## 3 Performance Analysis
### Numerical Results  
Based on the models described previously, we conducted a comprehensive review of a MATLAB (R2023a) function that facilitated the integration of deterministic and empirical data to construct a propagation model. This model elucidates the probabilistic pattern of spectrum occupancy, accommodating the specific terrain and equipment employed in the study. The Curve Fitting Toolbox library was used for this purpose, providing an application and various functions essential for fitting curves and surfaces to the data. This toolbox enables exploratory data analysis, alongside pre-processing and post-processing of information, evaluating competing models, and identifying and removing outliers. The \"fittype\" function was utilized to perform curve and surface fitting, subsequently deriving a probabilistic logarithmic function. A novel equation was developed from the code and the functions applied, thus delineating the adjusted model.  
The application of the SUI propagation model provides information on power levels as the receiver moves further from the transmitter. As a deterministic model, it uses predefined values from Tables 2 and 3. Based on the specific characteristics of the Checa parish central park, the scheme shown in Figure 6 was obtained.  
As a result of field measurements, deterministic formulations, and the use of MATLAB computational tools, the SUI deterministic model was developed based on calculations and parameters defined for the study area to simulate the behavior of a hotspot under optimal conditions, maximizing its performance; the heatmap in Figure 6 illustrates the  
Figure 6: Received Power levels vs distance using Equation (6) of SUI model.  
power levels of the hotspot, ranging from 100 dBm to \(-30\) dBm, which ensures excellent signal levels throughout the area.  
The revised model undertakes a comparative analysis of the deterministic and empirical models to enhance the empirical model's performance and align it more closely with the deterministic model. Figure 7 illustrates a juxtaposition of the power levels of the hotspot, as determined by the GUI model, against the empirical field data and the revised model. In the context of the revised model, the parameters utilized to formulate Equation (8) were taken into account. It is crucial to note that the GUI model yields reliable information beginning at a distance of 100 m, a design attribute specific to outdoor environments.  
Figure 8 presents the heatmap obtained from the adjusted model. Note that the heatmap exhibits results that align more closely with the power levels measured empirically in the field, thereby rendering it applicable to regions with analogous geographical attributes. Consequently, the model can be used to predict the power levels of a wireless transmitter.  
Figure 7: Comparison between received power levels of the hotspot based on the GUI model [Equation (6)], the empirical data collected in the field, and the adjusted model [Equation (8)] vs. distance.  
Finally, Figure 9 shows the application of the adjusted model in the geographic location where the wireless repeater is installed, which connects to the hotspot through a wireless link.