Abstract

An accurate, closed-form expression to evaluate the nonlinear interference (NLI) noise power in Nyquist-spaced, coherent optical communication systems using backward-pumped Raman amplification is presented. This enables rapid estimation of the signal-to-noise ratio (SNR) and avoids the need of integral evaluations and split-step simulations. The accuracy of the proposed formula is compared to numerical integration of the Gaussian noise (GN) model and split-step simulations over a wide range of parameters, including three different fiber types. Additionally, the impact of pump depletion on the NLI noise power is studied and the formula is applied to a second-order Raman-amplified system. In the case of first-order amplification and negligible pump depletion, a maximum deviation of 0.34 dB in NLI coefficient between the GN model and the closed-form formula is found, which corresponds to a maximum deviation of similar to 0.1 dB in optimal SNR or similar figures of merit (e.g., maximum reach). When pump depletion is considered, it is shown that the NLI coefficient becomes a function of launch power and as a result the cubic power dependence of the NLI noise power is no longer valid in such regimes. Finally, for the second-order Raman-amplified system, a maximum deviation of 0.39 dB in NLI coefficient is reported.