## 2 System Model  
### Signal Model  
The TOW system under consideration consists of three fundamental components, i.e., the out-of-body unit, the skin channel and the \(M\) in-body unit(s). In this respect, the system employs \(M\) direct TOW links, where the \(M\) optical signal's copies pass through skin channel once. The whole link appears in Figure 1.  
It is assumed that that the external unit consists of a data capturing unit, followed by a digital signal processing (DSP) unit. The former unit converts external stimulations into electrical signals,  
Figure 1: Block diagram of the proposed TOW system.  
while the latter unit performs the processes of digitization and compression of the \(M\) data copies into OOK, IM/DD, or \(L\)-PPM modulated signals. These signals are forwarded to the transmitter, which emits \(M\) data copies of the same part of information towards the internal unit that consists, in turn, of the corresponding receiver(s), DSP unit and the stimulation (STM) unit that eventually stimulates the appropriate nerve. Thus, the internal DSP and STM units are responsible for generating the appropriate stimulations [14; 36; 37; 38; 39]. In this context, the statistical channel model for the examined TOW system is given as [39]  
\[y_{m}=\eta_{m}h_{m}x+n, \tag{1}\]  
where \(y_{m}\) represents the \(m\)-\(th\) signal copy with \(m\) = 1, 2,..., \(M\), \(\eta_{m}\) is the effective receiver's photo-current conversion ratio, \(x\) is the modulated signal, convey over the corresponding \(h_{m}\) channel with additive noise \(n\) that is modeled as a zero-mean complex Gaussian process with variance \(\sigma^{2}\).  
The \(m\)-\(th\) channel for the case of the transdermal link can be expressed as [36; 37; 38; 39; 58]  
\[h_{m}=h_{l,m}h_{p,m}, \tag{2}\]  
where \(h_{l,m}\) stands for the deterministic channel coefficient due to the propagation losses of the \(m\)-\(th\) channel though the skin and \(h_{p,m}\) represents the corresponding stochastic process that models the geometric spread due to the presence of pointing errors. The former deterministic term is expressed as [36; 37; 38; 39]  
\[h_{l,m}=\exp\left[-\frac{1}{2}\alpha(\lambda_{m})\delta_{m}\right], \tag{3}\]  
where \(\delta_{m}\) is the total dermis thickness of the \(m\)-\(th\) channel and \(\alpha(\lambda_{m})\) is the corresponding skin attenuation coefficient in the corresponding operational wavelength \(\lambda_{m}\). More specifically, the term skin refers to the complex biological structure that consists of three basic layers, i.e., stratum corneum, epidermis and dermis, with transmitter and receiver terminals being in contact with the epidermal and the adipose side of skin [28]. Thus, their distance can be accurately approximated by skin's thickness while the parameter \(h_{l,m}\) expresses the skin-induced attenuation of the propagated optical signal through the \(m\)-\(th\) transdermal path. The wavelength dependent value of \(\alpha(\lambda_{m})\), depends also on the optical properties of the skin and for values between 400 nm and 1800 nm is obtained as [37; 38; 39]  
\[\alpha(\lambda_{m})=\sum_{i=1}^{8}a_{i}\exp\left[-\left(\frac{\lambda_{m}-b_{ i}}{c_{i}}\right)^{2}\right], \tag{4}\]  
where \(\lambda_{m}\) values are expressed in nm and the values of \(a_{i}\), \(b_{i}\) and \(c_{i}\), with \(i\) = 1, 2..., 8, are given in the following table as [37; 38].