Low-Complexity Frequency Offset Estimation for Probabilistically Shaped MQAM Coherent Optical Systems

Since the reduction of the proportion of high modulus constellation points with π/4 +
k
π/2 (
k
= 0, 1, 2, 3) modulation phase in probabilistically shaped (PS)-
M
-ary quadrature amplitude modulation (MQAM) deteriorates the power spectrum peak of frequency offset from the 4th power signal, the conventional 4th power Fast Fourier Transform (FFT) algorithm is not suitable for PS-MQAM under moderate or strong shaping. In this paper a low-complexity multi-format frequency offset estimation (FOE) scheme is proposed, where the coarse estimation is based on extended quadrature phase shift keying (QPSK) partitioning and quasi-linear approximation in polar coordinates at the first stage, and the fine estimation in subsequent stage using Digital Amplification and 4th power FFT with Sparse Operation. The computational complexity is approximately reduced by 71% compared with radius directed (RD) 4th power FFT algorithm with the same mutual information (MI) performance under 2e-2 bit error rate (BER). Dual polarization (DP) PS-16/32/64QAM numerical simulations prove that the normalized mean square error (NMSE) of proposed FOE scheme is an order of magnitude lower than that of RD 4th power FFT algorithm. The higher FOE accuracy has been demonstrated experimentally in DP PS-16/32QAM systems.