# 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
than the other locations. Most of the MPC arrive at the middle points of the PDP or later, and very few multipath components arrive before the middle points, which is a typical behavior for a pure NLoS propagation scenario. The above discussion indicates that the RMS delay spread is low for the Op2 at location 6, where the wide beam is more directive. While in the case of Op1, at location 1, where the strongest SSB is more directive, the RMS delay spread is shorter than at other locations. Overall, the 5G system employing a single wide beam gives a lower RMS delay spread than the multiple SSBs-based transmission systems at locations where the beam is more directive. Table 5 presents reported values of RMS delay spread in the literature at 3.5 GHz in outdoor-to-indoor and indoor-to-indoor environment. In [40], authors considered the outdoor-to-indoor environment and the RMS delay spread the values fluctuates from 13 to 27 ns. The values of the RMS delay spread reported in [11] vary from 20 to 70 ns in the indoor environments. It is also noteworthy to mention that the results reported in [11] establish a growing trend of the RMS delay spread with the distance, in a similar way to the results obtained in our work. As an example, for Op2, location 1, 4, and 6 is closer to the BS than compared to other locations. It is clear from the results that the RMS delay spread at locations 1, 4, and 6 is lower and higher for more distant locations. The higher delays associated with reflected and lateral waves with increasing propagation distance can explain this increase in RMS delay spread. In [44] the value of the RMS delay spread oscillates from 5 to 22 ns in LOS and 17 to 43 ns in NLOS conditions. Another paper [12] presents the delay spread values for LOS and NLOS conditions. The authors reported values 15 ns for LOS and 24 ns for NLOS conditions, suggesting that RMS delay spread had similar values in LOS and NLOS sites. In [28], the mean value of RMS delay spread for LOS scenario is 45 ns. It is worth noting that the results published in the literature are in line with our results; however, it should be highlighted that most of the above literature reports empirical observations for single link indoor-to-indoor deployments except one, which has single link outdoor-to-indoor deployment [40], while our results cover outdoor-to-indoor multi link real deployments, as observed in different locations; therefore, we can conclude that, from a RMS delay spread point of view, outdoor-to-indoor propagation has similar characteristics compared to indoor-to-indoor counterpart. The best fit distribution for RMS delay spread is the normal distribution. The evaluation of the best fit distribution is based on the Akaike Information criterion (AIC). AIC is an estimator to determine the best fit distribution for a given dataset. It estimates different distribution models for the same dataset, and compares them based on the AIC scores. The distribution model with lower AIC score is better and is considered as the best fit distribution for the observed data. In our case, normal distribution is the best approximation to the RMS delay spread for both operators Op1 and Op2 at location 1 based on AIC score; however, locations 3, 4, and 8 for Op1 and location 4 for Op2 have an exponential distribution. A possible explanation for this result is the relatively small number of samples at these locations that might prevent from reliably estimating the distribution. This hypothesis is \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Reference**} & \multicolumn{3}{c}{**RMS Delay Spread**} \\ \cline{2-4}  & \(\mu\) **(ns)** & \(\sigma\) **(ns)** & **Scenario** \\ \hline
[40] & 13–27 & N/A & outdoor-to-indoor \\
[11] & 20 (LOS) & N/A & indoor-to-indoor \\
[44] & 5–22 (LOS) & N/A & indoor-to-indoor \\  & 17–43 (NLOS) & N/A & indoor-to-indoor \\
[12] & 20 (LOS) & N/A & indoor-to-indoor \\  & 70 (NLOS) & N/A & indoor-to-indoor \\
[28] & 45 & N/A & indoor-to-indoor \\ \hline \hline \end{tabular}
\end{table}