# A Comprehensive Evaluation of Possible RNSS Signals in the S-Band for the KPS
## 4 FoMs Analysis
### DLL Error Analysis Results  
The DLL error depends on the receiver parameters, as well as the signal waveforms. Therefore, we analyzed the DLL error using the specified receiver parameters in Table 6.  
Figure 3 shows the DLL thermal noise jitter with respect to \(C/N_{0}\). As defined in Equation (10), the DLL error decreased as \(C/N_{0}\) increased. DLL stability was analyzed  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(T\) & \multicolumn{2}{c}{**Tx. Filter**} & \multicolumn{2}{c}{**Rx. Filter**} & \multicolumn{2}{c}{**Code Tracking Parameters**} & \\ \cline{2-7}
**(s)** & \multirow{2}{*}{**Type**} & **BW** & **BW** & **BW** & **B\({}_{L}\)** & **Loop** & **Discriminator** & **EML** \\  & & **(MHz)** & **(MHz)** & **(Hz)** & **Order** & **Type** & **Spacing** \\ \hline
0.02 & - & \(\infty\) & Brick-wall & 16.5 & 0.1 & 1 & NELP & 0.1 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Receiver parameters used in the delay-locked-loop (DLL) error analysis (also used in the Gabor bandwidth and multipath error analysis).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Candidates** & \(B\) **(MHz)** & **Spectral Efficiency** \\ \hline BPSK(1) & & 0.99 \\ BPSK(4) & & 0.95 \\ BPSK(5) & & 0.95 \\ BPSK(8) & & 0.91 \\ BOC\({}_{\rm s}\)(1,1) & & 0.97 \\ BOC\({}_{\rm s}\)(2,1) & & 0.92 \\ BOC\({}_{\rm s}\)(2,2) & & 0.93 \\ BOC\({}_{\rm s}\)(3,1) & & 0.84 \\ BOC\({}_{\rm s}\)(3,2) & & 0.86 \\ BOC\({}_{\rm s}\)(3,3) & & 0.88 \\ BOC\({}_{\rm s}\)(4,4) & & 0.87 \\ BOC\({}_{\rm c}\)(4,4) & & 0.84 \\ BOC\({}_{\rm c}\)(1,1) & & 0.94 \\ BOC\({}_{\rm c}\)(2,1) & & 0.90 \\ BOC\({}_{\rm c}\)(2,2) & & 0.89 \\ BOC\({}_{\rm c}\)(3,1) & & 0.82 \\ BOC\({}_{\rm c}\)(3,2) & & 0.82 \\ BOC\({}_{\rm c}\)(3,3) & & 0.83 \\ BOC\({}_{\rm c}\)(4,4) & & 0.75 \\ MBOC & & 0.95 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Spectral efficiency of candidates in the S-band.  
using a \(1-\sigma\) noise jitter and a stability threshold corresponding to \(d/6\). The threshold was a function of the chip rate when expressed in meters. Therefore, each candidate had different threshold values depending on its chip rate, even though they had the same correlator spacing. The \(C/N_{0}\) corresponding to the intersection of the noise jitter curve and the threshold line gave the minimum required \(C/N_{0}\) for the DLL to operate in a stable region.  
Table 7 summarizes the \(1\sigma\) DLL thermal noise jitter of each candidate when \(C/N_{0}\) was 20 dB-Hz, 40 dB-Hz, and the minimum required \(C/N_{0}\) for the stable DLL tracking. From the results, we found two things. First, the higher the chip rate and subcarrier frequency, the better the code tracking performance. Second, if the cosine-BOC signal and the sine-BOC signal had the same chip rate and subcarrier frequency, the cosine-BOC had a better code-tracking performance.  
Among the candidates, BOC\({}_{s}\)(5,2) showed the best code-tracking performance in terms of both accuracy and stability. BOC\({}_{s}\)(5,2) had a minimum required \(C/N_{0}\) of 10.79 dB-Hz, and when \(C/N_{0}\) was 40 dB-Hz, the DLL error was 0.03 m. The minimum required \(C/N_{0}\) and the DLL error of BPSK(1), which were the worst candidates in terms of the code-tracking performance, were 4.3 dB and 0.14 m higher than those of BOC\({}_{s}\)(5,2), respectively.  
Figure 3: The DLL errors and stability thresholds of the candidates.