# Channel Measurement and Modeling for 5G Urban Microcellular Scenarios
## 4 Evaluations
### Delay Spread Statistics  
To characterize the temporal spread of the channel, the root mean square (RMS) DS \(\tau_{\text{rms}}\) was calculated on the basis of APDPs according to  
\[\tau_{\text{rms}}=\sqrt{\frac{\int_{0}^{\tau_{\text{max}}}\tau^{2}P(\tau)\,d \tau}{\int_{0}^{\tau_{\text{max}}}P(\tau)\,d\tau}-\tau_{\text{m}}^{2}},\quad \tau_{\text{m}}=\frac{\int_{0}^{\tau_{\text{max}}}\tau P(\tau)\,d\tau}{\int_{0 }^{\tau_{\text{max}}}P(\tau)\,d\tau}\,, \tag{4}\]  
where \(\tau_{\text{m}}\) and \(\tau_{\text{max}}\) denote the mean and the maximum excess delay, respectively. A 25 dB threshold relative to the strongest MPC was used to exclude thermal noise and make the results fully comparable [32; 33]. The empirical complementary cumulative distribution functions (CCDFs) of all measured and simulated UMi LOS scenarios are illustrated in Figure 5. They show a clear trend towards smaller DS for the SC-RA scenario. This is most probably related to the street canyon width, which is much smaller than for SC-CC environment and compared to the dimensions of the square (OS-CC). In addition, glass facades are dominant in the city center (OS-CC and SC-CC), which are more reflective than the plastered walls in the residential area (SC-RA). The difference in DS is more distinct for the peak values, which occur with lower probability. Table 3 summarizes the statistical parameters. The 95%-quantile (\(\text{Q}_{\text{DS},0.95}\)) is almost twice as large for SC-CC compared to SC-RA. Furthermore, it can be noticed that the SC-RA channel is slightly more dispersive at 10 GHz, which can be related to relative surface roughness and oxygen absorption at 60 GHz. The latter may already take effect, since the excess traveling distance of reflected paths can easily exceed 100 m. On the other hand, the DS for OS-CC and SC-CC is very similar--\(\mu_{\text{DS}}\) is almost equal. The slightly deformed shape of the CCDF for OS-CC might be due to the fact that--in contrast to SC-CC--the measurement points are not equally distributed over the distance range and overall less DS values are available. In this context, it is noteworthy that the empirical statistical distribution of the DS (and other channel metrics) depends on the distribution of the measurement points over distances as long as a correlation between the respective metric and distance cannot be excluded. Simulations on system level might assume an equal distribution of users within a cell [10], resulting in a linear increase of the probability with respect to distance. It is therefore advisable to investigate a possible distance dependence and, if applicable, consider it in the channel model (see Section 4.4). \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & \multirow{2}{*}{**Freq. GHz**} & \multirow{2}{*}{**Conditions**} & \multicolumn{3}{c}{**Measurement**} & \multicolumn{3}{c}{**Simulation**} & \multirow{2}{*}{**Valid. Range (m)**} \\ \cline{3-4} \cline{6-10}  & & & \(\overline{L_{\text{tr}}(1\,\text{m})}\) & \(\pi\) (dB) & \(\sigma\) (dB) & \(\overline{L_{\text{tr}}(1\,\text{m})}\) (dB) & \(\pi\) & \(\sigma\) (dB) \\ \hline OS-CC & 60.0 & LOS & 69.2 & 1.88 & 1.03 & 69.2 & 1.74 & 1.17 & 5–50 \\ SC-CC & 60.0 & LOS & 67.0 & 2.13 & 2.03 & 69.2 & 1.72 & 0.97 & 5–50 \\ SC-RA & 60.4 & LOS & 67.0 & 2.07 & 2.53 & - & - & - & 10–210 \\  & & NLOS & 69.7 & 2.67 & 4.93 & - & - & - & 10–80 \\  & 10.0 & LOS & 57.7 & 1.62 & 2.95 & - & - & - & 10–210 \\  & & NLOS & 61.7 & 2.10 & 7.36 & - & - & - & 10–80 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Path loss (PL) parameters derived from measurements for all UMi scenarios and values from ray tracing simulations for “open square, city center” (OS-CC) and “street canyon, city center” (SC-CC) scenario. Equivalent evaluations were made with the RT data, available for SC-CC and OS-CC. To ensure full comparability, the CIRs were limited to 250 MHz bandwidth and the RMS DS \(\tau_{\text{rms}}\) was calculated on the basis of APDPs with the same threshold.