Blind frequency offset estimation using the optimal decision threshold-assisted QPSK-partition method for probabilistically shaped MQAM systems

Moderate or strong shaping conditions reduce the occurrence probability of the outermost ring constellation points of probabilistically shaped (PS)-M quadrature amplitude modulation (QAM) signals, which easily causes the peaks in the 4 h power periodogram of received signals be submerged, accordingly the classical frequency offset estimation (FOE) scheme using 4 h power fast Fourier transform (FFT) cannot be applied in PS-MQAM system. To solve this issue, we have proposed an optimal decision threshold assisted quadrature phase shift keying (QPSK)-partition blind FOE scheme. Firstly, the proposed scheme utilizes an optimal decision threshold assisted method for the symbol decision of received symbols, then chooses the symbols on multiple specific QPSK-shape rings. Secondly, the amplitude of each symbol selected above is normalized and uniformly augmented to 18. Finally, it carries out FOE using an improved time-domain 4 h power feedforward method that eliminates the time interval. The effectiveness of the proposed scheme has been verified by 28 GBaud polarization division multiplexing (PDM) PS-16/64QAM simulations and 28/8 GBaud PS-16/64QAM experiments. The results obtained by this scheme present that under moderate or strong shaping conditions, the generalized mutual information (GMI) increases with optical signal-to-noise ratio (OSNR) and eventually exceeds the corresponding GMI threshold. Besides that, the FOE range can reach [-Rs/8, Rs/8], where Rs denotes the baud rate. When OSNRs are higher than 16 dB and 19.5 dB, the NMSEs of PS-16QAM-3/3.6 are lower than 1e-7, respectively. For PS-64QAM-4.4/5, the NMSEs achieve lower than 1e-6 after OSNR increases to 20.3 dB and 23.4 dB, respectively. More importantly, the overall complexity can be reduced to O(N), which is at most as 26.5% as that of FFT FOE scheme.