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:

1. Create the comm.PhaseNoise object and set its properties.

2. 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

phznoise = comm.PhaseNoise

phznoise = comm.PhaseNoise(level,offset,samplerate)

phznoise = comm.PhaseNoise(___,Name=Value)

Description

phznoise = comm.PhaseNoise creates a phase noise System object with default property values.

phznoise = comm.PhaseNoise(level,offset,samplerate) creates a phase noise object with the phase noise level, frequency offset, and sample rate properties specified as value-only arguments. When specifying a value-only argument, you must specify all preceding value-only arguments.

phznoise = comm.PhaseNoise(___,Name=Value) specifies options using one or more name-value arguments in addition to the input arguments in previous syntaxes. For example, comm.PhaseNoise(RandomStream="mt19937ar with seed"), creates a phase noise object with the random stream set to use the Mersenne Twister random number generator.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

Level — Phase noise level

[-80 -100] (default) | vector of negative scalars

Phase noise level in decibels relative to carrier per hertz (dBc/Hz), specified as a vector of negative scalars. The Level and FrequencyOffset properties must have the same length.

Data Types: double

FrequencyOffset — Frequency offset

[2000 20000] (default) | vector of positive increasing values

Frequency offset in Hz, specified as a vector of positive increasing values. The maximum frequency offset value must be less than F_S/ 2, where F_S represents the SampleRate property value.

The Level and FrequencyOffset properties must have the same length.

Data Types: double

SampleRate — Sample rate

1e6 (default) | positive scalar

Sample rate in Hz, specified as a positive scalar greater than two times the maximum value specified by the FrequencyOffset property.

Data Types: double

RandomStream — Source of random stream

'Global stream' (default) | 'mt19937ar with seed'

Source of the random stream, specified as 'Global stream' or 'mt19937ar with seed'. If RandomStream is set to 'mt19937ar with seed', the mt19937ar algorithm is used for normally distributed random number generation, in which case the reset method reinitializes the random number stream to the value of the Seed property.

Data Types: char | string

Seed — Initial seed

2137 (default) | positive scalar less than 2³²

Initial seed for RandomStream, specified as a positive scalar less than 2³².

Dependencies

To enable this property, set RandomStream to 'mt19937ar with seed'.

Data Types: double

Usage

Syntax

out = phznoise(in)

Description

out = phznoise(in) adds phase noise, specified by the phznoise System object, to the input signal. The result is returned in out.

Input Arguments

in — Input signal

vector | matrix

Input signal, specified as an N_S-by-1 numeric vector or N_S-by-M numeric matrix. N_S is the number of samples and M is the number of channels.

This object accepts variable-size inputs. After the object is locked, you can change the size of each input channel, but you cannot change the number of channels. For more information, see Variable-Size Signal Support with System Objects.

Data Types: double | single
Complex Number Support: Yes

Output Arguments

out — Output signal

vector | matrix

Output signal, returned as a complex-valued signal with the same data type and size as the input signal.

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)

Specific to comm.PhaseNoise

visualize

Visualize spectrum mask of phase noise

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

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]; % in dBc/Hz
phNzFreqOff = [1e3 9.5e3 19.5e3 195e3]; % in Hz
Nspf = 6e6; % Number of Samples per frame
freqSpan = 400e3; % 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);
sascopeRBW100 = spectrumAnalyzer( ...
    SampleRate=fs, ...
    Method="welch", ...
    FrequencySpan="Span and center frequency", ...
    CenterFrequency=fc, ...
    Span=freqSpan, ...
    RBWSource="Property", ...
    RBW=100, ...
    SpectrumType="Power density", ...
    SpectralAverages=10, ...
    SpectrumUnits="dBW", ...
    YLimits=[-150 10], ...
    Title="Resolution Bandwidth 100 Hz", ...
    ChannelNames={'signal','signal with phase noise'}, ...
    Position=[79 147 605 374]);
sascopeRBW1k = spectrumAnalyzer( ...
    SampleRate=fs, ...
    Method="welch", ...
    FrequencySpan="Span and center frequency", ...
    CenterFrequency=fc, ...
    Span=freqSpan, ...
    RBWSource="Property", ...
    RBW=1000, ...
    SpectrumType="Power density", ...
    SpectralAverages=10, ...
    SpectrumUnits="dBW", ...
    YLimits=[-150 10], ...
    Title="Resolution Bandwidth 1 kHz", ...
    ChannelNames={'signal','signal with phase noise'}, ...
    Position=[685 146 605 376]);

