# Coverage Analysis and Efficient Placement of Drone-BSs in 5G Networks +
## 2 System Model  
In this section we present the system model adopted for our work. We consider an urban scenario where \(N\) users are distributed randomly in the area represented by (\(xj\)). The \(M\) drones-BSs are randomly distributed with fixed power transmission. Each drone is defined by its altitude \(h\) and location (\(xi\),\(i\)). Geometrically, the coverage area of the drone is given by \(Cdrone=(R2-h2)\), where \(R\) represents the radius of the transmitter drone [11]. Figure 1 depicts a possible scenario of drone-BSs deployment. Additionally, we assume that the propagation environments are both LOS and Non-Line-of-Sight (NLOS). On the other hand, the metric for satisfying quality of service is based on the determination of the Signal-to-Interference Plus Noise Ratio (SINR), which should be above a certain threshold \(SINR>SINRthr\). According to [3], the probability of the mean path loss is given by:  
\[PL\big{(}h,d_{ji}\big{)}=PL_{LOS}P_{LOS}+PL_{NLOS}P_{NLOS} \tag{1}\]  
where \(P_{LOS}\) represents the probability of the LOS link given by Equation (2) and \(P_{NLOS}=1-P_{LOS}\). As discussed in [12], the path loss between drone-BSs and users for the LOS and NLOS propagation in \(dB\) is given by Equation (3).  
\[P_{LOS}=\frac{1}{1+aexp\Bigg{(}-b\Bigg{(}\Big{(}\frac{180}{n}\Big{)}tan^{-1} \Bigg{(}\frac{h}{\sqrt{\big{(}{{{}_{i}}}-{{{}_{i}}}\big{)}^{2}+\big{(}{{{}_{j} }}-{{{}_{j}}}\big{)}^{2}}}}\Bigg{)}-a\Bigg{)}\Bigg{)}} \tag{2}\]  
\[\begin{array}{c}PL_{LOS}=20\text{log}\Big{(}\frac{4\pi f_{c}d_{ji}}{c}\Big{)} +\eta_{LOS}\\ PL_{NLOS}=20\text{log}\Big{(}\frac{4\pi f_{c}d_{ji}}{c}\Big{)}+\eta_{NLOS} \end{array} \tag{3}\]  
where \(f_{c}\) represents the carrier frequency, \(d_{ji}=\sqrt{\big{(}{{{}_{j}}}-{{{}_{i}}}\big{)}^{2}+\big{(}{{{}_{j}}}-{{{}_ {j}}}\big{)}^{2}+h^{2}}}\) is the distance between the drone-BSs and user \(i\). Furthermore, \(\eta_{LOS}\) and \(\eta_{NLOS}\) are the average additional losses for LOS and NLOS, respectively. The probability mean path loss can be further rewritten as:  
\[PL\big{(}h,\;d_{jit}\big{)}=(\eta_{LOS}-\eta_{NLOS})P_{LOS}+10\;log\Bigg{(} \begin{array}{c}\frac{h^{2}+}{\sqrt{\big{(}{{{}_{j}}}-{{{}_{i}}}\big{)}^{2} +\big{(}{{{}_{j}}}-{{{}_{j}}}\big{)}^{2}}}}\\ \sqrt{\big{(}{{{}_{j}}}-{{{}_{i}}}\big{)}^{2}+\big{(}{{{}_{j}}}-{{{}_{j}}} \big{)}^{2}}}\end{array}\Bigg{)}+B \tag{4}\]  
with \(B=20\;log\Big{(}\frac{4\pi f_{c}}{c}\Big{)}+\eta_{NLOS}\).  
As shown in Figure 1, the blue circles represent the drone's coverage area, and the black points indicate the users in the area. At this point, there are two major binary decisions to be conducted. The first one is to determine the deployment of drone-BSs and the second one is to determine the users covered by drone-BSs. The procedure can be developed mathematically as follows: let \(D=\{1\dots M\}\) represent the set of the candidate drone-BSs and \(U=\{1\dots N\}\) the set of the users. For the first case, the binary decision can be formulated as:  
\[\omega_{xyh}^{i}=\left\{\begin{array}{l}1,\;if\;the\;drone-BS\;is\;\;deployed\;at \;(x_{i},y_{i},h)\\ 0,\;otherwise\end{array}\right. \tag{5}\]  
Then, for the second case (user's coverage):  
\[\varphi_{j}^{i}=\left\{\begin{array}{l}1,\;if\;user\;j\;is\;covered\;by\; one\;drone-BS\;i\\ 0,\;otherwise\end{array}\right. \tag{6}\]