# A New Approach to Estimating the Path Loss in Underground Wireless Sensor Networks
## 4 Results and Discussion  
The soil from each of the locations was characterised in the laboratory using British Standard 1377-2 [30]. The results from the soil characterisation tests for all of the locations (A, B and C) are presented in Table 1.  
Table 1 shows a large difference between the soil types and conditions at the locations used for the trials. This helps to investigate the performance of the proposed method in a wide range of input parameters. As can be seen from Table 1, the soil from location C had a significantly higher water content compared to locations A and B. The soil from location C also had a considerably higher conductivity compared to the other two locations. Figures 4-6 illustrate the measured attenuation of the signal at locations A, B and C respectively. At location A, it was only possible to record two attenuation measurements; one at 0.2 m and one at 0.4 m (depth) from the transmitter. This was due to the practical limitations (i.e., equipment and location) during tests carried out at location A. The methodology for the tests was refined for locations B and C. At location B, five transmitter receiver distances were measured; and at position C, attenuation over three distances were measured as seen in Figures 4-6. The predicted values for the RF attenuation for each of the soils were calculated using the CRIM-Fresnel, conventional Modified-Friis and the alternative Modified-Friis (i.e., using TDR measurements) models, and are also displayed in Figures 4-6 for comparison. The error bars in these figures represent the maximum and minimum reading at each point. As can be seen from the results at all of the locations (Figures 4-6) the Modified-Friis model, using both the conventional and the alternative TDR methods of permittivity estimation, provided a better approximation for the attenuation of the signal in soil compared to the CRIM-Fresnel method. The Root Means Squared Error (RMSE) of these models was calculated in order to compare their 'performance' in predicting the RF attenuation with distance from the transmitter over the distance measured (see Table 2). As shown in Figure 4 at location A, the CRIM-Fresnel model under-estimates the attenuation of the signal (RMSE = 13.59). The conventional Modified-Friis model provided a significantly better approximation (RMSE = 3.06) compared to the CRIM-Fresnel model. However, the estimation of attenuation based on the Modified-Friis model using values obtained from TDR provided the best \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Location**} & \multicolumn{3}{c}{**RMSE**} \\ \cline{2-4}  & **CRIM-Fresnel** & **Modified-Friis (Conventional)** & **New Modified-Friis** \\ \hline A & 13.59 & 3.06 & 2.85 \\ B & 12.31 & 7.00 & 4.19 \\ C & 11.58 & 1.47 & 1.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: RMSE for the different models. Figure 5: Comparison of the measured attenuation with the propagation models (location B). Figure 6: Comparison of the measured attenuation with the propagation models (location C). estimation (RMSE = 2.85) compared to the other two methods. As can be seen from Figure 5, and similar to location A, the CRIM-Fresnel model failed to provide an acceptable estimation for the attenuation of the signal at location B (RMSE = 12.31). Figure 5 also shows that both the Modified-Friis estimation models (conventional and TDR based) provided a better estimation for the attenuation of the signal compared to the CRIM-Fresnel model. However, similar to location A, the TDR based Modified-Friis model performed better (RMSE = 4.19) than the conventional Modified-Friis model (RMSE = 7.00) at predicting the RF attenuation over the distances measured. Finally, from Figure 6 it can be seen that the performances of the estimation models at location C were very similar to the other two locations despite the considerable difference between the soil type and condition at this location compared to locations A and B.