# Hybrid Satellite-Terrestrial Networks toward 6G: Key Technologies and Open Issues
## 2 Cooperative HSTN
### HSTN Relay Network
#### 2.2.2 Multiple Relay Nodes  
The ergodic capacity and ASER of a fixed-gain AF-based HSTN was considered in [76]. A fixed-gain AF-based HSTN was investigated because of low-complexity system design. The effects of relay number, channel parameters, and modulation formats on system performance were also studied and validated through computer simulation. The authors found that the modulation format can change the system's array gain, and the ASER performance of binary-phase shift keying (BPSK) was found better than that of eight-phase shift keying (8 PSK). Similarly, the ASER of an AF-based HSTN was investigated in [77] under the influence of CCI due to frequency reuse. The degradation of ASER performance was observed due to shadowing in satellite links causing reduced array gain. Extending the work in [65], the authors of [78] considered the performance of a multi-relay and multi-user HSTN. The authors proposed a user-relay selection scheme and derived the exact and asymptotic OP expressions for both fixed- and variable-gain relaying. A performance evaluation of a DF-based HSTN over time-selective fading links due to mobile terrestrial nodes with multiple relays was considered in [79]. The satellite-terrestrial links were assumed to be non-identical time-selective shadowed Rician fading whose parameters depended on the satellite elevation angle. The relay-destination terrestrial links were assumed to be nonidentical time-selective generalized Nakagami fading. The authors observed that the time-varying nature of the links led to discernible degradation of the end-to-end performance. By considering a more-generalized HSTN with multiple relays and an available direct satellite-destination link, the authors of [80] addressed asymptotic analysis of the ergodic capacity for both AF and DF protocols based on MGF and proposed a simple relay-selection strategy requiring only statistical CSI with low system overhead. The authors of [81] investigated the ergodic capacity of the downlink in an HSTN for which fading of the satellite channel followed shadowed Rician distribution and fading of the terrestrial channel followed Rayleigh distribution. The closed-form expressions for the ergodic downlink channel were derived, and the system performances for both AF- and DF-based HSTNs were analyzed. A relay selection strategy with multiple relay nodes was discussed. The authors found that the ergodic capacity of a DF-based HSTN is larger than that of an AF-based HSTN under similar channel conditions. The ergodic capacity decreased with an increasing number of participating relays. However, the best relay selection strategy achieved larger ergodic capacity at the cost of channel estimation at each relay. For communication systems operating over fading channels, OP is an important performance parameter as it provides insight into the communication system's design. The authors of [82] evaluated the performance of an HSTN in terms of OP with the best relay selection scheme. The selective DF mode was used for the network, which consisted of a single destination node and multiple relays. For the first time, closed-form expressions of outage probability were derived and validated using Monte Carlo simulation. In [83], to improve system performance, the authors proposed the incorporation of content and uniform content wireless caching placement schemes for HSTNs, resulting in improved system OP performance. In the case of multi-relay systems under the same asymmetric fading channels, maximizing the satellite's received power and Nth worst relay selection schemes were also proposed. A novel partial relay selection scheme (PRS) for a DF-based HSTN that reduces relay selection overhead without compromising system performance was proposed in [84]. Assuming the unavailability of a direct satellite-destination path due to masking, asymptotic OP analysis was conducted in practical environments in which the satellite-relay and the relay-destination links were subject to generalized-k and Nakagami-m fading.