Optimal Pilot Sequences for Phase and Timing Synchronization in FTN Systems

In this paper, we study the joint phase and timing estimation problem in Faster-than-Nyquist (FTN) systems. We use the Cramér-Rao lower bound (CRB) as a cost function to design optimal pilot sequences subject to an energy constraint. We rely on harmonic approximations of the bound to establish closed-form relations between the ultimate synchronization performance and the transmitted waveform characteristics (i.e., pulse shaping filter and signaling density). We show that increasing the symbol rate at fixed bandwidth is beneficial to phase estimation and detrimental to timing synchronization. Therefore, we propose a joint timing/phase pilot design to accommodate this trade-off. Lastly, we illustrate the strengths of the proposed pilots with respect to traditional Zadoff–Chu sequences in presence of a residual carrier frequency offset.