## 1 Introduction  
Unmanned aerial vehicles (UAVs), usually known as drones, are aircraft controlled autonomously by a program or manually by a ground controller without a human pilot onboard. The easy deployability, mobility, and flexibility of UAVs have enabled them to provide services across a wide range of applications, including surveillance, remote sensing, military, photography, logistics, telecommunications, etc. [1]. In recent years, UAV communications were considered in Fifth-Generation (5G)-and-beyond networks. On one hand, UAVs can be connected as user equipment (UE) to provide real-time services, such as video streaming, precision agriculture, etc. [2]. On the other hand, UAVs can serve as aerial base stations (BSs) to provide a seamless and ubiquitous connectivity in the future wireless network when the terrestrial BSs are overloaded or out of service due to natural disasters [3]. In addition, UAVs can also act as mobile relay nodes to improve the coverage and reliability of ground communication systems. Compared to the conventional ground relays that are fixed at ground locations, the combination of UAVs and relays takes advantage of the maneuverability of UAVs to provide additional degrees of freedom to the communication links. This combination ensures a high probability of the line of sight (LoS) with the ground nodes, thus improving the rate and reliability of the communication systems [4; 5]. Meanwhile, reconfigurable intelligent surfaces (RIS), also known as intelligent reflecting surfaces (IRS) or large intelligent surfaces (LIS), have been envisaged as a new promising paradigm to assist the beyond-5G wireless communication system. RIS are a reconfigurable metasurface which consists of massive low-cost reflecting elements that can manipulate the propagation environment by adjusting the amplitude, phase shift, frequency, and polarization of the incident signals [6]. As a result, RIS are considered to serve as a relay node in order to reflect the signal toward the users [7]. Generally, there are two types of reflecting elements RIS can be equipped with, either active or passive. Active RIS elements can reflect the signals with amplification, whereas passive RIS elements reflect the signal without any signal modification. The active RIS elements introduce thermal noise, while the passive RIS elements suffer from the double path-loss problem, which degrades the signal strength significantly. To overcome these issues, hybrid RIS were introduced [8], in which one or a few elements are integrated with the power amplifier to act as active elements, while the remaining elements are passive. There are a number of published contributions that compare the system performance between the RIS and the active relays. For instance, the comparisons between passive RIS and an amplify-and-forward (AF) relay are investigated in [6] in terms of the achievable rate, [9] in terms of the energy efficiency, and [10] in terms of the signal-to-noise ratio (SNR), outage probability, ergodic capacity, and symbol error rate. Apart from that, the rate of a decode-and-forward (DF) UAV relay-aided system is compared to that of a passive RIS in [11], while the number of passive RIS elements that are required to outperform the DF relay is investigated in [12]. From the findings of [12], a large number of RIS elements are required to outperform the DF relay due to the double path-loss effect. Rather than being limited to ground deployment, RIS can potentially be mounted on a UAV (RIS-UAV) to achieve ubiquitous and reliable wireless connectivity. Owing to the mobility and flexibility of UAVs in a three-dimensional (3D) space, a RIS-UAV can provide a \(360^{\circ}\) panoramic full-angle reflection as opposed to the \(180^{\circ}\) half-space reflection and multiple reflections by the terrestrial RIS [13; 14]. Furthermore, the RIS-UAV can be dynamically deployed to maintain a favorable communication environment where the terrestrial RIS are usually fixed on the facades of a building or at a dedicated location.