# Positioning Performance Limits of GNSS Meta-Signals and HO-BOC Signals
## 5 GNSS Meta-Signal SPP Performance Results  
In the previous Section 4, we assessed the achievable performance limits for time-delay and phase estimation, considering a set of representative meta-signals. In the sequel, we assess how the previous time-delay estimates translate into the position domain considering the standard WLS SPP solution in Section 3.3. Notice that the covariance of the code observables noise \(\mathbf{C_{n,e}}\) was set according to the  
Figure 6: Time-delay/phase RMSE and CRBs (m) for different GNSS HO-BOC signals: (**a**) GPS L1-M BOCsin(10,5), (**b**) Galileo E1-PRS BOCcos(15,2.5), (**c**) Galileo E6-PRS BOCcos(10,5) and (**d**) BeilDou B1A BOCcos(14,2)  
corresponding MLE precision. We considered two satellite constellation scenarios, with a good and bad geometric dilution of precision (GDOP), respectively, which are shown in Figure 7.  
1. Nominal conditions with a good GDOP (Subplot (a) in Figure 7). 2. Constrained satellite visibility, or bad GDOP (Subplot (b) in Figure 7). Even if it is out of the scope to consider realistic multipath channels, this scenario was representative of an urban canyon situation, where part of the sky may be blocked by buildings. Without loss of generality and with the aim to determine the ultimate performance w.r.t. the SNR at the output of the estimator, we considered that all satellites were received with the same power. For instance, if the high-elevation satellites were received with a \(C/N_{0}\) around 45 dB-Hz, the low elevation satellites with a \(C/N_{0}\) around 40 dB-Hz, and the receiver used a coherent integration time \(T_{I}=10\) ms, this would translate into an ultimate SPP performance in the range SNR\({}_{\text{out}}\) = [20; 21; 22; 23; 24; 25] dB. The SPP performance results (i.e., position RMSE) for the good GDOP scenario are summarized in Figure 8. First, notice that the CRBs are shown together for the different meta-signals in Subplot (a). We can easily identify the same tendency as in Figure 5a, and as expected, better time-delay estimation performance implied a better position estimate. * Again, if we considered SNR\({}_{\text{out}}=25\) dB as a reference value, the position standard deviation was (i.e., following the order in Figure 8a) roughly: 18 cm, 11 cm, 8 cm, 6.5 cm, 5.5 cm, 8 cm, and 7 cm. Therefore, w.r.t. the time-delay results at SNR\({}_{\text{out}}=25\) dB previously discussed, the geometry matrix induced a slight performance degradation. * Any of the meta-signals could be considered as a precise code-based positioning alternative. * Obviously, the convergence time due to false locks into secondary peaks of the ACF directly translated to the corresponding convergence into the position domain CRB. This further supported the fact that in terms of SNR robustness, the best choices were Galileo E5 and the combinations with the full-bandwidth E5 and B2, i.e., E5 + E6 and B2 + B3. The slight performance improvement obtained with the other signal combinations was not worth  
Figure 7: Satellite constellation skylpots for both nominal (**a**) and non-nominal conditions (**b**). Figure 8: The comparison of the different SPP CRBs (m) is shown in Subplot **(a)**. Nominal good GDOP scenario SPP RMSE (m) and the corresponding CRBs (m) for the different GNSS meta-signals are shown in Subplots: **(b)** GPS L2C + L5Q, **(c)** Galileo E5B + E6B, **(d)** BeiDou B2 AQ + B3Q, **(e)** Galileo E5A + E6B, **(f)** BeiDou B2 + B3Q and **(g)** Galileo E5 + E6B. The SPP performance results for the bad GDOP constrained satellite visibility scenario are summarized in Figure 9. The previous results with a good GDOP for Galileo E5 are shown as a reference. Overall, we can see that considering a bad GDOP only degraded the performance, but did not change the behavior of the CRBs and MLEs.