# Channel Model for Estimating Received Power Variations at a Mobile Terminal in a Cellular Network
## Appendix A Absolute Error Between theoretical and practical measurements
### Evaluation of the Performance of the Theoretical Model  
This section evaluates the accuracy of the proposed theoretical model in estimating the received signal power at the user terminal's next position, based on its movement vector and previously measured power. The analysis compared the theoretical predictions with the experimental measurements across three types of coverage areas: fully covered zones, intra-handover zones, and inter-handover transition zones.  
Tables 6-8 summarize the relative error between the theoretical and experimental power values for each case. These values were computed over 11,253 georeferenced measurements from 14 urban base stations covering 59 sectors. Data inconsistencies (e.g., missing or corrupted values) in the dataset were excluded from the final analysis, the criteria for which were discussed in the data processing section.  
To statistically evaluate the agreement between the theoretical predictions and the measured values, an ANOVA test was conducted across all zones and scenarios. The test revealed statistically significant differences between the theoretical and experimental groups (\(p<0.001\)), although the effect size was relatively small. A post hoc Tukey HSD test indicated that the average discrepancy across all measurements remained between 3.2 dBm and 3.5 dBm. Over 85% of the data points showed a deviation of less than 5 dBm, which was adopted as a practical threshold for acceptable model accuracy.  
Based on this threshold and considering the overall dynamic range of the RSSI values in the dataset, the maximum cumulative relative error was conservatively estimated at 6.47%. This value reflects a statistically bounded upper limit for error under typical operational conditions, validating the model's utility for real-world applications.  
It is also evident that errors increased progressively from fully covered zones to intra-handover and inter-handover zones. This trend correlates with the presence of complex propagation effects, such as interference and fast fading, which are more prominent during cell transitions. Notably, suburban areas consistently showed slightly higher errors than urban zones. This can be attributed to the broader coverage footprints and reduced antenna density in suburban deployments, which introduced additional variability not captured by the model's current assumptions (e.g., flat terrain, horizontal radiation pattern, and constant gain).  
In summary, the proposed model demonstrates consistent and robust predictive capabilities. Its relative error remains within acceptable bounds across diverse environments,  
\begin{table}
\begin{tabular}{l c c} \hline
**Power Estimation \(P_{2}\)** & **Urban** & **Suburban** \\ \hline Relative Error & 4.8\% & 5.3\% \\ \hline \end{tabular}
\end{table}
Table 6: Relative error in the theoretical estimation of the received power \(P_{2}\) within fully covered areas.  
\begin{table}
\begin{tabular}{l c c} \hline
**Power Estimation \(P_{2}\)** & **Urban** & **Suburban** \\ \hline Relative Error & 5.2\% & 5.6\% \\ \hline \end{tabular}
\end{table}
Table 8: Relative error in the theoretical estimation of the received power \(P_{2}\) within inter-handover zones.  
\begin{table}
\begin{tabular}{l c c} \hline
**Power Estimation \(P_{2}\)** & **Urban** & **Suburban** \\ \hline Relative Error & 4.8\% & 5.3\% \\ \hline \end{tabular}
\end{table}
Table 7: Relative error in the theoretical estimation of the received power \(P_{2}\) within intra-handover zones.  
making it a suitable analytical tool for rapid power estimation, especially in scenarios where detailed infrastructure data are unavailable.