  Probabilistic shaping (PS) is a promising technique to approach the Shannon
limit using typical constellation geometries. However, the impact of PS on the
chain of signal processing algorithms of a coherent receiver still needs
further investigation. In this work we study the interplay of PS and phase
recovery using the blind phase search (BPS) algorithm, which is widely used in
optical communications systems. We first investigate a supervised phase search
(SPS) algorithm as a theoretical upper bound on the BPS performance, assuming
perfect decisions. It is shown that PS influences the SPS algorithm, but its
impact can be alleviated by moderate noise rejection window sizes. On the other
hand, BPS is affected by PS even for long windows because of correlated
erroneous decisions in the phase recovery scheme. The simulation results also
show that the capacity-maximizing shaping is near to the BPS worst-case
situation for square-QAM constellations, causing potential implementation
penalties.
