# UAV Based Relay for Wireless Sensor Networks in 5G Systems
## 2 System Model and the Problem Formulation  
In this section, we introduce the system model of the UAV based relay in WSN. As shown in Figure 1, users contain different types of sensors (sensors, road side units, etc. ), and the data sensed by each one will be collected by a concentrator (sink node/gateway). Moreover, the concentrator retransmit the collected data to the BS, which connects the WSN to the Internet. Hence, the concentrator acts as a gateway to concentrate the traffic data sensed in WSN for transmission to the border gateway (BS). Then, the WSN can connect to the Internet. Notably, in this paper, we assume that WSN can work at 900 MHz/2.4 GHz to support the 5  GHz frequency bands, and the concentrator contains two interfaces in order to connect WSN (Zigbee, WiFi, 6 LoWPAN, etc.) to the 5G mobile communications world. The approach we propose to improve the system performance is employing the UAV as a relay station, where we consider the path among SINK-UAV-BS to simplify the system model. Then, the omnidirectional path model can thus be used in this paper. We assume the wireless bandwidth of the concentrator at the sink node is \(B_{S}\) Hz, and the wireless bandwidth of the UAV is \(B_{U}\) Hz. The transmitting power of the concentrator is denoted as \(P_{S}\), and the transmitting power of the UAV is denoted as \(P_{U}\). The power of Gaussian White Noise is denoted as \(\sigma^{2}\). The wireless channel gain from the concentrator to the UAV is denoted as \(|h_{S}|^{2}\), and the wireless channel gain from the UAV to BS is denoted as \(|h_{U}|^{2}\). In this paper, the omnidirectional path model [18] based on the millimeter waves (mmWave) model is employed as in (1). However, the algorithm and results in this paper can also apply to the existing scenarios of WSN  
\[L=86.6+24.5\times\log_{10}d\ (\mathrm{dB}), \tag{1}\]  
where \(L\) denotes path loss in decibels (dB), and \(d\) denotes the distance between the source and end in meter. To make the paper more focused, we ignore the impact of fast fading and slow fading on the wireless channel gain. We make such an assumption from the following two reasons: first, the impact of fading can be counteracted from the long-term average. Second, we can obtain a more theoretical analysis to guide the engineering. Define \(L_{S}\) as the distance between the concentrator at the sink node and UAV, and \(L_{U}\) as the distance between UAV and BS, respectively. By (1), we can further derive \(|h_{S}|^{2}\) and \(|h_{U}|^{2}\) as in (2) and (3), respectively. \[|h_{S}|^{2}=10^{-\frac{L_{S}}{10}}, \tag{2}\]  
\[|h_{U}|^{2}=10^{-\frac{L_{U}}{10}}. \tag{3}\]  
To simplify the system model, in this paper we assume the concentrator transmit signal to the BS with one UAV as the relay. This system model can better reveal the relationship between the position of the UAV based relay and the system energy consumption. As shown in Figure 1, sensors first transmit signals to the concentrator. Then, the concentrator retransmit the signal to the BS, which will deliver the wireless data to the destination in the network. The model can be abstracted as the right triangle at the right side in Figure 1. The vertical dimension from BS to the ground is denoted as segment \(\overline{BO}\) in meter (m), and the horizontal distance between the concentrator and BS is denoted as \(\overline{SO}\) in meter. Then, the sight distance between the concentrator and BS is  
\[\overline{BS}=\sqrt{\overline{BO}^{2}+\overline{SO}^{2}}\;(\text{m}). \tag{3}\]  
The optimal position of the UAV will be dotted at the segment \(\overline{BS}\) because the minimize distance between two arbitrary points is the line segment. As shown in Figure 2, the minimized total distance between point \(A\) and \(B\) is the line segment \(\overline{AB}\). The minimized transmission distance between BS and the concentrator can minimize the transmitting power of the concentrator and UAV because the path loss is in direct proportion to the transmitting distance according to (1).