## 6 Conclusions  
This work has dealt with the composite estimation of ABER performance of FSO links, subjected to atmospheric turbulence, SJ, and TJ effects, also taking \(N\)-OC diversity and \(M\)-DF multi-hop techniques into account, for three modulation scheme families, i.e., OOK-RZ/NRZ, \(L\)-PPM, or \(L\)-PAM. The study included the Malaga distribution model, for  
Figure 7: ABER versus expected SNR for (\(a=11\), \(b=4\), \(\rho=1\)), \(\xi=5.03\), \(L\)-PAM schemes, and various diversity and DF multi-hop parameters, with (**a**) \(R=48\) Mbps, \(\sigma=5.815\times 10^{-9}\) s (\(\alpha=10^{-8}\) s, \(\beta=4\)), and (**b**) \(R=24\) Gbps, \(\sigma=29.075\times 10^{-12}\) s (\(\alpha=5\times 10^{-11}\) s, \(\beta=4\)). The studied curve cases are codified as follows: Case 71A: _4-PAM_, \(N=3\), \(M=1\); Case 71B: _4-PAM_, \(N=3\), \(M=5\); Case 72A: _4-PAM_, \(N=9\), \(M=1\); Case 72B: _4-PAM_, \(N=9\), \(M=5\); Case 81A: _16-PAM_, \(N=3\), \(M=1\); Case 81B: _16-PAM_, \(N=3\), \(M=5\); Case 82A: _16-PAM_, \(N=9\), \(M=1\); Case 82B: _16-PAM_, \(N=9\), \(M=5\).  
the atmospheric turbulence effect, the non-zero boresight SJ model, and the GGD model for the TJ effect. New, closed-form mathematical expressions for any studied case and practical numerical results for typical parameter values were also generated. Taking into account the above-derived expressions, the design and implementation of modern FSO links can be easier and more accurate. The influence of each effect have been described and the choice of the appropriate diversity scheme, along with the corresponding regenerator use, can be selected depending on the special characteristics of each specific area where the FSO link is installed.  
The obtained outcomes show that the joint effects due to the weather conditions or/and receiver's misalignment or/and desynchronization can be counterbalanced, allowing either further length expansion or bit rate incremental increase of the existing link. These features are feasible by increasing either the number of the receiver's apertures and/or the number of DF relays implemented between the original transmitter and the final receiver or the order of PPM/PAM scheme, depending on the desired results in terms of ABER thresholds or SNR benchmarks, beyond which no further ABER performance is achievable.  
The selection of the modulation format is crucial for the link's performance and for either the curve's slope, regulated by joint turbulence and SJ effect, or threshold, regulated by TJ effect and bit rate--steeper slopes allow a given ABER performance to be achieved at lower SNR values than in smoother slope cases, while deeper thresholds allow better ABER performance at the same SNR value than in shallower flat cases.  
Finally, it should be mentioned that although this research concerned terrestrial links, the results obtained can also be implemented--with minor alterations--in underwater links, since the studied effects, among others, also exist in underwater optical wireless channels.  
Conceptualization, P.J.G., H.E.N., A.D.T. and E.R.; methodology, P.J.G., H.E.N., A.D.T., V.C. and E.R.; software, P.J.G. and A.D.T.; validation, P.J.G. and H.E.N.; formal analysis, P.J.G. and V.C.; investigation, P.J.G., H.E.N., A.D.T., V.C. and E.R.; resources, P.J.G. and H.E.N.; writing--original draft preparation, P.J.G.; writing--review and editing, H.E.N., A.D.T., V.C. and E.R.; visualization, A.D.T.; supervision, H.E.N.; funding acquisition, H.E.N. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.