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The traditional fast Fourier transform based frequency offset estimation (FFT-FOE) estimates the frequency offset by searching the spectral peak of the signal after the fourth power operation, which is suitable for multiple modulation formats. But the accuracy of FOE is limited by the number of FFT points. In this paper, we propose a high accuracy and low complexity FOE algorithm based on all phase FFT (APFFT-FOE). The accuracy of FOE can be improved effectively with lower additional computational complexity. Simulation results show that the mean square error of APFFT-FOE is reduced by more than one order of magnitude compared with the FFT-FOE. Compared with other FOE algorithms that can achieve the same accuracy, the additional computational complexity required by APFFT-FOE is reduced by more than 50<inline-formula><tex-math notation="LaTeX">$\%$</tex-math></inline-formula>. Finally, the APFFT-FOE is experimentally verified with 20 GBaud 16/64-QAM modulation signal. The experimental results show that the required OSNR for 16-QAM signal to reach 6.7<inline-formula><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> hard-decision forward-error correction is relaxed by 0.23 dB. For 64-QAM signal, the required OSNR at 20<inline-formula><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> soft-decision forward-error correction threshold is relaxed by 0.68 dB.

High Accuracy and Low Complexity Frequency Offset Estimation Method Based on All Phase FFT for M-QAM Coherent Optical Systems