## 2 Methodology
### Simulation Setup  
In this experiment, three-dimensional (3D) radiation pattern simulation is employed to determine the radiative characteristics of the SMA open ended and the wire loop when inserted inside a restricted reflective space, such as the 18650 metal shell. The simulation accounts for the effects of ground planes by including a large surface of 2 m by 2 m, whereas the reflections are maximised by considering the simulation materials as perfect electrical conductors (PECs). The focus of the simulation is to show the phenomena that may occur when employing similar radiative designs, however, since the radiative structures have not been specifically designed for the operating frequencies, their surface current distribution, impedances and voltage standing wave ratio (VSWR) are not key factors to be highlighted in testing. As a preliminary simulation measure before conducting the more complex 3D radiation pattern involving the cell structure and the reflective plane, the SMA connector and the wire loop attached to the SMA were implemented and tested separately before being attached to the cell's shell structure, Figure 5. The azimuth and elevation planes in polar plots for both structures are illustrated in order to demonstrate that they act as described in classical RF literature. Three-dimensional representations of their attachment to the metal shell are shown separately in Figure 5A,B, whereas the additional connection to the SMA connector (i.e., closing the circuit between SMA's central pin and external housing) to accommodate the RF simulation excitation point is shown in Figure 5C. Radio line of sight (LOS) propagation can be numerically modelled by the free space path loss (FSPL) model [39]; however, it excludes the multipath effects. The secondary ground reflections at equal incident and reflective angles, including the FSPL model, can be modelled as shooting and bouncing rays (SBR) with the Two-ray model [40; 41]. This model can then serve as a reference for derived multi-ray analysis, such as the Three-ray model [42], which accounts the ceiling reflection as well. Moreover, since the 3D ray tracing is subjective and highly sensitive to its shooting ray source model [43], Figure 6 shows the geometrically derived relationships [39] between the Two-ray model and the Three-ray implementation based on this study case:  
Figure 5: MATLAB RF test setup initial azimuth and elevation planes polar plots for 868 MHz and 2.4 GHz communication with the SMA as radiative element (**A**), the wire loop connected to the SMA (**B**) and the modification on the 3D design for the SMA to insert the simulation RF excitation source (**C**). Since the radiation pattern for dipole and loop antenna are resembling in shape with a torus while 90\({}^{\circ}\) offset from each other, the azimuth (az) plane for SMA is similar with the elevation (el) plane for the loop. \[R_{ground}=\left\{ \begin{array}{l}\frac{\varepsilon_{r}-\sqrt{\varepsilon_{r}- \cos^{2}(\beta)}}{\varepsilon_{r}\sin(\alpha)+\lambda\frac{\zeta_{r}-\cos^{2}( \alpha)}{\varepsilon_{r}\sin(\beta)+\sqrt{\varepsilon_{r}-\cos^{2}(\beta)}}}, \text{ {vertical polarisation}}\\ \frac{\sin(\alpha)-\sqrt{\varepsilon_{r}-\cos^{2}(\alpha)}}{\sin(\alpha)+ \sqrt{\varepsilon_{r}-\cos^{2}(\alpha)}},\text{ horizontal polarisation}\end{array} \right. ;\ R_{ ceiling}=\left\{ \begin{array}{l}\frac{\varepsilon_{r}-\sqrt{\varepsilon_{r}-\cos^{2}(\beta)}}{ \varepsilon_{r}\sin(\beta)+\sqrt{\varepsilon_{r}-\cos^{2}(\beta)}},\text{ {vertical polarisation}}\\ \frac{\sin(\beta)-\sqrt{\varepsilon_{r}-\cos^{2}(\beta)}}{\sin(\beta)+\sqrt{ \varepsilon_{r}-\cos^{2}(\beta)}},\text{ horizontal polarisation}\end{array} \right.