# Adaptive Jamming Mitigation for Clustered Energy-Efficient LoRa-BLE Hybrid Wireless Sensor Networks
## 4 Results and Discussion
### Histogram with Probability Density Function  
From this analysis, we can determine whether the energy consumption follows a normal distribution, is skewed towards lower or higher values, or exhibits multiple peaks. A narrow and tall peak suggests that most energy values cluster around a specific range, indicating a consistent and predictable energy consumption pattern. In contrast, a wider or multi-modal distribution suggests fluctuations and inconsistencies in energy usage. If BLE exhibits a tight peak at lower values, it confirms that it is the most energy-efficient. If LoRa shows a wider and flatter distribution, it suggests more variability in energy demand, which could stem from varying transmission distances. The BLE+LoRa configuration, ideally, should demonstrate a balanced peak that does not lean too much towards either extreme, indicating an adaptive trade-off between efficiency and performance. Furthermore, the histogram helps in identifying potential inefficiencies. If a network protocol has a long tail extending toward higher energy values, it implies occasional spikes in energy consumption, which could lead to battery drain issues in IoT devices. The presence of these spikes in the BLE+LoRa configuration would indicate that switching between protocols sometimes results in suboptimal energy efficiency, depending on network conditions. Figure 12 presents the energy consumption distribution through a histogram and probability density function (PDF), highlighting the statistical characteristics of each communication mode under jamming conditions. BLE exhibits a narrow and sharply peaked distribution, reinforcing its status as the most energy-efficient protocol, albeit with noticeable sensitivity to interference, which causes occasional spikes in energy usage. LoRa, on the other hand, has a broader distribution, with a long rightward tail, indicating inconsistent but generally higher energy consumption, particularly during retransmissions caused by jamming. The BLE-LoRa switching mechanism displays a uniform distribution, with a peak aligning more closely with BLE, suggesting improved efficiency and reduced unnecessary protocol transitions. This finding underscores the importance of adaptive network management in hybrid communication systems, demonstrating that intelligent switching mechanisms can achieve a balance between energy efficiency and network resilience. These insights emphasize the necessity of real-time decision making in protocol selection to minimize energy wastage and enhance the sustainability of wireless sensor networks in challenging environments. Figure 12 was constructed based on experimental data collected from real-world jamming scenarios in a heterogeneous LoRa-BLE wireless sensor network. The dataset consists of the energy network performance metric recorded over multiple controlled experiments conducted within a university campus environment. The data were sampled at regular intervals, ensuring uniform time distribution across different interference conditions. Each recorded data point corresponds to a measurement taken from sensor nodes deployed in varying locations, including laboratories, classrooms, and open areas, where interference sources such as Wi-Fi networks and mobile devices were present. To generate the histograms, we used a binning strategy that appropriately reflects the data distribution without introducing bias or excessive granularity. The number of bins was determined using the Freedman-Diaconis rule, which balances the need for detailed resolution with statistical significance. The sampling methodology ensured data representativeness by incorporating different interference intensities and network conditions. We performed preprocessing steps such as outlier detection and removal using interquartile range (IQR) filtering to eliminate potential anomalies that could distort the statistical representation.