On Discrete-Time/Frequency-Periodic End-to-End Fiber-Optical Channel Models
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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 that 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 models can be formulated---one in the discrete-time domain, the other in the 1/T-periodic continuous-frequency domain. The time-domain formulation coincides with the pulse-collision picture and its correspondence to the frequency-domain description is derived. The latter gives rise to a novel perspective on the end-to-end input/output relation of optical transmission systems. 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 degenerate distortions into consideration. We provide an alternative formulation of the Gaussian Noise model and derive a novel algorithm for application in low-complexity fiber nonlinearity compensation. 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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