# Radio Frequency Compatibility Evaluation of S Band Navigation Signals for Future BeiDou
## 4 Radio Frequency Compatibility Evaluation
For the assessment of worst-case interference effects, a maximum threshold of \(-126\) dBW/m\({}^{2}\) in S band and 0 dBi receiving antenna are used for Globalstar and the effective area of receiving antenna is estimated approximately as 29.4 dBm\({}^{2}\) by  
\[A=\frac{G\Delta^{2}}{4\pi}, \tag{29}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**SSC[dB]**} & \multicolumn{6}{c}{**Interference Signals**} \\ \cline{2-10}  & **SC[dB]** & **CPM(6)** & **BOCs(4,0)** & **BPSK(8)** & **MSK-BOCs(4,0)** & **BPSK(1)** & **BPSK(4)** & **BOCs(5,2)** & **CBOC(6,1,1/11)** & **Globalstar** \\ \hline \multirow{7}{*}{Signed} & CPM(8) & \(-70.54\) & \(-73.81\) & \(-74.36\) & \(-72.28\) & \(-73.24\) & \(-74.99\) & \(-70.62\) & \(-74.84\) & \(-72.16\) \\  & BOC(4,4) & \(-78.51\) & \(-70.93\) & \(-72.17\) & \(-70.62\) & \(-79.93\) & \(-73.91\) & \(-73.10\) & \(-75.36\) & \(-where the \(G\) is antenna gain and \(\lambda\) is carrier wavelength. Table 4 summarizes the minimal and maximum power of all above S band signals, where a margin of 3 dB has been considered between the maximum and minimal received powers. To evaluate radio frequency compatibility of S band navigation signals for future BDS, the worst results of compatibility between BDS candidate signals and other systems in S band based on the \(\Delta\left(C/N_{0}\right)_{\text{eff}}\) for signal acquisition and code tracking are presented as follows:  
Case 1: Galileo candidate [PERSON](6,1,1/11) is interfered by BDS candidate signals, i.e.,  
\[\left\{ \begin{array}{l}I_{\text{intra}}=I_{\text{CBOC}\left(6,1,1/11\right), \text{others}}^{\text{Galileo}}\\ I_{\text{inter}}=I_{\text{candidate}}^{\text{BDS}}\end{array} \right., \tag{30}\]  
where \(I_{\text{candidate}}^{\text{BDS}}\) denotes the equivalent PSD of BDS candidate interfering signals, and the BDS candidate is assumed respectively as CPM(8), BOCs(4,4), BPSK(8) and MSK-BOCs(4,4). The \(\Delta\left(C/N_{0}\right)_{\text{eff,SSC}}^{\text{inter,worst}}\) and \(\Delta\left(C/N_{0}\right)_{\text{eff,CTSSC}}^{\text{inter,worst}}\) of Galileo candidate CBOC(6,1,1/11) interfered by BDS candidate signals for signal acquisition and code tracking are respectively shown in Figures 4 and 5. As shown, the mean \(\Delta\left(C/N_{0}\right)_{\text{eff,SSC}}^{\text{inter,worst}}\) between CBOC(6,1,1/11) and CPM(8), BOCs(4,4), BPSK(8) and MSK-BOCs(4,4) at global scale are around 0.0092 dB, 0.0195 dB, 0.0987 dB and 0.0134 dB respectively, which means that compared to other candidates the CPM(8) introduces minimal interference on CBOC(6,1,1/11) in acquisition. Also, the CPM(8) is more superior in code tracking, with a smallest mean degradation of 0.0184 dB on CBOC(6,1,1/11). This result comes as no surprise because CPM(8) has comparable or better SSC and CTSSC with CBOC(6,1,1/11) as well as less maximum received power than other BDS candidates at worst situation. \begin{table}
\begin{tabular}{c c c} \hline
**(dBW)** & **Maximum Received Power** & **Minimal Received Power** \\ \hline CPM(8) & \(-167.2\) & \(-170.2\) \\ BOCs(4,4) & \(-163.4\) & \(-166.4\) \\ BOCs(5,2) & \(-165.8\) & \(-168.8\) \\ CBOC(6,1,1/11) & \(-159.8\) & \(-162.8\) \\ BPSK(1) & \(-152.3\) & \(-155.3\) \\ BPSK(4) & \(-158.7\) & \(-161.7\) \\ BPSK(8) & \(-161.6\) & \(-164.6\) \\ MSK-BOCs(4,4) & \(-164.9\) & \(-167.9\) \\ Globalstar & \(-155.4\) & \(-158.4\) \\ \hline \end{tabular}
\end{table} 
Table 4: The minimal and maximum received power of all S band signals. Figure 3: The code tracking errors of S band navigation signals. Case 2: Galileo candidate BPSK(1) is interfered by BDS candidate signals, i.e.,  
\[\left\{ \begin{array}{l}I_{\text{intra}}=I_{\text{BPSK(1),others}}^{\text{ Galileo}}\\ I_{\text{inter}}=I_{\text{candidate}}^{\text{BDS}}\end{array} \right.. \tag{31}\]  
Figures 6 and 7 respectively show the \(\Delta(C/N_{0})_{\text{eff,SSC}}^{\text{inter,worst}}\) and \(\Delta(C/N_{0})_{\text{eff,CTSSC}}^{\text{inter,worst}}\) of Galileo candidate BPSK(1) interfered by BDS candidate signals.