# The Ionospheric Scintillation Effects on the BeiDou Signal Receiver
## 5 Effect on Tracking Process for BeiDou Receiver
### Determining DLL Variance for BeiDou B1I Signal  
For the code tracking loop, if carrier tracking is not lost due to amplitude or phase scintillation, the problem becomes by what degree code tracking errors increase. Phase scintillations are ignored in that they have been filtered in PLL and thus have little effect on code tracking errors. We only need to be concerned with tracking code errors caused by thermal noise and amplitude scintillations. In the presence of scintillation and thermal noise jitter variance, the tracking variance for a DLL in C/A code chips squared could be expressed as:  
\[\sigma_{T}{}^{2}=\frac{B_{n}d[1+\frac{1}{\eta(C/N_{0})(1-2S_{4}^{2})}]}{2(C/N_ {0})(1-S_{4}^{2})} \tag{48}\]  
In Equation (48), \(B_{n}\) is the one-sided noise bandwidth, and \(d\) is the correlator spacing in C/A chips. Such expression is derived in a manner completely analogous to the derivation of the thermal noise jitter variance for a PLL. Then the standard deviation of DLL tracking jitter in meters is:  
\[\sigma_{\hat{T}}=W_{B1I}\sigma_{T} \tag{49}\]  
In Equation (49), \(W_{B1I}\) is the chip length for the BeiDou B1I signal. Figure 11a,b show respectively the results of BeiDou B1I code tracking for \(d=1\) and \(d=0.1\) for the BeiDou receiver. Displayed are the values of \(\sigma_{\hat{T}}\) with respect to \(C/N_{0}\) for different levels of ionospheric scintillation. For a typical BeiDou  
Figure 10: Probability of loss of lock. receiver, \(B_{n}\) is equal to 0.1 Hz, \(\eta\) is equal to 0.02 s, \(W_{BIl}\) is 146.526 m. Simulation curves show that under high scintillation intensity, DLL tracking errors could be more than 10 m when \(d=1\) and close to 5 m when \(d=0.1\). The calculation of DLL error ignores the influence of phase scintillation on the tracking process, but in order to accurately analyze the influence on high precision positioning, which is closely related to the pseudo-range accuracy, we should take it into consideration. In order to obtain the accurate location of a user, the receiver needs to measure the accurate distance from the receiver to the satellite, which is the so-called pseudo-range. As is shown in Figure 12, a satellite sends out the navigation signal at \(t^{(s)}\) and get received by user receiver at \(t_{u}\). Generally, the clock in a satellite and receiver do not synchronize with the system clock, so there always exists a clock error. In correspondence with the BeiDou system clock \(t\), the satellite clock and receiver clock can be written as:  
\[t_{u}(t)=t+\delta t_{u}(t) \tag{50}\]  
\[t^{(s)}(t)=t+\delta t^{(s)}(t) \tag{51}\]  
Assume that the actual signal propagation time is \(\tau\), then according to Equation (51), at moment (\(t-\tau\)):  
\[t^{(s)}(t-\tau)=t-\tau+\delta t^{(s)}(t-\tau) \tag{52}\]  
Figure 11: (a) BeiDou PN code tracking error (\(d=1\)); (b) BeiDou PN code tracking error (\(d=0.1\)). Figure 12: Pseudo ranging. Then pseudo-range \(\rho(t)\) is defined as:  
\[\rho(t)=c(t_{u}(t)-t^{(s)}(t-\tau))=c\tau+c(\delta t_{u}(t)-\delta t^{(s)}(t- \tau)) \tag{53}\]  
In Equation (53), \(c\) is the speed of light. Signal propagation time \(\tau\) contains the time delay caused by the background ionosphere and troposphere. In order to study the influence only caused by ionospheric scintillation, this paper does not take into consideration the influence of background ionosphere and troposphere. Since \(t_{u}(t)\) could be directly obtained from the receiver clock, we only need to figure out \(t^{(s)}(t)\) to calculate the pseudo-range \(\rho(t)\). Actually, the direct measurement from the receiver is not \(\rho(t)\) or \(t^{(s)}(t-\tau)\) but the code phase (CP), which is obtained from the C/A code correlator in the receiver.