# Environmental Impacts on Hardware-Based Link Quality Estimators in Wireless Sensor Networks
## 5 Environmental Impacts on Hardware-Based LQEs
### Environmental Impacts on SNR Based LQEs
#### 5.3.2 Environmental Impacts on SNR Based LQEs  
Using Equation (8), the theoretical model between \(\mu_{sur}\) and \(PRR\) was plotted, as shown in Figure 16. The measured data in all three environments are not coincident with the theoretical model. There is an obvious deviation from the model to the measured data. To describe the environmental impact on the theoretical model between \(SNR\) and \(PRR\) quantitatively, RMSE of the estimated \(PRR\) and real \(PRR\) in the three environments were calculated, as shown in the first row of Table 5. It can be seen that RMSEs in all three environments are quite large.  
It looks like that the theoretical model between \(SNR\) and \(PRR\) is invalid. However, when getting down to the details, we can find that the calculation of \(SNR\) in Equation (16) is problematic. \(SNR\) is calculated by subtracting the measured noise power (\(N\) in dBm) directly from the measured signal power (\(RSSI\) in dBm). However, the transceiver only measures the power at the antenna without attempting to distinguish whether it is due to signal or noise. That is to say, the noise power also contributes to the \(RSSI\) value. Therefore, the actual ratio of the signal power to noise power should be:  
\[\gamma=\frac{P_{RSSI}-P_{N}}{P_{N}}=\frac{P_{RSSI}}{P_{N}}-1=10^{\frac{RSSI-N}{ 10}}-1 \tag{17}\]  
where \(P_{RSSI}\) and \(P_{N}\) are corresponding values in mW for \(RSSI\) and \(N\), respectively. Consequently, the \(SNR\) in dB should be expressed as follows  
\[SNR=10\log_{10}\left(10^{\frac{RSSI-N}{10}}-1\right) \tag{18}\]  
Figure 17 shows the theoretical model after correction. It is obvious that after correction, the theoretical model coincides well with the measured data. The relationship between \(SNR\) and \(RSSI\)-\(N\) is also shown in Figure 17. It can be seen that the actual \(SNR\) is nonlinear with \(RSSI\)-\(N\), especially when \(RSSI\)-\(N\) is small. That explains why the original theoretical model deviates from the measured data, especially when \(SNR\) is small, as shown in Figure 16.  
Figure 16: Effects of the theoretical model in different environments.  
\begin{table}
\begin{tabular}{c c c c} \hline  & **Runway** & **Artificial Lawn** & **Corridor** \\ \hline Theoretical model before calibration & 0.3009 & 0.1909 & 0.1749 \\ Theoretical model after calibration & 0.1253 & 0.0609 & 0.1442 \\ LR model after calibration & 0.1154 & 0.0659 & 0.1284 \\ \hline \end{tabular}
\end{table}
Table 5: RMSEs of \(SNR\) based LQEs in different environments.  
Using Equation (9), the LR model between \(SNR\) and \(PRR\) was plotted, as shown in Figure 18. From Figure 18, it is obvious that estimated values gained by the LR model basically coincide with the measured data.  
RMSEs of the estimated \(PRR\) and real \(PRR\) in three environments were also calculated for the theoretical model after correction and the LR model, as shown in Table 4. After correction, RMSEs of the theoretical model in all three environments are reduced effectively, which means that the proposed calculation method of \(SNR\) is reasonable. Compared with the runway, RMSE of the theoretical model in the artificial lawn reduces by 51.40%, but RMSE in the corridor increases by 15.08%. Compared with the runway, RMSE of the LR model in the artificial lawn reduces by 42.89%, but RMSE in the corridor increases by 11.27%. That is to say, the \(SNR\) based LQEs are almost unaffected by environmental changes.