Phase Noise

Apply receiver phase noise to complex baseband signal

• 

Libraries:
Communications Toolbox / RF Impairments and Components

Description

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.

Examples

Phase Noise Effects on 16-QAM in Simulink

Add a phase noise vector and frequency offset vector to a 16-QAM signal. Display the constellation.

Open Model

View Phase Noise Effects on Signal Spectrum in Simulink

The effects that spectral and phase noise have on a 100 kHz sine wave.

Open Model

Impact of RF Effects on Communication System Performance

Model thermal noise, phase noise, and nonlinearity impairments of an RF transceiver in Simulink^®.

Open Model

Ports

Input

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 represents the number of samples and M is the number of channels.

Data Types: double | single
Complex Number Support: Yes

Output

Out — Output signal

vector | matrix

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

Parameters

Phase noise level (dBc/Hz) — 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 Phase noise level (dBc/Hz) and Frequency offset (Hz) parameters must have the same length.

Frequency offset (Hz) — 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 Sample rate (Hz) parameter value.

The Phase noise level (dBc/Hz) and Frequency offset (Hz) parameters must have the same length.

Sample rate (Hz) — 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 Frequency offset (Hz) parameter.

Initial seed — Initial seed of noise generator

2137 (default) | positive scalar

Initial seed of noise generator, specified as a positive scalar.

This block uses the Random Source block to generate noise. The block generates random numbers using the Ziggurat method (V5 RANDN algorithm). Every time you rerun the simulation, the block reuses the same initial seed. That way, the block outputs the same signal each time you run a simulation.

View Filter Response — Display magnitude response of filter

button

Display magnitude response of filter defined by the Phase Noise block. The block uses the FVTool function to display the magnitude response.

Simulate using — Type of simulation to run

Interpreted execution (default) | Code generation

Type of simulation to run, specified as Interpreted execution or Code generation.

• Interpreted execution — Simulate the model by using the MATLAB^® interpreter. This option requires less startup time, but the speed of subsequent simulations is slower than with the Code generation option. In this mode, you can debug the source code of the block.

• Code generation — Simulate the model by using generated C code. The first time you run a simulation, Simulink generates C code for the block. The model reuses the C code for subsequent simulations unless the model changes. This option requires additional startup time, but the speed of the subsequent simulations is faster than with the Interpreted execution option.

For more information, see Simulation Modes (Simulink).

Block Characteristics

Data Types	double | single
Multidimensional Signals	no
Variable-Size Signals	no

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 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 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. If N_t < 2⁸, 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 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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a