## 2 Materials and Methods  
### Signals  
BDS-3 has been provided official open PNT service since 31 July 2020. The BDS-2 regional satellite navigation system was built earlier than BDS-3, which has opened three civil signals for B1I (1561.098 MHz), B2I (1207.14 MHz), and B3I (1268.52 MHz). The open civil signals of BDS-2 are mainly modulated by Binary Phase Shift Keying (BPSK). After the completion of BDS-3, the BDS-3 inherits the B1I and B3I signals of BDS-2, and the signal modulation methods of B1I and B3I are strictly consistent with BDS-2 to ensure the interoperability of system signals. BDS-3 began to adopt new civil signal frequency points such as B1C (1575.42 MHz), B2a (1176.45 MHz), and B2b (1207.14 MHz) [5; 6; 7; 8; 9], and the observational accuracy of the BDS-3 signals is comparable to GPS L1/L2/L5 and Galileo E1/E5a/E5b, according to the report [29]. Frequency multiplexing exists among GNSSs. Figure 1 shows the frequency distribution of the current four global satellite navigation systems. If the frequency band numbers in Figure 1 have the same position on the frequency coordinate axis, they have the same frequency center, and there is a potential possibility of interoperability between systems. Frequency overlap puts forward higher requirements for compatibility and interoperability among systems. B1C and B2a are the service signals that BDS-3 mainly opens to users. B1C and B2a can broadcast signals through 24 medium earth orbit satellites (MEO) and 3 inclined geosynchronous orbit satellites (IGSO). The signals broadcasted by the satellite are distinguished by capturing different pseudo-random noise codes (PRN). PRN numbers ranging from 19 to 46 belong to BDS-3 satellites, of which 38, 39, and 40 are IGSO satellites. The code length of the two signals is 10230, uniformly. However, the difference is that the coding rate of B2a is 10.23 Mcps, while that of B1C is 1.023 Mcps [7; 8]. By referring to the official spatial signal interface document (ICD) of the BeiDou system, the B1C signal is composed of data component and pilot component [8]. The carrier center frequency of both is 1575.42 MHz, where the GPS L1 and Galileo E1 are also broadcasted on it. The structural characteristics of B1C can be listed in Table 1.  
The pilot component adopts quadrature multiplexed binary offset carrier (QMBOC) modulation, which allows the signal to be composed of a narrow-band component with larger power distribution and a broadband component with smaller power distribution [30]. This shows that the B1C signal can be compatible with high-performance receiving mode and low-complexity receiving mode, which is a relatively novel feature of the BDS-3 B1C signal. The complex envelope form of B1C signal [31] can be written as:  
\[S_{(\text{B1C})}=s_{(\text{B1C}_{\text{D}})}(t)+\text{i}\beta_{(\text{B1C}_{ \text{P}})}(t) \tag{1}\]  
where \(s_{(\text{B1C}_{\text{D}})}(t)\) is the data component of the signal, which is generated through the modulation of navigation message \(D_{(\text{B1C}_{\text{D}})}(t)\), ranging code \(C_{(\text{B1C}_{\text{D}})}(t)\), and subcarrier signal. \(s_{(\text{B1C}_{\text{P}})}(t)\) is the pilot component of the signal, which is modulated by subcarrier and ranging code \(C_{(\text{B1C}_{\text{P}})}(t)\), the navigation message is not modulated in it. \(s_{(\text{B1C}_{\text{D}})}(t)\) and \(s_{(\text{B1C}_{\text{P}})}(t)\) are distributed in the power ratio of 1:3. The modulated B1C signal can finally be written as the following expression in bandpass form [31]:  
\[S_{(\text{B1C})}^{(\text{i})}(t)=\sqrt{2P_{(\text{B1C})}}\left[\frac{1}{2}D_{( \text{B1C})}^{(\text{i})}(t)C_{(\text{B1C}_{\text{D}})}^{(\text{i})}(t)\cos( 2\pi\text{ft})+\frac{\sqrt{3}}{2}C_{(\text{B1C}_{\text{P}})}^{(\text{i})}(t) \sin(2\pi\text{ft})\right] \tag{2}\]  
In the formula, \(S_{(\text{B1C})}^{(\text{i})}(t)\) represents the signal from the satellite labeled i, \(D_{(\text{B1C})}^{(\text{i})}(t)\) represents the modulated navigation message, \(P_{(\text{B1C})}\) represents the signal power of B1C,