Apply receiver phase noise to complex baseband signal
Communications Toolbox / RF Impairments
The Phase Noise block adds phase noise to a complex signal. This block emulates impairments introduced by the local oscillator of a wireless communication transmitter or receiver. The block 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.
Data Types 

Multidimensional Signals 

VariableSize Signals 

The output signal, y_{k}, is related to input sequence x_{k} by y_{k}=x_{k}e^{jφk}, 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 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
$$\lambda =\sqrt{2\pi {f}_{offset}{10}^{L/10}}\text{\hspace{0.17em}},$$
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
$${\gamma}_{i}=\left(i2.5\right)\frac{{\gamma}_{i1}}{i1}\text{\hspace{0.17em}},$$
where γ_{1} = 1, i = {1, 2,...,
N_{t}}, and N_{t} is the number of filter
coefficients. N_{t} is a power of 2, from
2
^{7 }to
2
^{19}. 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
from 0 Hz to the smallest frequency offset, and from the largest frequency offset to
f_{s} / 2. The frequency resolution is equal to $$\frac{{f}_{s}}{2}\left(\frac{1}{{N}_{t}}\right)$$, where N_{t} is the number of
coefficients, and is a power of 2 less than or equal to
2
^{16}. If
N_{t} <
2
^{8}, a time domain FIR filter is used.
Otherwise, a frequency domain FIR filter is used.
The algorithm increases N_{t} 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
2
^{16}.
[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.