# Comparison of Radio Frequency Path Loss Models in Soil for Wireless Underground Sensor Networks
## 3 Results and Discussion  
The measured attenuation of the EM signal transmitted through the soil in the container was compared with the estimated values for the attenuation calculated based on the modified-Friis and CRIM-Fresnel models. The initial test was carried out using a soil mixture of 90% sand and 10% clay, with a 19.4% gravimetric water content (GWC) and 10% sand and 90% clay, with a 19.1 % GWC. The result from the test can be seen in Figure 4.  
Figure 3: Final test setup showing hole spacing and grounded shielding. From Figure 4, it can be seen that the estimated attenuation of the signal by both models is broadly different as expected. In addition, it can be seen that the modified-Friis model provides a better estimation of the attenuation for the soil samples with high clay content while the CRIM-Fresnel model provides a better approximation for the soil with high sand content. These comparisons showed an inconsistency in the accuracy of the models across the range of soil compositions. The modified-Friis model is shown to have a better accuracy in soils with higher permittivity values compared to CRIM-Fresnel model while CRIM-Fresnel model provides a better approximation in lower permittivity soils. The test was repeated on more soil mixtures in terms of the proportions of sand and clay to get a better understanding of the applicability of the findings. Figure 5 shows the experimental attenuation values for a 434 MHz carrier frequency in samples with varying composition at 20% GWC as compared to the values predicted by the models in order to investigate the effect of clay content on model performance. As can be seen from Figure 5, the amount of clay present in the soil has a direct effect on the attenuation of the signal; with an increase in clay content comes a rise in the attenuation of the signal. This is in line with the literature [15; 21]. It can also be seen from this figure that both the CRIM-Fresnel and the modified-Friis models fail to estimate the attenuation of the signal accurately for all the soil compositions. However it can also be seen from this figure that the CRIM-Fresnel provides a better estimation at lower clay content samples compared to the modified-Friis model. For example at 10% clay content the modified-Friis model had a root mean square error (RMSE) of 16.6 while CRIM-Fresnel model had an RMSE of 2.35. In contrast the modified-Friis model estimated the attenuation of the signal in higher clay content samples with higher accuracy compared to the CRIM-Fresnel model. As an example, in the sample with a 90% clay content the modified-Friis model had an RMSE of 1.13, while the CRIM-Fresnel model had an RMSE of 6.67. To understand the effect of GWC on the models prediction accuracy the attenuation values for a 434 MHz carrier frequency in soil samples with 50% clay and 50% sand and with varying GWC were measured; the results as compared to the simulation values are displayed in Figure 6.  
Figure 4: Comparison of the radio frequency (RF) models for two soil mixtures. Figure 5: Effect of clay content on attenuation of signal and comparison of Modified-Friis and CRIM-Fresnel. Figure 6: Effect of gravimetric water content (GWC) on prediction accuracy of RF transmission models for the 50% Clay and 50% Sand sample. Both of the models failed to provide an accurate estimation for samples at all of the GWC range. However, based on the RMSE values of the models at different gravimetric water contents, the modified-Friis model provided a better estimation at lower GWC compared to the CRIM-Fresnel model. As an example at 10% water content the modified Friis had an RMSE value of 3.54, while CRIM-Fresnel model had an RMSE of 8.59. In contrast, at 30% GWC the modified Friis model had an RMSE value of 14.85 while the CRIM-Fresnel model had an RMSE of 3.52, which shows that the CRIM-Fresnel model provides a better estimation at higher water content values.