# Positioning Performance Limits of GNSS Meta-Signals and HO-BOC Signals
## 2 GNSS Signal Model, Meta-Signals, and HO-BOC Signals
### GNSS Meta-Signals  
In the previous contribution [27], we defined the original Galileo E5 signal, which uses an AltBOC(15,10), and the corresponding combinations with the Galileo E6 band signal, E5B + E6 and E5A + E6 meta-signals, being modulated as a single AltBOC(35,10,5) and AltBOC(50,10,5). These signals can be alternatively defined using the previous AltLOC modulation. In addition, several other signal combinations using individual GPS, Galileo, and BeiDou signals can be considered. The complete set of GNSS meta-signals considered in this article includes the following combinations:  
* Galileo E5 = E5A + E5B, generated as an AltBOC(15,10) [28] and taken as a reference.
* GPS L5 + L2C, generated through an AltLOC(25,10,175). The central frequency of this meta-signal is located at \(f_{c}=1175f_{0}\).
* Galileo E5B + E6, generated through an AltLOC(35,10,5,112). The central frequency of this meta-signal is located at \(f_{c}=1215f_{0}\).
* Galileo E5A + E6, generated through an AltLOC(50,10,5,132). The central frequency of this meta-signal is located at \(f_{c}=1200f_{0}\).
* Galileo E5 + E6, generated through an AltLOC(42.5,\(C_{E5}(t)\),5,132). \(C_{E5}(t)\) represents the full-bandwidth Galileo E5 signal. The central frequency of this meta-signal is located at \(f_{c}=1207.5f_{0}\).
* BeiDou B2A + B3, generated through an AltLOC(45,10,10,120). The central frequency of this meta-signal is located at \(f_{c}=1195f_{0}\).
* BeiDou B2 + B3, generated through an AltLOC(37.5,\(C_{B2}(t)\),10,125). \(C_{B2}(t)\) represents the full-bandwidth BeiDou B2 signal, characterized by an AltBOC(15,10) modulation [29; 30]. The central frequency of this meta-signal is located at \(f_{c}=1202.5f_{0}\).  
Notice that for all the signals, we only consider the corresponding pilot components, i.e., E5 is generated as E5 AQ + E5 BQ or the combination of E5B and E6 is generated as E5 BQ + E6B. For completeness, we provide the different meta-signals power spectral density (PSD) in Figure 1, where we make explicit the individual signals main lobes: E5A, L5, E5B, B2A, and B3 signals using a BPSK(10) (i.e., a BPSK with a chip rate 10 times faster than the one of the GPS L1-C/A), E6 BPSK(5), and L2 BPSK(1) signal.  
In addition and because it is difficult to extrapolate the behavior of the different signals from their PSD in Figure 1, we show the corresponding ACF in Figure 2. In the two top subplots (a) and (b), we show the comparison of the main ACF peak, where as expected, a wider PSD implies a narrower ACF. What is not evident to guess from the PSD is the shape of the different ACFs in Subplots (c)-(h). In the \"standard\" signal combinations, the L2 + L5, B2A + B3, E5B + E6, and E5A + E6, narrower main ACF peak implies higher secondary peaks and closer to the main one. The values and position of these secondary peaks are also given for completeness. As will be discussed in the results, these secondary peaks are one of the main drivers of the estimators' performance. Remarkably, the combinations with the full-bandwidth B2 and E5 signals, that is the combination of AltBOC(15,10) with the signals in the B3 and E6 bands, respectively, exhibit much lower secondary peaks. Despite their nice ACF shape, as far as the authors' knowledge, these combinations have never been discussed in the literature.