Design of Probabilistic Shaping 4D Ultra High Order Modulation Format With 8APSK Pilot Aided Carrier Phase Recovery
Feng Tian, Tianze Wu, Yiqing Ji, Chuxuan Wang, Qi Zhang, Ran Gao, Zhipei Li, Qinghua Tian, Xiangjun Xin
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.