# Maximization of Average Achievable Rate for NOMA-UAV Dual-User Communication System Assisted by RIS
## 1 Introduction  
RIS technology provides a new performance optimization opportunity for sixth-generation communication systems, thanks to its low cost and intelligent ability to reconstruct the wireless propagation environment. As such, it is considered a key technology with significant development potential. Specifically, RIS consists of electromagnetic units and a programmable patch array. Each unit intelligently controls the phase shift and accurately reflects the incident electromagnetic waves [1]. RIS offers an economical and effective solution for controlling the radio propagation environment while avoiding additional power consumption and the costly deployment of communication devices, thereby enhancing the system's achievable rate [2]. With its rapid deployment capabilities, spatial mobility, and reliable line-of-sight transmission, UAV communication offers an effective solution for optimizing wireless communication standards [3]. In [4], the author focuses on utilizing UAV cooperative operations to extend communication time and proposes two strategies to maximize system throughput. The UAV relay's flight trajectory and the power output between the sender node and the UAV relay are jointly optimized. Due to its high spectrum efficiency and large-scale access capabilities, NOMA is regarded as an advanced multiple access technology to address challenges in future wireless communication networks [5]. The core concept of NOMA involves leveraging users' varying channel conditions to improve spectrum efficiency and ensure fairness. The concept aims to promote spectrum resource sharing among users. These two communication technologies are complementary and can be integrated to meet the challenging demands of 6G cellular networks [6]. Leveraging the unique advantages of UAVs in communication and the technological potential of RIS and NOMA, their integration has become a major research direction. In [7], the author considers a multi-user communication system where UAVs provide services to a large number of ground users by using NOMA as a flying base station. They formulated the maximum and minimum rate optimization problem and proposed a path tracking method to address it. In the RIS-assisted UAV communication scenario, reference [8] proposes a strategy to jointly optimize the RIS phase, UAV time-slot power allocation, and flight trajectory by developing a three-terminal system model, effectively improving the average achievable data rate for ground users. In literature [9], a RIS-assisted UAV communication model is developed, and the trajectory and RIS beam are jointly optimized. The Successive Convex Approximation (SCA) approach is employed to iteratively solve the non-convex problem. Subsequently, using the optimal phase shift, a sub-optimal trajectory solution is derived to enhance the average rate. In [10], the author proposes a hybrid aviation full-duplex relay protocol, utilizing a UAV equipped with RIS in decode-and-forward mode, integrated with NOMA technology to enhance the frequency resource efficiency of information transmission between the base station and multiple users. Additionally, many studies focus on the NOMA-UAV cooperative system based on RIS. In [11], the author proposes a RIS-assisted UAV NOMA-based crisis communication infrastructure. Multiple RISs form an intelligent link. Users transmit data through the nearest RIS, with same-side users employing NOMA for transmission. In [12], the author develops a UAV-RIS-assisted communication system. By combining NOMA with imperfect successive interference cancellation (SIC) and jointly optimizing the three-dimensional UAV trajectory, power allocation, and RIS phase shift, a two-step method is proposed to maximize system throughput and adapt to both users and UAV mobility scenarios. In [13], the author proposes a novel scheme to optimize the NOMA-based multi-UAV network with RIS. The focus is on the association between ground user equipment and UAVs, UAV power distribution, and RIS reactive beamforming.