Equalization-enhanced phase noise (EEPN) can severely degrade the performance of long-haul optical fiber transmission systems. In this paper, the impact of EEPN in Nyquist-spaced dual-polarization quadrature phase shift keying (DP-QPSK), dual-polarization 16-ary quadrature amplitude modulation (DP-16QAM), and DP-64QAM optical transmission systems is investigated considering the use of electrical dispersion compensation (EDC) and multi-channel digital backpropagation (MC-DBP). Our results demonstrate that full-field DBP (FF-DBP) is more susceptible to EEPN compared to single-channel and partial-bandwidth DBP. EEPN-induced distortions become more significant with the increase of the local oscillator (LO) laser linewidth, and this results in degradations in bit-error-rates (BERs), achievable information rates (AIRs), and AIR-distance products in optical communication systems. Transmission systems using higher-order modulation formats can enhance information rates and spectral efficiencies, but will be more seriously degraded by EEPN. It is found that degradations on AIRs, for the investigated FF-DBP schemes, in the DP-QPSK, the DP-16QAM, and the DP-64QAM systems are 0.07 Tbit/s, 0.11 Tbit/s, and 0.57 Tbit/s, respectively, due to the EEPN with an LO laser linewidth of 1 MHz. It is also seen that the selection of a higher-quality LO laser can significantly reduce the bandwidth requirement and the computational complexity in the MC-DBP.

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In this work, a perturbation-based neural network (P-NN) scheme with an embedded bidirectional long short-term memory (biLSTM) layer is investigated to compensate for the Kerr fiber nonlinearity in optical fiber communication systems. Numerical simulations have been carried out in a 32-Gbaud dualpolarization 16-ary quadrature amplitude modulation (DP-16QAM) transmission system. It is shown that this P-NN equalizer can achieve signal-to-noise ratio improvements of ~1.37 dB and ~0.80 dB, compared to the use of a linear equalizer and a single step per span (StPS) digital back propagation (DBP) scheme, respectively. The P-NN equalizer requires lower computational complexity and can effectively compensate for intra-channel nonlinearity. Meanwhile, the performance of P-NN is more robust to the distortion caused by equalization enhanced phase noise (EEPN). Furthermore, it is also found that there exists a tradeoff between the choice of modulation format and the nonlinear equalization schemes for a given transmission distance.

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