# Framework for Behavioral Analysis of Mobile Networks
## 4 Experiments and Results
### Cell Pattern Detection  
After SOM execution, a total of 50 different behavior patterns are identified as shown in Figure 4(a). In the map shown in the figure, neurons that have been assigned at least one cell are distinguished by yellow dots. These are accompanied by a number that indicates the number of cells included in each group (i.e., the number of cells associated to the specific pattern). The map is built taking into account a neighborhood function, so that nearby neurons on the map have more similarities than neurons that are farther away. In this way, the corners of the map have the neurons with the highest number of cells, while intermediate patterns are found in the center of the map with the lowest number of accumulated cells. The limitation of this map lies in the large number of patterns detected, even if some of them only have a couple of cells. For this reason, it is necessary to have a post-processing phase that is capable of finding similarities between neighboring neurons, grouping together those that have fewer cells. As shown in Table 5, when the post-processing is applied, a high threshold allows more neurons to join, since the limit distance is greater. As the threshold is reduced, the number of resulting patterns is greater, reaching 13 at the threshold, which is considered as low. The differences between thresholds are reflected in the level of detail of the obtained patterns. The four patterns obtained with a high threshold are more generic than the 13 obtained with the low threshold. Therefore, the configuration of the post-processing depends on the level of detail desired for the network behavior analysis. Specifically, for a medium threshold, the obtained results are shown in Figure 4(b). The shape of the map is the same as in the SOM output, but in this case the neurons have different colors. Each color represents one of the patterns obtained after post-processing, so the neurons with the same color are finally associated with the same cell pattern. \begin{table}
\begin{tabular}{c c} \hline
**Threshold** & **Coefficients** \\ \hline High & \(0.5\cdot\mu+0.3\cdot\sigma^{2}+0.3\cdot\sigma\) \\ Medium & \(0.4\cdot\mu+0.25\cdot\sigma^{2}+0.25\cdot\sigma\) \\ Low & \(0.3\cdot\mu+0.2\cdot\sigma^{2}+0.2\cdot\sigma\) \\ \hline \end{tabular}
\end{table} 
Table 4: Thresholds in Post-processing. \begin{table}
\begin{tabular}{c c c} \hline
**Threshold** & **Coefficients** & **Number of Patterns** \\ \hline High & \(0.5\cdot\mu+0.3\cdot\sigma^{2}+0.3\cdot\sigma\) & 4 \\ Medium & \(0.4\cdot\mu+0.25\cdot\sigma^{2}+0.25\cdot\sigma\) & 6 \\ Low & \(0.3\cdot\mu+0.2\cdot\sigma^{2}+0.2\cdot\sigma\) & 13 \\ \hline \end{tabular}
\end{table} 
Table 5: Thresholds in Post-processing. This set of patterns is analyzed in detail by comparing the KPIs of the cells associated with each behavior pattern. In Table 6, patterns found in the commercial network are characterized with the shown statistics. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Key Performance Indicator** & **P0** & **P1** & **P2** & **P3** & **P4** & **P5** \\ \hline Number of cells & 132 & 20 & 120 & 36 & 57 & 85 \\ Cell throughput in downlink & & & & & & \\ User throughput in downlink & & & & & & \\ Volume data traffic in downlink & & & & & & \\ Cell throughput in uplink & & & & & & \\ User throughput in uplink & & & & & & \\ Volume data traffic in uplink & & & & & & \\ QPSK usage rate in downlink & & & & & & \\ QPSK usage rate in uplink & & & & & & \\ Spectral efficiency downlink & & & & & \\ CQI & & & & & \\ Average of connected users & & & & & \\ Maximum of connected users & & & & & \\ Restablishments success rate & & & & & \\ Restablishments per connected user & & & & & \\ PRB usage rate in downlink & & & & & \\ PRB usage rate in uplink & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Patterns and statistics per KPI. Figure 5: (**a**) Map of neurons at SOM output. (**b**) Map of neurons at post-processing output. Pattern 0 (Green).