Analysis of Optimal Pilot Sequences for Compression Factor Estimation in FTN Systems

in this paper, we investigate the design of pilot sequences for compression factor estimation in faster-than-Nyquist (FTN) systems, targeting the minimization of its Cramér-Rao lower bound (CRLB), while analyzing their impact on peak-to-average power ratio (PAPR). Accurate estimation of the compression factor is crucial in applications such as physical layer security (PLS) and adaptive modulations that rely on FTN signaling, whereas a high PAPR is detrimental to power amplification. Several CRLB-optimal pilot sequences are derived: unconstrained, binary-constrained, and clipped. Simulation results show that the unconstrained sequence achieves the lowest estimation error but exhibits high PAPR. On the contrary, the proposed binary-constrained and clipped sequences provide a favorable trade-off between estimation and PAPR performance. Compared to the start-of-frame (SoF) sequence adopted in the DVB-S2/S2X standard and traditional Zadoff-Chu sequence, the proposed sequences achieve significantly improved estimation accuracy at the cost of a slightly higher PAPR.