Extending Fibre Nonlinear Interference Power Modelling to Account for General Dual-Polarisation 4D Modulation Formats

Abstract

In optical communications, four-dimensional (4D) modulation formats encode information onto the quadrature components of two arbitrary orthogonal states of polarisation of the optical field. Many analytical models available in the optical communication literature allow, within a first-order perturbation framework, the computation of the average power of the nonlinear interference (NLI) accumulated in coherent fibre-optic transmission systems. However, all such models only operate under the assumption of transmitted polarisation-multiplexed two-dimensional (PM-2D) modulation formats, which only represent a limited subset of the possible dual-polarisation 4D (DP-4D) formats. Namely, only those where data transmitted on each polarisation channel are mutually independent and identically distributed. This paper presents a step-by-step mathematical derivation of the extension of existing NLI models to the class of arbitrary DP-4D modulation formats. In particular, the methodology adopted follows the one of the popular enhanced Gaussian noise model, albeit dropping most assumptions on the geometry and statistic of the transmitted 4D modulation format. The resulting expressions show that, whilst in the PM-2D case the NLI power depends only on different statistical high-order moments of each polarisation component, for a general DP-4D constellation, several other cross-polarisation correlations also need to be taken into account.

Modeling of Nonlinear Interference Power for Dual-Polarization 4D Formats

“…Moreover, we show that heuristic extensions of the EGN model to non PM-2D formats may lead to inaccuracies in the prediction of the NLI power coefficient beyond 1 dB, even for fairly regular 4D modulation formats. Our 4D model [6] is instead proven to be accurate on average within 0.1 dB for all 4D modulation formats studied in this work.…”

“…The model's expression was derived using a first-order perturbational approach under the hypothesis of single-channel transmission with quasi-rectangular pulse spectrum. A comprehensive discussion on the assumptions of the model as well as its mathematical derivation can be found in [6].…”

“…Recently, in [6], we extended the model in [1] to account for the entire DP-4D class of modulation formats. In this contribution, we present a first numerical validation of our 4D model.…”

“…. , 11 in[6, Table 8]. The expression for η y can be found from(1) by simply applying the transformation x → y and y → x.…”

Model-aided Geometrical Shaping of Dual-polarization 4D Formats in the Nonlinear Fiber Channel

“…Recently in [4], we have introduced a new analytical expression for the prediction of the NLI power when a general DP-4D linear modulation is adopted. The model expresses the dependency of the NLI power on the modulation format in closed-form thus enabling a fast search of the most nonlinearly tolerant DP-4D constellations.…”