## 3 Results and Discussion
### Model Selection and Application for Short-Range Propagation in a Corn Field
Furthermore, the results presented in Figures 5-8 and Tables 2 and 3 in Section 3.1 indicate that radio wave propagation in the corn field is impacted not only by the surrounding environment (i.e., corn), but also by the positions of the transmitting and receiving antennas relative to the ground. Hence, to include the effects of the antenna height, we compare the results with the multi-slope model (two slopes and a single breakpoint). In the model, the path loss, L, is assumed to increase with a given slope up to a 'breakpoint'. Beyond this point, the slope becomes steeper. The L in dB is given by [42]:  
\[\text{L}\text{(d)}= \begin{cases}10n_{1}logd+L_{1},&d\leq d_{bp}\\ 10n_{2}log\left(\frac{d}{d_{bp}}\right)+10n_{1}logd_{bp}+L_{1},&d>d_{bp}\end{cases}  \tag{4}\]  
where:  
L is a value for the basic transmission loss at the d = 1 m;  
d is the distance in meters;  
dbp is the breakpoint distance in meters and is given by:  
\[d_{bp}=(4h_{Tx}h_{Rx})/\lambda, \tag{5}\]  
where:  
\(\lambda\) is the wavelength in meters;  
hTx is transmitting antenna height in meters; \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{6}{c}{**Basic Input Parameters**} \\ \hline
**Model Names** & **A** & **B** & **C** & **n\({}_{1}\)** & **n\({}_{2}\)** & **Frequency Units** & **Note** \\ \hline Weissberger * & 1.33 & 0.284 & 0.588 & - & - & GHz & 14 m \(<d\leq\) 400 m \\  & 0.45 & 0.284 & - & - & - & GHz & 0 m \(<d<\) 14 m \\ \hline COST-235 ** & 15.6 & \(-\)0.009 & 0.26 & - & - & MHz & in leaf \\  & 26.6 & \(-\)0.2 & 0.5 & - & - & MHz & out of leaf \\ \hline Multi-slope model & - & - & - & 2.0 & - & - & \(d\leq d_{bp}\) \\  & - & - & - & 2.0 & 4.0 & - & \(d>d_{bp}\) \\ \hline \hline \end{tabular}  
* The range of frequencies for the Weissberger model is from 0.23 GHz to 9.2 GHz. ** The range of frequencies for the COST-235 model is from 9.6 GHz to 57.6 GHz.  
\end{table} 
Table 4: Basic input parameters values for Weissberger, COST-235, and Multi-slope models. * h\({}_{\rm Rx}\) is receiving antenna height in meters;
* n\({}_{1}\) and n\({}_{2}\) are model parameters. They are presented in Table 4.  
For each data set (communication scenario in corn field) and each model, we present in Tables 5 and 6 the mean absolute percentage error (MAPE), in %, to compare the prediction accuracies of the path loss models. The MAPE is given by:  
\[\text{MAPE}=\frac{100}{n}\sum_{i=1}^{n}\frac{|L_{\text{MI}}-\frac{L_{\text{MODEL}} |}{L_{\text{MI}}}|}{L_{\text{MI}}} \tag{6}\]  
where:  
Figure 9: Comparison between losses for co-polarized H-H antennas at transmitting antenna height: \(\lambda/3\) m with existing models: (**a**) 0.9 GHz, h\({}_{\rm Rx}\) = 2.0 m; (**b**) 0.9 GHz, h\({}_{\rm Rx}\) = 3.4 m; (**c**) 2.4 GHz, h\({}_{\rm Rx}\) = 2.0 m; (**d**) 2.4 GHz, h\({}_{\rm Rx}\) = 3.4 m.  
* \(n\) is the number of measurements;
* \(\rm L_{M}\) and \(\rm L_{MODEL}\) represent measured and predicted path loss, respectively, and \(i\) is the index of each sample. Figures 9 and 10 illustrate the comparison between predictions of the Weissberger, COST-235, and Multi-slope models and measured losses at the near-ground installation of the sensor node in the corn field, i.e., for transmitting antenna height \(\lambda/3\) m at two frequencies (0.9 GHz and 2.4 GHz) and two receiving antenna heights (2.0 m and 3.4 m) for H-H (Figure 9) and V-V (Figure 10) polarized antennas. From Figure 9 and Tables 5 and 6, we can observe that, when using co-polarized H-H antennas for near-ground sensor node installation in a corn field, the COST-235 model overestimates the path loss at 0.9 GHz and 2.4 GHz, while the Weissberger model underestimates the path loss. Among these models, the Multi-slope model demonstrates the highest accuracy for this data set: 6.7% (\(\rm h_{Rx}\) = 2 m, 0.9 GHz) and 9.8% (\(\rm h_{Rx}\) = 2 m, 2.4 GHz), as shown in Table 5, and 8.3% (\(\rm h_{Rx}\) = 3.4 m, 0.9 GHz) and 12.2% (\(\rm h_{Rx}\) = 3.4 m, 2.4 GHz), as shown in Table 6, respectively.