Joint equalization of RSOP and PMD fused probability-aware with square-root cubature Kalman filter for the PDM PCS-64QAM system under extreme scenarios.

Extreme scenario of lightning strikes would generate ultra-fast rotation of state-of-polarization (RSOP) up to 5.1 Mrad/s and large polarization mode dispersion (PMD) in optical ground wire (OPGW). Unfortunately, the conventional multiple modulus algorithm (MMA) cannot equalize these polarization impairments in polarization division multiplexing (PDM) probabilistic constellation shaping (PCS)-64QAM system. Moreover, due to unavoidable linearization errors and higher modulation order, the extended Kalman filter based on measurement equations of concatenated multiplication (EKF-CM) is highly unstable and fails under such scenarios. To address the above issues, we have proposed a joint equalization scheme of PMD and RSOP, which fuses probability-aware with square-root cubature Kalman filter (PA-SCKF). Firstly, according to the characteristic that the amplitude of PCS signals obeys mixed Rician distribution, the scheme combines maximum a posteriori criterion to obtain the optimal radius of constellation ring which the received symbol belongs to, for the sake of calculating the innovations of SCKF. Secondly, it performs joint equalization of PMD and RSOP impairments based on SCKF and time-frequency conversion architecture. 28GBaud PDM PCS-64QAM simulation results demonstrate that our scheme can jointly equalize maximum impairments of 8.34 Mrad/s RSOP and 90ps DGD under entropy of 4.5bits/symbol. Additionally, only 0.9 dB OSNR penalty is obtained after joint equalization of 6 Mrad/s RSOP with 70ps DGD impairments. Even under entropy of 5.5bit/symbol, it can still jointly equalize impairments of 6.05 Mrad/s RSOP with 60ps DGD. Furthermore, 16GBaud PCS-64QAM experimental results indicate that the maximum joint equalization performances of PA-SCKF scheme under entropy of 4.5bit/symbol and 5bit/symbol are 17 Mrad/s RSOP with 52ps DGD, and 9 Mrad/s RSOP with 52ps DGD, respectively. These results manifest that our PA-SCKF scheme outperforms both MMA and EKF-CM schemes. Importantly, its complexity is on an order of O(Llog2 L), which is comparable to that of EKF-CM scheme.

Joint equalization of frequency offset and phase noise using two-stage cascaded extended Kalman filter for discrete spectrum 16/64APSK NFDM systems.

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).

Joint equalization of EEPN, RSOP, and CD with the sliding window assisted extended Kalman filter for a high baud rate Stokes vector direct detection system.

Equalization-enhanced phase noise (EEPN) has emerged as one of the major impairments that cannot be ignored for a high baud rate Stokes vector direct detection (SVDD) system. When EEPN interacts with the rotation of state-of-polarization (RSOP) and chromatic dispersion (CD), the joint impairment effects become even more complicated. To achieve the joint equalization of EEPN, RSOP, and CD impairments of a high baud rate SVDD system, this paper first derives a joint impairment model of these three kinds of impairments, and then proposes a joint equalization scheme of EEPN, RSOP, and CD with a sliding window assisted extended Kalman filter (SWA-EKF). The SWA-EKF scheme first tracks RSOP in the time domain, subsequently compensates CD in the frequency domain, and finally performs EEPN mitigation in the time domain again. The effectiveness of the proposed scheme has been verified by a 60 GBaud SVDD-16QAM simulation system. The results show that when these three impairments are jointly equalized, the SWA-EKF scheme can track RSOP as fast as 3 Mrad/s, cumulative dispersion up to 1600 ps/nm, and EEPN caused by laser linewidth up to 3 MHz. In addition, with an optical signal-to-noise ratio penalty of 0.3 dB, it could increase 35 G baud rate under 3 MHz laser linewidth for the SVDD system. More importantly, its total complexity can be reduced to an order of O(N log N).