## 4 Discussion  
Near-ground models proposed in the literature are scarce given that most actual radio channels are designed to be far above the ground [24; 26]. It has been known that lowering the antennas height would significantly decrease the signal strength [17; 25], therefore reducing the system range. This effect was described in [17] proposing a two-slope log-distance model for the path loss occurring in a WSN at 868 MHz in an open area. In Table 3 some models and experimental results reported in literature are briefly described, showing their scope and validity. The main conclusion to infer is that near-ground models require experimental measurements in order to validate the main propagation mechanisms occurring. Simulation-based solutions present limited scalability and remains restricted to specific environments and certain requirements [17; 24; 25; 26; 27; 28; 29; 30; 31; 32]. In the plots of Figure 4a, a basic comparison was performed between the measurement results, the proposed model and the free-space attenuation. Among the mentioned existing models, the one given in [23] was chosen as the closer approach to perform a comparison. Figure 7 shows a comparison between the proposed model, free-space and the model in [23]. This approach determines the path loss \(P_{L}\) as a two-slope log-normal trend dependent of the link range, according to the expressions in (14) and (15):  
\[P_{L}(d)=L_{fs}\quad,\ d<\ d_{b} \tag{14}\]  
Figure 6: BER for (**a**) \(H_{1}\) and \(B\) = 100 MHz; (**b**) \(H_{1}\) and \(B\) = 100 MHz; (**c**) \(H_{2}\) and \(B\) = 20 MHz; (**d**) \(H_{2}\) and \(B\) = 20 MHz. \[P_{L}(d)=L_{fs}+L_{NG}\quad,\ d\geq\ d_{b} \tag{15}\]  
with \(L_{fs}\) the free space path loss, \(L_{NG}\) is the near-ground path loss in dB and \(d_{b}\) is the minimum distance for the existence of near-ground path loss. The near-ground path loss \(L_{NG}\) is obtained as indicated in (16), also in dB:  
\[L_{NG}=-20\cdot log_{10}\left(\frac{5\sqrt{h_{t}h_{r}}}{3\sqrt{d\lambda}}+ \frac{35h_{t}h_{r}}{6d\lambda}\right) \tag{16}\]  
where respectively \(h_{t}\) and \(h_{r}\) are the heights of the transmitter and the receiver and \(\lambda\) is the wavelength [16]. The minimum distance for the existence of near-ground path loss is defined by (17):  
\[d_{b}=\frac{h_{t}h_{r}}{0.09\lambda} \tag{17}\]  
This expression is derived from assuming that the FFZ is obstructed in a 30% which represents half of the requirement for the existence of diffraction loss; in other words, the clearance \(h\) meets the expression in (18):  
\[h\leq\frac{1}{2}\cdot 0.6\cdot r_{1}=0.3\cdot\sqrt{d\lambda}\rightarrow\quad \ d\geq\frac{h}{0.09\lambda}\rightarrow\quad d_{b}=\frac{h}{0.09\lambda} \tag{18}\]  
For a more general case in which the transmit and receive antennas have different heights, \(h\) is replaced by \(h_{t}h_{r}\). Generally speaking, from the comparison in Figure 6 an over-estimation of the path loss maybe concluded, except for the tall grass case. An explanation may be found in the low effective antenna height of this type of ground. The model proposed in this paper seems to be more realistic for scenarios. Other recent models can be found, and even that not comparable to our case, the analysis used may result in interest for future on-going research: study over irregular terrain in 200-600 MHz [31], forest at 2.4 GHz [32], snow covered forest at 2.45 GHz [33], a ray-tracing tool for simulation [34] or a UWB near-ground wireless network [35].