# Random Access Performance of Distributed Sensors Attacked by Unknown Jammers
## 3 RA Performance Analysis
### Access Delay of Random Access Request
However, code jammers further degrade the throughput compared to power jammers over all \(G\) tested. Figure 3: Success probability of the preamble transmission when \(G=3\). Figure 2: Success probability of the preamble transmission when \(G=1\). Figure 6 compares the access delay \(D_{T}\) of final MSG transmission for increasing offered traffic \(G\), where code and power jamming attacks with 1-3 jammers are considered, respectively. The result in Figure 6 certainly matches that in Figure 5. If the same number of jammers is considered, the delay with code jamming is greater than that with power jamming over all \(G\) tested, which is a similar trend that can be expected from Figure 5. When \(G=2\), 27%, 34%, 40%, 56%, 40% and 65% of greater  
Figure 4: Success probability of the preamble transmission when \(G=5\). Figure 5: Throughput of the message transmission. delay than without-jamming result due to 1 power jammer, 1 code jammer, 2 power jammers, 3 power jammers, 2 code jammers and 3 code jammers, respectively. When \(G=3\), the amount of delay increase is not distinguishable with the numbers of power jammers. Moreover, when \(G=4\), the delay with and without power jamming becomes equal due to overwhelming interference. However, code jammers further increase the delay compared to power jammers over all \(G\) tested. From the above numerical investigations, we can address two ideas to detect whether the jammers exist or not if HS has certain measurement data, the implementation of which would be left for future study. One is using the concave throughput graphs achieved in Figure 5. We assume that HS have measurement data on received power (RxP) vs. throughput without jammers. Since the offered load cannot be directly measured, RxP is used to estimate the load. The jammer seems to generate additional interference, by which HS may overestimate the offered load since it has accordingly low throughput. For example, with one power jammer, the throughput in Figure 5 is about 0.47 when \(G=2.0\), which can be achieved when either \(G=1.2\) or 3.0 if the jammer does not exist. Let us assume that 0.47 is the current throughput seen at HS. If HS has the measurement data, then HS can judge whether current 0.47 is due to the low load or possibly due to the jammer. Let us denote the RxP measured when the throughput is 0.47 by \(R_{1}\) and \(R_{2}\) (\(R_{1}\leq R_{2}\)), which represent two different loads \(G=1.2\) and 3.0 (noting that both provide the same throughput 0.47), respectively. Of course, HS does not know \(G\) exactly, but understands that throughput 0.47 is achieved by different load conditions: low and high, respectively. If current RxP is approximately equal to \(R_{1}\), then the throughput is due to low load. However, if it is much greater than \(R_{1}\), HS sends a signaling message that temporarily prevents each SN from sending preambles with certain probability \(p(0<p<1)\). Then, the load should be increased if throughput 0.47 is due to the high load. Otherwise, the load should be decreased, and there probably exits a jammer. The other idea is using the monotonically increasing delay graphs in Figure 6. If HS is assumed to have measurement data on RxP vs. delay without jammers, then it can guess that the current excessive delay is possibly due to jamming powers. Other methods to avoid or detect jamming such as using directional antennas are intensively summarized in [23]. Figure 4.0 Average delay in the message transmission.