Shaping Filter Design for Faster-than-Nyquist Signaling with Second Order Polynomial Function

Faster-than-Nyquist (FTN) signaling has been rediscovered in recent years, due to its ability of increasing the bit rate while preserving the signaling bandwidth. However, FTN signaling introduces inter-symbol interference (ISI) since more symbols are packed in time-domain than the orthogonal transmission arrangement. In this scenario, the conventional sinc pulse based shaping filter becomes no longer optimal for FTN signaling transmission. In this paper, we present a novel shaping filter design that employs a class of time-domain second order polynomial function (SOPF), aiming to reduce the ISI that imposed by FTN signaling. We mathematically characterize the signal to interference ratio (SIR), and then optimize the parameters of SOPF w.r.t. Maximizes the SIR of the receiver, thus provide an adaptive receiving capability. Numerical results demonstrate effectiveness of our design.