# Performance Limits of GNSS Code-based Precise Positioning: GPS, Galileo & Meta-Signals
## 7 Results: Time-Delay Estimation Accuracy Limit for Some Representative GNSS Signals
### GPS L1 C/A vs. Galileo E6B, E5b, E5 and GNSS Meta-Signals  
To complete the analysis, we summarize in Figure 6 the results obtained with the other Galileo signals, i.e., E6B, E5b-I, and E5, together with the ones obtained for the Galileo E5b/E6B and E5a/E6 meta-signals, that is, the AltBOC(35,10,5) and AltBOC(50,10,5), respectively. Recall that from the previous subsections the benchmark results (at SNR\({}_{\rm out}=25\) dB) are: (i) standard deviation of 2.24 m for the legacy GPS L1 C/A and \(F_{s}=10\) MHz; (ii) standard deviation of 75 cm for the GPS L1C pilot and \(F_{s}=12\) MHz; and (iii) standard deviation of 64 cm for the GPS L5 and \(F_{s}=10\) MHz. Using the E6B or E5b-I signals gives at the same operation point a standard deviation equal to 1 m and 64 cm, respectively, which is obvious considering the underlying BPSK(5) and BPSK(10) modulations. Notice  
Figure 4: (**Left**) CRB/MLE for GPS L1 C/A BPSK(1), GPS L1C data component BOC(1,1), and GPS L1C pilot component TMBOC. (**Right**) CRB/MLE for GPS L1 C/A BPSK(1), Galileo E1B CBOC(\(+\)), and Galileo E1B CBOC(\(-\)).  
that because the time-delay estimation performance is driven by the signal modulation, GPS L5 and Galileo E5b or Galileo E5a are equivalent in terms of estimation performance.  
What is remarkable is the performance improvement provided by the Galileo E5 AltBOC(15,10) if we exploit the complete bandwidth, which at this particular operation point provides an estimate with a standard deviation equal to 8 cm. Considering now the results obtained with the Galileo E5b-E6B AltBOC(35,10,5) and E5a-E6 AltBOC(50,10,5) meta-signals, and exploiting the complete bandwidth, we obtained a further improvement, with a standard deviation for the E5b-E6B of 3.5 cm, and for the E5a-E6 equal to 2.5 cm. These AltBOC-modulated signals can be considered as an option to precise positioning, with 3\(\sigma\) delay errors below 25 cm, i.e., below 12 cm for the meta-signals.  
It is important to notice the behavior of the MLE between the previous 15 dB threshold and the convergence to the CRB. This is because of the special shape of the ACF, as shown in Figure 3. With respect to the E5, these meta-signals have positive secondary ACF peaks which are very close to  
Figure 5: CRB/MLE for GPS L1 C/A BPSK(1) and GPS L5-I BPSK(10).  
Figure 6: CRB/MLE for GPS L1 C/A BPSK(1), E6B BPSK(5), E5b-I BPSK(10), E5 AltBOC(15,10), meta-signal E5b/E6 AltBOC(35,10,5), and meta-signal E5a/E6 AltBOC(50,10,5).  
the main peak. These secondary peaks induce a second operation region of the MLE between the CRB and the threshold. Indeed, in this intermediate operation region, the MLE jumps between secondary peaks because of the noise, which introduces estimation errors. Note that this is the effect known as false locks in high-order BOC signals such as the BOC(15,2.5) used in the Galileo E1 PRS. Then, the use of meta-signals can improve the delay estimation with respect to the Galileo E5a, E5b, E6, and the complete E5 signals if the receiver is able to cope with such false locks or the SNR at the output of the matched filter is high enough. In addition, to reach such centimeter-level accuracy the receiver needs to exploit a huge bandwidth; thus, depending on the application and design constraints, a wise choice may be to use the E5 AltBOC(15,10). To summarize, the E5 signal can reduce the delay standard deviation by a factor of 28, 12, and 8 with respect to the GPS L1 C/A, Galileo E6B, and Galileo E5b-I/GPS L5 signals, respectively. An additional factor of 2.5 and 3.5 can be obtained by means of meta-signals. These results confirm that AltBOC-type signals can provide decimetric accuracy, thus being a promising solution (and the only one) for code-based precise positioning.