# Data-Driven Analysis of Outdoor-to-Indoor Propagation for 5G Mid-Band Operational Networks
## 4 Statistical Analysis of Channel Propagation Characteristics
### Correlation Analysis  
Statistical channel models are attractive for their simplicity but they sometimes lack accuracy. In order to improve the statistical channel modeling, it is of key interest to derive information on the time/power variability of the propagation parameters. Interdependence of radio-channel model parameters, being observed in some measurement data, should also be reproduced by the channel model. To this purpose, the statistical correlation between the channel propagation parameters from measured data helps to obtain reliable models \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Locations**} & \multicolumn{2}{c}{**K-Factor for Op1**} & \multicolumn{2}{c}{**K-Factor for Op2**} \\ \cline{2-5}  & \(\mu\) **(dB)** & \(\sigma\) **(dB)** & \(\mu\) **(dB)** & \(\sigma\) **(dB)** \\ \hline
1 & 12.85 & 6.67 & 11.60 & 9.17 \\
2 & 10.68 & 4.01 & 2.68 & 3.48 \\
3 & 2.70 & 3.03 & N/A & N/A \\
4 & 2.37 & 3.36 & 24.14 & 10.84 \\
5 & N/A & N/A & 2.41 & 2.97 \\
6 & N/A & N/A & 21.22 & 8.18 \\
7 & N/A & N/A & 2.09 & 3.23 \\
8 & 3.85 & 3.73 & 6.26 & 5.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: K-factor results for Op1 and Op2. Figure 14: CDF of K-factor for Op1 and Op2 at the measurement location 1 (**a**) Op1 (**b**) Op2. Figure 15: PDF of K-factor for Op1 and Op2 at the measurement location 1 (**a**) Op1; (**b**) Op2. that reflect the true propagation environment. Based on the existing literature, one can expect the time dispersion parameters, i.e., mean excess delay and RMS delay spread, to be positively correlated with PL [6], while the K-factor is typically negatively correlated with time dispersion parameters [65; 66]. In this work, we are considering all the channel propagation parameters for correlation analysis to give a clear idea of which parameters are correlated and which are not. This analysis will allow us to answer the following questions:  
Do the estimated channel parameters, i.e., the number of the paths, interarrival times, mean excess delay, RMS delay spread, PL, and k-factor, interact with one another? Are they correlated? If yes, could we predict that they were? Our prediction is if the number of paths increases, there will be an increment in mean excess delay, RMS delay spread, and PL, and decrement in the interarrival times and k-factor. If the value of interarrival times decreases, the time dispersion and PL will increase, and the k-factor will decrease. In addition, if the time dispersion increases, PL will increase, and the k-factor will decrease. We performed a correlation analysis between all the estimated channel parameters based on the collected dataset. We performed Spearman rank correlation test to measure the degree of association between the parameters. The Spearman correlation indicates whether a monotonic relationship exists between the two variables, and can be considered as a more general indicator compared to the Pearson correlation, which indicates whether a linear relationship exists. We also performed Pearson correlation and, as expected, the values of Pearson correlation coefficient are lower than the Spearman correlation coefficient values. Correlation tests were performed in MATLAB and then confirmed using the SPSS software [67]. Results indicate that the correlation of the parameters is independent of the measurement locations and operators. By changing the measurement location and operators, the correlation coefficient values may change; however, the statistical association of the parameters remains the same; therefore, we are giving a correlation analysis of both operators and all locations collectively. The correlation coefficients of all combinations of the estimated channel parameters are shown in Table 7. To give a more clear idea about the association of the channel parameters with each other, we considered a threshold \(\pm\)0.2 for correlation coefficient.