## 2 System and Channel Model  
The TOW under investigation mainly consists of three fundamental parts: the out-of-body transmitter unit, the skin propagation medium which acts as the communication channel, and the in-body receiver unit. The external transmitter emits via a laser source the information-bearing light carrier which is modulated with on off keying (OOK) modulation format. After traversingthe propagation medium, the internal unit collects the light signal via an appropriate photodiode, and then the received signal is demodulated in order to provide the appropriate stimulations, after being processed by the internal digital signal processing unit and the stimulation unit. Under these circumstances, the received signal is expressed as follows [35]:  
\[y=\eta hx+n, \tag{1}\]  
where \(\eta\) represents the photo-current conversion ratio at the receiver side, \(h\) is the skin channel state, \(x\) stands for the modulated binary transmitted signal, and \(n\) denotes the additive noise described as a zero mean complex Gaussian process with variance \(\sigma^{2}\)[36]. The channel state is expressed asfollows [10]:  
\[h=h_{l}h_{p}, \tag{2}\]  
where \(h_{l}\) represents the deterministic channel coefficient owing to transdermal propagation loss, and \(h_{p}\) is the stochastic process that describes the misalignment-induced geometric spread at the receiver aperture due to pointing errors [35]. The deterministic pathloss parameter of Equation (2) is given as follows [34]:  
\[h_{l}=\exp\left[-\frac{1}{2}\alpha(\lambda)\delta\right], \tag{3}\]  
where \(\delta\) is the dermal thickness of the skin channel which practically translates into the transdermal link length, and \(\alpha(\lambda)\) is the corresponding attenuation coefficient which depends strongly on the utilized optical wavelength, \(\lambda\). Indeed, within the wavelength region between 400 nm and 1800 nm, the latter coefficient is expressed asfollows [9]:  
\[\alpha(\lambda)=\sum_{i=1}^{8}a_{i}\exp\left[-\left(\frac{\lambda-b_{i}}{c_{i} }\right)^{2}\right], \tag{4}\]  
where wavelength values are expressed in nm, and the remainingparameter values are obtained as described below [24; 35]. In fact, for TOW links, we focus on their operation at wavelengths between 600 nm and 1300 nm, since, within this wavelength region, known as the medical or tissue optical window, the photon absorption that stems mainly from water content or hemoglobin and melanin can be minimized [3; 23]. Optical signals with smaller or larger wavelengths are practically inappropriate for the establishment of TOW links due to this extremely strong skin-induced photon absorption. In addition to the selected optical wavelength, the value of the skin attenuation coefficient depends heavily on the optical properties of the skin and can be obtained numerically from experimental results [20]. On the basis of these values and by employing the trust region method, the latter expression along with its parameter values described in Table 1 can be obtained. It is notable that the accuracy of the latter expression was estimated to be higher than 99.7% by using the coefficient of determination (\(R\)-squared), which is the square of the correlation between the response values and the predicted response values and can be expressed as the ratio of the sum of squares of the regression and the total sum of squares [9]. Additionally, the random variable that describes stochastic pointing errors obtains the following probability density function (PDF) [16; 39; 43]:  
\[f_{h_{p}}(h_{p})=\psi^{2}A_{0}^{-\psi^{2}}h_{p}^{\psi^{2}-1},\ 0\leq h_{p}\leq A_{0}, \tag{5}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline \(i\) & \(a_{i}\) & \(b_{i}\) & \(c_{i}\) \\ \hline
1 & 10 & 0.35 & 0.065 \\
2 & 4.5 & 0.42 & 0.25 \\
3 & 13.48 & \(-1.5\) & 50.12 \\
4 & 14.7 & 1442 & 49.35 \\
5 & 7.435 & 1499 & 75.88 \\
6 & 48 & 3322 & 1033 \\
7 & 594.1 & \(-183\) & 285.9 \\
8 & 11.47 & \(-618.5\) & 1054 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The \(a_{i}\), \(b_{i}\), and \(c_{i}\) parameter values.