level specification, an IIR digital filter computes the spectrum mask. The spectrum mask has a 1/f characteristic that passes through the specified point.
For a vector frequency offset and phase noise level specification, an FIR filter computes the spectrum mask. The spectrum mask is interpolated across log10(f). It is flat from DC to the lowest frequency offset, and from the highest frequency offset to half the sample rate.
IIR Digital Filter
For the IIR digital filter, the numerator coefficient is
where foffset is the frequency offset in Hz and L is the phase noise level in dBc/Hz. The denominator coefficients, γi, are recursively determined as
where γ1 = 1, i = {1, 2,...,
Nt}, and Nt is the number of filter
coefficients. Nt is a power of 2, from
27 to
219. The value of
Nt grows as the phase noise offset decreases
towards 0 Hz.
FIR Filter
For the FIR filter, the phase noise level is determined through
log10(f) interpolation for frequency offsets over the range
[df, fs / 2], where
df is the frequency resolution and
fs is the sample rate. The phase noise is flat
from 0 Hz to the smallest frequency offset, and from the largest frequency offset to
fs / 2. The frequency resolution is equal to , where Nt is the number of
coefficients, and is a power of 2 less than or equal to
216. If
Nt <
28, a time domain FIR filter is used.
Otherwise, a frequency domain FIR filter is used.
The algorithm increases Nt until these conditions are met:
The frequency resolution is less than the minimum value of the frequency offset vector.
The frequency resolution is less than the minimum difference between two consecutive frequencies in the frequency offset vector.
The maximum number of FIR filter taps is
216.
References
[1] Kasdin, N. J., "Discrete Simulation of Colored Noise and Stochastic Processes and 1/(f^alpha); Power Law Noise Generation." The Proceedings of the IEEE. Vol. 83, No. 5, May, 1995, pp 802–827.