# Multi-IRS-Assisted mmWave UAV-BS Network for Coverage Extension
## 3 Architecture and System Model
### System Model  
Figure 2 presents the system model, thus illustrating how the access UAV extends coverage by selectively pairing one IRS with one UE from among multiple IRSs installed on structures such as buildings. This is how the UAV-BS creates a virtual LoS via an IRS for users located behind buildings who cannot obtain the LoS with a UAV. In this figure, ground BS is not available, and there are several possible routes for supplying radio waves from the UAV-BS. \(N\) denotes the total number of UEs in the specified area \(\Omega\), and \(M\) denotes the total number of IRSs. The position of neighboring BSs, UAVs, UEs, IRSs are respectively represented by the 3-dimensional coordinates \(P_{\text{BS}}\in\mathbb{R}^{1\times 3}\), \(P_{\text{UAV}}\in\mathbb{R}^{1\times 3}\), \(P_{\text{UE}}\in\mathbb{R}^{N\times 3}\), and \(P_{\text{IRS}}\in\mathbb{R}^{M\times 3}\). The horizontal positions of the UEs are located outdoors within the specified area \(\Omega\).  
We use real-based population data, that is, mobile spatial statistics [37], which are population statistics generated using the NTT DOCOMO cell phone network mechanism. A compartment is approximately 250 m \(\times\) 250 m and can capture the total population. Within a compartment, UEs are set with the sum of hot spots and uniform distribution. The location, radius, number of hotspots, and number of UEs to be accommodated are set randomly.  
Path Loss Model and Calculation of UE Received SNR  
The path loss model between the UAV in the sky and the UE on the ground is computed as the sum of the free space radio wave propagation loss and additional loss, which varies  
Figure 1: Proposed architecture overview.  
depending on whether the connection is LoS or NLoS by blocking [38]. Atmospheric absorption losses are not considered because they are negligible [39]. In our simulation, the path length from the UAV to the UE is up to 3.4 km. Atmospheric absorption will be maximally 3.4 dB [39] and included in the additional loss.  
\[L_{\text{LoS/NLoS}}[\text{dB}]=L_{\text{free}}+\eta_{\text{LoS/NLoS}} \tag{1}\]  
where \(L_{\text{free}}\) denotes free space radio wave propagation loss, which is calculated by  
\[L_{\text{free}}\left[\text{dB}\right]=20\log d+20\log f+20\log\frac{4\pi}{c} \tag{2}\]  
where \(d\) denotes the communication path length between the UAV and UE, \(f\) denotes the carrier frequency, and \(c\) stands for the speed of light. Based on the Friis transmission formula [40], the received power \(P_{\text{r}}\) at the UE is calculated by  
\[P_{\text{r}}[\text{dBm}]=P_{\text{t}}+G_{\text{t}}+G_{\text{r}}-L \tag{3}\]  
where \(P_{\text{t}}\) denotes the transmit power from the UAV antenna, \(G_{\text{t}}\) denotes the gain of the UAV transmitting antenna, and \(G_{\text{r}}\) signifies the gain of the UE receiving antenna. From the obtained received power \(P_{\text{r}}\), the SNR \(\gamma\) is calculated by  
\[\gamma=\frac{P_{\text{r}}}{P_{\text{n}}} \tag{4}\]  
where \(P_{\text{n}}\) denotes the noise power, which is calculated by  
\[P_{\text{n}}=\sigma_{\text{n}}^{2}B \tag{5}\]  
where \(\sigma_{\text{n}}^{2}\) denotes the noise power density, and \(B\) denotes the system bandwidth.