# On IRS-Assisted Covert Communication with a Friendly UAV
## 5 Numerical Results  
In this section, we present the numerical results for the IRS-assisted CCS with UAV. We use Algorithm 1, designed based on SCA and Dinkelbach, to solve the formulated optimization problem. The parameters are listed in Table 1.  
Figure 2 shows the trajectory comparison of the UAV that works as a jammer to assist the CCS. The initial trajectory, denoted as \(C_{0}\), represents the UAV moving with uniform speed from the initial point to the endpoint without optimization. For the trajectory optimized using the proposed algorithm, it can be observed that the UAV starts from the initial point, then flies at its maximum speed to [PERSON] following the shortest path. When approaching [PERSON], the UAV hovers closer to [PERSON] than to [PERSON]. Finally, the UAV travels to the endpoint at the maximum speed using the shortest distance. It can be observed that the transmitting power of [PERSON] and the AN power of the UAV are adjusted simultaneously to guarantee the maximum covert rate. In addition, due to the limit on its AN power, the UAV achieves a higher covert rate by approaching [PERSON] more closely, which can ensure covertness for the CCS. Furthermore, if the UAV is close to the initial point, [PERSON] can reduce her transmitting power and the UAV can enlarge its AN power to guarantee covertness, which leads to a small covert rate. In this case, the UAV flies close to [PERSON] at its maximum speed, and the UAV must expend a large amount of energy in order to jamthe communications between [PERSON] and [PERSON]. Thus, to save energy, the UAV is launched only when covert messages are being transmitted. Figure 3 displays the covert rate versus the flying time with different UAV altitudes and different numbers of IRS units. The IRS is used with 30 and 40 units, the UAV flying times are 30 s, 50 s, 70 s, 90 s, 110 s, and 130 s, and the UAV altitudes are 50 m and 75 m. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Meaning** & **Value** \\ \hline \(N\) & UAV flying time & 30 s \\ \(T\) & Number of time slots & 30 \\ \(L\) & Duration of time slot & 1 s \\ \(H\) & Altitude of UAV & 50 m \\ \(M\) & Number of IRS units & 30 \\ \(V_{max}\) & Maximum speed of UAV & 50 m/s \\ \(D\) & Maximum moving distance of & 50 m \\  & UAV per time slot & \\ \(\beta_{0}\) & Channel gain at a channel & \(-\)50 dB \\  & distance of 1m & \\ \(\alpha\) & Path loss parameter & 2.2 \\ \(d\) & Antenna spacing & \(\frac{\lambda}{2}\) \\ \(p\) & Transmission power of BS & 1 W \\ \(\rho_{w,dB}\) & Parameters for quantifying & 6 dB \\  & noise uncertainty at Willie & \\ \(\phi_{w,dB}^{2}\) & Standard noise power & \(-\)120 dBm \\  & variance at Willie & \(-\)120 dBm \\ \(\sigma_{b}^{2}\) & Noise power variance at Bob & \(-\)120 dBm \\ \(\varepsilon\) & Values for the covertness & 0.01 \\ \(J\) & Loop threshold & \(10^{-5}\) \\ \(\omega_{B}\) & Coordinates of Bob & \([0,150]^{T}\) \\ \(\omega_{W}\) & Coordinates of Willie & \([0,100]^{T}\) \\ \(\omega_{BS}\) & Coordinates of base station & \([0,0]^{T}\) \\ \(c_{A}\) & Initial coordinates of UAV & \([-300,0]^{T}\) \\ \(c_{F}\) & End coordinates of UAV & \([300,0]^{T}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 2: Comparison of the optimized trajectory and the trajectory of the UAV without IRS. From Figure 3, it can first be observed that the average covert rate increases with the flying time. As the flying time increases, the UAV spends a longer percentage of its time jamming [PERSON]'s received signals. Therefore, increasing the flying time improves transmission efficiency. Second, as the number of IRS units increases, the corresponding average transmission rate increases as well. The reason for this is that the IRS can intelligently adjust the reflection of the signals in the best direction to achieve a higher covert rate. Third, it can be observed that the covert rate of the covert communication system without any IRS [19] is much lower than that with IRS, demonstrating that IRS can significantly improve the covert rate.