## 2 Indoor Scenario Simulation and Characterization  
In order to estimate the feasibility of deploying WSNs inside indoor complex environments, a radio coverage map becomes essential. Various indoor models have been developed in the past based on semi-empirical approaches [10; 11; 12]. The advantage of these methods is that they require low computational cost but they have limited accuracy in comparison with high precision full wave techniques, which also exhibit very high computational cost [13; 14; 15; 16; 17; 18; 19]. A commitment between accuracy and computational time is acquired with deterministic methods, which are based on Geometrical Optics [20]. The Ray Tracing approaches combined with uniform theory of diffraction (UTD) is most commonly employed to radio coverage estimation [21; 22; 23; 24]. As illustrated in Figure 1, the ray launching (RL) technique is based on recognizing a single point of the radiated wave with a ray that propagates along the space following a combination of optic and electromagnetic theories. RL techniques can be used in environments where the frequency of interest is much smaller than the dimensions of the surroundings. A 3D in-house developed RL algorithm has been used for the characterization of wireless propagation in the ground floor of a department of the Public University of Navarre (UPNA, Pamplona, Spain). The algorithm has been explained in detail in [25] and it has been validated in the literature for different applications, like the analysis of wireless propagation in closed environments [26, 27, 28, 29], interference analysis [30] or electromagnetic dosimetry evaluation [31]. It is based on Geometrical Optics (GO) and Geometrical Theory of Diffraction (GTD). GO approaches consider only direct, reflected and refracted rays, bringing about abrupt areas, which correspond with the boundaries of the regions where these rays exist. Due to this constraint, the diffracted rays are introduced with the GTD and its uniform extension, the Uniform GTD (UTD). The whole scenario under analysis is divided into a uniform hexahedral mesh with cuboids of a given dimension. Rays at a predetermined power level are launched in a predefined solid angle from a specific transmitter location and the resulting power levels along the path are calculated and stored in the respective cuboids. The rays will be reflected, transmitted and diffracted by the structure of the walls, the furniture of the offices, the windows, the seats, _etc._ The material properties for all the elements within the scenario are considered, given the dielectric constant and permittivity at the frequency range of operation of the  
Figure 1: Wave front propagation with rays associated with single wave front points. Figure 2: Functional diagram of the 3D ray launching algorithm implemented at Public University of Navarre. system under analysis. Figure 2 summarizes the main points of the basic principle of the developed RL algorithm. Each ray propagates in the space as a single optic ray. The calculation of the electric field \(E\) created by an antenna with \(P_{rad}\) as radiated power, with a directivity \(D_{t}(\theta_{t},\Phi_{t})\) and polarization ratio \((X^{\perp},X^{\parallel})\) at a distance \(d\) in the free space is calculated by [32]:  
\[E_{l}^{\perp}=\sqrt{\frac{P_{rad}D_{t}(\theta_{t},\theta_{t})\eta_{0}}{2\Pi}} \;\frac{e^{-j\beta_{0}r}}{r}\;X^{\perp}L^{\perp} \tag{1}\]  
\[E_{l}^{\parallel}=\sqrt{\frac{P_{rad}D_{t}(\theta_{t},\phi_{t})\eta_{0}}{2\Pi} }\;\frac{e^{-j\beta_{0}r}}{r}\;X^{\parallel}L^{\parallel} \tag{2}\]  
where \(\beta_{0}=2\pi\ell_{c}\sqrt{\varepsilon_{0}\mu_{0}}\), \(\varepsilon_{0}=8.854\times 10^{-12}\), \(\mu_{0}=4\pi\times 10^{-7}\) and \(\eta_{0}=120\pi\). \(L^{\perp\parallel}\) are the path loss coefficients for each polarization. A reflected ray and a transmitted ray are created with new angles provided by [PERSON]'s law [33] when this ray finds an object in its path.