On Spectrum Broadening of Pre-Coded Faster-Than-Nyquist Signaling

Abstract

The faster-than-Nyquist (FTN) signaling has been of interest in the research literature due to recent advances in pre-coding and equalization techniques allowing practical removal of the intersymbol interference (ISI). Since the structure of ISI is deterministic in the FTN signaling, a data pre-coding at the transmitter to combat ISI is of practical importance. It is shown, however, that such pre-coding in FTN can significantly broaden the transmission spectrum and alter the shape of the power spectral density. In this paper, we analyze the power spectral density of convolutionally pre-coded FTN signals on linear time-invariant channels. We also identify sufficient conditions on the pre-coding coefficients for preventing the spectrum broadening. Simulation results with several pulse shapes are provided which agree with the analysis. The analysis and the simulation show that for many practically used pulses the pre-coded FTN suffers from the spectrum broadening. This suggests that pre-coding in the FTN signaling must be handled with care.