With the development of optical communication technology towards higher capacity, speed, and bandwidth, the phase noise caused by laser linewidth is becoming one of the key factors limiting the spectral efficiency of the system. Especially in high-order modulation formats, the tolerance of the system to phase noise gradually decreases, and excessive residual phase noise can lead to significant degradation in system performance. Meanwhile, with the increase in baud rate and transmission distance, the influence of equalization-enhanced phase noise (EEPN), generated by the interaction between the phase noise of the local oscillator laser at the receiver and the dispersion compensation module, gradually increases. Therefore, it is of great significance to accurately compensate for the phase noise. Currently, algorithms for carrier phase recovery include Viterbi?Viterbi phase estimation (VVPE) and blind phase search (BPS). VVPE is simple to implement, but for multi-level modulation formats, constellation partitioning must be carried out before implementation, which introduces an implementation penalty due to decision errors. BPS offers good compensation performance and is applicable to multiple modulation formats, but it consumes significant computational resources, as it requires numerous test phases and a sliding window with a large block size to estimate phase noise and smooth linear noise. We propose a phase noise compensation scheme based on end-to-end deep learning (E2EDL). This scheme learns the influence of phase noise on the signal, enhances the robustness of the system to phase noise and dispersion through constellation shaping, and improves the ability of the algorithm to track phase noise through a trainable BPS, thus enhancing the phase noise compensation performance.

A phase noise compensation scheme based on E2EDL is proposed to compensate for phase noise, including EEPN generated by the interaction between dispersion and phase noise, from multiple aspects. This scheme uses E2EDL for constellation shaping, including both geometric shaping and joint geometric-probabilistic shaping, to improve the tolerance of the system to phase noise. Meanwhile, a trainable BPS is proposed. The non-differentiable comparison operation in traditional BPS is replaced by a differentiable soft decision, which is abstracted as a neural network. Using the characteristics of E2EDL, the standard deviations of AWGN and Wiener phase noise are added and then incorporated into the E2EDL framework for overall training, thus improving its compensation ability for phase noise. In addition, the photonic Sigmoid function in optical computing is incorporated into the E2EDL framework for coherent optical communication. Utilizing its ability to simulate the physical response of photon devices, the tolerance of the system to dispersion is enhanced, and the compensation ability of BPS for EEPN is improved by reducing the influence of dispersion.

Numerical simulations are carried out on channels containing only dispersion, phase noise, and AWGN, as well as on channels containing nonlinear effects, respectively, to verify the performance of the proposed scheme. Additionally, simulation analyses are performed to evaluate the performance differences between the proposed scheme, the traditional QAM modulation scheme, and the E2E (no CD) scheme, which only learns the phase noise channel, under different laser linewidths. On the channel containing only dispersion, phase noise, and AWGN, when the laser linewidth changes within the range of 0 to 600 kHz, the generalized mutual information (GMI) performance of the proposed scheme in both geometric shaping and joint shaping is higher than that of E2E (no CD). The simulation analysis also studies the bit error rate curves of the proposed scheme and the traditional 64QAM scheme under different optical signal-to-noise ratios (OSNR). In the case of low OSNR, the proposed scheme demonstrates stronger robustness to amplified spontaneous emission noise and shows more clear advantages compared with the traditional 64QAM scheme. At a bit error rate standard of 3.8×10-3, the proposed scheme achieves an OSNR gain of about 0.6 dB compared with the traditional 64QAM. Under the channel with nonlinear effects, at the optimal transmit power, the proposed scheme provides a Q-factor improvement of about 0.44 dB compared to the traditional 64QAM scheme. Finally, we analyze the GMI performance of the three schemes under different laser linewidths at 800, 1040, and 1200 km. The GMI performance of the proposed scheme is higher than that of E2E (no CD) at different transmission distances. The proposed scheme improves the tolerance and compensation ability to phase noise by learning the interaction between phase noise and dispersion in the channel, thus improving the performance of the scheme under the influence of phase noise.

We propose a phase noise compensation scheme based on E2EDL. This scheme enhances the system’s ability to compensate for phase noise by learning the interaction between phase noise and dispersion in the channel, as well as conducting constellation shaping and BPS training. Compared with the traditional 64QAM+BPS, the proposed scheme provides an OSNR gain of approximately 0.6 dB in the case of 1200 km transmission. In addition, it incorporates the photonic Sigmoid activation function to reduce the influence of dispersion, further improving the performance of the system in the presence of dispersion. The performance of the proposed scheme is verified through numerical simulations. In the case of low SNR and large laser linewidth, the GMI performance of 64QAM is improved by about 0.17 bit/symbol, providing an additional gain of about 0.07 bit/symbol compared with E2E (no CD). In the presence of nonlinear effects, this gain increases further, reaching 0.59 bit/symbol and 0.17 bit/symbol, respectively. At the optimal transmit power, the Q factor of the proposed scheme improves by approximately 0.44 dB compared with the traditional 64QAM scheme.