Polynomial Closed-Form Model for Evaluating Nonlinear Interference in Any Island

TL;DR

The work tackles accurate evaluation of nonlinear interference (NLI) PSD in optical spans with islanded spectral profiles, including SCI, XCI and MCI, under ISRS and Raman amplification. It proposes the Polynomial Closed-Form GN Model (PCFM), which represents the spatial power-profile along a span as a polynomial of degree $N_p$ to enable closed-form evaluation of GN-model integrals. A central result is a generic closed-form for the NLI PSD contribution $G_{ ext{NLI},x}^{(n_s)}(f_{ ext{CUT}})$ that factors into channel PSDs and a core integral $K_x^{(n_s)}(f_{ ext{CUT}})$, which, after substituting $p_x^{(n_s)}(z)= left( 0n=0}^{N_p} p_{n,x}^{(n_s)} z^n ight)$, reduces to a finite sum over $(n,m)$ and frequency rectangles with $I_{nm}$ expressed via sine-integrals $ ext{Si}$ and related functions. The resulting expressions are real-valued and applicable to all island types, including low-dispersion and low-baud-rate regimes, and they accommodate ISRS, Raman amplification, and lumped span loss.

Abstract

Polynomial closed-form GN model is proposed by expressing the spatial power profile of each channel along a span as a polynomial. In this paper, we present the generic closed-form expression for all contributions of self-, cross-, and multi-channel interference. The full derivation is provided.