We propose a novel low complexity two-stage frequency offset estimation (FOE) scheme based on modified Zoom-FFT for square 16/64-quadrature amplitude modulation (QAM) coherent optical systems. The first stage roughly estimates the frequency offset through a small size FFT. After frequency shifting, the modified Zoom-FFT can select and reconstruct the spectrum of interest by time domain average. Since the average provides a good estimate of the amplitudes of the frequency components, we can accurately find the peak after the second-stage FFT. We conduct simulations and compare the normalized frequency variance of the proposed scheme with different algorithms, e.g., the single-stage FFT and the Chirp-Z transform (CZT). The simulation results show that the proposed FOE scheme has the similar normalized frequency variance as other algorithms of $4.0\times 10^{-9}$ and $1.6\times 10^{-9}$ for 16QAM and 64QAM, respectively. The numerical simulations and experimental results demonstrate that the proposed scheme can achieve comparable performance, while the complexity is reduced by 86.6% (81.2%) and 60.9% (61.2%) for 16QAM (64QAM) compared with single-stage FFT and FFT+CZT, respectively.

中文翻译：

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使用改进的 Zoom-FFT 的低复杂度两级 FOE 用于相干光 M-QAM 系统

我们针对方形 16/64 正交幅度调制 (QAM) 相干光学系统提出了一种基于改进的 Zoom-FFT 的新型低复杂度两级频偏估计 (FOE) 方案。第一阶段通过小尺寸 FFT 粗略估计频率偏移。频移后，改进的 Zoom-FFT 可以通过时域平均来选择和重建感兴趣的频谱。由于平均值提供了对频率分量幅度的良好估计，我们可以在第二阶段 FFT 之后准确地找到峰值。我们进行模拟并将所提出方案的归一化频率方差与不同算法进行比较，例如，单级 FFT 和 Chirp-Z 变换 (CZT)。仿真结果表明，所提出的 FOE 方案具有与其他算法相似的归一化频率方差。 $4.0\乘以 10^{-9}$ 和 $1.6\乘以 10^{-9}$ 分别为 16QAM 和 64QAM。数值模拟和实验结果表明，与单级FFT和FFT+CZT相比，所提出的方案可以达到相当的性能，而16QAM（64QAM）的复杂度降低了86.6%（81.2%）和60.9%（61.2%） ， 分别。