# Data-Driven Analysis of Outdoor-to-Indoor Propagation for 5G Mid-Band Operational Networks
## 4 Statistical Analysis of Channel Propagation Characteristics
### Correlation Analysis
It means if the correlation coefficient for any pair of parameters is between \(-\)0.  
the RMS delay spread is the power-weighted standard deviation of the delay of reflected paths; therefore, an increase in RMS delay spread with the number of paths is caused by the increased spread of delays of paths. The RMS delay spread and mean excess delay depend on the delay of the multipath components. As the delay of the multipath components increases, there will be an increased excess delay and delay spread. As expected, there is a positive correlation between RMS delay spread and mean excess delay. Similar to excess delay and RMS delay spread, PL also positively correlates with the number of paths. With an increase in distance between BS and measurement location, it is more likely that the reflected paths carrying a significant amount of power will be obstructed by the obstacles such as rough walls, trees, etc., which absorb and scatter them. As a result, the received signal contains scattered paths; therefore, the number of paths that carry a significant amount of power decreases with an increase in distance that also causes an increase in PL. When the mean excess delay and RMS delay spread increases caused by the higher delays associated with reflected and lateral paths, the power corresponding to these paths decreases, leading to increased PL. Further, these delays increase with increasing distance due to scattering. It shows a linear dependency of PL on the time dispersion parameters, and our results show, as expected, a positive correlation between time dispersion parameters and PL. There is a negative correlation between the number of paths and the K-factor because the dominant path becomes weaker due to scattering. The decrease in the power of the dominant path leads to a decrease in the K-factor value. As the RMS delay spread and mean excess delay increase due to the increased number of paths with larger delays and their corresponding reduced power, K-factor decreases. Further, PL increases with decreasing power, and the K-factor decreases, which explains the negative correlation between K-factor and PL and time dispersion parameters. Our analysis shows a weak negative correlation between interarrival times and other channel parameters. This is due to the fact that the interarrival times are closely linked to the measurement location's environment, surroundings, and BS position. They may vary for each CIR due to the time-varying nature of the wireless channel. In the case of a sparse multipath channel, there are small delays, and fewer paths fall into a resolvable delay bin; however, in rich multipath channels, the MPC may travel through different paths for a longer delay, and all paths may fall into the same delay bin. Hence, interarrival times changes with the density of MPC, which is random; therefore, there is no well-defined correlation between the interarrival times and other channel parameters. Conclusively, both time dispersion parameters are positively correlated with each other and also with the number of paths. PL has a positive correlation with time dispersion parameters and the number of paths. The K-factor is always negatively correlated with time dispersion parameters, PL, and the number of paths. In contrast, interarrival times do not show a well-defined correlation with any other channel parameter due to their random behavior with channel conditions.