# Two Low-Complexity Efficient Beamformers for an IRS- and UAV-Aided Directional Modulation Network
## 1 Introduction  
Due to the advantages of mobile controllability, on-demand placement, and low cost, unmanned aerial vehicles (UAVs) have gained wide attention and application in industry and academia, as shown in [1, 2]. With lower manufacturing costs, miniaturization, and the improved performance of UAVs, many new applications have emerged for UAVs in civilian and commercial applications and communication relay, as shown in [3]. In addition, UAVs have a high potential for having line-of-sight (LoS) and air-to-ground (ATG) communication because of their mobile controllability and on-demand placement flexibility, as shown in [4, 5]. However, due to the inherent broadcast nature of wireless communications, which makes confidential message (CM) information vulnerable to interception and eavesdropping by unauthorized users [6, 7, 8, 9, 10], in recent years, the physical layer security (PLS) of wireless communication has gained extensive attention. Moreover, PLS will potentially become one of the key techniques of future sixth generation (6G) mobile communications. The main solution to the traditional PLS problem is to prevent illegal users with a computational NP-complete difficulty from breaking the CM by using the encryption mechanism in the upper-layer protocol stack in [11]. Nevertheless, encryption technology that relies on encryption algorithms has security risks due to its conditional security. Therefore, a keyless PLS security eavesdropping channel wire-tap model was proposed by [PERSON] [12], in which secure communication could be achieved without relying on encryption technology. In [13; 14], artificial noise (AN) was used to effectively enhance the legitimate channels and weaken the eavesdropping channels in order to realize wireless network security. In [15], the authors investigated PLS with multiple single-antenna eavesdroppers in the millimeter wave channel. Here, two transmission schemes, maximum ratio transmission (MRT) and maximizing the security throughput under the constraint of the security interruption probability, were proposed by utilizing the specific propagation characteristics of mmWave. As an effective physical layer transmission technology suitable for the LoS propagation channels, directional modulation (DM) has increasingly attracted research attention from both industry and the academic world, as shown in [16; 17; 18]. Considering that the ATG channels of a UAV are mainly dominated by LoS channels, DM technology can be perfectly applied in UAV trunking networks to significantly improve the security of the communication systems. In [19], the authors studied the secure simultaneous wireless information and power transfer (SWIPT) problem for UAV relay networks, where the UAV operated in amplified forwarding (AF) mode, derived the connection probability, security outage probability, and instantaneous secrecy rate (SR) of the system, and analyzed the asymptotic SR performance. In a secure SWIPT transmission network for UAV in millimeter wave scenarios [20], the number and location of eavesdroppers obeyed the Poisson point process, and the UAV forwarded the CM while charging the legitimate user, which jointly designed the launch power of the UAV and the placement position. Adding AN to the DM network was extraordinarily effective [21]. In [22], phase alignment (PA), AN, and random subcarrier selection based on orthogonal frequency division multiplexing were combined to achieve precise and secure wireless communications. Compared to a relay [23], an intelligent reflecting surface (IRS) has the following main advantages: low power consumption, low cost, and the ease of realizing a large scale or even an ultra-large scale. Thus, an IRS can be physically deployed and integrated in wireless networks at a low cost. By adjusting its phase shift matrix, the IRS may intelligently control and change the wireless environment to improve the system's spectral efficiency and energy efficiency [24; 25; 26; 27; 28].