Zheng Zibo, Zhang Xulun, Yu Ruihua, Xi Lixia, Zhang Xiaoguang
Opt Express. 2019 Sep 30;27(20):28223-28238. doi: 10.1364/OE.27.028223.
Although fruitful studies have been conducted on carrier frequency offset (CFO) estimations in linear coherent optical fiber communication systems, there are few studies on CFO estimations and recoveries in the systems based on the nonlinear Fourier transform (NFT). Although the CFO is originated from the linear frequency domain, it definitely has effects on nonlinear spectra, including the shift of the nonlinear frequency and the phase rotations of the scattering data, which are similar to its effects on linear spectra. This work indicates that it is feasible to estimate frequency offset (FO) by capturing symbol variations in the nonlinear frequency domain (NFD) rather than in the linear frequency domain; the latter was usually exploited in the literature. Based on a thorough investigation of the FO induced behavior that appears in a nonlinear frequency division multiplexing (NFDM) system, we proposed a nonlinear frequency domain estimation method aided by training symbols (TS) using an angle search algorithm after NFT operations at the receiver. The discussions in this paper prove that the proposed method is generally applicable to the NFDM systems regardless of whether using single or multiple eigenvalues. A performance comparison between the NFD method and the conventional method in the linear frequency domain is performed with different modulation formats for both single and multiple eigenvalue NFDM transmission systems. The analysis results show that the proposed method holds the better stability and estimation accuracy in contrast with the linear domain estimation method. The TS overhead can also be deduced dramatically, which implies better transmission efficiency. Therefore, the NFD method is more powerful for eigenvalue NFDM transmission systems, especially for the scenarios where high order modulation formats and multiple eigenvalues are utilized.
尽管在线性相干光纤通信系统中已经开展了关于载波频率偏移（CFO）估计的卓有成效的研究，但基于非线性傅里叶变换（NFT）的系统中关于CFO估计与恢复的研究却很少。尽管CFO源自线性频域，但它肯定会对非线性谱产生影响，包括非线性频率的偏移以及散射数据的相位旋转，这与它对线性谱的影响类似。这项工作表明，通过捕获非线性频域（NFD）而非线性频域中的符号变化来估计频率偏移（FO）是可行的；而后者在文献中通常被采用。基于对非线性频分复用（NFDM）系统中出现的由FO引起的行为的深入研究，我们提出了一种在接收机进行NFT操作后使用角度搜索算法并借助训练符号（TS）辅助的非线性频域估计方法。本文的讨论证明，所提出的方法普遍适用于NFDM系统，无论是否使用单个或多个特征值。针对单特征值和多特征值NFDM传输系统，使用不同的调制格式对NFD方法和线性频域中的传统方法进行了性能比较。分析结果表明，与线性域估计方法相比，所提出的方法具有更好的稳定性和估计精度。TS开销也可以大幅降低，这意味着更好的传输效率。因此，NFD方法对于特征值NFDM传输系统更具优势，特别是对于使用高阶调制格式和多个特征值的场景。
