In this paper, we propose a novel carrier phase recovery scheme based on Kalman Filter with Principal Component Analysis (KF-PCA) for coherent optical transmission system, which is a low-complexity, Non-Data-Aided (NDA), feed-forward Carrier Phase Recovery (CPR) algorithm. The proposed algorithm enables synchronous demodulation of square Quadrature Amplitude Modulation (QAM) constellations, and it is suitable for a practical hardware implementation based on block-wise parallel processing. The proposed algorithm is employed to obtain an optimal estimate of carrier phase with minimum mean squared error by data fusion of the predicted results and the observed results obtained from principal component analysis in the corresponding squared constellation. We demonstrate different transmission distances of 500-1500km and different Optical Signal-to-Noise Ratios (OSNR) values of a dual-polarization 40GBaud 16- QAM signal with Root Raised Cosine (RRC) pulse shaping with a roll off factor of 0.02 by using the proposed algorithm in the offline Digital Signal Processing (DSP). Numerical simulation results show that the proposed phase recovery algorithm outperforms the Kalman Filter (KF) algorithm, showing much lower Bit Error Rate (BER) both numerically and experimentally. And it achieves similar BER performance compared with the well-known and widely used Blind Phase Search (BPS) algorithm. Additionally, the complexity of the proposed methods represents an effective computational complexity reduction against BPS.
With the rapid development of global communications and exponential growth of network traffic, the flexibility and dynamism of the modulation format and the transmission rate have become important characteristics of the development of the next generation of optical networks. The optical network must be capable of dynamically transferring signals of different modulation formats and data rates to satisfy the requirements of flexible and high-capacity optical network transmission. In this work, we propose a modulation format identification method based on the mean-shift cluster algorithm to implement the reception of different modulation format signals in high-speed optical communication adaptively. The proposed MFI is a spatial cluster method based on density distribution, which can automatically extract the cluster number and density information of samples by estimating the density distribution of samples in the space. In this paper, we construct a 10 GBaud coherent optical simulation system, transmitting QPSK, 8QAM, 16QAM, 32QAM, and 64QAM, to verify the feasibility of this method. The transmission fiber length of the simulation system is set to 80 km. In the case of considering the CD dispersion parameter to 16 ps/(nm·km) and the linewidth is 100 kHz, the simulation results show that the proposed MFI method can achieve 100% identification accuracy when the OSNR values are lower than the 7% FEC limit corresponding to the lowest required OSNR values for five commonly used modulation formats (MFs). Among them, when the OSNR values of 16QAM and 32QAM signals respectively are 17 dB and 21 dB, the identification rate reaches 100%, which can effectively complete the high-precision classification of different modulation formats.
In this paper, a flexible extended Kalman filtering (EKF)/cubature Kalman filtering (CKF) switching scheme with fast frequency offset (FO) estimation is proposed to cope with the impairments due to FO and rotational state of polarization (RSOP) caused by lightning strikes in optical fiber communication systems. The fast FO estimation method based on statistics is introduced to compensate the residual FO after coarse estimation with fast Fourier transform (FFT). The aggregation of symbol angles is used as a statistical measurement of FO. The switchable Kalman filtering enables compensation for varied fast RSOP by mathematically modelling lightning strikes and automatic switching between EKF and CKF. The EKF compensates better under slow RSOPs and less well under fast RSOPs caused by sudden lightning strikes. Hence CKF is introduced to compensate for the fast RSOP after a sudden lightning strike. To achieve automatic switching between EKF and CKF, RLC high voltage charge-discharge model is introduced to emulate RSOP of lightning strikes and use EKF to track RSOP in time domain. The effectiveness of the proposed scheme has been verified in a 14 GBaud PDM-16QAM simulation system which effectively improve the FO and RSOP tolerance for optical fiber communication systems. The results show that the proposed fast FO estimation method can tolerate FO up to 800 MHz. The Bit Error Rate (BER) performance with different FOs also verified the effectiveness of the proposed scheme. The maximum speed of RSOP caused by lightning strikes compensated by CKF can reach up to 80 Mrad/s, while EKF is less than 70 Mrad/s. Moreover, the tracking parameter of EKF had a sudden change after lightning strikes which can be used to set the threshold to automatic switching between EKF and CKF.
In order to solve the problems of fiber nonlinear effects due to constellation expansion and the reduction of information entropy due to constellation shaping, an 8-dimensional trellis coded 16-quadrature amplitude modulation format with probabilistic-geometric joint shaping (8D-TCM-PS-GS-16QAM) in high-speed optical communications is proposed. The BER performance of 8D-TCM-PS-GS-16QAM signals with unshaped, geometrical shaping only, and probabilistic-geometrical joint shaping (H=14/13/12 bits/symbol) is simulated. At a BER of 3.8e-3, the four shaped signals are able to obtain a gain of 0.36dB, 1.52dB, 2.02dB, and 2.46dB, respectively, compared with the unshaped signal. The BER performance of low-dimensional, i.e., 2D and 4D signals is also simulated. Comparing the gains obtained for 8D-TCM-PS- GS-16QAM (H=14 bits/symbol), 4D-TCM-PS-GS-16QAM (H=6 bits/symbol), and 2D-TCM-PS-GS-16QAM (H=2 bits/symbol) with the unshaped signals in the corresponding dimensions, the gains obtained at 3.8e -3 BER, are 1.52 dB, 2.29 dB, and 4.16 dB, respectively. Constellation shaping causes all three to sacrifice the same total information entropy of 1bits/symbol, but the information entropy sacrificed by the basic 2D constellations of the 8D signal is only 50%, 25% of that of the 4D and 2D signals. Meanwhile, the shaping gain obtained by the 8D signal reaches 66.4% and 36.5% of the 4D and 2D signals, respectively. This scheme enables the whole scheme to flexibly adjust the spectral efficiency (SE). Meanwhile, it increases the degree of freedom of the signal. This scheme can realize high BER performance transmission of high SE signals. It has great potential for future construction in high-capacity and high-speed optical communications.
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