# The Ionospheric Scintillation Effects on the BeiDou Signal Receiver
## 3 Solution of Signal Propagation Based on MPS Technique
### Experimental Results  
Figure 4 shows the distribution of phase and relative amplitude random fluctuation with \(S_{4}=0.47\). Note that the \"Std\" in the figures (and all the related figures in the paper) is standard deviation. Each result shown here is one sample profile, which is slightly different for every simulation. It should also be noted that the section in which the sampling point numbers are less than 150 should be rejected because the numbers are too small to be persuasive and representative. According to a 100 times simulations, the relative amplitude fluctuation could be \(-0.5\)\(\pm\) 0.05 to 0.4 \(\pm\) 0.05, the phase deviation could be \(-0.52\)\(\pm\) 0.09 rad to 0.52 \(\pm\) 0.09 rad. Furthermore, Figure 4c,f show the statistical probability density curves. The results show that under weak scintillation, phase fluctuation would largely follow a Gaussian distribution with \(\mu\) = 0.05, \(\sigma\) = 0.3 and amplitude fluctuation would mostly follow a Rayleigh distribution with \(\sigma\) = 0.8.  
Figure 5 presents the distribution of phase and amplitude scintillation in strong scintillation with \(S_{4}=0.808\). Rejecting the section whose sample point number is below 150, the relative amplitude fluctuation could be \(-0.75\)\(\pm\) 0.05 to 0.8 \(\pm\) 0.1, the phase deviation could be \(-1.13\)\(\pm\) 0.09 rad to 1.39 \(\pm\) 0.09 rad.  
Furthermore, it could be noticed that under strong scintillation, the fluctuation of phase agrees with a Gaussian distribution with \(\mu\) = 0.2, \(\sigma\) = 0.3 and the amplitude fluctuation is getting closer to a Rayleigh distribution with \(\sigma\) = 0.8. In addition, the comparison of Figures 4 and 5 shows that as the scintillation become stronger, the mean value of the relative amplitude differs slightly, but the variance is constantly increasing. At the same time for phase fluctuation, both of the mean value and variance would increase, which may result in receiver performance inaccuracy and instability.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Carrier Frequency (MHz) & 1561.098 \\ Ionosphere Altitude (km) & 200–400 \\ Power Law Index \(p\) & 4 \\ False Alarm Probability & \(10^{-6}\) \\ Classical Electron Radius (m) & \(2.818\times 10^{-15}\) \\ Code Rate of BeiDouB1I Signal (Mbps) & 2.046 \\ Sample Points & 6000 \\ Sampling Frequency & 500 \\ Outer Scale (m) & 5000 \\ Inner Scale (m) & 15 \\ Distance Between two Adjacent Screens (m) & 5000 \\ Average Electron Density & \(9\times 10^{11}\) \\ Computer Language & Matlab \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters.  
Figure 4: Phase and amplitude for \(S_{4}=0.47\). (**a**) Relative Amplitude Fluctuation; (**b**) Distribution of Amplitude Fluctuation; (**c**) Probability Density Curve; (**d**) Phase Fluctuation; (**e**) Distribution of Phase Fluctuation; (**f**) Probability Density Curve.  
Figure 5: Phase and amplitude for \(S_{4}=0.808\) (**a**) Relative Amplitude Fluctuation; (**b**) Distribution of Amplitude Fluctuation; (**c**) Probability Density Curve; (**d**) Phase Fluctuation; (**e**) Distribution of Phase Fluctuation; (**f**) Probability Density Curve.