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Extending fibre nonlinear interference power modelling to account for general dual-polarisation 4D modulation formats

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Document pages: 36 pages

Abstract: In optical communications, four-dimensional (4D) modulation formats encodeinformation onto the quadrature components of two arbitrary orthogonal statesof polarisation of the optical field. These formats have recently regainedattention due their potential power efficiency, nonlinearity tolerance, andultimately to their still unexplored shaping gains. As in the fibre-opticchannel the shaping gain is closely related to the nonlinearity tolerance of agiven modulation format, predicting the effect of nonlinearity is key toeffectively optimise the transmitted constellation. Many analytical modelsavailable in the optical communication literature allow, within a first-orderperturbation framework, the computation of the average power of the nonlinearinterference (NLI) accumulated in coherent fibre-optic transmission systems.However, all current models only operate under the assumption of a transmittedpolarisation-multiplexed, two-dimensional (PM-2D) modulation format. PM-2Dformats represent a limited subset of the possible dual-polarisation 4Dformats, namely, only those where data transmitted on each polarisation channelare mutually independent and identically distributed. This document presents astep-by-step mathematical derivation of the extension of existing NLI models tothe class of arbitrary dual-polarisation 4D modulation formats. In particular,the methodology adopted follows the one of the popular enhanced Gaussian noisemodel, albeit dropping most assumptions on the geometry and statistic of thetransmitted 4D modulation format. The resulting expressions show that, whilstin the PM-2D case the NLI power depends only on different statisticalhigh-order moments of each polarisation component, for a general 4Dconstellation also several others cross-polarisation correlations need to betaken into account.

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