## 2 Methodology
### Simulation Setup
\tag{1}\]  
\[d_{1}=\sqrt{\left(h_{1}-h_{2}\right)^{2}+D^{2}};\ d_{1}-d_{2}=\sqrt{\left(h_{1 }+h_{2}\right)^{2}+D^{2}}-\sqrt{\left(h_{1}-h_{2}\right)^{2}+D^{2}};d_{1}-d_ {3}=\sqrt{\left(h_{11}-h_{22}\right)^{2}+D^{2}}-\sqrt{\left(h_{1}-h_{2}\right) ^{2}+D^{2}} \tag{2}\]  
\[\Delta\varphi_{1}=\frac{2\pi d_{1}}{\lambda};\ \Delta\varphi_{2}=\frac{2\pi(d_{1}-d_ {2})}{\lambda};\Delta\varphi_{3}=\frac{2\pi(d_{1}-d_{3})}{\lambda} \tag{3}\]  
\[P_{r}=P_{t}\left[\frac{\lambda}{4\pi}\right]^{2}\left|\frac{\sqrt{G_{t1}G_{r1 }}e^{-i\Delta\varphi_{1}}}{d_{1}}+\frac{R_{ground}\sqrt{G_{t2}G_{r2}}e^{-i \Delta\varphi_{2}}}{d_{2}}+\frac{R_{ceiling}\sqrt{G_{t3}G_{r3}}e^{-i\Delta \varphi_{3}}}{d_{3}}\right|^{2} \tag{4}\]  
where \(R\) is the reflection coefficient for ground \(R_{ground}\) and ceiling \(R_{ceiling}\), including the ray's incidence associated angles \(\alpha\) and \(\beta\), \(\varepsilon_{r}\) is the material relative electric permittivity, \(d_{1-3}\) is the ray path for each of the three casted rays (i.e., \(r1\), \(r2\) and \(r3\)), \(\Delta\varphi_{1-3}\) is the phase difference derived from ray's distance and wavelength \(\lambda\), \(P_{r}\) is the received power, \(P_{t}\) is the transmit power, \(G_{t1-3}\) and \(G_{r1-3}\) are the Tx and Rx antenna, respectively, gains for the three casted rays (i.e., \(r1\), \(r2\) and \(r3\)). When computing the numerical values of (1)-(4), the following assumptions have been made: as the ground plane and the ceiling for the measurement setup are made from concrete, \(\varepsilon_{r}\) was set to the same value as suggested in [44]; using geometrical calculation methods in (2), ray paths can be predicted based on elevations of the Tx and Rx antennas from ground, such as 0.1-0.2 m, and room height \(h\) of 3.5 m, \(h_{11}=h\)-\(h_{1}\) and \(h_{22}=h\)-\(h_{2}\); considering the total separation distance between Tx and Rx is greater than the antenna heights, the signal phase difference \(\Delta\varphi\) from (2) can be expressed as a truncation of [PERSON]'s series [34]; since the simulation serves as a reference for the experimental results, the transmitting and receiving gains \(G_{t}\) and \(G_{r}\) that are provided by the exact alignment of the radiation pattern with the incoming signal are all considered equal with one, whereas the transmitting power \(P_{t}\) value is 1 mW. In addition, the three terms of the sum in (4) can be identified as the free-space path loss (FSPL) added to the Two-ray flat ground reflection, with the final inclusion of the Three-ray flat ceiling reflection. The reflection coefficient computed and shown in Figure 6B provides an initial insight regarding the Three-ray simulation. The influence of the ground and ceiling are similar up to 1 m for both polarisations, whereas above that point the ceiling reflection dominates. In this electromagnetic (EM) simulation, the MATLAB R2021b cross-disciplinary platform was selected due to its RF toolboxes providing the default tools for importing  
Figure 6: MATLAB signal attenuation simulation by using the Three-ray and Free space models for 868 MHz and 2.4 GHz for following the scenario described in (**A**), resulting in a computed reflection coefficient versus distance for the concrete ground and ceiling such illustrated in (**B**). an external 3D computer-aided design (CAD) of an antenna and analysing it with various solvers depending on the electrical size of the scenario. As the overall scenario implemented through the radiative cell's shell as an antenna on top of a large reflective platform of 2 m by 2 m delivered a mesh of more than 12,000 triangular faces, the method of moments (MoM) combined with physical optics (PO) was selected. The MoM-PO solver provided the best balance between simulation time i.e., approximatively 30 min each frequency and orientation scenario on a moderate computing platform equipped with a four-core processor Xeon E5-1620 V2 running at 3.7 GHz and 32 GB of RAM.