Low Earth Orbit (LEO) satellite networks, which would be the main architecture of Non-Terrestrial Networks (NTN), need to consider the high mobility of LEO satellites. The extremely high Doppler shift caused by the mobility of LEO satellites does not occur in the existing terrestrial networks. Therefore, it is challenging to overcome the Doppler shift of LEO satellite by the terrestrial networks structure. In this paper, we propose a novel LEO satellite beam design considering Doppler shift. We calculate Doppler shift with three dimension coordinates. By doing so, we analyze the characteristics of Doppler shift caused by pre-compensation scenario where the satellite compensates for most of Doppler shift before transmitting data. Considering the results of the analyzed Doppler characteristics, altitudes of LEO satellite, and OFDM numerology technology of 5G NR (New Radio), the LEO satellite beam size can be determined differently. Since the proposed beam size design is robust to Doppler shift and applies 5G NR technology, it has advantage in implementing NR-based NTN.
