# LoS Theoretical and Experimental MIMO Study from 1-40 GHz in Indoor Environments
## 5 Comparison with Ray-Tracing Simulations  
### Radio Channel Characteristics  
A 3D ray-tracing tool (RT) has been programmed in MATLAB by our research group. The tool includes the usual reflected and diffracted components and combinations of them as well as single-order diffuse scattering components. The following mechanisms were considered in order to achieve a good accuracy and a reasonable simulation time: direct ray, up to two order reflections, simple diffractions, simple diffractions plus single reflections, single reflections plus simple diffractions and single order diffuse scattering components. The Lambertian model was used to simulate the diffuse scattering; this model has only one parameter, the scattering parameter \(S\) that controls how much energy is scattered in all directions [35]. An iterative method, as the one shown in [21], was applied to find the best values of the S parameter in the measured band and scenario. Moreover, the measured radiating pattern of the antennas (see Figure 3) were included to improve the accuracy in each path gain of all propagation mechanisms. In Figure 12 the comparison between the measured and simulated PDP for position 10 is shown; the 30 dB threshold is also depicted. As seen in Figure 12 the main groups of components, above the threshold, are correctly simulated by the ray tracing tool. As in the measurements, the Hanning window was used to extract the PDP. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Band** & \(\mathbf{n_{DS}}\) & \(\mathbf{DS_{0}}\) **(dB)** & \(\mathbf{\sigma_{X}}\) **(dB)** & \(\mathbf{R^{2}}\) \\ \hline
3.3–4.99 GHz & 0.67 & 4.79 & 1.04 & 0.61 \\
24.25–27.5 GHz & 0.50 & 2.21 & 0.63 & 0.70 \\
37–40 GHz & 0.54 & 2.04 & 0.58 & 0.77 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: 1-slope model for the root mean square of the delay spread (RMS DS) for the selected WRC bands. The standard deviation and \(\mathrm{R^{2}}\) parameters of the linear model of Equation (5) are shown. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Band** & **Reference** & **RMS DS Mean (ns)** & \
\begin{tabular}{c} **RMS DS Standard** \\ **Deviation (ns)** \\ \end{tabular} &
\begin{tabular}{c} **Type of** \\ **Environment** \\ \end{tabular} \\ \hline
3.3–4.99 GHz & This work & 7.71 & 1.66 & Small office/lab. \\
24.25–27.5 GHz & This work & 4.37 & 1.14 & Small office/lab. \\
37–40 GHz & This work & 4.42 & 1.20 & Small office/lab. \\
26 GHz & [29] & 16.08 & 2.18 & Auditorium \\
28 GHz & [25] & 17.20 & 16.40 & Large office \\
28 & [28] & 23.10 & 4.20 & Industrial \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Measured mean and standard deviation of the RMS DS. The measured values are compared with those found in the literature. In Table 9, the comparison between the simulated and measured RMS DS is shown. A threshold of 30 dB was used in all cases. The results of the mean delay comparison are collected in Table 10. The mean accuracy of the RMS DS is close to 75%; the accuracy is below 60% for only three positions whereas the maximum accuracy is around 100%. The accuracy for the mean delay is high, reaching a mean value of 94.00%. A LoS component exists in all positions and the associated delay influences to a great extent the mean delay parameter. Since the LoS component is easily simulated with the ray-tracing tool, this explains the good match. Likewise, the PL accuracy is high as seen in Table 11. As in Figure 5 the gain has been extracted from the simulated PL. The mean error in dB is only 1.13 dB. In general, the accuracy is high, it can be improved including higher order components are three and four-order reflections, multiple diffractions and even second-order diffuse scattering; the simulation of these components require large amounts of computer memory and they are also very time consuming; for these reasons higher order components were not included in this work. Figure 12: Comparison between the measured and simulated PDP for position number 10.