# On the Performance of a UAV-Aided Wireless Network Based on NB-IoT
## 4 System Model
### Channel Model  
Motivated by the short-sized traffic demand, we assume the backhaul link UAB-terrestrial BS undergoes free-space propagation, and the capacity achieved is sufficient for both the UAB control links (for manouvrability and command and control signals) and data forward. In this article, the propagation model affects the UAB-ground node link, and is therefore known as ATG channel. We compute the received power, \(P_{rx}\) as a function of the transmit power, \(P_{tx}\), as: \(P_{rx}[\text{dBm}]=P_{tx}[\text{dBm}]-A_{L}[\text{dBi}]-L_{\text{ATG}}[\text{ dB}]\). The ATG propagation can statistically model the loss value, \(L_{\text{ATG}}\), as the reference considered here for drones in urban environment [7; 33]. According to this model, connections between drone and nodes can either be LoS or Non-LoS (NLoS). For NLoS links, the signals travel in LoS before interacting with objects located close to the ground which result in shadowing effects. We denote as \(p_{\text{LoS}}\) the probability of connection being LoS. The probability \(p_{\text{LoS}}\) at a given elevation angle, \(\theta\), is computed according to the following equation  
\[p_{\text{LoS}}=\frac{1}{1+\alpha\exp(-\beta[\frac{180}{\pi}\theta-\alpha])} \tag{3}\]  
with \(\alpha\) and \(\beta\) being environment-dependent constants, i.e., rural, urban, etc, and adopted as given in [7; 8]. Equation (3) determines for every link if it is in LoS or NLoS condition, impacting then the value of \(\xi_{\text{LoS}}\) in Equation (4). The LoS path loss model is given by:  
\[L_{\text{ATG}}(d)[\text{dB}]=20\log\left(\frac{4\pi f_{c}d}{c}\right)+x_{ \text{LoS}}\xi_{\text{LoS}}+(1-x_{\text{LoS}})\xi_{\text{NLoS}}+\eta \tag{4}\]where \(x_{\text{LoS}}\) equals 1 in the case of realization of LoS links and 0 otherwise. \(\xi\) represents the shadowing coefficient which depends on LoS or NLoS conditions as well and is set as described in [7; 8]. Then, \(c\) is the speed of light, \(f_{\text{c}}\) is the center frequency, and \(d\) is the transmitter-receiver distance in meters. An additional penetration loss, \(\eta\), as for in indoor monitoring or basement applications is considered.  
If the received power is above the receiver sensitivity, we consider the node to be in the connectivity range of the UAB. Because of the fact that NB-IoT may have three coverage classes, we have three sensitivity thresholds, one for each class \(ce\), denoted as \(P_{ce,\text{min}}\). Once the device is connected and synchronized to its coverage class signalling, it can attempt to access the channel through the NB-IoT NPRACH (see Section 3.3), so that, if succeeded, it may be given resources to transmit its data. The number of resources assigned determines the packet size that the node can transmit in the given time window (see Section 3.3 and Table 1 for scheduling details). Note that, since the IoT nodes are the devices more limited in their characteristics, for example considering the maximum transmit power, we assume:  
* the connectivity range is defined by the uplink,
* the downlink control communication is error-less.