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In this paper, we investigate the downlink transmission of a non-orthogonal multiple access (NOMA)-based integrated terrestrial-satellite network, in which the NOMA-based terrestrial networks and the satellite cooperatively provide coverage for ground users while reusing the entire bandwidth. For both terrestrial networks and the satellite network, multi-antennas are equipped and beamforming techniques are utilized to serve multiple users simultaneously. A channel quality-based scheme is proposed to select users for the satellite, and we then formulate the terrestrial user pairing as a max-min problem to maximize the minimum channel correlation between users in one NOMA group. Since the terrestrial networks and the satellite network will cause interference to each other, we first investigate the capacity performance of the terrestrial networks and the satellite networks separately, which can be decomposed into …