# Data-Driven Analysis of Outdoor-to-Indoor Propagation for 5G Mid-Band Operational Networks
## 4 Statistical Analysis of Channel Propagation Characteristics
### Time-Related Characteristics
#### 4.1.1 Number of Paths and Interarrival Times  
As discussed in Section 2.1, due to multipath propagation, the signal consists of paths, each characterized by different delays and gains. Hence, the different delays of paths have an impact on the system performance and have to be considered for channel propagation characterization [57]. The boxplots with an average number of paths for Op1 and Op2 at all measurement locations are shown in Figure 5. The average number of paths for Op1 at location 1, location 2, location 3, location 4, and location 8 is 5, 5, 1, 1, and 2, respectively. For Op 2, the average number of paths at the location 1, location 2, location 4, location 5, location 6, location 7, and location 8 is 5, 6, 2, 2, 5, 5, and 6, respectively. It can be seen that the number of paths arrived at the receiver depends on the geometry of the measurement location and surroundings, rather than on the distance. Because of propagation environment variability, measurements are inherently affected by some uncertainty, which is quantified by measuring the standard deviation \((\sigma)\) of the data. The uncertainty for each location and operator is given in Figure 5.  
Interarrival time, defined as the time difference between two consecutive paths, is also a parameter of interest. Interarrival time is a random variable that depends on the wireless channel conditions. The interarrival times vary with environment, surroundings, and BS  
Figure 5: Box plot for the number of paths for Op1 and Op2 at all measurement locations, showing median value (red line), standard deviation (blue box), and outliers (red plus signs). (**a**) Op1 (**b**) Op2.  
position. In the case of a sparse multipath channel, there are small delays, and fewer paths fall into a resolvable delay bin [57]; 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 [57; 58]. Hence, interarrival times change with the density of MPC, which is entirely random. Figure 6 shows the boxplots with average interarrival time and uncertainty in terms of standard deviation \((\sigma)\), between the MPC for Op1 and Op2 at all locations. The results indicate that with a single wide beam, in the case of Op2, the interarrival times between the arriving paths are shorter than with the SSB-based transmission, in the case of Op1, when the transmission is more directive toward the measurement location.  
It is worth noting that although Figure 6a apparently shows a high number of outliers for some locations, they are actually a low percentage of the total data samples. In particular, let us consider the interarrival times for Location 1 for Op1 from Figure 6a, where data samples between approximately 450 and 1000 ns are labeled as outliers. Figure 7 presents the corresponding histogram, and highlights that most of the data samples lie between 0 and 450 ns, while the data points above 450 ns that have been labeled as outliers according to the criterion previously indicated are relatively few.  
Figure 6: Box plot for the interarrival times of multipath components for Op1 and Op2 at all measurement locations, showing median value (red line), standard deviation (blue box), and outliers (red plus signs). (**a**) Op1 (**b**) Op2.  
Figure 7: Histogram for the interarrival times of Operator 1 at Location 1.