Due to the rapid mobility and the orbit feature of low Earth orbit (LEO) satellites, higher Doppler shift occurs in LEO satellite communications compared to the Terrestrial Networks. Therefor, Doppler analysis and application is crit- ical in the LEO satellite communications. The Doppler pre- compensation is a promising compensation in the LEO satel- lite communications downlink since it reduces the complex- ity of Doppler shift calculation at the ground user equip- ment (UE). The residual Doppler shift (RDS) caused by the Doppler pre-compensation is affected by the satellite orbit characteristics and the direction from the beam center to the location of UE. However, it is difficult for existing Doppler shift analysis methods to prove which condition results in the maximum RDS. This thesis proposes a novel analysis methodology for the Doppler shift and RDS characteristics. In addition, this thesis models a Doppler-based beam design for Non-Terrestrial Networks (NTN) within 5G New Radio (NR) standards (NR NTN). For the Doppler shift and RDS analysis, we use a three-dimensional coordinate system con- sidering the satellite as the origin, and define angles related to the LEO satellite orbit feature to use Line-Of-Sight (LOS) vector between the LEO satellite and the ground UE. The proposed analysis framework presents exact Doppler shift val- ues compared to the conventional method, and show that some geometric angles determine the Doppler shift charac- teristics. It also proves that the maximum Doppler shift and the maximum RDS values occur when the ground UE is on the satellite ground trace, and the maximum RDS value has linear relationship with the distance from the beam center. Using the linear relationship, the beam design simulation re- sults present the compatibility of the proposed beam design with the beam systems of current satellite communications service providers, SpaceX and OneWeb. Moreover, using the proposed beam design, the maximum beam size per the satel- lite altitude for NR NTN system is also derived.
