Surveying GNSS Carrier Offset Modulations: Investigating Gabor Uncertainty Principle for Precise Time Delay and Frequency Offsets Estimation

In the last decades, the adoption of offset carrier modulations represented one of the main aspects in the modernization of Global Navigation Satellite System (GNSS) signals. Offset carrier modulations provide indeed specific signal characteristics and guarantee the desired performance trade-off in terms of bandwidth utilization and tracking jitter at the receiver. In light of this, ongoing signal design proposals for modernized GNSS, Low-Earth Orbit and navigation services cannot neglect fundamental findings in this direction. At the same time, the theoretical bounds governing time delay and frequency offset estimation have a direct impact on receivers state estimation when this task rely on the inference of signal-derived observables. In this context, the aim of this work is to investigate the inherent relationship between offset carrier modulation, i.e., spreading code chip shaping, and the bounds set by uncertainty principle about time delay and frequency offsets estimation of GNSS signals. The research addresses a surveying analysis of currently-adopted offset carrier modulations and the evaluation of their theoretical bounds associated to the respective analytical ambiguity functions. The study offers a methodology to synoptically compare different chip shaping and to characterize how this influences signals' time-frequency localization precision and estimation errors at the receiver, which has a direct impact on delay and frequency lock loops performance at the receiver tracking stage.