# Two Low-Complexity Efficient Beamformers for an IRS- and UAV-Aided Directional Modulation Network
## 1 Introduction
An IRS can be applied to a diverse variety of communication areas, such as multiple input multiple output (MIMO) [29; 30], relay [31], covert communication [32], SWIPT [33], spatial modulation networks [34], and UAV networks [35]. In [30], adjusting the phase of the IRS mitigated the interference at the cell edge, and the performance of a cell-edge user was improved. In an IRS-assisted multi-antenna relay network [31], to further improve the rate, the authors designed three methods for power allocation. The three proposed methods had a higher rate gain than the EPA method. In IRS-aided covert communication [32], penalty successive convex approximation and a two-stage algorithm to jointly design the reflection coefficient of the IRS and the transmission power of Alice were proposed. More importantly, the existence of perfect covertness under perfect channel state information (CSI) was proved. In an IRS-aided UAV network, the average SR was improved by jointly designing the transmitting beamforming, UAV trajectory, and phase shift of the IRS [35]. Combining an IRS and DM can enable a dramatic rate performance improvement [36; 37; 38; 39]. In [36], using a multipath channel, a single CM signal was transmitted from the base station to a legal receiver using two symbolic time slots, where the IRS phase matrix was aligned with the direct and cascade paths, respectively. Although the method in [36] had low complexity, the transfer of information in two time slots led to an SR performance loss. In order to further enhance the SR [37], a semi-definite relaxation (SDR) method was designed to jointly optimize the CM beamforming, AN beamforming, and IRS phase, while maximizing the SR. In traditional DM networks, only one bitstream can be transmitted between the base station and a user, even with multiple antennas. With the help of an IRS, is it possible to achieve a multiple stream transmission via a controlled multipath in the LoS channel. In [38], with the aid of an IRS, the DM achieved two independent CM streams from Alice to Bob under a multipath channel. Since the design of the receive beamforming was not considered in [38], the authors designed two alternating iterative methods to design the receiving beamforming and IRS phase in [39] to maximize the receiving power sum. However, the proposed method in [37] was of high computational complexity with a high rate performance, and the proposed scheme was of a low spectral efficiency with a large rate performance loss due to the fact that the two-symbol period only transmitted one symbol [36]. In practical applications, an IRS needs to be fixed at a specific location. Therefore, an IRS can be installed on a drone to provide a more reliable and secure connectivity. The UAV-assisted IRS device may be viewed as a reflecting relay, for example, due to severe shadow fading in urban buildings or hilly terrain, or damage to communications infrastructure due to natural disasters. Deployment using low-altitude drones is faster, more flexible in configuration, and may have better communication channels due to the presence of strong LoS links. The UAV-aided IRS is very similar to a relay satellite. However, the main difference between the two lies in the coverage and application scenarios. A UAV-assisted IRS is more suitable for application scenarios that have relatively small coverage areas and require rapid deployment and response. Relay satellite communication, on the other hand, is more suitable for application scenarios that require communication on a global scale [40]. In other words, a relay satellite is more stable and reliable and suitable for applications in which remote communication is performed offline. Combining a UAV, an IRS, and DM can fully explore their advantages of a high position, passive reflection, and a directive property to form an enhanced secure wireless transmission. In practical applications, for energy-efficient and secure communication, using a UAV and an IRS creates multiple paths for propagation in three-dimensional (3D) conditions.