# Path Loss Determination Using Linear and Cubic Regression Inside a Classic Tomato Greenhouse
## 3 Results and Discussions  
During the field-tests, omnidirectional antennas were used in each node because they were traditionally used on agricultural deployments for WSN devices for the purpose of cover links P2 MP (point-to-multipoint communication) and MP2 MP (multi-point to multi-point) in a real solution. The height of the transmitter and receiver omnidirectional antennas during the tests carried out inside the greenhouse were 30 cm, 50 cm, 70 cm, 90 cm, 100 cm, 150 cm, and 200 cm from the ground. Based on the power levels recorded at the receiving node, the largest and smallest measured ranges were when the antenna height of the transmitting node (Tx) and receiver (Rx) were both 0.5 m and 1.5 m respectively using the 2.4 GHz band (Figure 5).  
Figure 4: Tomato greenhouse diagram and WSN deployment layout in the tests. (**A**) View from above, (**B**) transverse view.  
Figure 5: Signal level in dBm and maximum coverage between the transmitting node (Tx) and receiver (Rx) node at different heights with respect to the ground (30 cm, 50 cm, 70 cm, 90 cm, 100 cm, 150 cm, and 200 cm).  
Table 2 compares the attenuation values in the greenhouse (empirical PL) with respect to the separation distance of the nodes Tx and Rx measured in meters, when they were located 0.5 m and 1.5 m above the ground. The separations between the nodes were initially 2.6 m and then increased steadily by 1.8 m due to the plantation frame that has the scheme of Figure 4. The variations of the values in the attenuations were due to the conformation in the structure of the vegetation different heights. On average, in our case study, the highest density in vegetation consisting of stems, leaves and fruits was at a height of 1.5 m.  
With the Tx and Rx nodes at 0.5 m from the ground, the results obtained in the field tests were compared with the models with LOS (Line of Sight), the FSPL (Free-Space Path Loss) and two-ray with the graphs of curves shown in Figure 6A. In addition, the COST235, FITU-R, ITU-R, and Weissberger models were added to the losses of the unobstructed path corresponding to the corridors and spaces between floors with the FSPL and two-ray models in 6B and 6C respectively. From all these graphs it was concluded that the closest models were two-ray and Weissberger, adding the attenuation of two-ray. Analogously it is the analysis in Figure 7A-C working with the nodes Tx and Rx at 1.5 m above the ground.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{10}{c}{**Distance (m)**} \\ \cline{2-13}  & **2.6** & **4.4** & **6.2** & **8** & **9.8** & **11.6** & **13.4** & **15.2** & **17.0** & **18.8** & **20.6** & **22.4** & **24.2** \\ \hline Empirical PL (dB) & 26.8 & 28 & 31.86 & 36.38 & 38 & 42.5 & 47 & 51 & 55.13 & 56.5 & 58.44 & 65 & 74 \\ \hline Empirical PL (dB) & 34.22 & 50.43 & 57.25 & 60.85 & 64.89 & 70.11 & 73.33 & - & - & - & - & - \\ at 1.5 m & & & & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Total attenuation of the propagation of the radio wave in the presence of vegetation with nodes at 0.5 m and 1.5 m from the ground.  
Figure 6: Field measurement at 0.5 m of soil vs. (**A**) models with line of sight (LOS), (**B**) empirical models + FSPL, (**C**) empirical models + two-ray, (**D**) optimized model (linear regression) and the others closest in values.