## 5 Numerical Results  
In this section, by using the closed-form expressions derived above (18), (21), (26), (27), (30), (31), we present, over a wide range of average electrical SNR, performance results by means of the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**i** & **a\({}_{\mathrm{i}}\)** & **b\({}_{\mathrm{i}}\)** & **c\({}_{\mathrm{i}}\)** \\ \hline
1 & 10 & 0.35 & 0.065 \\
2 & 4.5 & 0.42 & 0.25 \\
3 & 13.48 & \(-\)1.5 & 50.12 \\
4 & 14.7 & 1442 & 49.35 \\
5 & 7.435 & 1499 & 75.88 \\
6 & 48 & 3322 & 1033 \\
7 & 594.1 & \(-\)183 & 285.9 \\
8 & 11.47 & \(-\)618.5 & 1054 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter \(a_{i}\), \(b_{i}\) and \(c_{i}\) values. ABER metric for both SISO and SIMO TOW configurations than may employ either OOK or \(L\)-PPM modulation formats. In all investigated cases, the joint impact of both skin-induced attenuation and pointing errors effects are considered. Note that without loss of generality we focus on spatial diversity, i.e., the examined TOW system may support SIMO configurations where the transmitter simultaneously emits the same part of information to more than one spatially separated receiver apertures. Thus, each detector receives independent information-bearing optical signals. Specifically, when multiple receivers are assumed, i.e., \(M>1\), the NZB component is also taken into account. In fact the examined system may employ from \(M=1\) to \(M=3\) TOW links of a typical skin thickness of \(\delta=8\) mm, while the operational wavelength of the system is fixed at \(\lambda=850\) nm. For each receiver aperture, it is assumed that \(\eta_{m}=0.8\), \(r_{m}=0.5\) mm, \(\theta_{m}=30^{\circ}\), \(\overline{P}_{S}=1\) mm/MHz and \(N_{0}=\left(1.3\,pA/\sqrt{Hz}\right)^{2}\). Thus, concerning pointing errors effects it holds that \(w_{\delta,m}/r_{m}>6\) which indicates that approximation in (5) is valid. Additionally, for \(M=1\), due to most precise positioning, the parameter \(\psi_{1}\) should obtain its maximal value, i.e., \(\psi_{1}=0.35\) for \(\left(w_{\delta}/r,\mu_{x}/r,\mu_{y}/r,\sigma_{x}/r,\sigma_{y}/r\right)=\left( 9.2,20,10,9,9\right)\) in comparison with SIMO configurations. Indeed, for \(M>1\), due to the spacing between photodetectors, we assume also stronger or even stronger non-zero boresight pointing errors effects, i.e., \(\psi_{2}\), \(\psi_{3}=0.29\) or \(0.25\), for \(\left(w_{\delta}/r,\mu_{x}/r,\mu_{y}/r,\sigma_{x}/r,\sigma_{y}/r\right)=\left[ \left(9.2,20,10,12,10\right)or\left(9.2,20,10,15,10\right)\right]\), respectively. Note that by substituting \(850\) nm for \(\lambda_{\rm m}\) and the corresponding parameter values of Table 1 for \(a_{i}\), \(b_{i}\), and \(c_{i}\), we obtain from (4) that for the examined cases it holds that \(\alpha(\lambda_{\rm m})=1.8\). Additionally, in all cases that we present below, the numerically evaluated results from the above derived closed form mathematical expressions, are accompanied by the corresponding ones obtained with Monte Carlo simulations with \(2\times 10^{7}\) samples. As is the case of terrestrial FSO in [2; 46] results in Figure 2 are now obtained for the examined TOW with OOK system by using the corresponding (26) and (27) expressions. Figure 2 illustrates the ABER evolution for the TOW system that employs both SISO and SIMO configurations with OOK over a wide range of average electrical SNR, along with different amounts of NZB misalignment-induced fading. Significant ABER degradations are demonstrated when NZB pointing errors are getting stronger. However, very important ABER performance improvements are depicted via the use of SIMO configurations, especially for larger number of receivers. Thus, the beneficial impact of the use of multiple receivers in terms of total TOW ABER performance is highlighted. Indeed, through diversity, for instance in space, the quality of the received signal is enhanced by achieving a lower ABER value for the same average electrical SNR value.