This paper proposes a cognitive hybrid satellite-terrestrial communication network based on Non-Orthogonal Multiple Access (NOMA) and Ambient Backscatter Communication (AmBC) to address the issues of spectrum resource scarcity and insufficient link reliability in modern communication networks.The system introduces Unmanned Aerial Vehicles (UAVs) as auxiliary relay nodes,which collaborate with ground equipment to transmit signals,and optimizes signal transmission efficiency through backscatter technology.Two methods are proposed:underlay-based backscatter-assisted transmission and overlay-based NOMA cooperative transmission.The study considers the power constraints imposed by the primary user network on the secondary user network.The closed-form expressions for the system outage probability are derived for both schemes under Shadowed-Rician and Rayleigh fading channels.The results show that adjusting transmission power and target rate can reduce the system outage probability,further improving communication quality.