In this paper, we highlight that it is inadequate to describe the rotation of the state of polarization (RSOP) in a fiber channel with the 2-parameter description model, which was mostly used in the literature. This inadequate model may result in problems in polarization demultiplexing (PolDemux) because the RSOP in a fiber channel is actually a 3-parameter issue that will influence the state of polarization (SOP) of the optical signal propagating in the fiber and is different from the 2-parameter SOP itself. Considering three examples of the 2-parameter RSOP models typically used in the literature, we provide an in-depth analysis of the reasons why the 2-parameter RSOP model cannot represent the RSOP in the fiber channel and the problems that arise for PolDemux in the coherent optical receiver. We present a 3-parameter solution for the RSOP in the fiber channel. Based on this solution, we propose a DSP tracking and equalization scheme for the fast time-varying RSOP using the extended Kalman filter (EKF). The proposed scheme is proved to be universal and can solve all the PolDemux problems based on the 2- or 3-parameter RSOP model and exhibits good performance in the time-varying RSOP scenarios.

Nonlinear frequency division multiplexing (NFDM) has been shown to be promising in overcoming the fiber Kerr nonlinearity limit. In multiple-eigenvalue modulated NFDM systems, the transmission capacity increases with the number of modulated eigenvalues. However, as the number of modulated eigenvalues increases, the complexities of the signal waveform and the nonlinear Fourier transform (NFT) algorithm for demodulation increase dramatically as well, while the accuracy drops significantly. Meanwhile, impairments such as amplifier spontaneous emission noise and phase noise in practical channels would perturb the eigenvalues and the corresponding nonlinear spectra during transmission. Coupled with an increase in the modulation format order, it is difficult for NFT algorithm-based receivers to recover information. To enable the use of multiple-eigenvalue modulated NFDM systems, we propose an innovative receiver based on regression neural networks (NNs), which can demodulate information correctly for both single- and dual-polarization NFDM systems. The results show that it has strong robustness and has a certain tolerance to the impairments of communication systems. In the contrast that the poor demodulation performance of the NFT and the Euclidean minimum distance (MD) receivers for multi-eigenvalue modulated NFDM systems, our proposed NN receiver can achieve low bit error rate with 2 GBaud 16QAM modulation over 1,000 km transmission in four-eigenvalue modulated single-polarization NFDM systems. The performance of three receivers (NFT, MD and NN) in a two-eigenvalue modulated NFDM system are also compared, the NN receiver shows the best performance and appears more suitable for higher-order modulation formats.

A window-split frequency domain Kalman scheme is proposed in this paper for the equalization of large polarization mode dispersion (PMD) and ultra-fast rotation of state-of-polarization (RSOP) which is an extreme environment due to the Kerr effect and the Faraday effect under the lightning strike near the fiber cables. In order to carry out the proposed Kalman scheme, we give a simplified and equivalent fiber channel model as a replacement for the general model of the polarization effect of the co-existence of PMD and RSOP. With this fiber channel model, we can conduct compensation for PMD in the frequency domain and tracking RSOP in time domain. A half analytical and half empirical theory for the initialization of the process and measurement noise covariance is also presented in theory and verified by the numerical simulation. The performance of the proposed Kalman scheme is checked in the 28Gbaud PDM-QPSK coherent system built on both simulation and experiment platforms. The simulation and experiment results confirm that compared with the generally used constant modulus algorithm (CMA), the proposed scheme provides excellent performance and stability to cope with large range DGD from 20ps to 200ps and RSOP from 200krad/s to 2Mrad/s, with less computational complexity.

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We propose a blind and low-complexity modulation format identification (MFI) scheme for elastic optical networks (EONs). Since the square operation reduces half the number of the clusters in Stokes space, the scheme directly performs principal component analysis (PCA) on Stokes parameters after square operation. This greatly reduces the dimensionality of received signals from 3 × N to 3 × 3. Subsequently, three obtained principal components (PCs) are employed synthetically to identify the modulation formats. The effectiveness is first verified through 28 GBaud polarization division multiplexing (PDM)-BPSK/-QPSK/-8QAM/-16QAM/-32QAM/-64QAM simulation systems. Only using 2048 symbols, the required minimum optical signal-to-noise ratio (OSNR) values to achieve 100% MFI success rate are all equal to or lower than their corresponding 7% forward error correction (FEC) thresholds. Besides that, the scheme also obtains significant tolerances to residual chromatic dispersion (CD) and differential group delay (DGD). Finally, the proposed scheme is further verified by 20 GBaud PDM-QPSK/-16QAM/-32QAM long-haul transmission experiments. The results demonstrate that the scheme exhibits good resilience towards fiber nonlinear impairments. More importantly, compared with other four kinds of MFI schemes, the used symbol number to achieve 100% MFI success rate notably equals to at most 2/5 as that of other schemes, and its time complexity can be reduced to O(N).

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A nonlinear frequency division multiplexing (NFDM) transmission system, designed specifically for nonlinear fiber channel, has the potential to overcome the nonlinear Shannon capacity limit. However, the spectral efficiency (SE) of the current proven NFDM transmission systems is still lower than that of the analogous orthogonal frequency division multiplexing system. It is extremely necessary to explore effective modulation scheme for the aim of increasing the SE of NFDM system. In this study, we first propose the nonlinear-frequency-packing nonlinear frequency division multiplexing (NFP-NFDM) transmission system. In NFP-NFDM, the spacing of nonlinear subcarriers is squeezed and more nonlinear subcarriers can be packed, but the inter carrier interference (ICI) is introduced. The method of NFP in nonlinear Fourier domain is carefully designed to reduce the complexity of ICI cancellation. Through numerical simulation, we illustrate the feasibility of NFP-NFDM transmission, and higher SE in NFP-NFDM than that of NFDM system is also demonstrated. The upper bound of the normalized SE for NFP-NFDM is estimated, which is higher than that of current NFDM system. Besides, we find out that the NFP scheme may have the advantage of reducing the signal-noise interaction in fiber transmission scenario, which indicates there may be a better way to load the data into the nonlinear Fourier domain.

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