Hybrid Probabilistic and Geometric Constellation Shaping for Phase Noise Channels with an Improved Differentiable Blind Phase Search

We perform hybrid probabilistic and geometric constellation shaping in a phase noise channel using a bitwise end-to-end learning scheme, including an improved two-stage differentiable blind phase search. The proposed approach outperforms geometrically shaped 64QAM by 0.086 bit/symbol in generalized mutual information at 350 kHz linewidth.