# Verification of a Probabilistic Model and Optimization in Long-Range Networks
## 3 Results
For a fixed transmission power of 14 dBm (0.0251 W), the energy consumption for SF = 7 is as follows:  
Figure 5:1  
For battery-powered devices, selecting an optimal SF that balances range and energy consumption is crucial. Transmission power (PWR) is another critical parameter that affects energy consumption. Higher transmission power levels improve signal strength and reliability, but also increase energy usage. Table 3 presents the energy consumption for different PWR levels, with a fixed SF of 7 and a bandwidth of 125 kHz. The data in Table 3 demonstrate that increasing the transmission power from 2 dBm to 18 dBm results in a four-fold increase in energy consumption per packet. This underscores the importance of optimizing transmission power to achieve a balance between communication reliability and energy efficiency, especially in battery-powered devices. While transmission power directly influences energy consumption, bandwidth (BW) also plays a crucial role by affecting both the data rate and receiver sensitivity. Lower bandwidth settings increase the airtime of packets, leading to higher energy consumption. Table 4 shows the energy consumption for different BW settings, with a fixed SF of 7 and a transmission power of 14 dBm. \begin{table}
\begin{tabular}{c c c} \hline
**Spreading Factor (SF)** & **Airtime (ms)** & **Energy per Packet (m)** \\ \hline
7 & 50 & 0.75 \\
8 & 100 & 1.50 \\
9 & 200 & 3.00 \\
10 & 400 & 6.00 \\
11 & 800 & 12.00 \\
12 & 1600 & 24.00 \\ \hline \end{tabular}
\end{table} 
Table 2: Energy consumption for different spreading factors. \begin{table}
\begin{tabular}{c c} \hline
**Transmission Power (dBm)** & **Energy per Packet (m)** \\ \hline
2 & 0.50 \\
6 & 0.75 \\
10 & 1.00 \\
14 & 1.50 \\
18 & 2.00 \\ \hline \end{tabular}
\end{table} 
Table 3: Energy consumption for different transmission power levels. As evident from Table 4, increasing the bandwidth reduces the airtime and, consequently, the energy consumption per packet. However, higher bandwidth settings may reduce the receiver's sensitivity, potentially requiring higher transmission power to maintain reliable communication. Therefore, selecting an appropriate bandwidth is essential for optimizing energy efficiency in LoRa networks. To further analyze these effects in a real-world setting, the energy consumption of the Reyax RYLR998 module was evaluated under varying traffic loads. The module was configured with an SF of 9, a transmission power of 14 dBm, and a bandwidth of 125 kHz. The energy consumption was measured over a 24-h period, with the device transmitting one packet every 10 min. The results in Table 5 indicate that energy consumption scales linearly with the number of transmitted packets. In low traffic scenarios, the device consumes minimal energy, making it suitable for long-term deployments. However, in high traffic scenarios, the energy consumption increases significantly, which could reduce the battery life of the device. This emphasizes the need for adaptive power management strategies, such as dynamic adjustment of transmission parameters based on traffic conditions, to optimize energy usage in battery-powered LoRa devices. These findings highlight the critical role of parameter selection in managing energy consumption, providing valuable insights for optimizing LoRa networks in battery-powered IoT applications. By carefully selecting the spreading factor, transmission power, and bandwidth, network designers can achieve a balance between communication reliability and energy efficiency. Additionally, adaptive strategies, such as dynamic parameter adjustment based on traffic conditions, can further enhance the energy efficiency of LoRa networks, extending the operational lifetime of battery-powered devices. While optimizing energy consumption is crucial for battery-powered LoRa devices, it is also essential to assess the LoRa performance over extended distances. To evaluate the LoRa performance over extended distances, additional simulations and practical experiments were conducted.