GNSS Modulation: A Unified Statistical Description with Application to Tracking Bounds.

摘要

A unifying framework for all signals belonging to the Global Positioning System (GPS) and Galileo system is presented and applied to assess the potential code tracking performance of modernized satellite radionavigation signals. The framework reconciles, under a single analytical formulation, subcarrier signaling schemes, including the Binary Offset Carrier (BOC), Multiplexed Binary Offset Carrier (MBOC), and Alternative Binary Offset Carrier (ALTBOC). The new formulation allows for the derivation of closed form equations for the Auto-Correlation Function (ACF) and Power Spectral Density (PSD) containing, as special cases, the corresponding functions for GPS and Galileo signals. The analytical expressions are used to obtain new bounds on code tracking accuracy based on the Ziv-Zakai Bound (ZZB). Although the code tracking performance of GPS and Galileo signals is typically investigated using the Cramer-Rao Bound (CRB), the approach is heuristic. The CRB does not adequately describe the potential code tracking performance of weak or wideband signals and does not account for tracking biases. On the other hand, there are no such restrictions for Bayesian bounds such as the ZZB. However, because the CRB is easier to evaluate, it is advantageous to quantitatively identify when the CRB is a meaningful benchmark before having to resort to the ZZB. Therefore, thresholds on signal energy are provided to indicate necessary conditions for the use of the CRB. In agreement with information-theoretic developments, the thresholds reveal that a large signal bandwidth cannot reliably compensate for low signal energy in order to sustain code tracking performance.