# Coverage Area Decision Model by Using Unmanned Aerial Vehicles Base Stations for Ad Hoc Networks
## 3 Proposed UAVs-BS Network Coverage Model
### Proposed System Model  
The cellular network's users are randomly distributed in the ground network. In the traditional cellular networks, the base station (BS) provides communication convergence to the users. The BS coverage is fixed and limited for downlink and uplink data communication. The UAVs-BS solution provides cost-effective and mobility-oriented services. This type of solution is only available whenever there is a need to cover the area. If the network BS meets user needs, the UAVs-BS solution is not required. By adopting this strategy, the proposed solution provides a more effective, low-cost, and feasible solution. This study considers a downlink wireless system where the BS provides the services as usual, and the UAVs-BS is used for congested situations. This solution also addresses the overlap coverage situation.  
The proposed solution is based on a statistically generic path loss model as used in [41]. The generic path loss model uses line-of-sight (LoS) and non-LoS links. To address the fading issue in the UAVs-BS, the proposed model uses Rician fading in LoS links, whereas the Rayleigh fading has been adopted for non-LoS links. The received signal stretch (RSS) from cellular users (CU) and the UAVs-BS is given as in Equations (1) and (2), respectively.  
\[TP_{LoS}(HD_{CU, UAVs-BS},SD_{CU, UAVs-BS})=TP_{CU, UAVs-BS}^{\xi}\text{FLOS} \tag{1}\]  
Figure 1: UAV-BS coverage area.  
\[TP_{LoS}(HD_{CU,UAVs-BS}SD_{CU,UAVs-BS})=TP_{CU,UAVs-BS}^{c}\text{Fnon}-\text{LoS} \tag{2}\]  
where the TP denotes the transmit power of the UAVs-BS, \(HD_{CU}\), \(UAVs-BS\) shows the horizontal distance of the CU and the UAVs-BS, and \(SD_{CU}\), \(UAVs-BS\) shows the spatial distance of the CU and the UAVs-BS. The FLoS and \(\text{Fnon}-\text{LoS}\) are the fading factors for the links. The probability of LoS connections between the CU and the UAVs-BS is presented in Equation (3).  
\[ProbLoS=\alpha(\frac{180}{\pi}\text{arctan}(HD_{CU,UAVs-BS}(HD_{CU,UAVs-BS,})-1 5)^{\beta} \tag{3}\]  
The \(\alpha\) and \(\beta\) are constant values and change with dense and sparse cellular network conditions. The probability of non-LoS is 1-ProLoS. The average received power (RP) depends on the vertical and horizontal altitude. The RSS increases based on network and quality of services (QoS) requirements. With the increased altitude of the UAVs-BS, the coverage radius also increases, and when the altitude reaches a specific value, then the coverage radius decreases.  
The UAVs-BS deployment's main objective is to cover the maximum area. However, the overlap problem still exists, as well as the need for a demand coverage area. Finding a feasible altitude and providing maximum coverage is the main goal. The set of CUs is denoted as \(Set_{CU}\) enclosed with the coverage area (CA), whereas the total coverage for the CU in the CA is shown in Equation (4).  
\[max\sum_{CI}^{L}\lvert Set_{CU}\rvert \tag{4}\]  
The L shows the number of CAs, and the max shows the maximum altitude of the UAVs-BS. This shows that the number of CAs is not more than the number of UAVs-BS, and the HD considers the distance between the CU in the CA and the UAVs-BS. The proposed solution solves the optimization issue to maximize the CA of the CUs by proposing the altitude and coverage radius of the UAVs-BS.