## 5 Numerical Results and Discussion
Figure 4 illustrates the BER vs. number of OAM mode states for four different refractive index structure (RIS) parameters from [4 \(\times\) 10\({}^{-12}\)] m\({}^{-2/3}\) to [6 \(\times\) 10\({}^{-12}\)] m\({}^{-2/3}\) atmospheric turbulence conditions. These turbulence conditions correspond to strong and weak atmospheric turbulences. Due to the severe vulnerability of the higher-order OAM states in different turbulence conditions, the BER curve increases with the increase in absolute value of the OAM state for the fixed value of the refractive index structure parameter. The result obtained demonstrates that the BER curve is symmetrical with respect to the different OAM states and that the center is located at the zero mode state. When the RIS parameter is kept constant for any turbulence conditions, the BER performance curve increases almost in a linear manner with the increase in the absolute value of the low-order OAM mode state maximum up to the OAM state of \(-\)17, whereas for the absolute value of higher-order OAM mode states beyond \(-\)17, the BER performance curve decreases gradually with the increase in OAM mode order. This is mainly due to mode energy leakage or spreading in adjacent OAM modes. For the mode state from \(-\)3 to 0, the BER performance remains almost constant. The symmetrical BER performance is observed for the OAM mode state from 0 to 20. When the OAM mode state is kept constant, it is observed that the BER increases with the increase in the RIS structure constant value due to the decrease in atmospheric turbulence strength. The BER performances of the OAM-SMM-MIMO and OAM-OFDM-SMM-MIMO FSO systems are compared in Figure 5 with respect to different OAM states during atmospheric turbulence. When the OAM state value is maintained constant, the BER of the OAM-OFDM-SMM-MIMO FSO system is significantly higher than the BER of the straightforward OAM-SMM FSO transmission system. The results distinctively show that atmospheric turbulence has an effect on the performance of both FSO systems; however, the variations in received OFDM-MIMO/SMM signals are primarily affected by intensity variations, as opposed to the impact of atmospheric turbulence on OAM signals, which is primarily caused by phase distortion or variations. Due to the fact that OFDM signals are also impacted by atmospheric turbulence, the OAM-OFDM-SMM FSO system is more adversely affected than OAM signals. Figure 3: Intensity and phase profiles of OAM state in different turbulence regions. The BER performance of the proposed system is compared as a function of different order OAM mode states in Figure 6 for three different link distances, from a maximum of 2 km to a minimum of 0.75 km, respectively, in atmospheric turbulence. When the order of the OAM state is kept constant, say at 0, the BER increases with an increase in optical link distances. The plot validates the fact that with an increase in optical link distances, both the atmospheric attenuation and the turbulence become stronger, which ultimately leads to a higher numerical value of BER and hence the worst system performance. The proposed system performs admirably for lower-order OAM states with absolute values ranging from 0 to 5 over a propagation distance of 0.75 km, but it performs poorly for the same order of OAM modes over a distance of 2 km. This is because of the least spreading of lower-order OAM state modes' energy, which is the minimum leakage of the mode energy from one mode to adjacent OAM modes. Figure 4: BER vs. OAM states under different refractive index structure parameters. Figure 5: BER vs. OAM state for the OAM-SMM-MIMO and the OAM-OFDM-SMM-MIMO FSO systems. Figure 7 compares the BER performance as a function of increasing OSNR values for the two OAM-SMM-MIMO and OAM-OFDM-SMM MIMO FSO systems, considering the intensity fluctuations at the receiver, respectively. For the performance analysis, a fixed and moderate atmospheric turbulence with a RIS parameter of \(2\times 10^{-12}\) m\({}^{-2/3}\) and the OAM \(l\) = +1 state mode is assumed.