A Theory of Nonlinear Interactions Between Signal and Amplified Spontaneous Emission Noise in Coherent Wavelength Division Multiplexed Systems

A general theory of nonlinear interactions between signal and amplified spontaneous emission noise in 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 four-wave mixing contributions to the total variance of nonlinear distortions, dependency on modulation format, erbium-doped fiber and backward Raman amplification schemes, heterogeneous spans, and chromatic dispersion to all orders; moreover, it is computationally efficient. This theory is used to estimate the impact of the signal-noise interaction on the unmitigated, as well as on the nonlinearity-mitigated systems with ideal multi-channel digital backpropagation, and to study the fundamental limits of zero-forcing nonlinear equalization of the fiber-optic coherent transmission systems.