## 2 Indoor Scenario Simulation and Characterization
The new angles \((\theta_{r},\Phi_{r})\) of the reflected wave and \((\theta_{t},\Phi_{t})\) of the transmitted wave are calculated once the parameters of transmission \(T\) and reflection \(R\) are calculated, and the angle of incidence \(\Psi_{l}\) and \(\Psi_{t}\). The diffracted field is calculated by [34]:  
\[E_{UTD}=e_{0}\frac{e^{-jks_{1}}}{s_{1}}\;D^{\perp\parallel}\sqrt{\frac{s_{1}} {s_{2}(s_{1}+s_{2})}}\;e^{-jks_{2}} \tag{3}\]  
where \(s_{1},s_{2}\) are the distances from the source to the edge and from the edge to the receiver point, respectively. \(D^{\perp\parallel}\) are the diffraction coefficients given by [34, 35, 36] as:  
\[D^{\perp\perp}=\frac{-e^{(-j\pi/4)}}{2n\sqrt{2\pi k}}\left\{ \begin{array}{l} \cot\left(\frac{\pi+(\Phi_{2}-\Phi_{1})}{2n}\right)F\left(kLa^{+}(\Phi_{2}- \Phi_{1})\right)\\ +\cot\left(\frac{\pi-(\Phi_{2}-\Phi_{1})}{2n}\right)F\left(kLa^{-}(\Phi_{2}- \Phi_{1})\right)\\ +R_{0}^{\perp\perp}\cot\left(\frac{\pi-(\Phi_{2}+\Phi_{1})}{2n}\right)F\left( kLa^{-}(\Phi_{2}+\Phi_{1})\right)\\ +R_{n}^{\perp\perp}\cot\left(\frac{\pi+(\Phi_{2}+\Phi_{1})}{2n}\right)F\left( kLa^{+}(\Phi_{2}+\Phi_{1})\right)\end{array} \right\} \tag{4}\]  
where \(n\pi\) is the wedge angle, \(F,L\) and \(\alpha\pm\) are defined in [34], \(R_{0,n}\) are the reflection coefficients for the appropriate polarization for the 0 face or n face, respectively. The \(\Phi_{2}\) and \(\Phi_{1}\) angles in Equation (4) would refer to the angles in Figure 3.  
With the parameters stored in each hexahedron of the considered scenario, the received power can be calculated at each point taking into account the losses of propagation through a medium (\(\varepsilon\), \(\mu\), \(\sigma\)) at a distance \(d\), with the attenuation constant \(\alpha\) (Np/m), and the phase constant \(\beta\) (rad/m). Based on this theory, the main contribution of the ray-launching technique is that it provides the impulse response of the channel \(h\) (\(t,fc,\Delta f,r\)) for each transmitter, at a given carrier frequency, \(fc\), at a given bandwidth (\(fc\pm\Delta f\)), where the materials have a similar response and at a given position, \(r\). A stationary channel can be wholly characterized with this information. Three dimensional maps of power levels can be obtained, as well as delay spread maps, power delay profiles and Signal to Noise ratio levels. The entire floor of the Public University of Navarre department building has been considered for the simulations, taking into account all the furniture and infrastructures as chairs, tables or air ducts, as depicted in Figure 4. The total length of the scenario is 55.3 m \(\times\) 27.85 m \(\times\) 3.8 m and it has been divided into 1 m size cuboids. Eight antennas have been distributed throughout the scenario, considering the real antennas properties and the locations used in the measurement campaign. The configured parameters for the simulations are given in Table 1.  
The coverage given by a single antenna is not capable of providing service for the complete scenario, but an adequate RF power distribution can be obtained deploying properly the eight elements of the proposed network. This behavior is shown in Figure 5, where the contribution of each antenna separately and the jointly contribution are depicted. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Frequency & 2.405 GHz \\ Transmitted power & 0 dBm \\ Antenna gain & 5 dBi \\ Horizontal plane angle resolution (\(\Delta\Phi\)) & 1\({}^{\circ}\) \\ Vertical plane angle resolution (\(\Delta\theta\)) & 1\({}^{\circ}\) \\ Maximum permitted reflections & 5 \\ Cuboids resolution & 1 m \(\times\) 1 m \(\times\) 1 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Considered parameters for the Ray Launching simulation. Figure 4: Schematic representation of the simulated scenario with the location of the antennas (represented by red points). Figure 3: Geometry for wedge diffraction coefficients.