Abstract

Probabilistic-shaped quadrature amplitude modulation (PS-QAM) based on Maxwell-Boltzmann (MB) distribution has been extensively studied in recent years in the SNR limited coherent communication system to approach the Shannon capacity. However, MB distribution is not the optimal distribution when the transmission system suffers from serious laser phase noise. To improve the laser phase noise tolerance of MB distribution, a novel Maxwell-Boltzmann/Angular-distance-directed (MB/ADD) distribution is proposed in this article. The benefits of PS-QAM exist in the case of limited SNR, as well as large laser phase noise. The proposed distribution is verified through simulations and experiments. In our simulation analysis, the ADD part enables the reduction of SNR penalty when laser phase noise increases. The results are validated by experimental data, in which both digitally generated and distributed-feed-back (DFB) laser generated phase noise are employed to evaluate laser phase noise tolerance. In the scenario of large phase noise, MB/ADD shaping can achieve lower pre-FEC BER and higher GMI compared with MB shaping, without inserting pilot symbols. Moreover, the improvement of applying MB/ADD distribution can be obtained no matter whether BPS or V&V based algorithm is adopted for carrier phase estimation (CPE). Different shaping parameters are also tested, where the capability to agilely adapt to various channel conditions of the MB/ADD distribution is shown. And the proposed MB/ADD shaping can be applied with similar complexity with MB shaping, if the Kullback–Leibler (KL) divergence between the generated and the expected 2-D QAM distribution is required to be lower than 10⁻³.

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