## 2 System and Channel Model  
### Signal Model  
The out-of-body transmitter terminal is assumed to employ just one laser source, while the receiver terminal, which is also assumed to be placed on the outside of the body, comprises \(m=1,2,...,M\) different, spatially separated detector apertures, i.e., see Figure 1.  
Figure 1: Block diagram of the proposed MRR TOW system. Apart from the IMD, the only part of the investigated TOW communication system that is needed to be installed inside the body is the retromodulator with its drive electronics. Initially, the laser source emits an interrogating light beam, which propagates through the skin and illuminates the internal retroreflector. The latter modulates the incoming light beam with on-off keying (OOK) and reflects it back to the receiver terminal. Consequently, the reflected light is modulated to reflect the information data to be transmitted. When the information-bearing light arrives at the receiver terminal, it is collected by its receiver aperture(s). At this point, by also using the OC technique, the intensity of the light signal is directly detected and demodulated in an attempt to recover the information data. It is worth mentioning that so far, OOK with intensity modulation and direct detection IM/DD is the only modulation format that has been practically utilized in both direct and MRR TOW link configurations, [1, 3, 7, 8, 9, 10], mainly because it outperforms in terms of simplicity, compactness and lightweight device equipment, which is very critical for any transdermal communication link design and feasibility. Nevertheless, when OOK is operating under fading conditions, the detector threshold must be estimated and adjusted by appropriate means, according to the variable skin channel states [12]. Therefore, perfect skin channel state information (CSI) needs to be assumed in order to perform optimal signal detection. In this context, the statistical skin channel model can be roughly expressed as [4, 5, 18, 25]:  
\[y_{m}=\eta_{m}h_{m}x+n \tag{1}\]  
where \(y_{m}\) represents the \(m\)-th signal copy arriving at the \(m\)-th receiver's aperture with \(m=1,2,...,M\); \(\eta_{m}\) is the corresponding effective photodiode's photo-current conversion ratio; \(x\) is the information bit signal; \(h_{m}\) denotes the \(m\)-th total channel state; and \(n\) is the additive noise that is modeled as a zero-mean complex Gaussian process with variance \(\sigma^{2}\)[5, 12, 25]. Each total skin channel state \(h_{m}\) can be obtained as \(h_{m}=h_{T,m}h_{R,m}=h_{T,I,m}h_{R,I,m}h_{p,m}\), where \(h_{T,m}\) and \(h_{R,m}\) represent the \(m\)-th channel state for the \(m\)-th forward-interrogating and backward-retroreflected path, respectively, [4, 18, 26]. Additionally, \(h_{T,I,m}\) and \(h_{R,I,m}\) stand for the deterministic channel coefficients due to the corresponding transdermal pathloss, while \(h_{p,m}\) refers to the corresponding stochastic process that models the misalignment-induced geometric spreading [5, 11, 12, 24, 25, 26, 27, 28, 29, 30]. Therefore, \(h_{T,m}=h_{T,I,m}\), and \(h_{R,m}=h_{R,I,m}h_{p,m}\), while by assuming without loss of generality that \(h_{T,I,m}=h_{R,I,m}=h_{I,m}\), the total \(m\)-th channel state can be expressed as [4, 18]:  
\[h_{m}=h_{l,m}^{2}h_{p,m}, \tag{2}\]  
Each transdermal pathloss component \(h_{l,m}\) can be obtained as:  
\[h_{l,m}=\exp\left[-\frac{1}{2}\alpha(\lambda_{m})\delta_{m}\right], \tag{3}\]  
where \(\delta_{m}\) is the dermal thickness of the \(m\)-th transmitted or reflected transdermal path, and \(\alpha(\lambda_{m})\) is its skin-attenuation coefficient, with \(\lambda_{m}\) being the corresponding operational wavelength. For operational wavelengths between 400 nm and 1800 nm, we obtain [24, 25, 11]:  
\[\alpha(\lambda_{m})=\sum_{i=1}^{8}a_{i}\exp\left[-\left(\frac{\lambda_{m}-b_{ i}}{c_{i}}\right)^{2}\right], \tag{4}\]  
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 obtained from ([19], Table 1).