# The Ionospheric Scintillation Effects on the BeiDou Signal Receiver
## 4 Effect on the Acquisition Process for the BeiDou Receiver  
According to BeiDou Interface Control Document (ICD) [25], the code rate of the BeiDou B1I (1561.098 MHz) signal is 2.046 Mbps with the code length 2046. As the chips of pseudo code are the smallest units of the BeiDou signal, this paper uses the BeiDou pseudo code to evaluate the influence of ionospheric scintillation on the BeiDou navigation signal. Besides, in order to analyze the influence only caused by ionospheric scintillations, this paper assumes that there exists no other factors that could cause errors for receiver. The schematic of the generation of the BeiDou pseudo code (version 2.0) is shown in Figure 6.  
The process of a received signal in a receiver mainly consists of two steps: acquisition and tracking, so this paper mainly analyzes the scintillation effects on these two aspects to evaluate the influence on receiver performance. Figure 7 shows the analysis method used in this paper. For signal acquisition, the correlation peak and acquisition probability are two of the most important parameters to determine whether or not the signal could be captured by a receiver [26]. As the first step for a receiver to work, signal acquisition is related to the strong autocorrelation ability of pseudo code. The received pseudo code must match with the local one created by receiver itself. Once the correlation peak value is higher than detection threshold, the signal can be captured. For the signal detection process, the detection probability \(P_{d}\) and false alarm probability \(P_{fa}\) are determined as follows [26]:  
\[P_{d}=\int\limits_{V_{t}}^{\infty}p_{s}(z)dz \tag{36}\]  
\[P_{fa}=\int\limits_{V_{t}}^{\infty}p_{n}(z)dz \tag{37}\]  
Figure 6: Sketch of BeiDou pseudo code generation. Figure 7: Analysis method. In Equations (36) and (37), \(p_{s}(z)\) is probability density function (PDF) of the envelope with signal present, \(p_{n}(z)\) is the envelope with signal absent, \(V_{t}\) is the threshold. Assume that the envelope of signal is \(\sqrt{I^{2}+Q^{2}}\), in which \(I\) and \(Q\) have a Gaussian distribution. Then \(p_{s}(z)\) and \(p_{n}(z)\) could be defined by:  
\[p_{s}(z)=\frac{z}{\sigma_{n}^{2}}e^{-(\frac{z^{2}}{2\sigma_{n}^{2}}+C/N)}\,I_{0 }(\frac{z\sqrt{2C/N}}{\sigma_{n}}) \tag{38}\]  
\[p_{n}(z)=\frac{z}{\sigma_{n}^{2}}e^{-(\frac{z^{2}}{2\sigma_{n}^{2}})} \tag{39}\]  
In Equations (38) and (39), \(\sigma_{n}^{2}\) is Root Mean Square (RMS) noise power, \(C/N\) is the pre-detection signal to noise ratio (SNR), \(I_{0}(\cdot)\) is a modified Bessel function with zero order. For a given false alarm \(P_{fa}\), the detection threshold is obtained as follows:  
\[V_{t}=\sigma_{n}^{2}\sqrt{-2\text{ln}P_{fa}} \tag{40}\]  
Then the detection probability \(P_{d}\) is:  
\[P_{d}=Q(\frac{p\cdot N\sqrt{2(C/N)}}{\sigma_{n}},\frac{V_{t}}{\sigma_{n}^{2}}) \tag{41}\]  
In Equations (41), \(Q(\cdot)\) is the generalized Marcum-Q function, \(N\) is pseudo code length, \(p\) is the scintillation factor which is defined as the ratio of the cross-correlation peak and the pseudo code autocorrelation peak. According to Equations (40) and (41), for given \(P_{fa}\) and \(\sigma_{n}^{2}\), the acquisition probability of the BeiDou signal is obtained. Figure 8a shows the correlation peak of the BeiDou pseudo code under three levels of \(S_{4}\) for 100 simulations. The figure shows that when \(S_{4}\) is around 0.15, the average correlation peak could be degraded by 3%; when \(S_{4}\) is around 0.38, the degradation could be 8%; when \(S_{4}\) is around 0.71, the degradation could be up to 13%. The correlation variance also tends to become higher as the scintillation becomes higher indicating that the acquisition process would be less stable. Figure 8b shows the acquisition probability under different scintillation intensity scenarios resulting from the decrease of correlation peak. Figure 8: (**a**) Correlation peak of the BeiDou pseudo code (\(N=2046\)); (**b**) Acquisition probability of the BeiDou signal (\(N=2046\)).