Extending a Nonlinear SNR Estimator to Include Shaping Distribution Identification for Probabilistically Shaped 64-QAM Signals

Abstract

An estimation method for the nonlinear signal-to-noise ratio (SNR) is extended to simultaneously identify the shaping distribution for rate-adaptive probabilistically shaped (PS) 64-ary quadrature amplitude modulation (QAM) constellations. An artificial neural network (ANN) is trained with the fiber nonlinearity induced amplitude noise covariance and phase noise correlation extracted from received symbols. The identification employs estimates of the nonlinear signal-to-noise ratio $(\text{SNR}_{nl})$ and nonlinear system coefficients obtained from the ANN to extract the standardized constellation moments and hence identify the shaping distribution. The data used for training are 504 input–output sets, which are obtained from a simplified MATLAB simulation for a 32 Gbaud dual polarization PS 64-QAM signal considering seven different shaping distributions and a wide range of link configurations with varying fiber lengths and number of wavelength division multiplexed channels. Validation using 180 input–output sets that include five shaping distributions corresponding to a bit rate granularity of 25 Gb/s for bit rates between 200 and 300 Gb/s, exhibits high identification success rates, albeit for a limited set of examples. Reduced success rates are achieved for five shaping distributions corresponding to a bit rate granularity of 12.5 Gb/s for bit rates between 200 and 250 Gb/s. For completeness, the identification success rate is also quantified for the case of all seven shaping distributions in the validation.