Carrier Phase Recovery Based on KL Divergence in Probabilistically Shaped Coherent Systems

We propose a novel carrier phase recovery (CPR) method in probabilistically-shaped (PS) coherent systems. This method targets to make the distribution of the received samples match that of the desirable constellation, which is realized by minimizing the Kullback-Leibler (KL) divergence between these two distributions. This is in contrast to conventional blind phase searching (BPS) or maximum likelihood estimation that targets to match the received samples with the transmitted symbols. Consequently, the proposed method avoids pre-decisions or feedback of data decisions in conventional methods. The distribution of the target constellation is the same as that used in soft-decision forward error correction (SD-FEC) and can be implemented via look-up tables. This distribution is re-used in the KL-based CPR, thus avoiding additional overhead and the calculation of the Euclidean distance as in conventional BPS. Minimizing the KL divergence can be achieved via a recursive algorithm, blind phase searching, or the combination of both. Simulation and experimental results show that the proposed methods outperform principal component analysis (PCA), PCA+BPS and Kalman filtering, and achieve similar performance as conventional 2-stage BPS but with greatly reduced complexity. The proposed methods are also format transparent, suitable for parallel processing in a feedforward manner, and so are promising for CPR especially in SD-FEC based PS coherent systems.