This project aims to enhance spectral efficiency in non-terrestrial networks (NTN) using low earth orbit (LEO) satellites, with a specific focus on both downlink and uplink beamforming to mitigate channel path loss. Our goal is to develop innovative algorithms that minimize initial access training time while maximizing accuracy, aligning with the challenges posed by the sixth-generation (6G) standard. We will also explore information-theoretic limits on training duration in LEO satellite links and investigate beam-tracking strategies for fast-moving LEO satellites, leveraging their predictable orbits.