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This paper investigates the outage performance of an overlay multiuser hybrid satelliteterrestrial spectrum sharing system. Herein, we exploit both direct and relay links from a primary satellite source to multiple terrestrial users with the coexistence of a secondary transmitter-receiver pair on the ground. Based on an overlay approach, the secondary transmitter provides an amplify-and-forward-based relay cooperation to the primary satellite network that employs opportunistic scheduling of multiple users. The underlying user scheduling strategy is based on satisfying the criterion of minimal outage probability (OP) for the primary network and, eventually, exploring more opportunities of the spectrum sharing for the secondary terrestrial network. By considering the widely adopted Shadowed-Rician fading model for the satellite links while the Nakagami-m fading model for the terrestrial links, we derive the analytical …