# Data-Driven Analysis of Outdoor-to-Indoor Propagation for 5G Mid-Band Operational Networks
## 4 Statistical Analysis of Channel Propagation Characteristics
### Time-Related Characteristics
#### 4.1.3 RMS Delay Spread  
Environment has a strong effect on the delay spread. Typically, the delay spread is smaller in indoor and micro-cellular scenarios. The RMS delay spread varies with the geometric configuration and environment of the measurement location. Figure 9 shows the cumulative distribution function (CDF) of RMS delay spread of the Op1 and Op2 at measurement location 1 with best-fit normal distribution. The total number of data-points to find the curve fitting distribution for Figure 9 is 4156 (the number of data points for each  
Figure 8: Box plot for Mean excess delay 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. location and operator can be found in Table 3). As location 1 has the highest data-points, it gives a good approximation for the CDF of RMS delay spread. Table 4 shows the mean \((\mu)\) and standard deviation \((\sigma)\) of the RMS delay spread of Op1 and Op2 at all locations. The RMS delay spread for Op1 at location 1, location 2, location 3, location 4, and location 8 is 44 ns, 77 ns, 3 ns, 43 ns, and 75 ns, respectively. For Op 2, the RMS delay spread at location 1, location 2, location 4, location 5, location 6, location 7, and location 8 is 26 ns, 75 ns, 7 ns, 21 ns, 20 ns, 78 ns, and 35 ns respectively. The RMS delay spread for Op1 at locations 1, 3, and 4 is lower than other locations. The received power is mostly due to the early received dominant path, thus resulting in a lower RMS delay spread, which explains the smaller values observed at these locations. Locations 2 and 8 have a higher RMS delay spread. Location 8 is more distant from the estimated BS position, leading to a higher delay spread with a large portion of received power through reflected paths having more significant propagation delay. In the case of location 2, while this location is spatially close to the BS, there is a wall facing the BS; as a result, signal components reach the location through reflections from nearby buildings and thus with larger propagation delays, causing a larger RMS delay spread. In the case of Op2, locations 1, 4, and 6 have a smaller delay spread. These measurement points are on the same side where the estimated BS position is, and the distance between these points and BS is smaller than other locations. Hence, at these measurement points, the signal suffers a lower attenuation. The concentration of power in the early arrived MPC is thus higher, with most of the power being received through the early received dominant path, while a smaller portion of power is received through other reflected paths; therefore, the delay time dispersion is small at locations 1, 4, and 6. Measurement point 5 also has a small delay spread, with a small propagation delay that means the strongest MPC arrived first. After that, the MPC decay quickly. We observed that measurement locations 2, 7, and 8 provided larger RMS delay spreads than other locations. All these locations are more distant from BS \begin{table}
\begin{tabular}{|c|c c c|c c c|} \hline  & \multicolumn{3}{c|}{**RMS Delay Spread for Op1**} & \multicolumn{3}{c|}{**RMS Delay Spread for Op2**} \\ \cline{2-7}
**Location** & \(\mu\) **(ns)** & \(\sigma\) **(ns)** & **Distribution** & \(\mu\) **(ns)** & \(\sigma\) **(ns)** & **Distribution** \\ \hline
1 & 44 & 24 & Normal & 26 & 13 & Normal \\
2 & 77 & 24 & Normal & 75 & 17 & Normal \\
3 & 3 & 1 & Exponential & N/A & N/A & N/A \\
4 & 43 & 93 & Exponential & 7 & 4 & Exponential \\
5 & N/A & N/A & N/A & 21 & 19 & Normal \\
6 & N/A & N/A & N/A & 20 & 12 & Normal \\
7 & N/A & N/A & N/A & 78 & 32 & Normal \\
8 & 75 & 73 & Exponential & 35 & 14 & Normal \\ \hline \end{tabular}
\end{table} 
Table 4: Mean and standard deviation values of RMS delay spread for Op1 and Op2. Figure 9: CDF of RMS delay spread values for Op1 and Op2 at measurement location 1. (**a**) Op1 with best fit distribution \(\sim\mathcal{N}(44,\,24)\). (**b**) Op2 with best fit distribution \(\sim\mathcal{N}(26,\,13)\).