# Energy-Efficient UAVs Deployment for QoS-Guaranteed VoWiFi Service
## 5 Solving a Pseudo-Static Scenario
### Checking the Fitness of Individuals: Check Function
#### 5.2.1 Signal Coverage Evaluation (Associate Function)  
This function associates each ground user to an aerial AP. A successful association requires that the Received Signal Strength Indicator (RSSI) and the Signal-to-Interference-plus-Noise-Ratio (SINR) are above a lower threshold. If multiple access points were available, each user will associate with the AP which provides the strongest RSSI. The output of the _Associate_ function is the set of users that are associated to drone \(j\), \(\mathcal{C}(j)\):  
\[\mathcal{C}(j)=\{i\in\mathcal{U}\mid\gamma_{ik}=1,\ RSSI_{ij}>RSSI_{ik},\ \forall k\
eq j\} \tag{11}\]  
where \(\gamma_{ij}\) as a boolean that represents if user \(i\in\mathcal{U}\) satisfies minimum thresholds (i.e., both, \(SINR_{ij}\geq SINR_{\text{min}}\) and \(RSSI_{ij}\geq RSSI_{\text{min}}\)) when associated to UAV \(j\in\mathcal{D}\). Observe that the user-to-AP association determines the Modulation and Coding Scheme (i.e., \(MCS^{(i)}\)) at the physical layer of each WiFi station, which depends on the received \(RSSI^{(i)}=\underset{j=1..D}{\max}\{RSSI_{ij}\}\) and the required minimum sensitivity for each MCS. Next, we develop how RSSI and SINR are computed for each ground user. UAV-to-Ground Channel Model  
Most works [22; 33; 52] consider that ground users receive three different groups of signals that could be classified as: (a) Line-of-Sight (LoS), (b) Non-Line-of-Sight (NLoS), and (c) other reflected components which cause multipath fading. Each group has its own probability of occurrence depending on the environment, density, height, and elevation angle; so their impact on the overall path loss can be averaged. According to [53], the probability of fading is significantly lower than the probability of receiving the LoS (\(P_{LoS}\)) and NLoS (\(P_{NLoS}\)) components. Therefore, the UAV-to-Ground path loss can be represented by:  
\[L(d,\theta)=P_{LoS}(\theta)\,L_{LoS}(d)+P_{NLoS}(\theta)\,L_{NLoS}(d) \tag{12}\]  
which depends on the distance \(d\) between the UAV and the ground terminal, and \(\theta\) that represents the elevation angle (in radians). \(L_{LoS}\) and \(L_{NLoS}\) represent the average path loss for LoS and NLoS components, respectively; and can be expressed as [52]:  
\[L_{LoS}(d) =20\log_{10}\left(\frac{4\pi f_{c}\,d}{c}\right)+\xi_{LoS} \tag{13}\] \[L_{NLoS}(d) =20\log_{10}\left(\frac{4\pi f_{c}\,d}{c}\right)+\xi_{NLoS} \tag{14}\]where the first term accounts for the free space propagation loss, \(\xi_{LoS}\) and \(\xi_{NLoS}\) represent any additional losses due to the environment (a list of values can be found in [22]), and \(f_{c}\) is the channel frequency. Finally, the probability of receiving each component is given by [54]:  
\[P_{LoS}(\theta)=\frac{1}{1+\alpha e^{-\beta\theta\cdot 180/\pi+\beta\alpha}} \tag{15}\] \[P_{NLoS}(\theta)=1-P_{LoS}(\theta) \tag{16}\]  
where \(\alpha\) and \(\beta\) are environment-dependent constants (e.g., rural, urban, etc.) as defined in [22] (e.g., \(\alpha=\beta=0\) for no buildings). Obtaining RSSI and SINR  
The Received Signal Strength Indicator (RSSI) represents the power received at the ground terminal. Let us consider a generic user \(i\) and the AP installed at drone \(j\). Then, \(RSSI_{ij}\) can be calculated by subtracting the UAV-to-Ground path loss to the total transmitted power:  
\[RSSI_{ij}=P_{\text{tx}}+G_{ij}-L\left(\|\mathbf{w}_{i}-\mathbf{x}_{j}\|, \theta_{ij}\right) \tag{17}\] \[G_{ij}=10\log_{10}\left(10^{G_{\text{max}}/20}\cdot\cos^{2} \theta_{ij}\right) \tag{18}\]  
where \(P_{\text{tx}}\) (dBm) represents the power delivered by the transmitter antenna; \(G_{ij}\) (dB) stands for the gain of the antenna between user \(i\) and drone \(j\) as indicated in Equation (18) (which is bounded by \(G_{\text{max}}\)); \(L(d,\,\theta)\) represents the path loss function introduced in Equation (12); and \(\|\mathbf{w}_{i}-\mathbf{x}_{j}\|\) is the Euclidean distance between user \(i\) and drone \(j\).