  A general theory of nonlinear signal-noise interactions for wavelength
division multiplexed fiber-optic coherent transmission systems is presented.
This theory is based on the regular perturbation treatment of the nonlinear
Schrodinger equation, which governs the wave propagation in the optical fiber,
and is exact up to the first order in the fiber nonlinear coefficient. It takes
into account all cross-channel nonlinear four-wave mixing contributions to the
total variance of nonlinear distortions, dependency on modulation format,
erbium-doped fiber and and backward Raman amplification schemes, heterogeneous
spans, and chromatic dispersion to all orders; moreover, it is computationally
efficient, being 2-3 orders of magnitude faster than the available alternative
treatments in the literature. This theory is used to estimate the impact of
signal-noise interaction on uncompensated, as well as on
nonlinearity-compensated systems with ideal multi-channel
digital-backpropagation.
