Abstract
Abstract
We propose a joint optimization algorithm of probabilistic shaping and geometric shaping for faster-than-Nyquist (FTN) signaling. The theoretical analysis and bit error performance both represent that the FTN probabilistic-geometric shaping method is superior to the conventional Nyquist regular QAM system. When spectral efficiency (SE) is 3.077 bits/s/Hz, the proposed 16QAM FTN probabilistic-geometric shaping scheme can obtain 1.65 dB theoretical gain compared to the conventional Nyquist regular 16QAM system, while the simulation gain is 2.90 dB with spectral efficiency at 3.077 bits/s/Hz. The proposed 16QAM FTN probabilistic-geometric shaping scheme can obtain 1.63 dB theoretical gain compared to the conventional FTN regular 16QAM system, while the simulation gain is 3.28 dB with spectral efficiency at 3.282 bits/s/Hz. Therefore, the proposed method is reliable, which can be regarded as a potential scheme for the 6G communications.