## 3 Methodology  
### Energy Consumption Model of Lora Sensor Node  
The energy consumption modeling process represents an essential consideration when designing sensor nodes to monitor a specific application. For most applications, such as the ones presented in [55], the communicating sensors should perform the following: sense events, process the local information of sensed events, and transmit packets to the access point [56]. Each task consumes power over a given period. Therefore, an accurate energy consumption model of the sensor node is essential to estimate the sensor lifetime, as proven in [15,57]. Furthermore, the energy model allows the power consumption optimization of the sensor node. In order to study the sensor node autonomy, it is necessary to model the different operating modes of the sensor node. Then, the consumed energy of each mode can be determined, and the consumption energy model can be defined. Most of the time, the sensor node is put into sleep mode. That is a low-power mode, but the energy consumed in this mode can also impact the total energy consumption of the sensor node. The total consumed energy E_Total of the sensor node for one cycle is:  
\[\text{E}_{\text{Total}}=\text{E}_{\text{Active}}+\text{E}_{\text{-Sleep}}, \tag{1}\]  
where E_Sleep and E_Active represent the dissipated energy by the sensor node in the sleep mode and the total energy consumption during the active mode of the node microcontroller, respectively [15]. The duration of the sleep mode should be \(\geq\)99%, and the duration of the active mode should be \(\leq\)1% [15]. In addition, E_Sleep is expressed as:  
\[\text{E}_{\text{Sleep}}=\text{P}_{\text{-Sleep}}\cdot\text{T}_{\text{-Sleep}}, \tag{2}\]  
where P_Sleep and T_Sleep are the power consumption and the time duration in the sleep mode, respectively [15]. The total energy consumption in active mode E_Active is calculated as the sum of the energy consumption used for the operation of each part of the sensor node. Therefore, it is given by the following equation [15]:  
\[\text{E}_{\text{Active}}=\text{E}_{\text{-WU}}+\text{E}_{\text{-M}}+\text{E}_ {\text{-PROC}}+\text{E}_{\text{-WUT}}+\text{E}_{\text{-Tx}}+\text{E}_{\text{- WUR}}+\text{E}_{\text{-Rx}}, \tag{3}\]  
where the consumed energies that should be considered are the ones for the system wake-up, data measurement, microcontroller processing, the wake-up of the transmitter, the transceiver's transmission, the wake-up of the receiver, and the reception of the transceiver, respectively [15], as presented in Figure 1.  
Energy consumption in specific operating modes can be determined regarding the current consumption of LoRa/LoRaWAN transceiver modules, as declared in the specifications and affirmed by conducted measurements, presented in Table 1. As can be seen, the sleep current ranges from 0.1 uA to 34 mA. Sleep current for the hardware platforms is up to several orders of magnitude greater than sleep current of their transceivers [58], which can be near 1 uA, or even lower than that [47]. In addition, the power consumption can be determined from the transceivers' electrical specifications under the stated supply voltage conditions, as presented in Table 2.  
Figure 1: Energy consumption states of the sensor node. The output power is sensitive to the power supply voltage, and their performance is typically expressed at 3.3 V [64]. For instance, the HopeRF RFM95/96/97/98(W), used in the field measurements whose presentation is given in Section 4 of the paper, has a minimum output supply voltage of 2.4. V and a maximum of 3.7 V, which applies to the high-power +20 dBm operation [54]. According to [54], the following can be quoted:  
1. [label=()]
2. Transmit mode of operation of the transceiver In transmit mode, the power consumption, presented in Table 2, is optimized only when packet data needs to be transmitted by enabling the following blocks: RF, PLL (used for calibration of the receiver), and PA (amplifier capable of yielding RF power) [64].