# An Efficient Location Verification Scheme for Static Wireless Sensor Networks
## 6 Performance Evaluation
### Effect of Network Density  
The location verification schemes considered in this paper make use of the information from neighbors, so the number of neighbors affects the verification performance. The number of neighbors for each sensor can be adjusted by controlling the network's density, which is a combination of the total number of sensors and the distribution of sensor deployment in the field. Figure 13(a) shows the verification performance of the MSRLV in terms of network density. In the figure, the total number of sensors is displayed on the x-axis. On the y-axis, the percentage of the malicious sensors being successfully rejected by the MSRLV is displayed. Each line graph corresponds to the srr according to the combination of sensor deployment strategies and types of malicious sensors. The behavior of the attackers is set to either dumb or smart in each scenario. Smart attackers in this experiment fake their location by adjusting the angle by 10 degrees.  
As shown in Figure 13(a), verification performance generally improves as sensor density increases. This is because location verification depends on the implicit help of neighbors. Given that a sensor must be in the EMSR to correctly filter out malicious sensors, the more neighbors there are, the greater the chance that malicious sensors will be correctly filtered out. This result also accords with the relationship defined in Equation 5. Dumb attackers have a relatively high, stable srr across conditions, which indicates that D-filtering works well.  
One interesting point is that the performance of the MSRLV significantly drops around 300 sensors in the network and recovers as the number of sensors increase. Under 300 sensors in the network, sensors are deployed 16 m away from each other. The majority of sensors in this situation do not have any neighbor in common, which makes the token value zero. This affects the performance because the scheme is designed to accept the same token as the successful verification, which means the sensor is classified as the honest one. Thus, the malicious sensors in this sparse network might be also classified as the honest ones. If this zero token is taken as the abnormal state of the sensor, the honest sensor will be considered as the malicious one, which leads to the increase of the successful and false rejection rate. The acceptance of this zero token can be determined by the policy of the service. However, as the number of sensors increases, any two sensors will have enough common neighbors, which results in the recovery of the successful rejection of malicious sensors.  
Figure 14: Successful rejection rate.  
The other point worth mentioning is the performance peak of the grid deployment scenario with the dumb attacker under 200 sensors. In this case, sensors are located 20 m away from each other. A malicious sensor's attempt to fake its location toward a certain sensor will cause the situation that its location becomes out of communication range to the other sensors. This situation is interpreted as verification failure, so the srr increases.  
In the case of the uniform random deployment scenarios, performance increases rapidly at the lower end of the density conditions because smart attackers have more physical empty space to fake in, as shown in Figure 13, though the benefits of this effect decrease exponentially as density increases linearly.  
According to this result, it is obvious that the proposed scheme is not practical in the network with less than four neighbors. The network may become sparse because sensors can lose their function due to energy exhaustion or a harsh environment. However, it is reasonable to expect that the network would have more than five neighbors when considering usual applications of WSNs, such as machine diagnosis, vehicle tracking, smart homes or habitat monitoring [29].