## 5 Results
### Model Comparison  
The RSSI data were collected herein for 433 MHz LoRa channels, and then analyzed. The data comparison was then used to represent the path loss models' behavior. To compare our RSSI and path loss models, the received signals were obtained through Equation (28):  
\[RSSI(dB)=Pt+Gt+Gr-Path\ loss \tag{28}\]  
where \(Pt\) is the transmitting power (\(dB\)), and \(Gt\) and \(Gr\) are the gains of the transmitting and receiving antennas, respectively.  
Figure 11: FLR curves for one person moving with membership level 0.0.  
Figure 12: FLR curves for RSSI with two people blocking at membership level 0.0.  
The RMSE was calculated as follows to observe the deviation of the measurement and related empirical models:  
\[RMSE=\sqrt{\frac{\sum_{l=1}^{N}(\text{Measured }RSSI-\text{Model})^{2}}{N}} \tag{29}\]  
In this work, we attempt to provide different perspectives. Therefore, we assessed the performance by comparing the proposed model with the three following propagation models of a similar environment at the same frequency, namely: One Slope Path Loss Prediction Model (433 MHz), Optimized FITU-R NGF, and ITU-R MA FSPL.  
(1) One-slope Path Loss Prediction Model (433 MHz)  
An empirical path model for a palm plantation was proposed based on the measurement of the LoRa 433 MHz at the available spreading factors (SF7-SF12) and bandwidths (125, 250, and 500 kHz) for wireless sensor networks [19]. The model for the LOS with grass at the 1 m antenna height is presented below:  
\[PL_{LOS(433 MHz)}=PL_{0}+10 nlog(d) \tag{30}\]  
where \(PL_{0}\) is the reference path loss at the 1 m distance from the transmitter; d is the distance between the transmitter and the receiver; and n is the PLE equal to 2.37 for SF7 and BW 125 kHz.  
(2) Optimized FITU-R Model for Near-ground Forest (Optimized FITU-R NGF)  
This model proposes the optimization of the FITU-R (fitted ITU-R) model for the near-ground path loss modeling in a forest environment [17]. It considers the plane earth model that explains the direct ray in addition to the ground-reflected ray received by the receiver in Equation (31).  
\[PL_{PlaneEarth}(db)=(40\;log\;d)-(20\;log\;ht)-(20\;log\;hr) \tag{31}\]  
The ITU-R foliage attenuation (AITU - R foliage) was added into the plane earth model as follows:  
Figure 13: MBFLR for all fuzzy RSSI.  
\[AITU-R_{\mathit{foliage}}(dB)+PL_{\mathit{PlameEarth}}(dB)=0.2\ f^{0.3}d^{0.6}+(40 \ log\ d)-(20\ log\ ht)-(20\ log\ hr) \tag{32}\]  
where \(f\) is the frequency carrier in GHz; \(ht\) is the antenna transmitter height in meters; \(lr\) is the antenna receiver height in meters; and \(d\) is the distance between the transmitter and the receiver in meters.  
1. ITU-R Maximum Attenuation and Free Space Path Loss (ITU-R MA FSPL)  
This model is recommended by the International Telecommunications Union for the 30 MHz-30 GHz range. In the case of the LOS, the ground-reflected ray in this environment is negligible because the forest ground is covered with full grass and/or weed that absorbs the radio waves. However, in the case of the NLOS, the maximum attenuation is calculated and combined with the LOS, as shown in Equation (33) [31]:  
\[PL_{MA-ITU-R}(dB)=A_{M}\Big{(}1-e^{-Rd/A_{M}}\Big{)}+32.44+20\ log\ d+20\ log\ f \tag{33}\]  
where \(A_{M}\) is the maximum excess attenuation in \(dB\); \(R\) is the initial slope of the attenuation curve in \(dB\)/m; \(d\) is the distance between the transmitter and the receiver in km; and \(f\) is the frequency carrier in MHz.