Carrier Phase Recovery Combined Optimal Decision Threshold with Principal Component Analysis for Probabilistically Shaped Square-QAM Systems

We propose a carrier phase recovery (CPR) scheme combined optimal decision threshold with principal component analysis (ODT-PCA) for probabilistically shaped (PS) quadrature amplitude modulation (QAM) systems. Firstly, the rings with quadrature phase shift keying (QPSK)-shaped are selected in the PS-MQAM constellation using an optimal decision threshold method. Secondly, the amplitudes of the QPSK-shaped symbols are augmented to the outermost ring. Finally, the principal component analysis is used to recover the carrier phase of PS signals. The simulation results of 28 GBaud PDM PS-16/64QAM system demonstrate that the CPR performance of this ODT-PCA scheme achieves significant improvements over the classical principal component phase estimation (PCPE) scheme. Specifically, under moderate and strong shaping conditions, this scheme achieves consistently above the normalized generalized mutual information (NGMI) thresholds for PS-16QAM and PS-64QAM under optical signal-to-noise ratios (OSNRs) of 19 dB and 25 dB, respectively. The maximum linewidth tolerance of PS-16QAM and PS-64QAM could reach up to 8.1 MHz and 4.3 MHz, respectively.