The evolution of non-orthogonal multiple access (NOMA) has raised many opportunities for massive connectivity with less latency in signal transmissions at great distances. Power-Domain NOMA transmits user signals superimposed in the same resource block by varying the power coefficient of each user according to their channel state information (CSI). At the receiver’s end, successive interference cancellation (SIC) is performed to extract the desired signal from the superimposed signal. Imperfect CSI should therefore be studied in this context. Satellite-terrestrial networks and relay networks have already gained significance in the field of communications through their efficient data transmission techniques. We aimed to integrate NOMA with a satellite communications network under both imperfect CSI and co-channel interference (CCI) from nearby systems with respect to analysis of ground user performance. In our considered system, two users perform downlink communications under Power-Domain NOMA. We analyzed the performance of this system with two modes of shadowing effect: Heavy Shadowing (HS) and Average Shadowing (AS). Performance was analyzed in terms of the outage probability and ergodic capacity of the system. We derived closed-form expressions and performed a numerical analysis. We discovered that the performance of two destinations depends on the strength of the transmit power at the satellite. However, floor outage occurs because the system depends on other parameters, such as satellite link modes, noise levels, and the number of interference sources. More specifically, if, for example, the number of interference sources is 5, the outage performance of the system experiences a decrease of approximately 40% at a signal to noise ratio (SNR) of 30 dB at the satellite. Outage probability and ergodic capacity became saturated at SNRs of 50 dB and 45 dB, respectively. To verify the authenticity of the derived closed-form expressions, we also performed Monte-Carlo simulations.