Precoding Optimization for Faster-Than-Nyquist Signaling With Probabilistic Shaping

A probabilistic shaping (PS) scheme applied to Faster-than-Nyquist (FTN) signaling is proposed firstly to obtain shaping gain. Secondly, a precoding optimization algorithm based on maximizing average mutual information (AMI) criterion for FTN PS system is proposed to get precoding gain, which uses bare bones particle swarms optimization (BB-PSO) algorithm. The theoretical AMI analysis of the proposed precoded FTN PS scheme are analyzed and turn out that the proposed precoded FTN PS scheme is superior to the conventional Nyquist regular system. Compared with the Nyquist regular system, we can get FTN gain, PS gain, and precoding gain for the proposed precoded FTN PS system. The gains of the simulation results coincide well with that obtained from the theoretical analysis. When spectral efficiency (SE) is 2.778 bits/s/Hz, compared with the 16QAM Nyquist regular system, the proposed 16QAM precoded FTN PS scheme has a total 1.85 dB theoretical gain, where the simulation results in the 16QAM precoded FTN PS scheme show that the simulated gain is 1.65 dB. When SE is 3.333 bits/s/Hz, compared with the 64QAM Nyquist regular system, the proposed 16QAM precoded FTN PS scheme has a total 1.65 dB theoretical gain, where the simulation results in the 16QAM precoded FTN PS scheme show that the simulated gain is 2.15 dB. The results show that the proposed precoded FTN PS scheme is an efficient scheme with a significant improvement in terms of the AMI and the system error performance, and thus suitable for the sixth generation (6G) communication system.