# Research on Tracking Technique Based on BPSK-CSK Signals
## 3 Results  
### BER Comparison and Analysis  
In order to verify the performance of the methods proposed in this paper, we compare the BER under three methods. Figure 6: Code-tracking loop. Method 1 uses the conventional BPSK-modulated signal for tracking [31]. Method 2 uses the BPSK-CSK-modulated signal for tracking in this paper, and Method 3 uses the CSK-modulated signal for tracking [28]. Since CSK modulation is used for the L6 signal in QZSS, the L6 signal with tracking CSK modulation is selected in Method 3. The code length of the L6 signal is 10,230 and the code rate is 5.115 MHz. According to the frequency point, code length, and code rate, the Galileo E6b signal with the same frequency point, code length, and code rate is selected in Method 1. The BPSK-CSK-modulated signal in Method 2 also has the same code length and code rate. The rough values of the Doppler frequency and coded phase of BPSK-modulated signals, BPSK-CSK-modulated signals, and CSK-modulated signals are estimated using the FFT-based circular correlation method. The exact Doppler frequency and code phase are continuously estimated every 1 ms during tracking using frequency-locked loop (FLL), phase-locked loop (PLL), and demurrage-locked loop (DLL). The carrier-tracking loop and coded-tracking loop parameters for the three methods are shown in Tables 1 and 2 for a Doppler value of 1000 Hz and a sampling time of 10 s. The parameters of the carrier-tracking loop and coded-tracking loop for the three methods are shown in Tables 1 and 2. Figure 7 shows the variation of BER with CNR when Doppler is kept constant (35-50 dB-Hz) for constant Doppler. Table 3 shows the percentage BER of Method 2 and Method 3 with respect to Method 1 when Doppler is kept constant. From Figure 7, it can be seen that the BPSK-modulated signal (Method 1) has the lowest BER, the CSK (Method 3) has the highest BER, and the proposed BPSK-CSK-modulated signal is in the middle of the two. Therefore, the BPSK-CSK tracking method has a higher information transmission rate and lower BER with constant Doppler and the same CNR. The specific percentage values of BER for mode 2 and mode 3 with respect to mode 1 are given in Table 3, from which it can be seen that the BER of CSK-modulated signals is much higher than that of conventional BPSK-modulated signals, while the BER of BPSK-CSK-modulated signals is improved. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Coherent Integration** & **Non-Coherent** & **Traction** & **Loop Bandwidth/Hz** \\
**Time/ms** & **Integration Time/ms** & **Range/Hz** & **Loop Bandwidth/Hz** \\ \hline
**4** & \(1\) & \(\pm\)62.5 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Carrier-tracking loop parameters. \begin{table}
\begin{tabular}{c c c} \hline \hline
**CNR/(dB-Hz)** & **Method 3 Higher than** & **Method 2 Higher than** \\  & **Method 1/\%** & **Method 1/\%** \\ \hline
36 & 36.00 & 18.42 \\
37 & 35.41 & 18.99 \\
38 & 34.79 & 19.56 \\
39 & 34.19 & 20.12 \\
40 & 32.82 & 16.24 \\
41 & 31.61 & 12.39 \\
42 & 30.47 & 8.53 \\
43 & 29.24 & 4.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: BER proportion of Method 2 and 3 higher than Method 1 when Doppler is constant. Figure 8 shows the variation of BER with CNR (35-50 dB-Hz) when \(a_{acce}=10\) m/s\({}^{2}\). \(a_{acce}\) is the relative acceleration between the satellite and the receiver. Table 4 shows the percentage of BER of Method 2 and Method 3 that is higher than that of Method 1 when \(a_{acce}=10\) m/s\({}^{2}\). From Figure 8, it can be seen that the BER of Method 2 and Method 3 is higher than that of Method 1 when \(a_{acce}=10\) m/s\({}^{2}\). The BER when \(a_{acce}=10\) m/s\({}^{2}\) is almost the same as when Doppler is kept constant. Therefore, the BPSK-CSK tracking method has a higher message rate and lower BER when \(a_{acce}=10\) m/s\({}^{2}\) and CNR is the same.