## 1 Introduction  
### Research Background  
UAV-aided cellular data network communication based on an IRS is not only an effective method for expanding the signal transmission range, but also an important way to improve the signal quality [1; 2]. This is important for users in marginal areas, who may experience severe path loss because they are far from the base station or at a poor receiving antenna angle. An IRS can flexibly adjust the amplitude and phase of the received signal and change the propagation direction of the reflected signal [3], while a UAV can achieve more flexible movement and deployment at low altitude [4]. Based on the above characteristics, researchers have shown great interest in the performance analysis of low-altitude wireless relay communication systems in recent years. As low-altitude relays, UAVs are widely used in wireless communication systems [5; 6]. In mobile edge computing systems, UAVs can be deployed at the edge nodes to forward the tasks received from a user to a cloud center or base station for processing, which not only shortens the operating time, but also allows the maximal secure capacity of mobile edge computing systems to be realized [7]. In air-to-ground communication systems, by jointly optimizing scheduling and power allocation and determining the trajectory of a UAV over a certain period of time, the energy consumption required for secure communication is minimized. Thus, the system's secrecy energy efficiency is significantly improved [8]. In multi-UAV communication systems, according to the advantages of UAVs--low cost, high mobility, and on-demand deployment--the minimum signal-to-noise ratio of the UAVs is maximized through joint optimization of channel allocation and power allocation in order to realize the optimization of the performance of multi-UAVsystems [9]. UAVs have been widely used in cellular data networks in recent years because of their characteristics of high mobility and on-demand deployment. The authors of [10] studied the deployment of a UAV as an air base station in fifth-generation communications systems, which solved the deployment problems of UAVs in a three-dimensional space and maximized the system throughput. An IRS is essentially a metamaterial that integrates a very low-cost and subwavelength structure. It consists of independent and controllable passive electromagnetic reflective elements on a plane, and it operates through software or hardware [11]. The main function of an IRS is to control the reflection phase and amplitude of an incident signal through software programming according to the communication link information fed back by signal transmission, which is essentially an adjustment of the capacitance, resistance, and inductance [12]. IRSs are also widely used in wireless communication systems as assisted passive wireless relays. An IRS can assist orthogonal frequency division multiplexing systems in channel estimation by considering the relationships between the amplitude, phase shift, and frequency of an actual IRS response [13]. In 5G communication networks, signals can be transmitted to a blocking user by utilizing the reflection characteristics of an IRS, thus greatly reducing the probability of interruption of the system [14]. An IRS can also be deployed in communication systems in which listeners are present, which illustrates the effects of the size of the IRS and the optimization of its phase element on the expansion of the security rate of the energy collection area [15]. In terms of power optimization, considering the minimal signal-to-interference-plus-noise ratio (SINR) per user, the power minimization problem of an IRS-assisted downlink non-orthogonal multiple-access system has been proposed. Numerical results have shown that, compared with other schemes, the proposed joint optimization algorithm based on an IRS can significantly reduce the required transmission power. In addition, an IRS and UAV can be jointly deployed in the same wireless communication system to optimize system performance [16; 17; 18; 19].