# Positioning Performance Limits of GNSS Meta-Signals and HO-BOC Signals
## 1 Introduction  
Global Navigation Satellite Systems (GNSS) are the main source of position, navigation, and timing (PNT) information in several engineering fields. The main advantages are their global coverage and that the satellite-based infrastructure is already deployed and maintained by governmental institutions. The latter allows the user to exploit GNSS freely and the ability to design both mass-market and dedicated receivers. These remarkable advantages will make GNSSa key player in the next-generation intelligent transportation systems and several safety-critical applications. However, even if the navigation research community has been developing positioning methodologies for decades, there are still several limitations that may limit the use of GNSS in the most stringent applications, i.e., lane-level precision for autonomous driving in highly populated cities with harsh propagation conditions. One of the key open problems is how to achieve precise PNT solutions under harsh environments, i.e., affected by multipath, deep fading, signal blockage, or non-line-of-sight (NLOS) conditions. Using standard GNSS signals, it is known that code-based techniques (i.e., only relying on the time-delay estimation between the receiver and a set of visible satellites) do not provide precise PNT information. The standard way to provide such precise navigation capabilities is by exploiting carrier phase information. Indeed, this measurement is linked to the wavelength, which is much smaller than the baseband signal resolution (i.e., for a legacy Global Positioning System (GPS) L1-C/A signal, the wavelength is 19.4 cm, while the baseband signal resolution is around 300 m). The two main solutions are precise point positioning (PPP) [1] and real-time kinematic (RTK) positioning [2]. However, the main problem of these techniques is that they are very sensitive to the quality of phase observables, i.e., it is unlikely that they provide a robust solution under harsh propagation conditions, at least exploiting standard GNSS signals. Therefore, in order to provide robust and precise solutions, new alternatives must be accounted for. A possible alternative is to robustify the signal processing, for instance resorting to outlier mitigation techniques [3, 4]. Another option is to increase the receiver complexity and exploit large bandwidth signals, which allow obtaining a better (i.e., with respect to standard signals) baseband resolution, and therefore more precise code-based observables. The latter can be achieved by using (i) high-order binary offset carrier (HO-BOC) modulations or (ii) GNSS meta-signals, which is the combination of two GNSS signals at different frequency bands as a single signal. It is a fact that there is an increasing interest in the topic of GNSS meta-signals. The authors are not aware if this is the case on the industry side, but on the academic side, the European Space Agency (ESA) is funding (or has recently funded) projects related to the study of HO-BOC signals and GNSS meta-signals, in order to obtain more precise code-based pseudoranges [5; 6; 7]. For instance, one of the main goals of the latest one [7] is to assess if such GNSS meta-signals are an option to achieve sub-meter- or decimeter-level positioning in harsh propagation conditions (i.e., multipath and urban canyons), mainly because carrier phase-based positioning techniques are known to fail in such challenging scenarios as the phase ambiguity resolution needs precise phase observables. However, there are very few contributions discussing the concept of meta-signals [8; 9]; therefore, before considering realistic harsh propagation conditions, an important missing point in the literature is the characterization of the ultimate positioning performance limits of such signals (i.e., resorting to fundamental estimation performance bounds), which is the goal of this article.