Probabilistic Shaping in Faster-Than-Nyquist System

Probabilistic shaping (PS) in Faster-than-Nyquist (FTN) system is proposed. The proposed system is based on probabilistically shaped 16QAM formats and 8QAM formats. The theoretical average mutual information (AMI) analysis of the proposed FTN PS scheme are analyzed and turns out that the proposed FTN PS scheme is superior to the conventional Nyquist regular system. The gains of simulation results are comparable to that obtained from the theoretical analysis. Compared with conventional Nyquist regular system, we can get FTN gains and PS gains for PS in FTN system. When spectral efficiency (SE) is 2.778 bits/s/Hz, the proposed 16QAM FTN PS scheme has 1.20 dB theoretical FTN gain and 0.35 dB theoretical PS gain, where the simulation results in 16QAM show that the FTN gain and PS gain are 0.75 dB and 0.40 dB, respectively. When SE is 2.083 bits/s/Hz, the proposed 8QAM FTN scheme has 1.55 dB theoretical FTN gain and 0.30 dB theoretical PS gain, where the simulation results in 8QAM show that the FTN gain and PS gain are 0.95 dB and 0.55 dB, respectively. The theoretical analysis and simulation results show that the proposed PS in FTN system is an efficient scheme for improving system performance, and thus suitable for the sixth generation (6G) communication system.