## 1 Introduction  
Satellite communication is considered to be one of the most reliable forms of wireless communications. Satellite communication networks have several advantages over conventional wireless communications that include long-distance communication, large coverage area, and flexible communication environments [1]. Due to this, their role in emergency applications is growing each passing year. This is especially true in a situation where the communication infrastructure is destroyed due to large-scale disasters [2]. Even when a few communication access points are available in the disaster-ridden region, there is the possibility of network congestion and overload due to increased demand. This makes satellite communication more feasible and important to carry out disaster relief operations [3].  
Although mobile satellite networks can prove advantageous in disaster management, the issues of operation costs and transmission capacity cannot be ignored in such networks. Thus, it is important to establish a flexible, stable, and broadband communication network in disaster regions [4]. Furthermore, when the terrestrial user is not outdoor or the angles of satellite elevation are low, the conventional mobile satellite networks suffer crucial performance degradation. In this context, different relaying techniques can be employed to improve the coverage and reliability of the network. This form of networks are generally called hybrid satellite-terrestrial relay network (HSTRN) and have shown to significantly decrease the masking effect [5; 6]. The HSTRNs can integrate the advantages of both conventional satellite networks and the terrestrial broadband networks. Broadly speaking, they have the ability to provide longer transmission coverage along with higher data rates without environmental limitations. These hybrid networks are able to provide multimedia services while ensuring the quality of service requirements for mobile users through ITU-R S.2222 standard cross-layer design [7]. The HSTRNs are, thus, considered to be one of the promising solutions for ensuring public safety in disaster regions due to their performance gains.  
In parallel, non-orthogonal multiple access (NOMA) techniques have received considerable research interest due to their ability to improve the spectral efficiency of wireless networks [8]. For instance, using NOMA can be combined with cognitive radio to increase spectrum efficiency [9]. Although the applications of NOMA in HSTRNs have not been explored extensively, significant performance improvements can be achieved with NOMA-enabled HSTRNs. NOMA also improves user fairness, thereby, allow different users to experience the same quality of services. NOMA also does not require significant modifications in the existing network architecture [10], thus, operating with virtually no change in the cost of deployment and operation of the network. These exciting benefits of NOMA-enabled HSTRNs motivate us to further explore the performance limits of such networks and identify the performance variations under different network parameters. In the following, we outline some of the recent state-of-the-art developments in this domain.