  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.
