Gao Hongbing, Xu Hengying, Dong Tingting, Yao Donghu, Zhang Yining, Bai Chenglin, Yang Lishan, Li Xusheng, Sun Zukai, Fan Yaxuan
Opt Express. 2024 Feb 12;32(4):6366-6381. doi: 10.1364/OE.512167.
For the discrete spectrum nonlinear frequency division multiplexing (DS-NFDM) 16/64 amplitude phase shift keying (APSK) system, the inevitable laser impairments including frequency offset (FO) and carrier phase noise (CPN) would cause different rotations of the received signal constellations. In addition, the combined effect of FO and amplifier spontaneous emission (ASE) noise induces the eigenvalue shift, accordingly the residual channel impairment (RCI) is inevitably yielded. To address the above problems, we deduce the joint impairment model of FO, CPN and RCI, and then propose a joint equalization scheme using two-stage cascaded extended Kalman filter (TSC-EKF) for these impairments. It performs frequency offset compensation in the first stage, subsequently carries out joint equalization of CPN and RCI in the second stage. Meanwhile, the minimum Euclidean distance and phase difference between the received symbols and the ideal 16/64APSK constellations are ingeniously fused to calculate the innovations of TSC-EKF. The effectiveness has been verified by 2 GBaud DS-NFDM 16/64 APSK simulations and DS-NFDM 16APSK transmission experiments. The results demonstrate that when performing the joint equalization of FO, CPN and RCI, the maximum FOE range of TSC-EKF scheme achieves 1.2 and 9.6 times as that of nonlinear frequency domain (NFD) scheme and fast Fourier transform -Like (FFT-Like) scheme, respectively. Furthermore, its maximum LW tolerance reaches 3.3 times as that of the M-th power scheme. Importantly, the complexity of TSC-EKF is 63.4% as that of NFD scheme and on an order of O(N).
对于离散频谱非线性频分复用（DS-NFDM）16/64幅度相位键控（APSK）系统，不可避免的激光损伤，包括频率偏移（FO）和载波相位噪声（CPN），会导致接收信号星座图的不同旋转。此外，FO和放大器自发辐射（ASE）噪声的联合效应会引起特征值偏移，从而不可避免地产生残余信道损伤（RCI）。为了解决上述问题，我们推导了FO、CPN和RCI的联合损伤模型，然后针对这些损伤提出了一种使用两级级联扩展卡尔曼滤波器（TSC-EKF）的联合均衡方案。它在第一阶段进行频率偏移补偿，随后在第二阶段对CPN和RCI进行联合均衡。同时，巧妙地融合了接收符号与理想16/64APSK星座图之间的最小欧几里得距离和相位差，以计算TSC-EKF的创新值。通过2 GBaud DS-NFDM 16/64 APSK仿真和DS-NFDM 16APSK传输实验验证了其有效性。结果表明，在对FO、CPN和RCI进行联合均衡时，TSC-EKF方案的最大FOE范围分别是非线性频域（NFD）方案和类快速傅里叶变换（FFT-Like）方案的1.2倍和9.6倍。此外，其最大LW容限达到M次幂方案的3.3倍。重要的是，TSC-EKF的复杂度是NFD方案的63.4%，且为O(N)量级。
