Estimating the Outage Probability Due to Polarization Dependent Loss Using Threshold Exceedances

The method of threshold exceedances is used to reliably estimate the outage probability due to per-span polarization dependent loss (PDL). Bit-wise achievable information rate (BW-AIR) data for 10,000 instances of the link PDL are obtained using a simulation model that accurately captures the effect of PDL on both the signal and amplified spontaneous emission noise. The root mean square error between the mean excess function and a theoretical fit to it, and the average squared absolute error are compared for the critical step of determining the threshold above which transformed BW-AIR data are represented by the generalized Pareto distribution (GPD). Four techniques are considered for determining values of the two parameters that specify the GPD. The outage probability is defined in terms of the BW-AIR being less than a threshold value for the generalized mutual information (GMI), as determined by a specified value for the normalized GMI. To thoroughly demonstrate the approach, the dependence of the outage probability on the per-span PDL, the number of spans, and the constellation entropy is considered for 32 Gbaud, dual-polarization 64-ary quadrature amplitude modulation with uniform and probabilistically shaped constellations. The extent to which the outage probability can be reduced by decreasing the constellation entropy is quantified.