## 5 Method for Calculating Path Loss Based on Local Conditions  
The method developed by Akwa Ibom State University for calculating path loss involves determining the path loss exponent and a shadow factor using standard deviation. This approach improves the accuracy of models by accounting for local variations in propagation conditions, allowing the customization of modeling based on the geographical characteristics of the study area. This also facilitates comparisons with other path loss models. We utilize the formulations of [21]:  
The path loss beyond reference distance is given by  
\[PL(dB)=PL(d_{0})+10\gamma\log_{10}\left(\frac{d}{d_{0}}\right)\ +X\sigma, \tag{15}\]  
and the path loss exponent was determined as  
\[\gamma=\frac{\sum_{i=1}^{K}[L_{P}(d_{i})-LP(d_{0})]}{\sum_{i=1}^{K}10\log_{10 }\left(\frac{d_{i}}{d_{0}}\right)}, \tag{16}\]  
where \(\gamma\) is the path loss exponent, \(L_{P}(d_{i})\) is the signal loss at distance \(d_{i}\), \(L_{P}(d_{0})\) is the signal loss at the reference distance \(d_{0}\), \(K\) is the total number of measurement points, and \(X\sigma\) is the shadow factor. Considering the data from Table 6, we determine the path loss exponent \(\gamma\):  
\[\gamma=\frac{58.7821}{65.59763}=0.896101. \tag{17}\]  
To compensate for shadow fading due to terrain conditions, the large-scale average path loss was predicted at 50 m as  
\[PLr(dB)=73.75+8.96\log_{10}\left(\frac{50}{10}\right)=80.01\ \text{dB}. \tag{18}\]  
Based on the predicted path loss calculations in Equation (18), the squares of the mean deviations were generated, as shown in Table 7.  
Figure 14: Comparison between received power levels of repeater WiFi based on the empirical data collected in the field, adjusted linear model [Equation (13)], and the adjusted logarithmic model [Equation (14)] vs distance at which WiFi signal repeater is installed. To calculate the shadow factor \(X_{\sigma}\), we need to determine the standard deviation \(\sigma\) of the data as follows:  
\[\sigma=\sqrt{\frac{1}{N}\sum_{k=1}^{n}(PLm-PLr)^{2}}, \tag{19}\]  
where \(\sigma\) is the standard deviation, \(N\) is the total number of measurements (N = 10), the summation is indicated by \(\sum\) and the limits of the sum are specified from \(k=1\) to \(n\). Considering that N = 10 and the data from Table 7,  
\[\sigma=\sqrt{\frac{74.726}{10}}=2.733. \tag{20}\]  
By utilizing the cumulative density function and considering that the mean value (\(\mu\)) is 0 dB and \(\phi(z)=1.65\), the following results can be obtained:  
\[\frac{X\sigma-0}{2.733}=1.65\quad\Rightarrow\quad X\sigma=4.51\;\mathrm{dB}, \tag{21}\]  
Finally, using Equation (15), the path loss is  
\[PL(dB)=73.75+8.96\log_{10}\left(\frac{d}{10}\right)\;+4.51. \tag{22}\]  
In \[\gamma=\frac{\sum_{i=1}^{K}[L_{P}(d_{i})-LP(d_{0})]}{\sum_{i=1}^{K}10\log_{10 }\left(\frac{d_{i}}{d_{0}}\right)}, \tag{16}\]03 of [21], the theoretical path loss equations are presented for the Free Space, Okumura-Hata, COST 231 Hata, and COST 231 Walfisch-Ikegami models. These equations are used to evaluate the adjusted model in Equation (22). The equations for these models are listed below. Free Space: \[\gamma=\frac{\sum_{i=1}^{K}[L_{P}(d_{i})-LP(d_{0})]}{\sum_{i=1}^{K}10\log_{10 }\left(\frac{d_{i}}{d_{0}}\right)}, \tag{16}\]1 Okumura-Hata: \[\gamma=\frac{\sum_{i=1}^{K}[L_{P}(d_{i})-LP(d_{0})]}{\sum_{i=1}^{K}10\log_{10 }\left(\frac{d_{i}}{d_{0}}\right)}, \tag{16}\]2 COST 231-Hata: \[\gamma=\frac{\sum_{i=1}^{K}[L_{P}(d_{i})-LP(d_{0})]}{\sum_{i=1}^{K}10\log_{10 }\left(\frac{d_{i}}{d_{0}}\right)}, \tag{16}\]3 COST 231-WI: \[\gamma=\frac{\sum_{i=1}^{K}[L_{P}(d_{i})-LP(d_{0})]}{\sum_{i=1}^{K}10\log_{10 }\left(\frac{d_{i}}{d_{0}}\right)}, \tag{16}\]4  
Figure 15 presents a comparison of the path loss across the aforementioned models, alongside the path loss of the adjusted model.