## 6 Time Dispersion Parameters and Analysis  
We have been investigating the time characteristics of a 5G scheme by using the RMS delay diffusion, the mean delay (MN-EX), and the maximum delay excess (MAX-EX). The MAX-EX delay is the delay where the farthest MPCs can be obtained with the gain power above the threshold value (20 dB less than the maximum power of the MPCs). The time dispersion parameters provide delay information for the channel, which is very useful for designing a robust 5G system. It is possible to calculate the RMS delay spread by the square root of the second moment of the power delay spectrum, as follows [31]:  
\[\tau_{rms}=\sqrt{E(\tau^{2})-(E(\tau))^{2}}, \tag{3}\]  
where  
\[E(\tau^{2})=\frac{\sum_{j}p\big{(}\tau_{j}\big{)}\cdot\big{(}\tau_{j}\big{)}^{ 2}}{\sum_{j}p\big{(}\tau_{j}\big{)}}, \tag{4}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **PLE** & \(\sigma\) \\ \hline
**CI** & **0.9** & \(\sigma\) \\ \hline  & \(\alpha\) & \(\beta\) & \(\gamma\) & \(\sigma\) \\ ABG & 0.2 & 5.8 & 5.4 & 2.5 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Multilateral path loss models 19, 28, and 38 GHz; CI; and alpha–beta–gamma (ABG) model parameters. and the MN-Ex is given as follows:  
\[E(\tau)=\frac{\sum_{j}p\big{(}\tau_{j}\big{)}\cdot\tau_{j}}{\sum_{j}p\big{(}\tau_ {j}\big{)}}, \tag{5}\]  
where \(p\big{(}\tau_{j}\big{)}\) is the power of the multipath with delay \(\tau_{j}\). To investigate the temporal dispersion, the received power at all of the receiver locations is depicted in Figure 4a-c, with excess delay. The Rx is indexed from 1 to 11, as shown in Figure 4a-c. For all of the measurement points at all of the investigated frequencies, most of the received power arrived at an excess delay of less than 30 ns, and between 50 to 60 ns. It can be shown that the high received power can be collected at the large excess delay for all of the measured frequencies. As an example, the Rx 6-Rx 11 have a high received power at an excess delay between 55 ns and 60 ns at 19 and 28 GHz, as shown in Figure 4a,b, and almost all of the Rx 1-Rx 11 received a high power at 38 GHz, as shown in Figure 4c. The maximum excess delay values (the delay of the received signal with power more than the noise floor of \(-\)120 dBm) are less than 93, 85, and 76 ns at 19, 28, and 38 GHz, respectively. It is worth noting that there is no linear correlation between the Rx distance, excess delay, and received power. This means that the composition of the setting plays a crucial role in 5G wireless channel at mm-wave bands. In other words, the reflection and scattering phenomena can be exploited at mm-wave frequencies to get a strong power from the farthest multipath components. Figure 4: _Cont._  
From the received power, excess delay, and using Equations (3) and (4), the temporal dispersion can be investigated based on the RMS delay spread. Figure 5 shows the RMS delay spread variation as a function of the Tx-Rx separation distance at 19, 28, and 38 GHz. Figure 4(a)-c shows that the RMS delay spread variation with a Tx-Rx separation distance is not linear. Moreover, the correlation between these parameters is weak, if it exists at all. The RMS delay spread at the farthest location (Tx-Rx separation distance = 13.5 m) has the lowest value at all of the frequencies (Figure 4(a)-c). This result implies that the farthest MPCs have less power than the threshold value (20 dB less than the maximum  
Figure 4: Received power level versus excess delay at all of the receiver sites. power of the MPCs). Table 3 lists the values of the maximum excess delay, the mean values of RMS delay spread and mean excess delay, and the MN-EX/RMS delay spread for all of the frequencies. The MAX-EX delay varies between 64 and 90 ns; the lowest value is associated with the highest frequency. This finding indicates that, at high frequencies within the same threshold, the paths after the MAX-EX delay are ignored, because the power of these components is less than or identical to that of the noise floor.