Low Complexity Two-Stage FOE Using Modified Zoom-FFT for Coherent Optical M-QAM Systems
Bi Tang, Jing Zhang, Shaohua Hu, Bo Xu, Hongbo Zhang, Guangze Ge, Kun Qiu
Abstract
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4.0\times 10^{-9}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.6\times 10^{-9}$ </tex-math></inline-formula> 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.