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Satellite-terrestrial networks (STNs) have received significant attention from research and industry due to their capability of providing a stable connection to rural and distant areas, where the allocation of terrestrial infrastructures is uneconomical or difficult. Moreover, the STNs are considered as a promising enabler of fifth-generation communication networks. However, expected massive connectivity in future communication networks will face issues associated with spectrum scarcity. In this regard, the integration of cognitive radio and non-orthogonal multiple access (NOMA) techniques into STNs is considered as a promising remedy. Thereafter, in this article, we investigate NOMA-assisted cognitive STN under practical system conditions, such as transceiver hardware impairments, channel state information mismatch, imperfect successive interference cancellation, and interference noises. Generalized coverage …