# Investigations on Millimeter-Wave Indoor Channel Simulations for 5G Networks
## 3 Methodology and Simulation Setup
For example, PLE is estimated by taking the path loss information recorded by WI; then, Equation (5) (below) is used through a Matlab code. The number of clusters is estimated by taking the rays' arrival time using a Matlab code; if the time delay between two consecutive rays is more than 6 ns, the two rays belong to different clusters. Figure 2 presents a simulated LOS propagation. The propagation paths include a direct path, a reflected path, and multi-reflected paths, and the rays' colors denote the relative power of each path. Received signal strength (RSS) can be computed with and without the consideration of the small-scale effect; the first method takes the power sum of all multipath rays, known as \"power sum prediction (PS)\" [35; 36]:  
\[\langle P_{PS}\rangle=\sum_{M}P_{M}. \tag{1}\]  
where \(\langle P_{\text{PS}}\rangle\), M, and \(P_{M}\) are the averaged power using the PS method, number of multipath rays, and power of each ray, respectively. This method requires a huge bandwidth and antenna array to exclude the small fading effect. Path loss (PL) models describe the propagation environment through a mathematical expression. These models are widely used in environments with similar features to the original one from which the model's parameters are extracted. The close-in (CI) free space \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Frequency (GHz)**} & **28** & **39** & **60** & **75.3** \\ \hline \multirow{2}{*}{Concrete} & \(\varepsilon_{r}\) & 5.31 & 5.31 & 5.31 & 5.31 \\ \cline{2-6}  & \(\sigma\) & 0.48 & 0.633 & 0.90 & 1.06 \\ \hline \multirow{2}{*}{Glass} & \(\varepsilon_{r}\) & 6.27 & 6.27 & 6.27 & 6.27 \\ \cline{2-6}  & \(\sigma\) & 0.23 & 0.34 & 0.57 & 0.72 \\ \hline \multirow{2}{*}{Wood} & \(\varepsilon_{r}\) & 1.99 & 1.99 & 1.99 & 1.99 \\ \cline{2-6}  & \(\sigma\) & 0.17 & 0.24 & 0.38 & 0.47 \\ \hline \multirow{2}{*}{Drywall} & \(\varepsilon_{r}\) & 2.94 & 2.94 & 2.94 & 2.94 \\ \cline{2-6}  & \(\sigma\) & 0.12 & 0.16 & 0.21 & 0.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Building material properties’ relationship with frequency. \begin{table}
\begin{tabular}{c c} \hline \hline
**Property** & **Setting** \\ \hline Number of paths & 10 \\ \hline Ray Spacing (°) & 0.1 \\ \hline Plane-wave ray spacing & 0.5 m \\ \hline Propagation model & Full 3D \\ \hline Ray tracing method & SBR \\ \hline Ray tracing acceleration & Octree \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._reference distance PL model is a common PL model, which allows simple comparisons with different frequency bands, which is characterized by a single PLE (n) [37; 38]. \[PL_{(f,d)}^{CI}=FSPL(f,d_{0})+10n\,\log_{10}\left(\frac{d}{d_{0}}\right)+X_{ \sigma}^{CI} \tag{2}\]  
where FSPL is the free-space path loss, f is the operating frequency, d\({}_{0}\) is the reference distance, usually 1 m from the transmitter, and \(X_{\sigma}^{CI}\) is a zero-mean Gaussian random variable due to shadowing with standard deviation (\(\sigma\)) in dB. FSPL is given by Equation (3), where \(\lambda\) is the wavelength in m.  
\[FSPL(f,1)=20\,\log_{10}\left(\frac{4\pi}{\lambda}\right) \tag{3}\]  
The PLE is estimated using the Minimum Mean-Squared Error (MMSE), which fits the simulated results with the lowest error. From Equation (2):  
\[X_{\sigma}^{CI}=PL_{(f,d)}^{CI}-FSPL(f,1)+n\big{(}10\,\log_{10}(d)\big{)}=A-nB \tag{4}\]  
where A = \(PL_{(f,d)}^{CI}-FSPL(f,1)\) and B = \(\big{(}10\,\log_{10}(d)\big{)}\). The PLE is estimated using MATLAB as in Equation (5), where A and B are written as column vectors. \[n=A^{T}\Big{(}B^{T}B\Big{)}^{-1}B \tag{5}\]  
RMS delay spread (\(\sigma_{\tau}\)) is estimated from the second moment of the delay power spectrum and describes the multipath time dispersion and coherence bandwidth:  
\[\sigma_{\tau}=\sqrt{\overline{\tau^{2}}-(\overline{\tau})^{2}} \tag{6}\]  
where \(\overline{\tau^{2}}\) is the 2 nd central moment of a power delay profile and \(\overline{\tau}\) is the mean excess delay.