Time-Domain Maximum Likelihood Estimation of Ultra-Fast RSOP and Phase in Coherent Optical PDM Systems

Coherent optical polarization-division multiplexing (PDM) is a promising technique to enhance spectral efficiency by transmitting data streams independently using orthogonal polarizations of light. However, in challenging conditions like lightning strikes, rotation of state of polarization (RSOP) due to Kerr and Faraday effects can cause significant signal distortions at speeds up to Mrad/s. In this paper, we propose a maximum likelihood (ML) and an expectation maximization (EM) estimator for the estimation of RSOP and laser phase noise (PN). The ML estimator utilizes pilot symbols for deriving explicit RSOP estimates, while the EM estimator iteratively refines estimates by incorporating unknown transmitted data as latent variables, which approximates the ML estimator's performance while enhancing spectral efficiency. A decision-aided (DA) scheme is subsequently proposed for dynamic tracking of RSOP and PN, as well as signal detection. The Cramér-Rao lower bounds (CRLBs) are derived for performance evaluation, and simulation results demonstrate the superior RSOP tracking performance of our proposed estimators over conventional methods, with capable tracking speed beyond 100 Mrad/s. The proposed methods also exhibit robustness to impairments such as laser PN, polarization dependent loss (PDL), fiber nonlinearity and residual chromatic dispersion (CD).