# Two Low-Complexity Efficient Beamformers for an IRS- and UAV-Aided Directional Modulation Network
## 4 Simulation and Analysis  
The numeral results to examine the SR performance and computational complexities of proposed algorithms are provided herein. The simulation parameters are set as Table 3.  
After setting the 3D coordinates of the IRS and UAV, Bob, Eve, and Alice, their corresponding 2D coordinates can be obtained so that the departure angles and distances can be obtained. In turn, the channel state information of each channel can be determined. In the following, our two proposed methods are compared with two benchmark schemes:  
1. No IRS: This scheme disregards the presence of the IRS. \(\mathbf{\Theta}=\mathbf{0}_{N_{s}\times N_{s}}\). 2. Random Phase: Here, the IRS phase shift value takes on a random value, and the phase of the IRS is random within the range \([0,2\pi)\). Figure 2 shows that SR versus \(N_{s}\). The SR performance of the Max-SR-SLNR and MRT-NSP-PA was much higher than the cases of the no IRS, random phase, and the existing method in [36] and gradually increased with \(N_{s}\). Their SR performance was ordered from the best to the worst as follows: the SDR in [37], the Max-SR-SLNR, the MRT-NSP-PA, and the existing method in [36]. The SR performance gap between the Max-SR-SLNR and the SDR in [37] was small. When \(N_{s}\) was 256, the existing method in [36], the MRT-NSP-PA method, the Max-SR-SLNR method, and the SDR in [37] had a higher SR than the random phase and no IRS: 18%, 47%, 50%, and 53%, respectively. The SR of the Max-SR-SLNR method was much higher than the MRT-NSP-PA method when the IRS was small- to medium-scale. For the case of a large scale, the latter approached the Max-SR-SLNR. The application scenario of this conclusion was that the departure angle from Alice to IRS had a certain angular separation from the departure angle from Alice to Bob. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Alice coordinate & (0, 0, 0) m \\ IRS and UAV coordinate & (39.8, 3.5, 3.5) m \\ Bob coordinate & (90, 0, 0) m \\ Eve coordinate & (96.6, \(-25.9, 0)\) m \\ Transmitting power, \(P_{s}\) & 30 dBm \\ Noise power, \(\sigma_{b}^{2}\) and \(\sigma_{c}^{2}\) & \(-40\) dBm \\ PA factor, \(\beta_{1}\) & 0.8 \\ distance of Alice-to-IRS, \(d_{ai}\) & 40 m \\ distance of Alice-to-Bob, \(d_{ab}\) & 90 m \\ distance of Alice-to-Eve, \(d_{ae}\) & 100 m \\ angle of departure of Alice-to-IRS & 17\(\pi/36\) \\ angle of departure of Alice-to-Bob & 1\(\pi/2\) \\ angle of departure of Alice-to-Eve & 7\(\pi/12\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Table of simulation parameters. Figure 3 plots the SR versus the SNR for \(N_{s}=128\). As can be seen from the simulation diagram, the SR performance of the six schemes increased with the increase in the SNR. The SR performance of the proposed MRT-NSP-PA method and the Max-SR-SLNR method was about two times that of the existing methods in [36]. When SNR = 10 dB, compared with the cases of the no IRS and the random phase, the SDR in [37], the Max-SR-SLNR method, and the MRT-NSP-PA method achieved SR improvements of roughly: 47%, 46%, and 34%, respectively. Therefore, this means that effectively designing the PSM of the IRS, CM, and AN beamforming can harvest obvious performance gains. Figure 4 shows the SR versus the distance between Alice and Bob for \(N_{s}=100\). It can be observed that as the \(d_{ab}\) increased, the SRs in all cases tended to decrease. This is because increasing the \(d_{ab}\) increased the path loss. It can be seen from Figure 4 that the SR of the existing method in [36] was only half of the SR performance of the Max-SR-SLNR and MRT-NSP-PA method, thus demonstrating the advantages of our proposed methods. Figure 3: Secrecy rate versus the SNR. Figure 2: Secrecy rate versus the number of IRS elements. (name in year is the comparison method). Figures 5-7 illustrate the SR versus directional angle of the CM beamforming with different numbers of IRS elements as follows: 16, 256, and 1024.