A Theory of Nonlinear Signal-Noise Interactions in Wavelength Division Multiplexed Coherent Systems

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 Schrödinger 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 fourwave 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.