# On Performance Analysis of Protective Jamming Schemes in Wireless Sensor Networks
## 5 Numerical Results
### Comparisons of Different Schemes  
In the first set of results, we compare the probability of eavesdropping attacks \(P(E)\) of FJ-Ran scheme with that of Non-Jam scheme. Note that the larger node density \(\lambda_{2}\) in FJ-Ran scheme and the smaller \(d\) in FJ-Reg scheme imply the higher cost (i.e., more jammers are deployed in the network). As shown in Figure 3, the results of Non-Jam scheme are shown in a dash curve and the results of FJ-Ran scheme are shown in solid curves with markers, where we choose the different values of node density \(\lambda_{2}\) of friendly jammers (ranging from 0.2 to 2.0) and the value of node density \(\lambda_{1}\) of legitimate user is 0.5. It is shown in Figure 3 that the Non-Jam scheme always has higher values of \(P(E)\) than the FJ-Ran scheme, implying that _using friendly jammers in WSN can effectively reduce the probability of eavesdropping attacks_.  
It is also shown in Figure 3 that the probability of eavesdropping attacks \(P(E)\) decreases with the increment of jammers density \(\lambda_{2}\), implying that _adding more jammers can further improve the effect of mitigating eavesdropping attacks_. For example, when \(\alpha=4\) and the threshold \(T=5\) dB (as shown in Figure 3b), \(P(E)\) of the Non-Jam scheme is 0.719 while \(P(E)\) of FJ-Ran scheme is reduced to 0.393 with jammers density \(\lambda_{2}=0.8\) and 0.211 with jammers density \(\lambda_{2}=2.0\).  
In the second set of results, we compare the probability of eavesdropping attacks \(P(E)\) of the FJ-Reg scheme with that of the Non-Jam scheme. Figure 4 shows the results, where a dash curve represents \(P(E)\) of the Non-Jam scheme and solid curves with markers depict the results of FJ-Reg scheme. Similar to Figure 3, we find that using friendly jammers can always reduce the eavesdropping probability compared with the Non-Jam scheme. Moreover, it is shown in Figure 4 that the probability of eavesdropping attacks \(P(E)\) heavily depends on both the channel conditions and system parameter \(d\). Specifically, it is shown in Figure 4b that the probability of eavesdropping attack \(P(E)\) decreases with the decreased values of \(d\). In fact, the \(d\) in FJ-Reg scheme plays a similar role to jammer density \(\lambda_{2}\) in FJ-Ran scheme. In other words, decreasing \(d\) is equivalent to the effect of increasing jammer density \(\lambda_{2}\). Take Figure 4b as an example again. When the threshold is \(T=5\) dB and \(\alpha=4\), \(P(E)\) of Non-Jam scheme is 0.7176 while \(P(E)\) becomes 0.072 with \(d=0.2\), implying that using more friendly jammers can further reduce the eavesdropping probability.  
In the third set of results, we compare the probability of eavesdropping attacks \(P(E)\) of FJ-PC scheme with that of Non-Jam scheme. Figure 5 shows the results, where a dash curve represents \(P(E)\) of Non-Jam scheme and solid curves with markers depict the results of FJ-PC scheme. Similar to Figures 3 and 4, we find that using friendly jammers can always reduce the eavesdropping probability compared with the Non-Jam scheme. Furthermore, we also find that the FJ-PC scheme can further reduce the eavesdropping probability compared with FJ-Reg scheme. This is due to the power assigning strategy in our FJ-PC scheme. In particular, the eavesdropping capability of the eavesdropper is significantly weakened by the jammers in the first layer, which have been assigned with higher  
Figure 3: Probability of eavesdropping attacks \(P(E)\) with FJ-Ran scheme (PPP) versus Non-Jam scheme when \(\alpha=3,4,5\) with SINR threshold \(T\) ranging from 0 dB to 20 dB.  
power as they are much closer to the eavesdropper than other jammers in other layers. Another benefit of the FJ-PC scheme is that it has less impairment to legitimate communications compared with FJ-Reg and FJ-Ran schemes. The following results will further confirm this observation.