Disaggregable Outage-Aware SNR Modeling under PDL Uncertainty for Optical Network Digital Twins

Polarization-dependent loss (PDL) makes the post-equalization signal-to-noise ratio (SNR) of a coherent optical lightpath stochastic, with an outage-relevant lower tail that depends on the longitudinal interleaving of PDL elements and amplified-spontaneous-emission (ASE) noise sources. Under a finite- hinge representation, the inverse-SNR is a weighted sum of correlated exponentials of a random walk, whose exact evaluation is too costly for repeated quality-of-transmission assessment in an optical network digital twin (ONDT), where physical-layer models are continuously combined with network data to predict transmission feasibility and support network operation. We model the PDL magnitude of each element through a Maxwell prior in dB and compare five efficient approximations: gamma moment matching, recursive moment-matched lognormal, correlated Fenton–Wilkinson lognormal, delta-cumulant log-skew- normal, and third-moment recursive log-skew-normal. Their descriptors can be accumulated element by element or exchanged as a constant-size moment state across vendor and operator domains, while allowing different PDL statistics in different network portions. Monte Carlo validation based on 109 realizations, with N ∈ {2, 10, 40} and σPDL from 0.1 to 1.5 dB, shows that no approximation is uniformly best. In the practically relevant sub-1 dB range, the third-moment recursive log-skew-normal model is generally the most accurate global approximation and provides the best overall outage-tail prediction, with outage- probability errors typically within a few tenths of a decade and outage-quantile errors of about 0.2 dB or less. Realistic core–metro and metro–access examples further show that propagation direction, received optical power, and transceiver SNR jointly alter both the reference SNR and the distribution shape. The scope is limited to ASE-dominated links, independent per-element Maxwell priors, and ideal zero-forcing polarization equalization; Kerr nonlinear noise, non-ideal receivers, and correlated or telemetry-conditioned PDL models remain for future work.