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Endeavors to surpass the Kerr-induced nonlinearity limit have been performed by either inserting an optical phase conjugator (OPC) at the middle point of the link [1] or using electronic-based nonlinearity compensators (NLC) such as digital back-propagation (DBP) placed in the receiver [2] or transmitter [3], phaseconjugated twin-waves (PC-TW) [4], and nonlinear equalizers (NLEs) based on the inverse Volterra-series transfer function (V-NLE) [5]. Unfortunately, OPC significantly reduces the flexibility in an optically routed network requiring both symmetric 2 nd order chromatic dispersion (CD) and power evolution, DBP is extremely complex and PC-TW halves the transmission capacity. V-NLE has been considered as a simple and effective method for combating fiber nonlinearities, however it still requires a significant amount of floating-point multiplications. Additionally, in coherent communication systems the interaction between nonlinear phenomena, CD, and frequency fluctuations of source and local oscillators (LO) results in stochastic nonlinear distortion, which can be partially mitigated using either frequency referenced carriers [3] or nonlinear mapping based on statistical learning such as artificial neural networks (ANN) [6] and support vectors machines (SVM) [7].On the other hand, coherent optical orthogonal frequencydivision multiplexing (CO-OFDM) is an excellent candidate for longhaul communications because of its high spectral efficiency and tolerance to CD and polarization-mode dispersion (PMD). However, due to its high peak-to-average power ratio (PAPR) the nonlinear cross-talk effects among subcarriers such as cross-phase modulation (XPM) and four-wave mixing (FWM) are enhanced, causing a stochastic-like interference to the extent of becoming an insurmountable obstacle. Owing to the vulnerability of CO-OFDM in nonlinear distortion, it is envisaged that NLC will enhance the capacity and transmission-reach in coherent optical core networks [8], thus avoiding highly dissipative regeneration electronics [3]. However, NLC feasibility demands the employment of versatile (i.e. independent from link parameters) techniques of low complexity for real-time applications.In this letter, it is experimentally compared, for the first time, V-NLE and full-field DBP-NLE with a novel SVM-based regression (SVR) NLE in 40-Gb/s 16-quadrature amplitude modulation (16-QAM) CO-OFDM at 2000 km. In contrast to nonlinear classifiers such as ANN [6] and SVM [7], SVR projects the obtained data on a hyperplane where constellation regions are easier to decode. It is shown that SVR-NLE can extend the optimum launched optical power (LOP) by 4 dB compared to both linear equalization and V-NLE by means of reduction of fiber nonlinearity. In comparison to full-field DBP-NLE at a LOP of 6 dBm, SVR-NLE outperforms by ~1 dB in Q-factor. In addition, it is shown that SVR is significantly less complex than full-field DBP and V-NLE. Fig. 1 depicts (a) the block diagram of the CO-OFDM receiver equipped with NLE, and (b) the proposed SVR-NLE...

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We propose a flexible simplified extended Kalman filter (S-EKF) scheme that can be applied in both pilot-aided and blind modes for phase noise compensation in 16-QAM CO-OFDM transmission systems employing a small-to-moderate number of subcarriers. The performance of the proposed algorithm is evaluated and compared with conventional pilot-aided (PA) and blind phase search (BPS) methods via extensive an Monte Carlo simulation in a back-to-back configuration and with a dual polarization fiber transmission. For 64 subcarrier 32 Gbaud 16-QAM CO-OFDM systems with 200 kHz combined laser linewidths, an optical signal-to-noise ratio penalty as low as 1 dB can be achieved with the proposed S-EKF scheme using only 2 pilots in the pilot-aided mode and just 4 inputs in the blind mode, resulting in a spectrally efficient enhancement by a factor of 3 and a computational effort reduction by a factor of more than 50 in comparison with the conventional PA and the BPS methods, respectively.

In this paper, we experimentally demonstrate the combined benefit of artificial neural network-based nonlinearity compensation and probabilistic shaping for the first time. We demonstrate that the scheme not only compensates for transceiver's nonlinearity, enabling the full benefits of shaping to be achieved, but also the combined effects of transceiver and fiber propagation nonlinearities. The performance of the proposed artificial neural network is demonstrated at 28 Gbaud for both 64-QAM and 256-QAM probabilistically shaped systems and compared to that of uniformly distributed constellations. Our experimental results demonstrate: the expected performance gains for shaping alone; an additional SNR performance gain up to 1 dB in the linear region; an additional mutual information gain of 0.2 bits per channel use in the constellation-entropy limited region. In the presence of coupled transceiver and fiber-induced nonlinearities, an additional mutual information enhancement of ∼0.13 bits/symbol is experimentally observed for a fiber link of up to 500 km with the aid of the proposed artificial neural network.