# A Doppler Frequency-Offset Estimation Method Based on the Beam Pointing of LEO Satellites
## 5 Discussion  
The accuracy of the DFS-BP algorithm proposed in this paper depends on the accuracy of the satellite antenna's azimuth and elevation angles, which are closely related to factors such as antenna pointing accuracy, satellite attitude control accuracy, clock stability, and radio frequency (RF) tolerance. (1) Influence of Antenna Pointing Accuracy on the DFS-BP Algorithm  
Traditional communication satellites typically have antenna pointing accuracies ranging from 0.1\({}^{\circ}\) to 0.5\({}^{\circ}\). Military satellites and navigation satellites usually feature antenna pointing accuracies that are better than 0.01\({}^{\circ}\). Low-Earth-orbit (LEO) satellites, due to the requirements of inter-satellite communication, often have antenna pointing accuracies that are superior to 0.01\({}^{\circ}\). Figure 10: Simulation results of the Doppler frequency shift when the minimum elevation angle is adjustable (the ground terminal is on the left side of the subsatellite point). Antenna pointing accuracy is primarily determined by two components: hardware errors and software algorithms. Hardware errors mainly arise from phase errors in phase shifters and radio frequency (RF) chain errors. Phase errors can be minimized by using digital phase shifters to increase the effective bits of the phase shifter and improve quantization accuracy. RF chain errors mainly stem from amplitude and phase errors between channels, which can be reduced by employing high-precision components and implementing amplitude predistortion adjustments. In terms of software, beam-pointing compensation algorithms can be used to reduce RF delays, avoid beam squint, and thus minimize antenna pointing errors. 1. Influence of Satellite Attitude Control Accuracy on the DFS-BP Algorithm  
Traditional communication satellites have attitude control accuracies of less than 0.1\({}^{\circ}\), while remote sensing satellites achieve attitude accuracies that are better than 0.05\({}^{\circ}\). Low-Earth-orbit (LEO) satellites for satellite constellation applications feature attitude control accuracies that are superior to 0.01\({}^{\circ}\). For instance, the Chang'e-5 probe achieved an attitude control accuracy of \(\leq\)0.1\({}^{\circ}\) during lunar sampling, and the \"Jilin-1\" satellite can reach an attitude control accuracy of 0.02\({}^{\circ}\). The factors influencing satellite attitude control accuracy mainly include star sensors, gyroscopes, etc. The measurement error of star sensors directly affects attitude control accuracy, with high-precision star sensors achieving an accuracy of 0.0003\({}^{\circ}\). The bias stability of fiber optic gyroscopes is 0.01\({}^{\circ}\)/h, while that of laser gyroscopes can be better than 0.001\({}^{\circ}\)/h. The combination of high-precision star sensors and laser gyroscopes enables high-precision satellite attitude control. A satellite's attitude control accuracy and antenna pointing accuracy actually affect the antenna's pointing information. Based on the requirement that both the antenna pointing accuracy and satellite's attitude control accuracy are better than 0.5\({}^{\circ}\), this paper adds random errors of 0.05\({}^{\circ}\) to 0.5\({}^{\circ}\) to the antenna's azimuth and elevation angles for simulation, and the simulation results are shown in Figure 11. The simulation results indicate that as the random errors added to the antenna's azimuth and elevation angles gradually increase, the Doppler frequency-shift estimation errors also increase progressively, with the estimation errors remaining within \(\pm\)350 Hz. If the satellite's altitude control errors and antenna pointing errors reach a certain threshold, the accuracy of the DFS-BP algorithm will be affected. Figure 11: Influence of pointing errors in azimuth and elevation angles on the results of Doppler frequency-offset estimation. (3) Influence of Clock Stability on the DFS-BP Algorithm  
Clock stability is reflected in a signal's frequency stability.