# Signal Quality Assessment for Transdermal Optical Wireless Communications under Pointing Errors +
## 4 Results and Discussion
In Figure 3, the impact of pointing errors in the received signal quality is quantified. In more detail, in Figure 3, the average SNR is illustrated as a function of the skin thickness for different values of the jitter SD. We observe that the value of average SNR decreases at an increase of the skin thickness and the jitter SD. For instance, for \(\delta=6\) mm, as jitter SD increases from 0.1 mm to 1 mm, the average SNR decreases by 6%. In addition, it is noticed that, for \(\sigma=0.5\) mm, the average SNR decreases by approximately 19% as the skin thickness increases from 4 mm to 10 mm, while, for \(\sigma=1\) mm, for the same skin thickness increase, the average SNR decreases about 16.8%. This indicates that, as \(\sigma\) increases, the signal quality becomes less severe to the skin thickness variation. Figure 3 illustrates the effect of skin thickness and pointing errors in the received signal quality in terms of average SNR, for \(\lambda=940\) nm. In this figure, it is evident that, for a fixed \(\xi\), as the skin thickness increases, the average SNR decreases. For instance, for \(\xi=0.5\), the SNR decreases from 90.18 to 87.57 dB, as the skin thickness increases from 5 to 9 mm, whereas, for \(\xi=2\), the SNR decreases from 94.16 to 91.55 dB, for the same skin thickness increase. This indicates that the average SNR degradation, due to skin thickness increase, is independent of the intensity of the pointing errors. Additionally, in this figure, we see that, for a fixed skin thickness, as \(\xi\) increases, i.e., the intensity of pointing errors decreases, the average SNR increases. For example, for \(\delta=0.7\) mm, when \(\xi\) changes from 0.1 to 1.5, the average SNR increases for about 10 dB, from 82.64 to 92.19 dB. Finally, we observe  
Figure 3: Impact of pointing errors. Figure 2: Impact of wavelength selectivity. that, for practical values of \(\delta\) and \(\xi\), i.e., \(\delta\in[4,10]\) mm and \(\xi\in[0.1,2]\), the achievable average SNR is very high, even though the transmission PSD is relatively low. Figure 3(a) demonstrates the average SNR as a function of the PD effective area, \(A\), for different values of the jitter SD, \(\sigma\). It is evident that, for a certain \(\sigma\), as \(A\) increases, the average SNR increases as well. Of note, for higher values of \(A\), the increase in performance becomes less severe. This observation indicates that, after a certain point, the impact of \(A\) on the system's performance becomes obsolete. Furthermore, for a given \(A\), as the jitter SD, \(\sigma\), increases, the signal quality degrades and thus the average SNR decreases.For example, for \(A=1\) mm\({}^{2}\), an increase in the jitter SD from 0.1 to 1 mm results in a 10% degradation of the signal quality. Note that \(\sigma\) is a measure of the intensity of the pointing errors and, therefore, as the intensity of the pointing errors increases, the received signal quality is expected to decrease. Figure 3(b) illustrates the average SNR as a function of the skin thickness and the PSD of the transmission signal. As expected, while the transmission PSD, \(\tilde{P}_{s}\), increases, the average SNR increases as well. For example, for \(\delta=8\) mm, an increase of the transmission PSD from 0.001 mW/MHz to 0.01 mW/MHz results in a 15% increase of the corresponding average SNR. Moreover, we observe that, in the worst case scenario, in which the skin thickness is 10 mm, even with particularly low transmission signal PSD of about \(10^{-6}\) mW/MHz, the achievable average SNR is in the order of 30 dB. This result highlights the fact that the transmission PSD can be utilized to countermeasure the impact of skin thickness. Figure 3: Selection of the appropriate design parameters. In Figure 4c, the average SNR is illustrated as a function of the skin thickness and the divergence angle. It is shown that, for a fixed \(\theta\), the average SNR decreases as \(\delta\) increases.