# Clustering-Based Energy-Efficient Self-Healing Strategy for WSNs under Jamming Attacks
## 3 System Model  
We assume \(N\) sensor nodes are distributed in a flat square area of \(H\times H\) meters. The sensor nodes communicate with a gateway (or sink) node located in the center of the square area, as shown in Figure 1. The distance of pairwise nodes is expressed as \(D\). The WSN nodes use time division multiple access (TDMA). Moreover, the nodes are static, and their positions are known to all nodes. This information allows each node to execute clustering algorithms in a distributed way and previously know the most convenient associations. When the system operates in cooperative mode, all the nodes can assume a relay role and use TDMA to transmit their data. Additionally, we assume that nodes can implement techniques that allow them to estimate the presence and location of a static jammer. Although this point is out of the scope of this work, note that nodes can implement energy detection techniques and share this information with neighbors, which would allow the execution of location techniques. For a better understanding of jammer localization in multi-hop wireless networks, the following survey [41] can be consulted. Moreover, there are recent jammer location techniques that are efficient even in the face of jammer mobility [42] and of multiple jammers [43].  
The scenario considers a flat outdoor environment. We assume that no obstacles are in the line-of-sight (LOS) between the nodes. Moreover, we assume that the jammer's location is determined by its decision, but we limit ourselves to considering the most representative potential locations to carry out a viable number of experiments.  
It might be thought that the self-healing capability is not required for WSNs, considering that a UAV can fly over each sensor node and collect information from it, as described in [37]. However, from the analysis of [37], we can conclude that collecting information from all nodes in a network is an energetically expensive task, especially in WSNs with many nodes. In such scenarios, guaranteeing the freshness of the information would be an infeasible task for a single UAV. Therefore, if a network is attacked and its nodes are isolated from the sink, it is convenient for the network to be capable of self-healing, at least in interconnected groups, in such a way that the UAV would only have to collect information from the leader of each group.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reference** & **Power Allocation** & **Cooperation** & **Self-Healing** & **UAV** & **Jamming Scenarios** \\ \hline LEACH [8] & ✓ & - & - & - & - \\ SecLEACH [14] & ✓ & - & ✓ & - & - \\ Armor-LEACH [15] & ✓ & - & ✓ & - & - \\ MS-LEACH [16] & ✓ & - & ✓ & - & - \\ SEC [17] & ✓ & - & ✓ & - & - \\ Enhanced SLEACH [19] & ✓ & - & ✓ & - & - \\ [PERSON] [22] & - & ✓ & ✓ & - & - \\ [PERSON] [23] & - & - & ✓ & - & - \\ [PERSON] [25] & - & ✓ & - & - & - \\ [PERSON] [31] & - & - & ✓ & - & - \\ [PERSON] [33] & - & ✓ & ✓ & - & ✓ \\ [PERSON] [34] & - & ✓ & - & - & - \\ [PERSON] [35] & ✓ & ✓ & - & - & - \\ [PERSON] [36] & - & - & - & ✓ & - \\ [PERSON] [37] & - & - & - & ✓ & - \\ [PERSON] [38] & - & - & - & ✓ & - \\ [PERSON] [39] & - & - & ✓ & ✓ & ✓ \\ [PERSON] [40] & ✓ & - & - & ✓ & - \\ Our Proposal & ✓ & ✓ & ✓ & ✓ & ✓ \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison with related work.