## 3 Method  
### Developing the Simplified PL Model  
In this section, the steps to develop the simplified PL model are explained. Figure 3 describes our approach towards approximating layered medium in an adult human model. Figure 3b shows the cross-section of the human frontal thorax. Figure 3c is an equivalent layered medium that is used for modeling and is obtained from the highlighted region of Figure 3b. Figure 4 shows a plane wave normally incident to a lossy multilayered medium with N layers of thickness \(l_{i}\), where i = 1,2,..,N, and N + 1 interfaces, \(T_{i}\) = transmission coefficient, \(R_{i}\) = reflection coefficient, \(\alpha_{i}\) = attenuation constant of the medium and \(\eta_{i}\) = characteristic impedance of the medium. The amplitude of the incident plane wave (\(E_{inc}\)) is 1 V/m. As the wave propagates through the medium, it undergoes attenuation and reflections due to the lossy medium and the interface of the layers, respectively. The development of the PL model is explained by means of a flow chart, as shown in Figure 5, and its various blocks are explained as follows. Figure 4: Plane-wave propagation in a multilayer model. Figure 3: The anatomical adult model: (**a**) Duke, followed by (**b**) the cross-section of the human frontal thorax and (**c**) the equivalent tissue layer of the human frontal thorax. 3.1.1. Loss in the Medium  
The attenuation that the plane wave undergoes as it propagates through the multilayered lossy medium is accounted for by \(\alpha\), which is the attenuation constant (nepers/meter) of the medium. The time-averaged power per unit area entering each layer is calculated using the Poynting vector, which is given as:  
\[P_{i}=\frac{1}{2}Re\left(E\times H^{*}\right),where\;i=1,2,...,M \tag{1}\]  
The power absorbed in the layers is equal to the difference of the power entering the layer and the power leaving it. \[P_{i}^{loss}=P_{i}-P_{i+1},where\;i=1,2,...,M \tag{2}\]  
3.1.2. Antenna Characteristics  
Once the power loss is determined for the plane wave traveling through the layers, the next step is to introduce the antenna characteristics, of the antennas being used, in order to calculate the PL. The antenna characteristics of the two Tx and Rx dipole antennas at 2.45 GHz, as mentioned in Section 2.1[7], include the reflection coefficients \(|S_{11}|\) and \(|S_{22}|\) of the antennas, respectively. The gains of the Tx and the Rx antennas are \(G_{t}\) and \(G_{r}\), respectively, and the effective aperture of the Rx antenna is given by \(\lambda_{med}^{2}/(4\pi)\), where \(\lambda_{med}\) is the wavelength of the medium in which the Rx is placed. 3.1.3. Spherical Wavefront  
The factor \((\frac{1}{4\pi R^{2}})\) in (3) takes into account the increase in the spherical wavefront surface [19]. It accounts for the fact that the actual waves are not plane, but spherical, where R is the distance between the Tx and the Rx. Figure 5: Block diagram of path loss (PL) calculation. The parameters of the antenna, loss in the medium and the antenna characteristics in a multilayer lossy medium are used in the Friis transmission equation along with the theory of the reflection and transmission of electromagnetic waves for the development of the simplified PL model. The Friis transmission equation in lossy medium is as follows [19]:  
\[\frac{1}{PL}=\frac{P_{r}}{P_{t}}=\frac{(1-|S_{11}|^{2})(1-|S_{22}|^{2})\;\lambda _{med}^{2}\;G_{t}\;G_{r}\;exp(-\alpha r)}{(4\pi R)^{2}} \tag{3}\]  
where \((1-|S_{11}|^{2})\) and \((1-|S_{22}|^{2})\) are the mismatch efficiency obtained from the reflection coefficients \(|S_{11}|\) and \(|S_{22}|\). \(G_{t}\) and \(G_{r}\) are calculated depending on their positions, _i.e._, if they are in free space or in medium [8]. The method of calculating the gain of an antenna in a medium has been described in [8], and the same methodology is applied here. In the Friis transmission formula, the loss of power in a medium is calculated by \(exp(-\alpha r)\).