# Channel Measurement and Modeling for 5G Urban Microcellular Scenarios
## 4 Evaluations
### Distance Dependence of the Delay Spread  
In this section, the dependence of the DS on distance is investigated in more detail. In Figure 6, the DS for the OS-CC and SC-CC scenarios is plotted (in logarithmic) scale against the distance. A distinct increase can be observed for the OS-CC scenario, which motivates the use of a linear regression model. It is expressed by  
Figure 5: Empirical complementary cumulative distribution functions (CCDFs) of the root mean square (RMS) delay spread (DS) for all measured and simulated UMi line-of-sight (LOS) scenarios. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Scenario** & **Frequency (GHz)** & **Conditions** & \(\mu_{\text{DS}}\) **(ns)** & \(m_{\text{DS}}\) **(ns)** & \(\sigma_{\text{DS}}\) **(ns)** & \(Q_{\text{DS,0,95}}\) **(ns)** \\ \hline OS-CC & 60.0 & LOS & 26.5 & 27.3 & 16.9 & 59.5 \\ SC-CC & 60.0 & LOS & 26.6 & 23.2 & 19.1 & 63.9 \\ SC-RA & 60.4 & LOS & 18.3 & 18.2 & 7.84 & 32.5 \\  & & NLOS & 20.9 & 15.9 & 13.4 & 43.8 \\  & 10.0 & LOS & 21.9 & 21.1 & 10.2 & 42.2 \\  & & NLOS & 37.7 & 38.2 & 17.4 & 67.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical parameters of the root mean square (RMS) delay spread (DS): mean \(\mu_{\text{DS}}\), standard deviation \(\sigma_{\text{DS}}\), median \(m_{\text{DS}}\) and 95%-quantile \(Q_{\text{DS,0,95}}\). \[\log_{10}\left(\frac{\tau_{\text{rms}}}{1\,\text{s}}\right)(d)=\alpha+\beta d+ \Gamma_{e}, \tag{5}\]  
where \(\alpha\) is the IP at \(d=0\,\text{m}\), \(\beta\) is the slope and \(\Gamma_{e}\) is a zero-mean random variable with standard deviation \(\epsilon\). The values obtained by LS fitting are given in Table 4.  
Figure 6b illustrates the same evaluation for the SC-CC environment, where more samples are available. The DS values similarly increase as a function of distance, though the slope is less steep and a saturation effect can be observed at around \(20\,\text{m}\). Hence, the model should not be extrapolated to distances beyond the validity range. It shall be noted that the saturation is not related to an exclusion of values due to an insufficient dynamic range of the APDPs, but the evaluable dynamic range is always large enough. Figure 6 also includes the DS derived from simulations--the corresponding parameters for the distance-dependent model are given in Table 4. As already seen in Section 4.3, the prediction yields a noticeably higher DS than the measurement for the OS-CC scenario. However, according to Figure 6a, the behavior of the DS over distance is very similar and the linear regressions are parallel. This is also reflected by the model parameters. Whereas the slope \(\beta\) of the simulations fits the measurements, the IP \(\alpha\) has a slight difference that matches the offset between the regressions. The larger standard deviation is mainly caused by some data points close to \(10^{-9}\), where no significant multipaths were predicted. For the SC-CC scenario, see Figure 6b, the simulated DS matches the measured DS very well. The ray tracer reproduces the behavior over a distance in a good manner, and also saturates around \(100\,\text{ns}\). Smaller DS in the simulation are caused by non-predicted paths, which increases the standard deviation in Table 4. \(\alpha\) is in agreement with the measurements. The slope \(\beta\) varies slightly, which is also obvious in Figure 6.  
The measurement results for the SC-RA scenario are depicted in Figure 7. The gradient for \(60\,\text{GHz}\) is moderate (compared to OS-CC and SC-CC). Nevertheless, it is clear that limiting the set to DS values attributed to distances below \(50\,\text{m}\) and calculating the empirical CCDF on this basis, would further increase the difference to the OS CC and SC-CC curves in Figure 5. For \(10\,\text{GHz}\), the gradient is very small--the calculated DS is almost independent from distance. Figure 6: Measured and simulated DS as a function of distance with linear least-squares (LS) fit: (a) OS-CC scenario; (b) SC-CC scenario.