In this paper, we have studied the impact of the antenna configuration on the performance of hybrid state-terrestrial relay networks (HSTRN) with a non-orthogonal multiple access (NOMA) scheme. To ensure the best outage performance of the primary user and maximize the communication capacity of the secondary users, we have proposed a multi-antenna selection scheme under the decode-and-forward (DF) strategy, which can greatly reduce the computational complexity. Firstly, we assume that there is no direct link between the satellite and the terrestrial user, and communication can only be assisted through the relay. Then, we derive users' exact outage probability expressions and asymptotic outage probability expressions under high signal-to-noise ratio (SNR). Finally, simulations are provided to validate the correctness of the theory and the impact of parameter configuration on the system outage performance.