Physics-informed neural network for OSNR monitoring based on the nonlinear Schrödinger equation and fractional Fourier transform

The nonnegligible fiber nonlinearity and the relentless growth in transmission rates in modern optical systems has brought unprecedented challenges to the existing optical signal-to-noise ratio (OSNR) monitoring techniques. In this work, a novel phase-aware, nonlinear-tolerant, and interpretable physics-informed neural network (PINN) OSNR estimator based on the nonlinear Schrödinger equation (NLSE) and the fractional Fourier transform (FrFT) is proposed and experimentally validated for the first time. The proposed PINN OSNR estimator reveals the impact of phase-related information on OSNR estimation via an indirect phase-aware strategy based on NLSE. The FrFT is applied to achieve joint time-frequency and amplitude-phase features and further enhance OSNR estimation performance. Integration of the NLSE into the loss function allows the model to be closely aligned with the intrinsic physical characteristics of optical transmission systems, endowing it with improved interpretability and enhancing its robustness under unseen conditions. Experimental results yield consistently favorable results across high-nonlinearity, higher-order modulation coherent systems, and out-of-distribution data. The proposed model achieves average OSNR monitoring errors of 0.13, 0.26, and 0.19 dB for quadrature phase shift keying (QPSK), 16 quadrature amplitude modulation (16QAM), and 64QAM systems, respectively, and achieves an average estimation error of 1.12 dB with a maximum error of 2.6 dB on out-of-distribution data.