Random Faster-than-Nyquist Signaling

In this paper, we propose the random faster-than-Nyquist (RFTN) signaling as an effective method to approach the capacity of the additive white Gaussian noise (AWGN) channel under assigned power spectral density (PSD). By establishing a concise input-output representation of RFTN signaling, we analyze its asymptotic mutual information using the replica method. Particularly, leveraging asymptotic state evolution, we provide the performance analysis of RFTN signaling with finite-alphabet constellations. This analysis reveals that RFTN signaling can achieve a superior shaping gain compared to conventional FTN signaling, especially under higher symbol rates. In addition, an efficient RFTN detector based on orthogonal approximate message passing (OAMP) is also presented. Our numerical results confirm our theoretical analysis and demonstrate significant performance gains in both spectral efficiency and bit error rate (BER).