# A Doppler Frequency-Offset Estimation Method Based on the Beam Pointing of LEO Satellites
## 4 Simulation Analysis
### Simulation of Doppler Frequency Shift When the Minimum Elevation Angle Parameter Is Adjustable
When the azimuth angle exceeds 180\({}^{\circ}\), the Doppler frequency-offset estimation error of the satellite beam-pointing method is shown in Figure 10. During the entire visible period, the frequency-offset estimation error ranges of the two methods are between [\(-\)2000 Hz, \(+\)200 Hz]. The simulation results indicate that as the minimum elevation angle value of the satellite increases, the frequency-offset estimation error of the satellite beam-pointing method also increases. We conducted simulations on the RMSE of the frequency-offset estimation for values of 0\({}^{\circ}\), 10\({}^{\circ}\), 20\({}^{\circ}\), 30\({}^{\circ}\), 40\({}^{\circ}\), and 50\({}^{\circ}\). The simulation results are shown in Figure 10. The results indicate that as \(\varphi_{max}\) increases, the RMSE of the frequency-offset estimation gradually increases. When \(\varphi_{max}=0^{\circ}\), the RMSE of the frequency-offset estimation does not exceed 100 Hz, and when \(\varphi_{max}=50^{\circ}\), the RMSE is approximately 2000 Hz. The simulation results of the DFS-BP algorithm are compared with those obtained from STK's SGP4 model. The comparison shows that the terminal's geographic latitude has little effect on the Doppler frequency-offset estimation error. When the satellite's minimum elevation angle is 0\({}^{\circ}\), the Doppler frequency-offset estimates from both methods are similar, with estimation errors ranging between \(-\)200 Hz and \(+\)200 Hz. The RMSE of the DFS-BP algorithm is less than 100 Hz. As the minimum elevation angle increases, the Doppler frequency-offset estimates from both methods also increase gradually, with estimation  
Figure 9: Simulation results of Doppler frequency shifts when the minimum elevation angle is adjustable (the ground terminal is on the right side of the subsatellite point). errors expanding to a range of approximately \(-2000\) Hz to +2000 Hz. The RMSE of the DFS-BP algorithm is less than 2 kHz. Analyzing the frequency-offset estimation errors as the minimum elevation angle increases reveals that the difference between the frequency-offset estimates at the start and end of the satellite-to-ground communication remains under 500 Hz. Future work can focus on reducing frequency-offset estimation errors through more in-depth research. Depending on the specific satellite communication scenarios, techniques such as satellite beam-pointing awareness and fixed error compensation could be applied to optimize the frequency-offset estimation in the satellite beam-pointing method, thereby enhancing estimation accuracy. This section simulates the estimation error accuracy of the DFS-BP algorithm in terms of the satellite's geocentric latitude, orbital altitude, orbital inclination, terminal position, etc., which uses statistical methods such as the RMSE and 95% CI to analyze the error range of the DFS-BP algorithm. This proposes follow-up improvement directions for the DFS-BP algorithm. However, this method does not consider the influence of clocks, equipment, and systems on the DFS-BP algorithm. This part of the influence will be discussed in Section 5.