Bounds on Compression Factor Estimation in FTN Systems

In this letter, we derive closed-form Cramér–Rao lower bounds (CRLBs) for estimating the compression factor in faster-than-Nyquist (FTN) systems under root-raised-cosine pulse shaping, in both data-aided and non-data-aided (NDA) scenarios. Bounds attainability is assessed via maximum likelihood estimators. We also study the impact of a compression factor mismatch at the receiver by assessing the resulting bit-error-rate penalty incurred by a channel shortening symbol detector. Notably, small compression factors can be estimated with higher precision, which is particularly beneficial for symbol detectors sensitive to estimation errors in this regime. Finally, the NDA approach demonstrates sufficient robustness for moderately long frame lengths, enabling either a reduction in pilot overhead or even repurposing all pilots to estimate other parameters. This study paves the way towards designing adaptive FTN systems that leverage the compression factor to optimize spectral efficiency or avoid cyclostationary patterns for covertness.