## 3 Analytical Results  
In this section, we initially present the ABER performance outcomes obtained by the analytical expressions extracted; i.e., Equations (16) and (19), through the mathematical analysis performed above. Most of them were verified by simulations in order to highlight the accuracy of the derived expressions and the analysis proposed. In this context, by assuming weak to strong NZB pointing errors along with transdermal pathloss, the beneficial impact of spatial diversity on ABER performance enhancement, with OC technique, was revealed. Next, the power efficiency of the proposed MRR TOW system was evaluated in terms of its attainable average electrical SNR within a specific and desirable power-density-spectrum regime, considering once again transdermal pathloss and stochastic NZB pointing errors. In this context, the derived average SNR expression in Equation (12) was utilized. The representative results demonstrated the feasibility of the proposed MRR TOW links in terms of this important metric. In view of the above, we made the assumptions below and we adopted the following parameter values, i.e., see Table 2. The investigated MRR TOW system could employ from one to three photodetector apertures, i.e., \(M=\{1,\,2,\,3\}\). Consequently, for \(M=1\), we obtained a SISO MRR TOW link without diversity, while when \(M>1\), the spatial-diversity technique was utilized and thus, SIMO MRR TOW links were created. Note that for the former SISO link configuration, we addressed only zero-boresight pointing errors, while for the latter SIMO link configurations, pointing errors with NZB also appeared and must be taken into account. For each forward or backward transdermal link, the skin thickness, \(\delta_{m}\), was assumed to be equal to 7 mm or 8 mm, while the divergence angle, \(\theta_{m}\), was set to \(20^{\circ}\). Furthermore, unless otherwise stated, it was assumed that \(P_{s}=1\)\(\mu\)w\(/\)MHz, while \(N_{0}\) is fixed at \(\left(1.3\,\mathrm{pA}/\sqrt{\mathrm{Hz}}\right)^{2}\)[37]. Additionally, for each TOW link, the operational wavelength, \(\lambda_{m}\), was selected to be equal to \(1.1\mu\)m, since according to [19], this is the optimal transmission wavelength value for TOW links. It became evident that the choice of the appropriate operational wavelength was even more critical for MRR TOW links, where the light signal traverses the skin channel twice, which makes it even more susceptible to skin-induced attenuation and transdermal pathloss. Regarding pointing errors, considering the above parameter values, we obtained \(w_{\delta,m}/r_{m}>6\), which made the approximation in Equation (5) valid. Additionally, for \(M=1\), we assumed zero-boresight pointing errors either with \(\left(\delta_{m},\mu_{x,m}/r_{m},\,\mu_{y,m}/r_{m},\,\sigma_{x,m}/r_{m},\,\sigma _{y,m}/r_{m}\right)=\left(7\,\mathrm{mm},0,0,4,4\right)\); i.e., \(\xi_{1}=1.14\); or \(\left(\delta_{m},\mu_{x,m}/r_{m},\,\mu_{y,m}/r_{m},\,\sigma_{x,m}/r_{m},\, \sigma_{y,m}/r_{m}\right)=\left(8\,\mathrm{mm},0,0,4,4\right)\); i.e., \(\xi_{1}=1.30\). For \(M=2\), we also assumed NZB pointing errors for the second photodetector with \(\left(\delta_{m},\mu_{x,m}/r_{m},\,\mu_{y,m}/r_{m},\,\sigma_{x,m}/r_{m},\, \sigma_{y,m}/r_{m}\right)=\left(7\,\mathrm{mm},2,1,4.5,4.5\right)\); i.e., \(\xi_{2}=0.96\); \(\left(\delta_{m},\mu_{x,m}/r_{m},\,\mu_{y,m}/r_{m},\,\sigma_{x,m}/r_{m},\, \sigma_{y,m}/r_{m}\right)=\left(7\,\mathrm{mm},2,1,5,5\right)\); i.e., \(\xi_{2}=0.99\); \(\left(\delta_{m},\mu_{x,m}/r_{m},\,\mu_{y,m}/r_{m},\,\sigma_{x,m}/r_{m},\, \sigma_{y,m}/r_{m}\right)=\left(8\,\mathrm{mm},2,1,4.5,4.5\right)\); i.e., \(\xi_{2}=0.87\); and \(\left(\delta_{m},\mu_{x,m}/r_{m},\,\mu_{y,m}/r_{m},\,\sigma_{x,m}/r_{m},\, \sigma_{y,m}/r_{m}\right)=\left(8\,\mathrm{mm},2,1,5,5\right)\); i.e., \(\xi_{2}=1.10\). Finally, for \(M=3\), we correspondingly assumed \(\xi_{2}=\xi_{3}=0.96\), \(0.99\), \(0.87\) or \(1.10\). Under these assumptions and settings, the following analytical and simulation results are presented.