# On Discrete-Time/Frequency-Periodic End-to-End Fiber-Optical Channel Models

## TL;DR

This paper develops a novel discrete-time and frequency-periodic end-to-end fiber-optical channel model based on perturbation theory, offering a new perspective on nonlinear interference and efficient computational implementation.

## Contribution

It introduces a new frequency-domain periodic model with aliasing considerations and extends the regular model to include multiplicative distortions, improving analysis accuracy.

## Key findings

- Model aligns well with split-step Fourier method in MSE sense
- Provides a single-step computational algorithm
- Incorporates aliasing effects in frequency domain

## Abstract

A discrete-time end-to-end fiber-optical channel model is derived based on the first-order perturbation approach. The model relates the discrete-time input symbol sequences of co-propagating wavelength channels to the received symbol sequence after matched filtering and T-spaced sampling. To this end, the interference from both self- and cross-channel nonlinear interactions of the continuous-time optical signal is represented by a single discrete-time perturbative term. Two equivalent discrete-time models can be formulated---one in the time-domain, the other in the 1/T-periodic continuous-frequency domain. The time-domain formulation coincides with the well-known pulse-collision picture. The novel frequency-domain picture incorporates the sampling operation via an aliased and periodic kernel description. This gives rise to an alternative perspective on the end-to-end input/output relation between the spectrum of the discrete-time transmit symbol sequence and the spectrum of the receive symbol sequence. Both views can be extended from a regular, i.e., solely additive model, to a combined regular-logarithmic model to take the multiplicative nature of certain distortions into consideration. An alternative formulation of the Gaussian Noise model is provided to take the aliasing of frequency components correctly into account. A novel algorithmic implementation of the discrete and periodic frequency-domain model is presented. The derived end-to-end model requires only a single computational step and shows good agreement in the mean-squared error sense compared to the oversampled and inherently sequential split-step Fourier method.

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Source: https://tomesphere.com/paper/1907.06087