Temporal Gaussian Noise Model for Equalization-Enhanced Phase Noise

Benedikt Geiger, Fred Buchali, Vahid Aref, and Laurent Schmalen

This repository contains an implementation of the Temporal Gaussian Noise (TGN) Model for Equalization-Enhanced Phase Noise (EEPN) proposed in [1], along with a full end-to-end system simulation as a reference.
Implementations are provided in MATLAB (both as a Live Script and as a plain .m file) and in Python (as a Jupyter Notebook).

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Minimal Model Implementation

The TGN Model can be realized in just three lines of code:

MATLAB

% (1) Load or generate LO phase noise realization
Rx_phi = cumsum(sqrt(sigma2_LO) * randn(size(Tx_symbols),1)) + 2*pi*rand(1);

% (2) Calculate the time-varying distortion power
sigma_time_varying = system_noise_power + movvar(Rx_phi, CD_memory + 1);

% (3) Sample AWGN from time-varying distortion power and add to transmit signal
Rx_symbols = Tx_symbols + sqrt(time_varying/2) .* ...
             (randn(size(Tx_symbols)) + 1j*randn(size(Tx_symbols)));

Python

\# (1) Load or generate LO phase noise realization
Rx_phi = np.cumsum(np.sqrt(sigma2_LO) * np.random.randn(len(Tx_symbols))) + 2*np.pi*np.random.rand()

\# (2) Calculate the time-varying distortion power
sigma_time_varying = system_noise_power + movvar(Rx_phi, CD_memory + 1)

\# (3) Sample AWGN from time-varying distortion power and add to transmit signal
Rx_symbols = Tx_symbols + (np.sqrt(sigma_time_varying/2)*np.random.randn(len(Tx_symbols)) + 1j*np.sqrt(sigma_time_varying/2)*np.random.randn(len(Tx_symbols)))

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Variable Definitions

sigma2_LO — variance of the LO Wiener process

$$ \sigma^2_{\text{LO}} = \frac{2\pi\cdot\text{linewidth}}{\text{oversampling factor}\cdot\text{symbol rate}} $$

CD_memory — chromatic-dispersion–induced memory (in samples)

$$ \mathrm{CD_memory} = D_{CD}\cdot\text{fiber length}\cdot\frac{\lambda^2}{c_0}\cdot\text{symbol rate}^2 $$

system_noise_power — noise power accounting for ASE, fiber nonlinearity, and transceiver impairments

Tx_symbols — normalized transmit symbols (e.g., 16‑QAM)

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Reference

[1] B. Geiger, F. Buchali, V. Aref, and L. Schmalen, “A temporal Gaussian noise model for equalization-enhanced phase noise,”
Proc. Eur. Conf. Opt. Commun. (ECOC), Copenhagen, Denmark, Sep. 2025.
arXiv:2507.08470