Abstract

A new four-dimensional (4D) probabilistically shaped (PS) ultra-high order modulation format is proposed with pilot aided carrier phase recovery (PA-CPR) algorithm to improve the general mutual information (GMI) performance. While the structure of the 4D-PS ultra-high order modulation format uses constellation set partitioning (SP) based on amplitude translation, and the PA-CPR applies 8-level amplitude phase shift keying (8APSK) pilot. To demonstrate the feasibility of the scheme, the PS-1024QAM system is designed on the simulation platform. The results show that the proposed 8APSK-PA-CPR algorithm outperforms the QPSK-PA-CPR algorithm. The gain of the optimal 8APSK-PA-CPR is ∼0.4 dB compared with the quadrature phase-shift keying (QPSK) PA-CPR algorithm. The steep drop of blind phase search (BPS) with different PS factors is overcome by 8APSK-PA-CPR when the signal-to-noise (SNR) ratio is lower than 24 dB. The maximum improvement of GMI is 1.3 bit/symbol when the SNR is higher than 26 dB and the complexity of the 8APSK-PA-CPR algorithm is reduced by 99.9% compared with the BPS algorithm. The gain obtained from the proposed 4D modulation scheme is ∼2.8 dB under the condition of GMI = 17.7971 bit/symbol. It demonstrated that this scheme has a strong tolerance to noise, low computational complexity, and high coding gain. It is a feasible and flexible scheme for PS high-order modulation format transmission systems.

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