Opt Express. 2023 Apr 10;31(8):13455-13471. doi: 10.1364/OE.487168.
The practical Kramers-Kronig (KK) receiver has been a competitive receiving technique in the data-center, medium reach, and even long-haul metropolitan networks. Nevertheless, an extra digital resampling operation is required at both ends of the KK field reconstruction algorithm due to the spectrum broadening caused by adopting the nonlinear function. Generally, the digital resampling function can be implemented by using linear interpolation (LI-ITP), the Lagrange cubic interpolation (LC-ITP), the spline cubic interpolation (SC-ITP), time-domain anti-aliasing finite impulse response (FIR) filter method (TD-FRM) scheme, and fast Fourier transform (FFT)-based scheme. However, the performance and the computational complexity analysis of different resampling interpolation schemes in the KK receiver have not been thoroughly investigated yet. Different from the interpolation schemes of conventional coherent detection, the interpolation function of the KK system is followed by the nonlinear operation, which will broaden the spectrum significantly. Due to the frequency-domain transfer function of different interpolation schemes, the broadened spectrum will have a potential spectrum aliasing, which will cause serious inter-symbol interference (ISI) and further impair the KK phase retrieval performance. We experimentally investigate the performance of different interpolation schemes under different digital up-sampling rates (i.e. the computational complexity) as well as the cut-off frequency, the tap number of the anti-aliasing filter, and the shape factor of the TD-FRM scheme in a 112-Gbit/s SSB DD 16-QAM system over 1920-km Raman amplification (RFA)-based standard single-mode fiber (SSMF). The experimental results involve that the TD-FRM scheme outperforms other interpolation schemes and the complexity is reduced by at least 49.6%. In fiber transmission results, take 20% soft decision-forward error correction (SD-FEC) of 2×10 as the threshold, the LI-ITP and LC-ITP schemes only reach 720-km while others can reach up to 1440-km.
实用的 Kramer-Kronig (KK) 接收机一直是数据中心、中程甚至长距离城域网络中的一种有竞争力的接收技术。然而，由于采用非线性函数会导致频谱展宽，因此在 KK 域重构算法的两端都需要额外的数字重采样操作。通常，可以使用线性内插 (LI-ITP)、拉格朗日三次内插 (LC-ITP)、样条三次内插 (SC-ITP)、时域抗混叠有限脉冲响应 (FIR) 滤波器方法 (TD-FRM) 方案和基于快速傅里叶变换 (FFT) 的方案来实现数字重采样函数。然而，KK 接收机中不同重采样插值方案的性能和计算复杂度分析尚未得到彻底研究。与传统相干检测的插值方案不同，KK 系统的插值函数紧随非线性运算之后，这会显著扩展频谱。由于不同插值方案的频域传递函数，扩展后的频谱可能会产生潜在的频谱混叠，从而导致严重的码间干扰 (ISI)，进一步损害 KK 相位恢复性能。我们在 112-Gbit/s SSB DD 16-QAM 系统中实验研究了不同插值方案在不同数字上采样率（即计算复杂度）以及截止频率、抗混叠滤波器的抽头数和 TD-FRM 方案的形状因子下的性能在基于 1920 公里 Raman 放大 (RFA) 的标准单模光纤 (SSMF) 中。实验结果表明，TD-FRM 方案优于其他插值方案，复杂度至少降低了 49.6%。在光纤传输结果中，以 2×10 的 20%软判决前向纠错 (SD-FEC) 作为阈值，LI-ITP 和 LC-ITP 方案仅达到 720 公里，而其他方案则可以达到 1440 公里。
