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Phase Noise

Apply receiver phase noise to complex baseband signal


RF Impairments


The Phase Noise block applies receiver phase noise to a complex, baseband signal. The block applies the phase noise as follows:

  1. Generates additive white Gaussian noise (AWGN) and filters it with a digital filter.

  2. Adds the resulting noise to the angle component of the input signal.

Using this block, you can specify phase noise as a scalar frequency offset or a vector of frequency offsets.

  • For a scalar frequency offset, the block generates phase noise over the entire spectral observation window, from 0 Hz (or as close as possible to 0 Hz) to ±FS2, where Fs represents the sampling frequency. The noise is scaled so that it is at the block-specific phase noise level at the specified frequency offset. The block generates a phase noise with 1f characteristic over the entire frequency range.

  • For a vector of frequency offsets, the block interpolates the spectrum mask across log10(frequency), and is flat from the highest frequency offset to half the sample rate.

You can view the block's implementation of phase noise by right-clicking on the block and selecting Mask > Look under mask. This displays the following figure:

You can view the construction of the Noise Source subsystem by double-clicking it.

The effects of changing the block's parameters are illustrated by the following scatter plots of a signal modulated by 16-ary quadrature amplitude modulation (QAM). The usual 16-ary QAM constellation without distortion is shown in the first scatter plot:

The following figure shows a scatter plot of an output signal, modulated by 16-ary QAM, from the Phase Noise block with Phase noise level (dBc/Hz) set to -70 and Frequency offset (Hz) set to 100:

This plot is generated by the model described in Illustrate RF Impairments That Distort a Signal with the following parameter settings for the Rectangular QAM Modulator Baseband block:

  • Normalization method set to Average Power

  • Average power (watts) set to 1e-12

This block has a companion function, plotPhaseNoiseFilter, that plots the response of the filter specified by the block.


Phase noise level (dBc/Hz)

Scalar or vector that specifies the phase noise level. Specify the phase noise level in decibels relative to carrier per Hertz (dBc/Hz). The lengths of the phase noise level and frequency offset vectors must be equal.

Frequency offset (Hz)

Specifies the frequency offset in Hertz. If the frequency offset is a vector, then the vector must be monotonically increasing. The lengths of the phase noise level and frequency offset vectors must be equal.

Sample rate (Hz)

Must be greater than twice the largest value of the Frequency offset vector to avoid aliasing. Specify in Hertz. When you specify a vector of frequency offsets, the block uses this parameter. The block does not use this parameter when you specify a scalar frequency offset.

The sample rate must match the sample rate of the input signal. This quantity is the actual sample rate, not the frame rate of a frame-based signal.

Initial seed

Nonnegative integer specifying the initial seed for the random number generator the block uses to generate noise.


For an example model that uses this block, see View Phase Noise Effects on Signal Spectrum.


[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, May, 1995, Vol. 83, No. 5

Introduced before R2006a

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