# Signal Quality Assessment for Transdermal Optical Wireless Communications under Pointing Errors +
## 4 Results and Discussion  
In this section, we evaluate the performance of the transdermal OWC link by illustrating analytical and Monte-Carlo simulation results for different insightful scenarios. The simulation results were obtained using the software tools Matlab and Mathematica. In more detail, we assume that the photodiode effective area, \(A\), is defined as  
\[A=\pi\beta^{2}, \tag{20}\]  
and is equal to \(1\) mm\({}^{2}\), while the divergence angle, \(\theta\), equals \(20^{\circ}\). Additionally, unless otherwise stated, the skin thickness, \(\delta\), is assumed to be equal to \(4\) mm, while the noise optical PSD, \(N_{0}\), is set to \(\left(1.3\ \mathrm{pA}/\sqrt{\mathrm{Hz}}\right)^{2}\)[27]. The beam waist in distance \(\delta\) is calculated as  
\[w_{\delta}=\delta\tan\left(\frac{\theta}{2}\right). \tag{21}\]  
Moreover, according to [PERSON] et al. [15], the OWC link shows extremely high immunity to external interference; hence, the background optical power can be omitted, i.e., \(P_{b}=0\). Furthermore, the photodiode's dark current, \(I_{DC}\), is set to \(0.05\) nA, whereas, \(\eta=0.8\)[8]. Finally, unless stated otherwise, we assume \(\tilde{P}_{s}=0.1\) mW/MHz, \(\lambda=1100\) nm and \(\xi=1\). Figure 2a demonstrates the impact of skin thickness on the received signal quality in the OWC link operating in different wavelengths. We observe that the analytical and simulation results coincide; therefore, the analytical framework for the derivation of the average SNR is verified. As expected, for a given wavelength, as the skin thickness increases, the average SNR decreases, i.e., the received signal quality degrades. This degradation is caused due to the pathloss. Additionally, we observe that, for a given skin thickness, \(\delta\), the average SNR depends on the wavelength. For example, for \(\delta=6\) mm and \(\lambda=1500\) nm, the average SNR equals \(57.5\) dB, whereas, for the same \(\delta\) and \(\lambda=1400\) nm, the average SNR is \(72.34\) dB. In other words, the \(100\) nm variation of the wavelength, from \(1500\) to \(1400\) nm, resulted in a \(25.8\%\) signal quality improvement. On the other hand, for the same \(\delta\), when \(\lambda\) changes from \(400\) to \(500\) nm, the average SNR increases about \(39.4\%\). This observation indicates the wavelength selectivity of the transdermal link, as well as the importance of appropriately choosing the wavelength, when designing the link. Finally, for \(\delta\leq 5.25\) mm, we observe that a \(1500\) nm OWC link outperforms the corresponding link operating in \(400\) nm, while, for \(\delta>5.25\) mm, the opposite is valid. This is because, in these scenarios and for skin thicknesses less that \(5.25\) mm, the factor that determines the received signal quality degradation is mainly the RX's responsivity, whereas, for \(\delta>5.25\), the dominant factor is the skin attenuation coefficient. Figure 2b depicts the average SNR as a function of the wavelength for different values of the jitter standard deviation, \(\sigma\). We observe that, although the signal PSD in the OWCs is much lower than the one when RF link is used, the average SNR is surprisingly high, i.e., in the order of \(90\) dB. This indicates that the OWCs can achieve much higher energy efficiency compared to the corresponding RF link. Moreover, for a fixed wavelength, as \(\sigma\) increases, the average SNR decreases. For \(\lambda=600\) nm, the average SNR decreases approximately \(10\%\) as \(\sigma\) is changed from \(0.25\) to \(1.25\). Additionally, from this figure, it is evident that a transmission window exists for wavelengths between \(700\) and \(1300\) nm. Note that, in this wavelength region, several commercial light emitting diodes (LEDs) and photodetectors (PD) exist (see, for example, [28; 29]). Finally, we observe that the wavelength windows from \(400\) to \(600\) nm and around \(1500\) nm are not optimal for TOLs, whereas the optimal transmission wavelength is \(1100\) nm.