## 4 Results and Discussion
For instance, at a distance of 13.72 km, the measured Q-factors were found to be 5.9 for the MDB-NRZ link, 4.7 for MDB-RZ, and 3.52 for MDB-PSK. and designs that mitigate nonlinear phenomena, ultimately promoting system efficiency and reliability in lightwave communication technologies. An analysis of SPM was conducted for the three mode channels of fiber, each operating at a data rate of 40 Gb/s with different modulation formats. The bandwidths of the electrical low-pass filter (LPF), optical band-pass filter (BPF), and optimized values for the LPF post-detection were selected. This analysis was based on the assumption that the optimal LPF bandwidth for a given bit rate (B) lies within the range of [0.28B, 0.42B]. For the DB MDM-FSO system using NRZ, the electrical LPF bandwidth was set to 15.24 GHz, while the optical BPF frequency was set to 27.92 GHz. Similarly, for the MDB MDM-FSO system, the LPF and BPF bandwidths were adjusted to 35.7 GHz and 45.6 GHz, respectively, as shown in the simulation setup in Figure 2b. Figure 11 illustrates the effect of SPM at power levels ranging from \(-\)20 dBm to \(-\)4 dBm for the spatial CW laser. As the transmission distance increased, varying the bandwidth of the optical filter resulted in a degradation of the Q-factors. The analysis provides the optimized filter bandwidth necessary for the four-modulation model. A 13 km three-mode fiber was used for the SPM analysis, with an optimized attenuation value set to 1.2 dB/km. Figure 12 presents the optimized eye diagram for the MDM MDB-based FSO at a bit error rate (BER) of \(10^{-9}\), yielding a Q-factor of approximately six across the three mode channels. Figure 11: Q-factor against bandwidth of the optical low-pass filter (GHz) for MDB RZ FSO, MDB PSK-FSO, MDB NRZ FSO, and DB RZ FSO. Figure 12: Optimized calculated eye diagrams of the three-mode MDM MDB-FSO NRZ signal at the recovery points of receiver (**a**) LP\({}_{01}\), (**b**) LP\({}_{11}\), (**c**) LP\({}_{02}\), respectively. It is crucial to mention that the basis for fiber length selection in the proposed MDM-FSO link encompasses thorough scrutiny of link budget evaluations alongside mode stability considerations. Mode stability is considered a vital factor in fiber length chosen in the adoption of the three spatial modes to encode information. The effective utilization of these modes requires stable propagation characteristics over the length of the fiber. Longer fibers may introduce modal dispersion and coupling losses, which can disrupt the integrity of the transmitted data. Consequently, in this study, an optimal fiber length was examined through simulations to ensure that the desired modal characteristics are preserved throughout the transmission distance. A maximum precise balance between ensuring adequate transmission distance and maintaining sufficient power levels at the receiver is achieved at 13 km three-mode fiber + 1.1 km FSO. Thus, the interplay of these factors not only ensures robust communication links but also enhances the overall efficiency and viability of the proposed MDM-FSO model in practical deployments. As a recommendation for further work, the framework of edge-disjoint, rooted, distance-constrained minimum spanning trees can be employed to effectively optimize transmission paths, minimize interference, and enforce stringent constraints on latency and power efficiency [30]. The utilization of AI to address other challenges, e.g., routing, fault tolerance, and optimal resource allocation can also be considered for future works.