## 2 RISs and Their Integration with NTNs
### RISs Against Traditional Beamforming Architecture  
Compared to traditional beamforming architectures, a significant innovation of this scheme lies in its ability to fully harness the potential of RISs with their unique programmable feature as an external and standalone analog beamformer [32; 33; 34]. This eliminates the need for internal analog beamforming at BSs, leading to simplified architecture and a substantial cost reduction. The research discussed in [35; 36; 37; 38; 39; 40], addresses the joint beamforming optimization for RIS-aided full-duplex (FD) NTN communication systems. Optimizing beamforming in RIS-aided FD communication systems is essential for enhancing performance across various metrics as it improves signal quality, spectral efficiency, and interference mitigation. In this optimization approach, refining beamforming vectors at both the transmitter and receiver ends and adjusting the phase shifts on RIS elements are jointly carried out. The most important objectives are to maximize the received signal power, minimize interference, and adhere to the communication system constraints, including the handling self-interference inherent in FD setups that share the same frequency spectrum [41; 42; 43]. To address these challenges comprehensively, diverse optimization algorithms and techniques such as convex optimization, genetic algorithms, particle swarm optimization, and deep learning (DL) methodologies are deployed. The benefits of RISs are fully harnessed to achieve superior spectral efficiency and interference management by synergizing the optimization of beamforming vectors and phase shifts in RIS-FD systems [44; 45]. In [45], the presented framework showed a power reduction of 6 dB at 5 bps/Hz compared to the baseline method. Designing efficient beamforming algorithms considering self-interference and the needs of joint optimization further enhances RIS-aided FD system performance [39; 40; 46].  
The study in [43] focuses explicitly on minimizing total transmit power by combining optimizing active beamforming at the sources and passive beamforming at an RIS positioned between them. The authors showed the effectiveness of RISs for FD schemes, showing that they outperform half duplex when the transmit power is less than 25 dBm. The number of transmit antennas was fixed to 40 and the data rate was set to 4 bps/Hz [43]. They proposed an efficient algorithm such as alternating optimization to solve the non-convex problem. In addition, joint optimization of beamforming, RIS phase shift, and user association in a multi-cell network aided by multiple RISs were studied [38]. The authors proposed less complex algorithms compared to existing methods and effectively exploited multiple RISs to improve network performance.  
The process of joint beamforming optimization for RIS-aided FD communication includes simultaneously optimizing the beamforming vectors at the transmitter and receiver and adjusting the phase shifts of the RIS [47]. It was shown in [47] that the target sum rates of 9.5 and 12.5 bps/Hz can be achieved by saving 58% and 39% of the RIS elements, respectively. This optimization strategy aims to strengthen signal quality at the receiver, boost spectral efficiency, and mitigate interference in RIS-FD systems [48]. By jointly optimizing these parameters, the system can benefit from the RIS's unique advantages, such as enhancing signal strength and directing signals toward intended users or nullifying interference.