Carrier phase recovery friendly probabilistic shaping scheme based on a quasi-Maxwell–Boltzmann distribution model

A novel probabilistic shaping (PS) scheme based on the quasi-Maxwell–Boltzmann (quasi-MB) distribution model is proposed in order to solve the incompatibility between PS and carrier phase recovery (CPR) algorithms, such as blind phase search (BPS) and principal component-based phase estimation (PCPE). In the proposed quasi-MB model, the same occurrence probability is assigned to each constellation point on the same square-ring, rather than on the same circle. Signals obeying the quasi-MB model have superior CPR friendliness compared to traditional PS signals. For a PS 64 quadrature amplitude modulation system, the simulation results indicate up to 51% and 21% normalized generalized mutual information (NGMI) improvements for PCPE and BPS, respectively. Experimental verification of the proposed quasi-MB scheme was demonstrated in a 10 Gbaud coherent detection system. The results show that when the optical signal-to-noise ratio (OSNR) is low, the quasi-MB model can help the BPS algorithm to achieve better NGMI performance and, when the OSNR is high, the proposed model can also solve the incompatibility between the PCPE algorithm and PS.