The Evolution of Faster-Than-Nyquist Signaling

The fifty-year progress of faster-than-Nyquist (FTN) signaling is surveyed. FTN signaling exploits non-orthogonal dense symbol packing in the time domain for the sake of increasing the data rate attained. After reviewing the system models of both the conventional Nyquist-based and FTN signaling transceivers, we survey the evolution of FTN techniques, including their low-complexity detection and channel estimation. Furthermore, in addition to the classic FTN signaling philosophy, we introduce the recent frequency-domain filtering and precoding aided schemes. When relying on precoding, the information rate of FTN signaling becomes related to the eigenvalues of an FTN-specific intersymbol interference matrix, which provides a unified framework for the associated information-theoretic analysis and simplifies the associated power allocation specifically designed for increasing the information rate attained. We show that the FTN signaling scheme combined with bespoke power allocation employing a realistic raised-cosine shaping filter achieves the Shannon capacity associated with ideal rectangular shaping filters.