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In this paper, a hybrid satellite-terrestrial spectrum sharing system allows terrestrial secondary network to cooperate with a primary satellite network and to further provide higher spectrum efficiency. For massive connections design, we implement non-orthogonal multiple access (NOMA) technique to form cognitive radio based satellite-terrestrial (CR-NSHT) system relying on NOMA and further achieve more benefits compared with traditional schemes. The secondary network only remains its stable operation when the outage probability of such system is guaranteed, and thereby, to explore advantages of spectrum sharing opportunities. Considering Shadowed-Rician fading for satellite links, and Nakagami- m as well as Rician fading for terrestrial links, we derive the closed-form expressions of the outage probability to evaluate the performance of secondary network. We consider further system performance metrics …