# Hybrid Satellite-Terrestrial Networks toward 6G: Key Technologies and Open Issues
## 2 Cooperative HSTN
### HSTN Relay Network
#### 2.2.1 Single Relay Node
By employing satellites equipped with multiple antennas, the impacts of antenna correlation, CCI, and outdated CSI on the ergodic capacity of an HSTN [61] was considered for both correlated and uncorrelated shadowed Rician fading at the satellite links in [63]. Better system performance was observed by increasing the number of antennas at the satellite. Extending their work from [61; 63], the average symbol-error probability (ASEP) performance of an AF relay-based multi-user HSTN with multiple antennas at the satellite was evaluated in detail in [64]. By considering CCI at the relay and an outdated CSI for terrestrial links with shadowed Rician and Nakagami-m fading for satellite and terrestrial links, respectively, asymptotic SEP expressions at high SNRs were derived to gain insights into the system's error performance. In the case of multiple users, the OP was studied for AF-based HSTN in [65] for frequent heavy shadowing (FHS) and average shadowing (AS) scenarios. The authors found that AS outperforms FHS and that system performance improves with an increased number of user nodes due to more coding gain. Similarly, assuming an opportunistic selection DF relay scheme, OP of the integrated satellite-terrestrial network with multiple antennas at the relay was studied in [66] using maximal ratio combining (MRC) at the destination. Suggesting superiority of multi-antenna relays, the performance of an HSTN in the case of correlated Rayleigh fading at the terrestrial channel with multi-antenna relays was investigated in [67]. Asymptotic OP expressions at high SNRs were developed to find the diversity order and the impact of the number of antennas and users and the satellite transmit power on the system performance. Considering maximum ratio transmission (MRT) and MRC at the relay and selection-combining at the destination, OP was analyzed. For a multi-user DF integrated satellite terrestrial network with a multi-antenna relay for which the satellite-relay link undergoes shadowed Rician fading, while the relay-user links experience correlated Rayleigh fading, a new probability density function (PDF) to statistically characterize the square sum of independent and identically distributed (i.i.d.) random variables was proposed in [68]. In [69], the performance of the two-way AF-based HSTN was evaluated, with the satellite-relay links modeled as \(k-u\) shadowed fading for more accuracy but with a more complex mathematical model, and the user-relay links were modeled as Nakagami-m fading. The exact OP, ASEP, and achievable rate expressions were derived and provide insights into the impact of fading channels on the considered system. Proposing a new method to calculate the instantaneous rain attenuation rather than a value averaged over the entire rainfall event, in [70], the performance of an AF-based mmWave HSTN was evaluated considering the effects of both rain attenuation and the unavailability of LOS links due to masking. Joining the effects of a dynamic rain attenuation model with a statistical channel model for describing mmWave satellite and terrestrial links in a new channel model, the influence of rain attenuation on mmWave HSTN system design was found. Motivated by the lack of work discussing the effect of hardware impairment in HSTNs, ref. [71] investigated the performance of a two-way HSTN with hardware impairment. Outage analysis, signal-to-noise-and-distortion ratio (SNDR), and throughput of the single-antenna satellite, terrestrial, and relay node system were analyzed. The work suggested that smaller impairment of the terrestrial relay would lead to better system performance. An in-depth performance evaluation of a power-splitting NOMA-based multi-antenna HSTN with energy harvesting relays was provided and the closed-form expressions of outage probabilities and ergodic capacities for both AF and DF relaying protocols were derived to perform a comprehensive analysis in [72].