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10.5.3 Performance Evaluation > Sensitivity of Performance Improvement Under Ne... - Pg. 270

270 CHAPTER 10 500 400 300 200 100 0 0 100 Defending Against Physical Attacks in Wireless Sensor Networks 500 400 300 200 100 0 200 300 400 (a) With defense. 500 0 100 200 300 400 (b) Without defense. 500 FIGURE 10-6 Instant alive sensors at time 10000 s. cannot be delivered to the base station. If the only functional component is not large enough, the network is regarded as unfunctional. Our cur- rent metric AC does not consider the network partitioning, which is part of our future work. We expect that the performance improvement of our defense protocol will be even more signifi- cant under the new metric. Here, we only show one instant case because of space limitation. We observe similar patterns under various parame- ters and other time instances. Sensitivity of Performance Improvement Under Network Parameters. In the following, we will investigate the sensitivity of performance improvement under two key network parame- ters, which are network density and active signal frequency. We will change the number of sensors N while fixing the size of the field. The number of sensors varies between 1000 and 5000. It is easy to calculate that the corresponding average number of neighbors for a single sensor varies between 5, which corresponds to a sparse net- work, and 25, which is a dense network. The active signal frequency f ranges from 1 packet per 10 s to 1 packet per 100 s, which captures the sampling rate of most sensor network appli- cations. In Figure 10-7(a), we show the AC achieved by our defense protocol under different combi- nations of sensor number N and active signal frequency f . It is obvious that AC decreases when f increases. What's interesting is that there exists a threshold of f at around 1 packet per 60 s. When f is smaller than the threshold, AC decreases slightly with the increase of f . How- ever, beyond the threshold, AC decreases sharply with the increase of f . This is because for small f , sensors send out active signals infrequently, so most sensors are detected by passive signals. In this case, decreasing f brings little extra benefit. Contrarily, when f is above the threshold, most sensors are detected by active signals due to the high frequency of packet sending and the fact that R as is usually larger than R ps . In this case, active signals dominate the effectiveness of attack and increasing f will significantly affect the perfor- mance. The existence of the threshold can help the network designer to choose a reasonable f to make a good tradeoff between security and network performance. Although a small f helps to improve security, it may decrease the network performance by introducing a long delay between sensor sampling/event detection and sending our active signal. An f , a little smaller than the thresh- old, can achieve reasonable security while intro- ducing little compromise to the network perfor- mance. Interestingly, we observe a similar effect of N on AC . First, AC increases with N due to the redundancy in a more dense network. With the