# A Comprehensive Evaluation of Possible RNSS Signals in the S-Band for the KPS
## 4 FoMs Analysis
### Multipath Error Analysis Results  
The multipath error is a function of the multipath delay, and the multipath error characteristic of the signal can be analyzed using the multipath error envelope (MPEE). The MPEE is composed of a positive envelope and a negative envelope. These two envelopes indicate the upper and lower bounds of the pseudorange error due to in-phase and quadrature multipaths, respectively [44]. The multipath error was analyzed using the receiver parameters in Table 6, assuming there existed only one single multipath with the MDR of \(-\)3 dB. Figure 5 illustrates the MPEE for all candidate signals, and Table 9 enumerates the maximum multipath error of each candidate. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Candidates**} & \multicolumn{3}{c}{**Gabor Bandwidth (MHz)**} \\ \cline{2-4}  & \(\mathbf{B_{r}=4\) MHz**} & \(\mathbf{B_{r}=16.5\) MHz} & \(\mathbf{B_{r}=2f_{c}\) or \(2(f_{s}+f_{c})\)} \\ \hline BPSK(1) & 0.46 & 0.93 & 0.33 \\ BPSK(4) & 0.90 & 1.85 & 1.31 \\ BPSK(5) & 0.88 & 2.19 & 1.63 \\ BPSK(8) & 0.76 & 2.62 & 2.62 \\ BOC\({}_{\text{s}}\)(1,1) & 0.80 & 1.60 & 0.80 \\ BOC\({}_{\text{s}}\)(2,1) & 1.16 & 2.45 & 1.72 \\ BOC\({}_{\text{s}}\)(2,2) & 1.10 & 2.26 & 1.60 \\ BOC\({}_{\text{s}}\)(3,1) & 0.35 & 2.70 & 2.64 \\ BOC\({}_{\text{s}}\)(3,2) & 0.56 & 2.71 & 2.53 \\ BOC\({}_{\text{s}}\)(3,3) & 0.82 & 2.65 & 2.40 \\ BOC\({}_{\text{s}}\)(4,4) & 0.59 & 3.21 & 3.21 \\ BOC\({}_{\text{s}}\)(5,2) & 0.27 & 4.41 & 4.38 \\ BOC\({}_{\text{c}}\)(1,1) & 1.03 & 2.06 & 1.03 \\ BOC\({}_{\text{c}}\)(2,1) & 0.93 & 2.78 & 1.84 \\ BOC\({}_{\text{c}}\)(2,2) & 0.78 & 2.93 & 2.07 \\ BOC\({}_{\text{c}}\)(3,1) & 0.15 & 3.11 & 2.70 \\ BOC\({}_{\text{c}}\)(3,2) & 0.28 & 3.58 & 2.86 \\ BOC\({}_{\text{c}}\)(3,3) & 0.37 & 3.93 & 3.11 \\ BOC\({}_{\text{c}}\)(4,4) & 0.20 & 4.17 & 4.16 \\ MBOC & 0.76 & 2.23 & 2.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Gabor bandwidths of the candidates in the S-band. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Candidates**} & \multicolumn{2}{c}{**Max. MP Error (m)**} & \multicolumn{2}{c}{**RA of MPEE (m) (\(B_{r}\) = 16.5 MHz)**} \\ \cline{2-6}  & \(B_{r}\)=\(\infty\) & \(B_{r}\) = 16.5 MHz & \(\tau_{delay}\) = 26 m & \(\tau_{delay}\) = 51 m & \(\tau_{delay}\) = 400 m \\ \hline BPSK(1) & 7.35 & 7.12 & 4.72 & 5.66 & 4.82 \\ BPSK(4) & 1.83 & 5.83 & 4.18 & 4.47 & 0.86 \\ BPSK(5) & 1.46 & 5.31 & 3.89 & 4.16 & 0.73 \\ BPSK(8) & 0.98 & 5.98 & 4.20 & 3.09 & 0.41 \\ BOC\({}_{s}\)(1,1) & 7.35 & 7.10 & 4.72 & 5.65 & 3.00 \\ BOC\({}_{s}\)(2,1) & 7.35 & 6.97 & 4.67 & 5.59 & 2.23 \\ BOC\({}_{s}\)(2,2) & 3.68 & 6.00 & 4.24 & 4.67 & 1.14 \\ BOC\({}_{s}\)(3,1) & 7.35 & 8.12 & 5.07 & 4.81 & 2.02 \\ BOC\({}_{s}\)(3,2) & 3.69 & 7.58 & 4.95 & 4.81 & 1.14 \\ BOC\({}_{s}\)(3,3) & 2.46 & 6.95 & 4.72 & 4.60 & 0.86 \\ BOC\({}_{s}\)(4,4) & 1.83 & 6.04 & 4.18 & 3.11 & 0.50 \\ BOC\({}_{s}\)(5,2) & 3.68 & 4.90 & 3.22 & 2.87 & 0.63 \\ BOC\({}_{c}\)(1,1) & 7.35 & 7.03 & 4.69 & 5.62 & 2.13 \\ BOC\({}_{c}\)(2,1) & 7.35 & 6.66 & 4.48 & 4.64 & 1.76 \\ BOC\({}_{c}\)(2,2) & 3.68 & 6.06 & 4.19 & 3.42 & 0.80 \\ BOC\({}_{c}\)(3,1) & 6.82 & 7.03 & 4.60 & 3.95 & 1.73 \\ BOC\({}_{c}\)(3,2) & 3.68 & 5.56 & 3.90 & 2.93 & 0.83 \\ BOC\({}_{c}\)(3,3) & 2.46 & 4.80 & 3.35 & 2.20 & 0.54 \\ BOC\({}_{c}\)(4,4) & 1.83 & 4.72 & 3.24 & 2.48 & 0.37 \\ MBOC & 6.18 & 5.32 & 3.41 & 3.18 & 1.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Running average (RA) of the multipath error envelope (MPEE) of the candidates in the S-band. Figure 5: Multipath error envelope of the candidates in the S-band: (**a**) \(B_{r}=\infty\); (**b–d**) \(B_{r}=16.5\,\mathrm{MHz}\). Figure 5a,b shows the MPEE of the BPSK and NavIC signals. When the receiver bandwidth was infinite (Figure 5a), the higher the chip rate, the smaller the maximum multipath error. Similar to the DLL error, the limited front-end bandwidth affected the multipath error.