# Channel Model for Estimating Received Power Variations at a Mobile Terminal in a Cellular Network
## Appendix A Absolute Error Between theoretical and practical measurements  
Figure 13: Histogram of the absolute error between the theoretical and experimental power variations. Approximately 2000 data points show significant deviations. From this point onward, the power variations obtained using Equation (24) are adopted, as they allow for the estimation of power trends based on the user terminal's movement vector within the coverage area. This approach is consistent with the methodology previously described in the channel model section, where directional variations were incorporated to characterize propagation dynamics. Once the theoretical variation, \(\Delta P_{\text{Theo}}\), is determined, the predicted power at the next location, \(P_{2_{\text{Theo}}}\), can be estimated using the experimentally observed power at the previous point, \(P_{1_{\text{Exp}}}\), following Equation (26):  
\[P_{2_{\text{Theo}}}\left[\text{dBm}\right]=P_{1_{Exp}}\left[\text{dBm}\right]+ \Delta P_{\text{Theo}}\left[\text{dBm}\right] \tag{26}\]  
Following this approach, Figure 14 presents a comparative histogram illustrating the received signal strength indicator (RSSI) obtained experimentally using NetMonitor and the RSSI estimated by the proposed vector-based theoretical model. Both datasets exhibit a similar central tendency, particularly between \(-80\,\text{dBm}\) and \(-75\,\text{dBm}\), indicating that the model reliably approximates real-world signal behavior under average propagation conditions. This alignment is particularly evident in the urban scenario, where the base station density is higher and the propagation variability is somewhat reduced. However, the histogram also shows that the experimental RSSI values are more widely dispersed, especially toward lower power levels (e.g., below \(-80\,\text{dBm}\)), reflecting the influence of random environmental factors--such as shadowing from buildings, fast fading, and inter-cell interference--that are not fully captured by the theoretical formulation. This behavior is consistent with the statistical findings discussed previously. In the urban area, the experimental RSSI values showed an average of \(-79.31\,\text{dBm}\) with a standard deviation of \(11.10\,\text{dB}\), while in the suburban area, the mean RSSI dropped to \(-97.00\,\text{dBm}\), with greater dispersion (\(12.00\,\text{dB}\)). Such degradation and variability were especially pronounced in the inter-handover zones of the suburban scenario, where both the RSSI and RSSNR were classified as poor, highlighting instability and increased susceptibility to interference. These statistical patterns help explain the histogram's left-skewed tail, particularly in suburban transitions or areas with sparser infrastructure. The comparison underscores both the strengths and limitations of the proposed model. On the one hand, it effectively replicated dominant propagation trends with a low average estimation error, not exceeding \(7.6\%\) under nominal conditions. On the other hand, it tended to underestimate the received power under non-ideal conditions--such as abrupt terrain variations, handovers, or interference from neighboring cells--especially in suburban areas, where long distances and fewer obstacles yielded higher path loss but also more  
Figure 14: Comparative histogram of experimental and theoretical power 2, estimated based on the direction of movement for consecutive points. variability in the RSSNR. Despite these deviations affecting only a minority of data points, the model remains a valuable tool for preliminary signal mapping and handover zone characterization, particularly in urban environments where rapid estimation is prioritized and full drive test datasets may be unavailable. Unlike high-complexity models based on ray tracing or machine learning, which often require extensive parameter tuning, our low-complexity directional approach accurately captures real-time power fluctuations caused by terminal mobility.