  Probabilistic shaping (PS) is investigated as a potential technique to
approach the Shannon limit. However, it has been proved that conventional
carrier phase recovery (CPR) algorithm designed for uniform distribution may
have extra penalty in PS systems. In this paper, we find that the performance
of QPSK partition algorithm is degenerated when PS is implemented. To solve
this issue, a modified QPSK partition algorithm that jointly optimizes the
amplitude decision threshold and filter weight is proposed, where the
optimization of decision threshold is based on maximum a posterior probability
(MAP) estimation. Different from the conventional decision methods which
commonly use Euclidean distance metric, the MAP-based decision introduces the
statistical characteristics of the received signals to obtain an accurate
amplitude partition. In addition, the filter weight is optimized for different
decision thresholds to enhance the tolerance of ASE-induced phase noise. We
verify the feasibility of the proposed algorithm in a 56 GBaud PS 16-ary
quadrature amplitude modulation (16-QAM) system. The proposed algorithm reduces
the error of phase noise estimation by nearly half. Compared with conventional
QPSK partition, the proposed algorithm could narrow the gap with theoretical
mutual information (MI) by more than 0.1 bit/symbol. The channel capacity is
increased by 4.2%, 4.3% and 3.6% with signal-to-noise ratio (SNR) from 8 dB to
10 dB respectively. These observations show that the proposed algorithm is a
promising method to relieve the penalty of QPSK partition algorithm in PS
systems.