To analyze the spectrum and phase noise, the example includes two spectrum analyzer objects, with 100 Hz and 1 kHz resolution bandwidths, respectively. The spectrum analyzer objects use the default Hann windowing setting, the spectrum units are set to dBW, and the number of spectral averages is set to 10.

x = sinewave();
y = pnoise(x);

When the resolution bandwidth is 100 Hz, the dBW/Hz view for the spectrum analyzer shows the tone at -20 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.

sascopeRBW100(x,y)

When the resolution bandwidth is 1 kHz, the dBW/Hz view for the spectrum analyzer shows the tone at -30 dBW/Hz. The tone energy of the sine wave is now spread across 1 kHz instead of 100 Hz, so the sine wave PSD level reduces by 10 dB. With the resolution bandwidth at 1 kHz, the visual average of the phase noise still achieves the phase noise defined by the phase noise object.

With the resolution bandwidth increased from 100 Hz to 1 kHz, 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?

sascopeRBW1k(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.', ...
    rms_ph_nz_deg)

ans = 
'The computed RMS phase noise is 0.37 degrees.'

Algorithms

The output signal, y_k, is related to input sequence x_k by y_k=x_ke^jφ_k, where φ_k is the phase noise. The phase noise is filtered Gaussian noise such that φ_k=f(n_k), where n_k is the noise sequence and f represent 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 more information, see IIR Digital Filter.

• 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). For more information, see FIR Filter.

IIR Digital Filter

For the IIR digital filter, the numerator coefficient is

$$\lambda =\sqrt{2\pi f_{offset}{10}^{L/10}},$$

where f_offset is the frequency offset in Hz and L is the phase noise level in dBc/Hz. The denominator coefficients, γ_i, are recursively determined as

$${\gamma }_i=\left(i-2.5\right)\frac{{\gamma }_{i-1}}{i-1},$$

where γ₁ = 1, i = {1, 2,..., N_t}, and N_t is the number of filter coefficients. N_t is a power of 2 in the range [2⁷ , 2¹⁹]. The value of N_t 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, f_s / 2], where df is the frequency resolution and f_s is the sample rate. The phase noise is flat over the range [0, df] in Hz, and from the largest frequency offset to f_s / 2. The phase noise has 1 / f³ characteristic from df to the smallest frequency offset. The phase noise is linearly interpolated between the smallest and the largest frequency offset. The frequency resolution is equal to (f_s / 2)(1 / N_t), where N_t is the number of coefficients, and is a power of 2 less than or equal to 2¹⁶.

Use a time domain FIR filter if the number of taps, N_t, of the resulting filter is less than 2⁸. Use a frequency domain FIR filter if 2⁸ <= N_t <= 2¹⁶. Use a cascaded system of filters and synthesizers if N_t > 2¹⁶. Divide the [0, f_s/2] frequency range into two equal halves. Design a filter to shape the phase noise in each sub band. Combine the two sub bands using a synthesizer that results in the desired phase noise characteristics over the [0, f_s/2] range. Repeat this process for each sub band until the number of taps of each filter is less than or equal to2¹⁶.

The single filter, or the cascaded filter-synthesizer system, is primed during initialization to remove filter latency.

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^® 83, no. 5 (May, 1995): 802–27.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

See System Objects in MATLAB Code Generation (MATLAB Coder).

Version History

Introduced in R2012a

R2024a: Variable-size support

This support enables you to vary the length of input signal each time you call the object.

R2024a: Model high frequency phase noise impairment

Use the comm.PhaseNoise System object to accurately model phase noise at higher frequency signals. Use the visualize function of the comm.PhaseNoise System object. For more information, see the Algorithms in comm.PhaseNoise System object.