# On IRS-Assisted Covert Communication with a Friendly UAV
## 5 Numerical Results
Third, the average covert rate decreases with the height of the UAV. The reason for this is that increasing the altitude results in a larger distance between the UAV and [PERSON], which in turn results in higher path loss for the interfering signal. In this case, [PERSON] must reduce her transmitting power in order to ensure the covertness of the communication, leading to a lower covert rate. To evaluate the convergence of the proposed algorithm, Figure 4 plots the average covert rate versus iterations for different outage probabilities and the maximum speed of the UAV. The outage probability \(P_{out}^{*}\) is set as 0.05, 0.1, and 0.3, and the maximum speed of the UAV \(V_{max}\) is set as 50m/s and 70m/s. It can be observed that a high average transmission rate can be obtained with an increase in outage probability. In addition, when the speed of the UAV increases, the average transmission rate increases accordingly. This is because as the speed of the UAV increases, the time required for UAV to arrive at the optimal jamming coordinate is reduced. Thus, the UAV can jam [PERSON]'s communications for a longer time at the optimal jamming coordinate, which results in an improvement in the covert rate. In this way, increasing both the upper limit of the outage probability and the speed of the UAV elevates the covert rate of the proposed CCS. Figure 3: The covert rate achieved by the system as the flying time varies, where \(M\) and \(H\) denote the number of IRS units and the height of the UAV, respectively. Figure 5 illustrates the covert rate versus \(\varepsilon\) for different noise variances at [PERSON]'s location and [PERSON] location. The noise variance at [PERSON]'s location is set as \(-120\) dBm, \(-100\) dBm, and \(-80\) dBm, while the noise variance at [PERSON]'s location is set as \(-120\) dBm and \(-80\) dBm. First, it can be observed that as \(\varepsilon\) grows, the average covert rate increases; this is because \(1-\varepsilon\) is comparatively smaller, which means that the covertness constraint is relatively loose, leading to a higher average covert rate. In the \(\varepsilon\) range of 0 to 0.2 the average covert rate is significantly influenced by \(\varepsilon\), while when \(\varepsilon\) is larger than 0.2 the change in the average covert rate is negligible. This is because when the value of \(\varepsilon\) is large the covertness constraint is relatively loose, and the average rate can reach its maximum value. Moreover, there is an increase in the covert rate as the noise variance at [PERSON]'s location becomes larger. This is because the increased interference imposed on [PERSON] can help [PERSON] to increase her transmitting power, improving the covert rate. However, when the noise at [PERSON]'s location increases, the signal received by [PERSON] is influenced as well, reducing the outage probability. Therefore, artificial noise generated by [PERSON] or noise signals used to interfere with [PERSON] influence covert communications between [PERSON] and [PERSON], decreasing the covert rate. Figure 6 plots the average covert rate versus [PERSON]'s transmitting power with different flying times of 30 s, 70 s, and 110 s. The maximum AN power is set to 1 W and 2 W. It can be observed that the average covert rate increases with the flying time of the UAV; thus, the transmitting power is determined by the flying time of the UAV as well. Therefore, higher transmitting power results in a significant improvement in the covert rate, and higher AN power can ensure better covertness, though resulting in correspondingly higher energy consumption. In addition, the covert rate was maintained almost unchanged as the transmission power increased from 1 W to 2 W when a UAV was not included in the system [31]. This is due to the fact that, while the increase in AN transmitting power decreases [PERSON]'s detection performance, it also introduces extra interference with [PERSON]'s attempts to receive covert messages.