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In this paper, we consider an overlay cognitive satellite-terrestrial relay network comprising a primary satellite source-receiver pair and a secondary transmitter-receiver pair on the ground while taking into account the practical relay transceiver hardware impairments. Herein, a primary satellite source communicates with its terrestrial user by utilizing both direct and relay links, using an amplify-and-forward based cooperative communication technique. Considering distortion noises in relay signal processing, we obtain new closed-form expressions for the outage probability of primary satellite network and secondary terrestrial network and explicitly derive the asymptotic outage behaviour for primary network by adopting pertinent heterogeneous fading models. Both primary and secondary networks satisfy their quality-of-service criteria for the low data rate requirements only. However, for the high data rate requirements …