Blind Carrier Frequency Offset Estimation in Coherent Optical Communication Systems With Probabilistically Shaped M-QAM

We find that the conventional 4th power and circular harmonic expansion (CHE) algorithms, which are originally devised for blind frequency offset estimation (FOE) in the uniform M-quadrature amplitude modulation (MQAM) systems, cannot work properly for probabilistically shaped (PS)-MQAM under moderate or strong shaping. To solve this issue, two novel blind FOE algorithms, namely the radius directed (RD)-4th power algorithm and the generalized circular harmonic expansion (GCHE) algorithm, are proposed. The former one adopts QPSK-selection based on a radius threshold optimized for a specific constellation entropy; while the later one conducts maximum likelihood (ML) estimation with a theoretically derived nonlinear radius transfer function in the GCHE. Several issues related to the practical implementation, including the optimization of the radius threshold in the RD-4th power algorithm, the impact of SNR-mismatch in the GCHE algorithm, and the computational complexities of the proposed algorithms, are analyzed. The Monte-Carlo simulation results show that: (1) the RD-4th power algorithm works properly in most of the cases except for very weak shaping, whereas the GCHE algorithm offers robust performance regardless of the shaping strength and outperforms the RD-4th power algorithm in all cases; (2) the performance gap between the two algorithms, which have the same computational complexity, enlarges for a larger constellation entropy. These observations indicate that the GCHE algorithm is a promising blind FOE algorithm, in terms of high estimation accuracy and robust performance, for applications that leverage the rate adaptability of the PS-MQAM, such as flexible optical networks.