  Knowing only two high-order statistical moments of modulation symbols, often
represented by the fourth moment called "kurtosis", the overestimation of
nonlinear interference (NLI) in a Gaussian noise (GN) model due to Gaussian
signaling assumption can be corrected through an enhanced GN (EGN) model.
However, in some modern optical communication systems where the transmitted
modulation symbols are statistically correlated, such as in systems that use
probabilistic constellation shaping (PCS) with finite-length sphere shaping,
the kurtosis-based EGN model produces significant inaccuracies in analytical
prediction of NLI. In this paper, we show that for correlated modulation
symbols, the NLI can be more accurately estimated by substituting a statistical
measure called windowed kurtosis into the EGN model, instead of the
conventional kurtosis. Remarkably, the optimal window length for windowed
kurtosis is found to be consistent with the self-phase modulation (SPM) and
cross-phase modulation (XPM) characteristic times in various system
configurations. The findings can be used in practice to analytically evaluate
and design NLI-tolerant modulation formats.
