Recently, the satellite communication has main demand but still facing main problems which are the spectrum limited, both cognitive-radio (CR) and non-orthogonal-multiple-access (NOMA) methods are identified as a one of the potential solutions for these issues. Using the deep learning techniques with the CR and NOMA systems will be improvement in the spectrum effectiveness. One of the performance enhancement of the NOMA, the integration with the satellite-terrestrial-relay-network (ISTRN) in a spectrum-sharing context of several main-users (PUs) is examined. We specifically presented and given the interference limitation imposed by several nearby pus and its effect on each other’s. The closed-form formulations are investigated the ergodic-capacity (EC) and outage-probability (OP). The asymptotic-analysis for OP at high SNRs is achieved to get additional insights. To support our research and reveal the effects of the significant characteristics on the quality of the system; the numerical data and analysis are provided with deep discussions.