## 4 Proposed Solution
### Mobility Model  
The proposed LDAP can be implemented using any type of ground or over-the-ground vehicle depending on the WARM applications. However, most of the WARM applications may require remote connectivity where the SNs are difficult to access using ground vehicles. Therefore, for the WARM case, an UAV-mounted DS is considered. Figure 7 shows an UAV-mounted DS, which is moving from its initial position, a, to b and then to c, at a ground speed of V\({}_{\mathrm{UAV}}\), at an altitude of H, and with the LoRa link distance from the RN represented by L. The projected position of the DS is shown as DS' at different times (at a', b', and c'). The projected distance between the RN and the DS' is D, which is considered equal to H for optimized altitude vs. the wireless link coverage condition, so that D = H = 0.7 L. An UAV-mounted DS needs to perform two tasks; link establishment and data transfer. To keep the proposed LDAP lightweight, these two tasks are designed to meet the UAV speed and also the LoRa TOA. According to the experimental setup used for the WQM case, we calculated a data transfer time through the repeater node (T\({}_{\mathrm{AQRN}}\)) as 856 ms for the maximum sensor data size of 245 bytes. We can calculate the number of SNs data messages to be transferred using a low to medium height UAV, such as the Zephyr 7 [56], with the following conditions:  
- UAV altitude is 3.5 km for a 5 km LoRa link;  
- UAV maximum ground speed = 50 km/hr = 13.8 m/s = 833 m/min; and  
- The data transfer ratio through the repeater node = 100%.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Event** & **Duration (mS)** & **Voltage (V)** & **Current (mA)** & **Power (mW)** & **Energy (mJ)** \\ \hline Active & T\({}_{\mathrm{AC}}\) = 2407 & 5.01 & 31 & P\({}_{\mathrm{AC}}\) = 155.31 & E\({}_{\mathrm{AC}}\) = 373.83 \\ LoRa Rx & T\({}_{\mathrm{RX}}\) = 336 & 5.01 & 44 & P\({}_{\mathrm{RX}}\) = 220.44 & E\({}_{\mathrm{RX}}\) = 74.07 \\ LoRa Tx & T\({}_{\mathrm{TX}}\) = 135 & 5.00 & 148 & P\({}_{\mathrm{TX}}\) = 740.00 & E\({}_{\mathrm{TX}}\) = 99.90 \\ Full cycle & 2878 & & & & 547.80 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Event-wise energy calculation of the SN with a 3-sec cycle using the LDAP.  
Figure 7: Data transmission from the SN to the mobile DS mounted on a unmanned aerial vehicle (UAV).  
With the above conditions where the minimum distance between the DS and SN (L) is very high compared with the distance traveled per second (or the time of T\({}_{\text{AQRN}}\)) by the UAV, the DS can be considered static for the period of T\({}_{\text{AQRN}}\). As shown in Figure 7, when all the SNs are distributed at a minimum distance of 3.5 km (0.7 L) from the RN, they will communicate with the DS through the RN only in the worst case scenario. The DS can travel half of the SN-DS distance (3.5 km) in 126 s without losing the connection with the RN, and during this time it can receive data from at least 147 SNs. Table 1 shows that with the LDAP, the SNs are much more distributed or the number of SNs within the 3.5 km range is lower than the number of SNs that the UAV-mounted DS can acquire data through the RN. The maximum number of SN density can be calculated as 56 (3.5* 480/30) for zone 1. Therefore, the UAV-mounted mobile DS with the LDAP can easily be implemented for the WQM case as described in Section 3. Similarly, using the proposed LDAP, the mobile DS mounted on a specific UAV, traveling at an altitude of H (=0.7 L), can acquire data from the number of SNs (SN\({}_{\text{UAV}}\)) which can be calculated using Equation (12).  
\[\text{SN}_{\text{UAV}}\ =\ \left(\frac{0.7\ L}{\text{V}_{\text{UAV}}}\right)/ \left(2\text{T}_{\text{AQRN}}\right) \tag{12}\]