## 5 Numerical Results
### Tracking Performance  
Assessing the tracking performance in terms of unsmoothed TOA estimation error stdev. for a fixed \(C/N_{0}\) is, in this study, the primary performance measure used to judge whether a potential E1D signal may also be a good candidate considering MSP. The carrier power \(C=\mathbf{s}^{\mathrm{H}}\mathbf{s}/N_{\mathrm{s}}\) is derived for each signal to individually test that a fair-ranging performance evaluation for each signal is achieved. However, when directly comparing the status quo tracking, for instance, the GAL E1C signal at a certain noise power \(N_{0}B\) with MSP of a potential E1C+E1D signal, one should keep in mind whether an E1D signal would be added with a 1:1 power ratio with respect to the E1C signal; the combined meta-signal's power would be 3 dB higher than the E1C signal alone, resulting in a boost of TOA estimation error stdev., where the degree depends on the reception situation in terms of noise regime but also the chosen E1D signal.  
Figure 6 illustrates the code-phase ranging performance of each investigated signal for the two extreme cases, where either an ideal all-pass payload (\(\kappa=0\)) or a realistic distortion of a measured filter is applied (\(\kappa=1\)) during the signal formation. In the low-noise regime (\(C/N_{0}\geq 50\) dB-Hz), two performance tiers of signals can be identified. The meta-signals with the larger frequency offset (E1C+E1D-d/e/f/g) lead to a decreased TOA estimation error stdev. and therefore an increased ranging performance compared to E1C tracking at the same \(C/N_{0}\). The E1C+E1D-g signal candidate accumulates deformations due its wider bandwidth and experiences the greatest ranging performance degradation for a realistic payload characteristic in comparison to an all-pass payload scenario. The E1C+E1D-f performs best above 45 dB-Hz and sees a performance difference between ideal and fully distorted payload in a transition region from 42 to 47 dB-Hz.  
Tracking E1C+E1D-a/b meta-signals is worse than CBOC-tracking of the E1C signal in the all-pass case but even more so for the realistic payload case for a \(C/N_{0}\) greater than 45 dB-Hz. In the fully distorted case, E1C+E1D-a/b-tracking is worse than BOC-tracking of an E1C signal above 50 dB-Hz \(C/N_{0}\). Tracking E1C+E1D-a/b instead of E1C only would merely be improved due to the increased signal power but not due to MSP as the ACF main peak is less sharp than that of E1C using a CBOC replica.  
Figure 5: Multipath envelopes of investigated meta-signals assuming a very narrow NELP with an early–late spacing \(\Delta=0.01\times T_{\mathrm{c,BPSK-R(1)}}\) and the application of a brick-wall filter with a two-sided bandwidth of 24.552 MHz.  
Figure 7 shows the evolution of the stdev. and sample mean when varying the distortion parameter \(\kappa\) from 0 to 1 for a fixed \(C/N_{0}\) of 45 dB-Hz.  
The gradual increase in band limitation only slightly worsens the TOA estimation error stdev. For \(\kappa>0.75\), the influence of the measured phase response influences the mean and stdev., resulting in a range bias but also a worsening of ranging performance due to the introduced CCF asymmetry.