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In this paper, we investigate the outage probability (OP) performance of amplify-and-forward (AF) cognitive hybrid satellite-terrestrial overlay networks (CHSTONs) with the non-orthogonal multiple access (NOMA) scheme, in which half-duplexing terrestrial secondary networks cooperate with a primary satellite network for dynamic spectrum access. In order to improve the fairness of overlay paradigm, a NOMA-based power allocation profile is determined by instantaneous channel conditions. Considering the generalized shadowed-Rician fading for satellite links and Nakagami- $m$ fading for terrestrial links, we derive the closed-form OP expressions for both the primary and secondary users. Then, the asymptotic OP expressions at the high signal-to-noise ratio (SNR) regime are also obtained to evaluate the achievable diversity order and coding gain. Finally, the numerical simulations are provided to validate the theoretical results as well as the superiority of the NOMA scheme in CHSTONs and proclaim the effect of key parameters on the performance of the NOMA users, such as fading configurations and the power split factor.

Outage Performance of NOMA-Based Cognitive Hybrid Satellite-Terrestrial Overlay Networks by Amplify-and-Forward Protocols