# Energy-Efficient UAVs Deployment for QoS-Guaranteed VoWiFi Service
## 3 QoS and UAVs Endurance in VoWiFi Networks
### Modeling UAV Endurance  
Endurance can be described as the total time taken during the flight (\(T_{\text{Flight}}\)) until the depletion of the UAV's battery. High-power performance commercial UAVs are typically powered by LiPo batteries, whose energy density varies between 150 and 300 Wh/Kg. In this work, the UAV energy expenditure will consider two factors: flight and radio communication, being the former dominant in the energy budget.  
According to [28], the energy (in Wh) associated with flying can be broken down into three different flight stages:  
\[E_{\text{Flight}}=E_{\text{Climb}}+E_{\text{Translational}}+\underbrace{P_{ \text{Hover}}\cdot T_{\text{Hover}}}_{E_{\text{Hover}}} \tag{2}\]  
where \(E_{\text{Climb}}\) stands for the energy associated with vertical climbing, \(E_{\text{Translational}}\) is the energy spent in lateral transitions, and \(E_{\text{Hover}}\) accounts for the energy spent while hovering (i.e., static). As proved in [48], the hovering factor is dominant and overshadows the other two, and thus, the expression in Equation (2) can be simplified to its last term.  
Besides Equation (2), the other contributing factor to energy consumption is the power spent on the radio used by the VoWiFi service.  
\[E_{\text{Radio}}=E_{\text{WiFi}}+E_{\text{Backhaul}} \tag{3}\]  
where \(E_{\text{WiFi}}\) represents the energy consumed by the wireless IEEE 802.11 card of the aerial AP, and \(E_{\text{Backhaul}}\) accounts for the energy consumed by the radio link used for the backhaul network.  
Assuming that network cards are not running power saving mechanisms, the first term of Equation (3) (\(E_{\text{WiFi}}\)) can be further decomposed as:  
\[E_{\text{WiFi}}=P_{\text{WiFi}}\cdot T_{\text{Flight}}=\rho_{\text{tx}}\cdot T _{\text{tx}}+\rho_{\text{rx}}\cdot T_{\text{rx}}+\rho_{\text{idle}}\cdot T_{ \text{idle}} \tag{4}\]  
where \(T_{\text{tx}}\), \(T_{\text{rx}}\) and \(T_{\text{idle}}\) stand for the time spent by the network interface card on transmission, reception and idle states respectively (their sum must be \(T_{\text{Flight}}\)); and \(\rho_{\text{tx}}\), \(\rho_{\text{rx}}\) and \(\rho_{\text{idle}}\) stand for the respective power consumption coefficients (which depend on the network interface card). The time taken on each state depends on the traffic processed at the AP during the flight, which in turn depends on the VoIP traffic pattern, the MCS used at each station, and retransmissions that may occur due to noise or collisions. In Appendix A we derive closed-form expressions for the temporal factors in Equation (4) for the IEEE 802.11 mac sub-layer.  
Regarding the second factor in Equation (3), (the backhaul radio link is out of the scope of our this work and the radio power will depend on the particular technology used. However, the assumption indicated in Equation (5) is acceptable for the sake of completeness) we can assume that in general, it will be proportional to the WiFi consumption, as expressed in Equation (5):  
\[E_{\text{Backhaul}}=\underbrace{K\cdot P_{\text{WiFi}}}_{\text{Backhaul}}\cdot T _{\text{Flight}} \tag{5}\]  
where \(K\) is a constant that represents the relation between both radio consumptions. For the remainder of this paper we use \(K=1\) so \(P_{\text{Backhaul}}=P_{\text{WiFi}}\).  
Therefore, the total energy \(E\) spent by the UAV can be expressed as in Equation (6):  
\[E=E_{\text{Flight}}+\underbrace{E_{\text{WiFi}}+E_{\text{Backhaul}}}_{E_{ \text{Radio}}} \tag{6}\]  
Finally, assuming hovering as the dominant factor in Equation (2), the UAV's expected flight duration (in hours) can be expressed as:  
\[T_{\text{Flight}}=\frac{E_{\text{Battery}}}{P_{\text{Hover}}+(1+K)\cdot P_{ \text{WiFi}}} \tag{7}\]  
where \(E_{\text{Battery}}\) represents the battery energy in Watts per hour. \(T_{\text{Flight}}\) is one of the factors of our objective function and its computation will be addressed in greater detail in Section 5.2.3.