# Environmental Impacts on Hardware-Based Link Quality Estimators in Wireless Sensor Networks
## 5 Environmental Impacts on Hardware-Based LQEs
### Environmental Impacts on RSSI Based LQEs  
#### 5.2.1 RSSI and PRR in Different Environments  
Figure 7 shows the relationship between \(RSSI\) and \(PRR\) in different environments, including the minimum, maximum, and mean value of \(RSSI\). It can be seen that the trend of change between \(RSSI\) and \(PRR\) is basically the same for the three different environments. In terms of \(\mu_{rssi}\), \(PRR\) increases as \(\mu_{rssi}\) increase: when \(\mu_{rssi}\) is lower than \(-95\) dBm, \(PRR\) approaches 0; when \(\mu_{rssi}\) is higher than \(-90\) dBm, \(PRR\) approaches 100%; when \(\mu_{rssi}\) is located between \(-95\) dBm and \(-90\) dBm, \(PRR\) rapidly increases from 0 to 100%. In terms of the fluctuations of \(RSSI\), it is significantly greater in the corridor than that in the runway and artificial law.  
To observe the environmental impact on the relationship between \(RSSI\) and \(PRR\) more clearly, the relationship between \(\mu_{rssi}\) and \(PRR\) is shown in Figure 8. There already exist some studies which utilize the relationship between \(RSSI\) and \(PRR\) to estimate link quality [12; 19; 20; 26; 27]. Although the pattern between \(\mu_{rssi}\) and \(PRR\) is basically the same in different environments, it is not difficult to find out that there are still some differences among the relationships between \(\mu_{rssi}\) and \(PRR\) in different environments. For example, compared with the relationship between \(\mu_{rssi}\) and \(PRR\) in the runway, the relationship in the corridor translates to the right by about 2 dB. This means that the received signal power in the corridor should be 2 dB higher than that in the runway to get the same \(PRR\). The 2 dB difference may cause misjudgment of the link quality. For example, when \(\mu_{rssi}\) is \(-93\) dBm, \(PRR\) in the corridor is less than 10% which means a bad link, while \(PRR\) in the runway is greater than 90% which means a good link.  
Theoretically, the translation of the relationships between \(\mu_{rssi}\) and \(PRR\) should be caused by the difference in background noise. To confirm this conjecture, background noise in these different environments was measured. The noise power in the corridor, artificial lawn, and runway are \(-96.20\) dBm, \(-99.61\) dBm, and \(-98.37\) dBm, respectively. The difference between the corridor and the runway happens to be 2.17 dB. This indicates that translation of the relationships between \(\mu_{rssi}\) and \(PRR\) in different environments is indeed caused by the difference in background noise.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Runway** & **Lawn** & **Corridor** \\ \hline Theoretical model & 0.2862 & 0.4507 & 0.5304 \\ Fitting model & 0.3191 & 0.4402 & 0.4474 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The root mean square errors (RMSEs) of the mapping models in different environments.  
Figure 7: Received Signal Strength Indicator (\(RSSI\)) vs. \(PRR\) in different environments.  
To describe the impact of environmental changes on the fluctuation of \(RSSI\) more intuitively, the fluctuation ranges of \(RSSI\) in different environments were statistically obtained, and their cumulative distribution functions (CDFs) are shown in Figure 9. The fluctuation range of \(RSSI\) is calculated by subtracting the minimum \(RSSI\) from the maximum one. It can be seen that the fluctuation range of \(RSSI\) in the corridor is the largest, with about 30% of the fluctuation range higher than 10 dBm, and about 9.73% of the fluctuation range higher than 15 dBm. In contrast, the fluctuation range of \(RSSI\) in the artificial lawn is much smaller, with only about 10.91% of the fluctuation range higher than 5 dBm, and 100% of the fluctuation range lower than 10 dBm. The fluctuation range of \(RSSI\) in the runway is between that in the corridor and artificial lawn. The fluctuation range of \(RSSI\) is mainly determined by the number of propagation paths. The more the factors that cause signal reflection, diffraction, and scattering, the greater the fluctuation range of \(RSSI\).