## 3 Results and Discussion
### Model Selection and Application for Short-Range Propagation in a Corn Field  
In this section, we present the propagation data and compare the measured path loss to different propagation models to find the model(s) that best represent the propagation characteristics in a corn field in several scenarios of smart agriculture applications. Calculation of Path Loss  
The measured path loss \(\mathrm{L_{M}}\) in dB as a function of the distance (d) is computed using the following formula [42]:  
\[\mathrm{L_{M}(d)=P_{T}+G_{T}+G_{R}-P_{R}(d),} \tag{1}\]  
where:  
* \(\mathrm{P_{T}}\) is the transmitted power (which remains constant \(\mathrm{P_{T}=0\ dBm}\));
* \(\mathrm{P_{R}}\) (in dBm) is the received power, varying as a function of distance;
* \(\mathrm{G_{T}}\) and \(\mathrm{G_{R}}\) represent the gains of the transmitting and receiving reference dipole antennas, which are both 2.15 dBi. Figures 9-12 show comparisons of the measured path loss for various scenarios, with predictions from two of the most commonly used models predicting the additional attenuation of a wireless link passing through vegetation--the Weissberger and COST-235 models [43, 44]. These models are modified exponential decay models and have the generic form given by [45]:  
\[\mathrm{L(f,d)=A\times F^{B}\times d^{C},} \tag{2}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Frequency *} & **Transmitting Antenna** & **Receiving Antenna** & **Maximum Communication** \\  & **(Tx) Height ** & **(Rx) Height ** & **Distance Between Tx and Rx ** \\ \hline \multirow{4}{*}{0.9} & 0.11 & 2.0 & 90 \\  & 0.11 & 3.4 & 105 \\  & 0.50 & 2.0 & 140 \\  & 0.50 & 3.4 & 140 \\ \hline \multirow{4}{*}{2.4} & 0.04 & 2.0 & 40 \\  & 0.04 & 3.4 & 45 \\ \cline{1-1}  & 0.50 & 2.0 & 45 \\ \cline{1-1}  & 0.50 & 3.4 & 65 \\ \hline \hline \end{tabular}  
* The frequency indicated in the table is in GHz. ** The antenna height and distance indicated in the table are in meters.  
\end{table} 
Table 2: Maximum communication distance between Tx and Rx at co-polarized H-H antennas. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Frequency *} & **Transmitting Antenna** & **Receiving Antenna** & **Maximum Communication** \\  & **(Tx) Height ** & **(Rx) Height ** & **Distance Between Tx and Rx ** \\ \hline \multirow{4}{*}{0.9} & 0.11 & 2.0 & 80 \\  & 0.11 & 3.4 & 100 \\  & 0.50 & 2.0 & 120 \\  & 0.50 & 3.4 & 110 \\ \hline \multirow{4}{*}{2.4} & 0.04 & 2.0 & 40 \\  & 0.04 & 3.4 & 45 \\ \cline{1-1}  & 0.50 & 2.0 & 20 \\ \cline{1-1}  & 0.50 & 3.4 & 65 \\ \hline \hline \end{tabular}  
* The frequency indicated in the table is in GHz. ** The antenna height and distance indicated in the table are in meters.  
\end{table} 
Table 3: Maximum communication distance between Tx and Rx at co-polarized V-V antennas. where:  
L is attenuation loss in dB;  
F is the frequency in MHz or GHz;  
d is the depth of the vegetation along the line-of-sight path in meters;  
A, B, and C are model parameters. They are presented in Table 4.  
The additional attenuation caused by vegetation for each model is added to the basic free-space loss to calculate the predicted path loss shown in Figures 9-12. The basic free-space transmission loss (Lbs) in decibels (dB) is calculated by [46]:  
\[\text{L}_{\text{bs}}\text{(f,d)}=32.4+20\text{logF}+20\text{logd} \tag{3}\]  
where:  
F is the frequency in MHz;  
d is the distance in kilometers. In the Weissberger and COST-235 models for transmission loss in the vegetation, the loss between antennas is expressed as the sum of free-space basic transmission loss, Lbs, and additional loss, L, such as foliage losses in crop or forestry scenarios [43]. In addition, in the modified exponential decay models, Lbs and L are frequency- and distance-dependent and independent of the antenna height.