# A Doppler Frequency-Offset Estimation Method Based on the Beam Pointing of LEO Satellites
## 1 Introduction  
The relative motion between communication entities gives rise to the Doppler frequency effect, which induces carrier frequency shifts in communication systems. Due to their high orbital velocities, low-Earth-orbit (LEO) satellites experience significantly more pronounced Doppler effects, resulting in larger frequency deviations under fixed carrier frequency conditions [1, 2]. Traditional satellite communication systems have predominantly adopted or are based on Digital Video Broadcasting (DVB) standards. DVB systems offer strong anti-interference capabilities and excellent resilience to Doppler-induced distortions. With the ongoing evolution of mobile communication technologies, terrestrial communication systems are increasingly being extended into space, driving the development of Non-Terrestrial Networks (NTNs). NTN systems typically employ orthogonal frequency-division multiplexing (OFDM), which offers robust multipath resistance throughits subcarrier structure. However, the Doppler resilience of OFDM remains limited compared to that of DVB systems [3].  
In satellite-ground communication, two primary approaches are generally used to address the carrier frequency offset (CFO) between the transmitter and the receiver.  
The first involves enhancing signal processing capabilities to improve adaptability to CFO [4], such as developing demodulation algorithms that can tolerate larger offsets or designing signals in specialized formats.  
The second involves applying frequency-offset compensation prior to signal processing, such as implementing CFO pre-compensation at the receiver side [5].  
Both approaches face inherent limitations. Demodulation algorithms capable of handling large frequency offsets tend to increase signal processing complexity and implementation difficulty. Signals with special formats often lack flexibility and general applicability. Meanwhile, applying CFO compensation at the receiver adds to the system's overall complexity. As a result, these conventional techniques struggle to meet the performance requirements of high-speed LEO satellite communication and the broader application demands of NTN systems.  
To address Doppler-induced frequency offsets in dynamic and diverse scenarios, the fundamental principles [6; 7] of Doppler generation are revisited. The Doppler correction techniques used in navigation systems [8; 9] are analyzed, and the method by which ground stations calculate Doppler offsets [10; 11; 12] for LEO satellites is studied. Based on these insights and extensive simulations, a novel approach for frequency-offset estimation and compensation is proposed. This method leverages beam-pointing information to infer Doppler frequency offsets. A satellite-centered coordinate system is established using satellite orbital altitudes, beam elevation angles, and azimuth angles as input parameters. The positions of the communicating terminals are mapped into this coordinate system. The frequency offset is then estimated based on variations in beam-pointing directions as the satellite moves according to the laws governing Doppler shifts.  
This paper focuses on the modeling, optimization, and simulation analysis of Doppler frequency-offset estimations for LEO satellite signals based on beam-pointing perception. The remainder of this paper is organized as follows. In the Section 2, the Doppler frequency-offset estimation model based on the satellite coordinate system is established. The Section 3 optimizes the model according to the parameters affecting the model. In the Section 4, the model is simulated and analyzed and compared with the simulation results of the STK 11.6.0 software. The Section 5 is the discussion of the model, and the Section 6 is the conclusion of this article.