# Channel Model for Estimating Received Power Variations at a Mobile Terminal in a Cellular Network
## 4 Results
### Urban Area Results Using the Theoretical Channel Model  
After presenting the theoretical analyses using two distinct approaches--one based on the decomposition and examination of [PERSON]'s equation, as shown in Equation (7) (Theoretical Model 1), and the other employing vector calculus concepts, as detailed in Equation (24) (Theoretical Model 2)--it is pertinent to compare these models both with each other and with the experimental data obtained through NetMonitor measurements.  
When comparing the results obtained from the two theoretical models, as shown in Figure 12a, the expected power variations are relatively small with respect to the movement of the user terminal. This behavior aligns with expectations, as both theoretical models consider only the position and movement direction of the user within the coverage area, without accounting for complex propagation phenomena such as fading, reflection, or diffraction.  
Figure 12: Comparison of the histograms obtained in the study. (**a**) Histogram of power delta—Theoretical Model 1 vs. Theoretical Model 2. (**b**) Histogram of power delta—experimental vs. Theoretical Model 1. (**c**) Histogram of power delta—experimental vs. Theoretical Model 2.  
In contrast, Figure 12b,c illustrate the theoretical and experimental power variations, respectively. The overlay of these distributions shows generally strong agreement: most samples yielded an error of less than 5%, indicating that the proposed model successfully captured the overall spatial trends of the signal variation. However, certain discrepancies can be observed, particularly in about 4% of the data, where abrupt power fluctuations occurred. These deviations are mostly concentrated around inter-handover regions, changes involving invalid or non-existent cells, or areas affected by measurement artifacts introduced by the NetMonitor software (version 1.81). This particular version, commonly used for LTE signal diagnostics, may produce placeholder values or incomplete readings under certain conditions, especially during cell transitions or low-coverage scenarios. This highlights the importance of robust data preprocessing in future implementations to improve accuracy.  
The histograms in Figure 12 include a common color not defined in the legend table. This color represents overlapping measurement values common to both compared distributions, indicating zones where the theoretical and experimental results converge in power variation behavior.  
Following this visual criterion, it can be observed that the comparison between the two theoretical models results in smaller power variation differences than when each theoretical model is compared individually against the experimental data. Nevertheless, even in the theoretical-to-experimental comparisons, the deviations remain relatively small, reinforcing the validity of the proposed approach.  
Furthermore, to assess the alignment between theoretical predictions and experimental results, a statistical analysis was conducted comparing the directional power variation derived from Equation (24) with the field measurements. As shown in Figure 13, the majority of measurement points--representing over 85% of the dataset--show a difference of less than 5 dBm between the theoretical and experimental values. This observation was statistically supported by an ANOVA test (\(p<0.001\)), which confirmed that the differences between the two groups (theoretical vs. experimental) were statistically significant but not substantial in magnitude. A post hoc Tukey test revealed that the average discrepancy between the matched theoretical and experimental values across the intra- and inter-handover zones ranged between 3.2 dBm and 3.5 dBm. Based on the maximum observed mean difference and relative to the overall dynamic range of the RSSI values in the dataset, the maximum cumulative error was conservatively estimated at 6.47% and did not exceed 7.6%.