## 5 Numerical Results
Figure 2: Total outage probability (OP) of a dual-hop relay-aided system with varrying path configurations as a function of a wide range of \(\gamma/\mu\), for negative exponential (NE) modeled saturated turbulent channels along with different amounts of pointing mismatch. In Figure 3, the corresponding results with those of Figure 2 are presented, but for \(H_{j}=4\). It can be seen that although qualitatively behavior is the same for both cases, in Figure 3 degraded corresponding OP performance results are obtained due to the larger number of hops in each path that lead to longer path lengths. However, we ought to mention that by increasing the hops number, the coverage area also increases. Thus, at the expense of an increase in OP values we can broaden the coverage FSO area, while considering our system's OP specifications and demands, we can conclude whether it is wise to extend the total coverage area of our FSO system, under specific turbulence-induced and misalignment-induced fading conditions. Furthermore, by comparing Figures 2 and 3 in [17] obtained by the analytical expression Equation (15) in [17], Figure 3 depicts significantly increased OP corresponding values due to the stronger turbulence conditions that are assumed. Figure 4 shows the evolution of OP performance over a wide normalized average electrical SNR range, obtained by using (19), for the total relay-assisted examined FSO system when it employs \(N=1\), 3 or 5 dual-hop paths, i.e., \(H_{j}=2\), under weak turbulence conditions, modeled through the G-G distribution, along with zero boresight pointing errors for \(N=1\), and additional weak to strong non-zero boresight pointing errors for \(N=3\) or 5. Thus, the performance comparison between Figures 2 and 4 demonstrates that the obtained results of the latter outperformed the corresponding results of the former, in terms of OP. This is due to a weaker amount of turbulence strength that the FSO propagation has to deal with in the latter case. Consequently, the comparison between these two figures reveals the detrimental impact of turbulence-induced fading, on the outage FSO performance. Figure 3: Total outage probability (OP) of a quadruple-hop relay-aided system with varying path configurations as a function of a wide range of \(\gamma/\mu\), for negative exponential (NE) modeled saturated turbulent channels along with different amounts of pointing mismatch. In Figure 5, the corresponding results of those of Figure 4 are shown, but for \(H_{j}=4\). Once again, despite the identical qualitative behavior of the two figures, we now obtain increased corresponding OP values due to the larger number of the serially connected DF relays that are employed in each path. Furthermore, due to the weak turbulence conditions instead of the saturated we investigated before, we can observe the current performance comparison, i.e., between Figures 4 and 5, which shows less significant outage performance degradation, by doubling the hops in each path, than the corresponding performance comparison between the Figures 2 and 3. Figure 6, depicts the evolution of MOD values over a wide normalized average electrical SNR range, obtained by using (22), for the total relay-aided FSO system with \(N=1,3\) or \(5\) quadruple-hop paths, under negative exponential modeled saturated turbulence along with varying non-zero boresight pointing errors effects for multi-path configurations. It becomes evident that for a specific normalized average electrical SNR value the corresponding MOD value is significantly reduced by increasing the number of paths, even in saturated turbulence, along with strong pointing errors. Indeed, we can observe that for a normalized average electrical SNR, \(\gamma/\mu=18\) dB, the MOD value per hour is shown to be almost equal to \(23.8\) min for the single-path configuration, while for \(N=5\) the MOD value is reduced almost to \(2.9\) s or \(1.6\) s for strong and weak non-zero boresight pointing errors, respectively.