# Dual-Frequency Signal Enhancement Method of Moving Target Echoes for GNSS-S Radar
## 3 Simulation and Experimental Results
### Simulation  
In order to deeply observe the detailed effect of this method, a simulation is performed in this section. Firstly, the phase changes in dual-frequency echo signals caused by moving targets were analyzed. Then, the effect of using the dual-frequency differential method to eliminate phase fluctuations was simulated. Finally, the effect of the coherent accumulation of dual-frequency differential signals is presented. During the simulation, the original signal is generated according to the real signal format of the GNSS satellite, and Gaussian white noise is added as background interference. The simulation uses signals of BDS B1 and B3 frequency, and the sampling frequency fs is 200 MHz. The detailed parameters are shown in Table 2.  
After the target echo signal is demodulated and correlation compressed, the data are vertically arranged according to PRN code period, and then the target trajectory of the B1 echo signal and B3 echo signal is obtained, as shown in Figure 8. In order to intuitively analyze the signal phase fluctuation, a higher echo SNR is adopted in the simulation; so, the signal trace can be seen after the signal demodulation in Figure 8.  
Figure 8a is the target echo trajectory of the B1 signal, and Figure 8b is the target echo trajectory of the B3 signal. Because the bandwidth of the B3 signal is larger than the bandwidth of the B1 signal, the track line in the figure is thinner than that of B1; that is, it has a higher range resolution. Then, the SNR of the B1 and B3 echo signals in Figure 8 is calculated to form the SNR curve shown in Figure 9. Due to the acceleration, the velocity of the target is increasing, and the residual Doppler shift of the echo is also increasing, which makes the SNR of the compressed echo decrease. Since the frequency of the B1 signal (1561.098 MHz) is larger than that of the B3 signal (1268.52 MHz), the same target motion speed will cause a greater Doppler shift. So, the decline amplitude of the SNR curve of B1 (blue curve) in Figure 9 is greater than that of the B3 signal (orange curve). Due to the fact that the B1 and B3 signals are simultaneously transmitted by the same satellite, the amplitudes of the two correlated compressed single-frequency signals in Figure 8 can be directly added to obtain the trajectory of amplitude enhancement, as shown in Figure 10. Comparing the color bars on the right side of Figures 8 and 10, it can be observed that after combining the signal amplitudes of the two frequencies, the signal energy increases by one time, from 10,000 to 20,000. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Signal type & BDS B1, B3 \\ Carrier frequency & B1:1561.098 MHz; B3:1268.52 MHz \\ PRN code period & 1 ms \\ SNR & \(-\)20 dB \\ Initial speed of the target & 16 m/s \\ Acceleration of the target & 10 m/s\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the Simulation. Figure 8: Target echo trajectory. (**a**) Echo of B1 Signal; (**b**) Echo of B3 Signal. Due to the low power of the real GNSS signal, further coherent accumulation is required after amplitude accumulation to detect the signal. Then, in order to analyze the relationship between the signal phase changes in B1 and B3, the signal cells from the original data in Figure 8 were selected, as shown in Figure 11a,b. It can be seen that due to the existence of target movement, the signal phase (the blue lines) is constantly changing between \(\pm 180^{\circ}\) (the red lines) with slow time \(t_{m}\). It can be seen that due to the influence of signal phase changes between each piece of data, long-term coherent accumulation cannot be performed. Figure 11: Variation in signal phase with slow time. (**a**) B1 Signal; (**b**) B3 Signal. Figure 9: SNR of echo signals after correlation compression. After unwrapping the signal phase, the continuously changing phase diagram is shown in Figure 12a.