# Resource Allocation in Uplink NOMA-IoT Based UAV for URLLC Applications
## 3 System Model  
As shown in Figure 1, a UAV-assisted IoT network is considered where the UAV serves as an aerial base station, all IoT devices are served by a UAV that covers a cell with radius \(R_{c}\). The UAV is located at 3D coordinates (\(x_{UAV}\), \(y_{UAV}\), \(h_{UAV}\)); assume that (\(x_{UAV}=0\), \(y_{UAV}=0\), \(h_{UAV}\)); i.e., the UAV is at the center of the cell with altitude \(h_{UAV}\); such that (\(h_{min}\leq h_{UAV}\leq h_{max}\)) where \(h_{min}\) and \(h_{max}\) are the minimum and maximum allowable heights of the UAV. Assume that there are \(N\) ground IoT devices; each device is equipped with a single antenna. These devices are distributed randomly in the cell covered by the UAV; each device is located at (\(x_{i},y_{i}\)) where \(i=\{1,2,\,.\,.\,.\,N\}\). Each IoT device has a packet arrival rate \(\lambda_{i}\) and transmits minimum rate \(R_{i}\) with delay limit \(D_{i}\). Each IoT device has a transmitted power \(P_{i}\) (\(P_{min,i}\leq P_{i}\leq P_{max,i}\)) where \(P_{min,i}\) and \(P_{max,i}\) are the minimum and maximum transmitted power of IoT device \(i\) respectively. Path loss between IoT device \(i\) to the UAV expresses the large-scale fading component which is given by  
\[PL_{i}=\frac{A}{1+ae^{-b\ (\theta_{i}-a)}}+B_{i}, \tag{1}\]  
\[A=\eta_{LOS}\ -\eta_{NLOS}, \tag{2}\]  
\[B_{i}=20\ log_{10}(d_{i})+20\ log_{10}\bigg{(}\frac{4\pi f_{c}}{c}\bigg{)}+ \eta_{NLOS}, \tag{3}\]  
where \(f_{c}\) is the carrier frequency, \(c\) is the light speed, \(\eta_{LOS}\), \(\eta_{NLOS}\), \(a\), \(b\) are constants related to the propagation environment either urban, suburban, dense urban or high-rise urban environments. Considering air to ground (A2G) communication between the UAV and the ground IoT devices, thus, each device can have line of sight (\(LoS\)) view or non-line of sight (_NLoS_) view with respect to the aerial base station with certain probability. _NLoS_ occurs when the propagation path is partially or fully obscured by physical obstacles. The _LoS_ probability or _NLoS_ probability are highly dependent on the device location, environment and the elevation angle between the device and the UAV, as illustrated in Figure 1. \(Pr_{LoS_{i}}\), \(Pr_{NLoS_{i}}\), are the probabilities of IoT device \(i\) having _LoS_ link or having non-line of sight (_NLoS_) link respectively between the UAV and IoT device, which could be calculated as [20]  
\[Pr_{LoS_{i}}=\frac{1}{1+aexp(-b[\theta_{i}-a])}\, \tag{4}\]  
\[Pr_{NLoS_{i}}=1-Pr_{LoS_{i}} \tag{5}\]  
where \(\theta_{i}\) is the elevation angle (measured in \"degree\") between IoT device \(i\) and the _ULAV_ as illustrated in Figure 1; it can be calculated as  
\[\theta_{i}=\frac{180}{\pi}\sin^{-1}\left(\frac{h_{ULAV}}{d_{i}}\right) \tag{6}\]  
\(d_{i}\) is the distance between the IoT device \(i\) at (\(x_{i},y_{i}\)) and the _ULAV_ located at (\(x_{ULAV},y_{ULAV}\), \(h_{ULAV}\)) is  
\[d_{i}=\sqrt{\left(x_{ULAV}-x_{i}\right)^{2}+\left(y_{ULAV}-y_{i}\right)^{2}+ \left(h_{ULAV}\right)^{2}} \tag{7}\]  
The _ULAV_ uses the NOMA access technique to communicate with the IoT devices. Assume that the total bandwidth allocated to the _ULAV_ is \(B\), which is divided equally into \(K\) orthogonal subcarriers. Let \(b_{k,i}(t)\) is the subcarriers assignment index, where \(b_{k,i}(t)=1\) means that subcarrier \(k\) is allocated to device \(i\), otherwise \(b_{k,i}(t)=0\). There are maximum \(L\) IoT devices allowed to be scheduled over a single subcarrier at the same time and each IoT device gets exactly one subcarrier for simplicity. IoT devices can give preferences for the resource blocks, and their preferences are considered based on their channel quality indicator (CQI) [22] which depends on the channel quality between the _ULAV_ and IoT devices.