Unleashing Timing Advance Precision: CRLB Limit and Neural Implementation

In 4G/5G networks, the usual role of the Random Access Channel (RACH) signal is to establish uplink synchronization by means of Timing Advance (TA) estimation. In this study, we explore the upper limits of precision for this TA parameter, as well as for the Carrier Frequency Offset (CFO), by means of an original Cramer-Rao Lower Bound (CRLB) calculation. Remarkably, this performance can be encapsulated within a straightforward formula, uncovering a potential for precision that surpasses the Nyquist period by one to two orders of magnitude. This enhanced precision holds promise for geolocation application. Furthermore, we demonstrate that the Maximum Likelihood (ML) estimator closely approximates this theoretical boundary, and we propose a novel implementation method employing a compact Neural Network. A series of numerical evaluations affirm the potential of this innovative approach, ensuring both statistical optimality and the feasibility of real-time implementation.