## 5 Numerical Results and Discussion  
In this section, the BER and channel transmission capacity performances of the proposed OAM-OFDM-SMM multiplexed MIMO FSO system are evaluated with respect to various performance metrics, such as the number of OAM states, various refractive index structure parameters, Rytov parameters, different FSO link distances, and different signal -to-power ratios (SNR) under various weak to strong atmospheric channel conditions. In the optical transmitter section, the OAM states are multiplexed to carry OAM-OFDM-SMM multiplexed channels, where each channel is 16-QAM modulated and carries information at a data speed of 120 Gb/s over a wavelength of 1550 nm. Equation (28) is used to calculate the minimum power required/channel to achieve a set target BER. To analyze the performance of the proposed system, the following assumptions are also made: (i) the system physical and default parameters used to calculate and evaluate the proposed FSO system are summarized in Table 1; (ii) transmitted power for all the channels is kept equal; (iii) the forward error correction (FEC) limit is set to be \(3.8\times 10^{-3}\) corresponding to threshold SNR of 18 dB; (iv) inter-channel crosstalk with the signal behaves similarly to noise at our BER threshold; and (v) the large-scale eddies and small-scale eddies are represented by \(\alpha_{rj,m}\) and \(\beta_{rj,m}\), respectively. The simulation results for the intensity profile and phase front distortion of the purest OAM-OFDM-SMM-MIMO mode \(l=+1\) are illustrated in Figure 3 under weak (\(C_{n}^{2}=1.0\times 10^{-10}\)) m\({}^{-2/3}\) and (\(\sigma^{2}<1\)) and under strong atmospheric turbulence (\(C_{n}^{2}=1.0\times 10^{-15}\)) m\({}^{-2/3}\) and (\(\sigma^{2}>1\)) conditions for the link distance of 1 km, respectively. For the purest mode, the beam waist parameter is \(\omega_{0}=1\) m. In very weak AT, there is almost no phase front distortion, most of the transmitted power remains in OAM = +1 mode, and almost negligible optical power leakage occurs from this mode to other adjacent modes. However, under severe AT conditions, we clearly observe the EM field's distorted phase front, which causes a high-power leakage to other modes. At the receiver end, the normalized power received for 7 different OAM modes is also shown in Figure 3. The normalized received power for \(l=+1\) mode under strong AT conditions decreases by almost 10 dB compared to weak AT conditions, whereas \(l=-3\) mode demonstrates the worst performance profile under the same conditions. \begin{table}
\begin{tabular}{c c c} \hline
**System Parameters** & **Symbol** & **Simulation Values** \\ \hline Spatial laser power & \(P_{l}\) & \(-15\) dBm \\ \hline Bit rate per channel & \(R_{b}\) & \(120\) Gb/s \\ \hline Number of OAM modes & \(L\) & \(21\) \\ \hline Maximum OAM state & \(K\) & \(10\) \\ \hline Lens focal length & \(f_{1}=\)\(f_{2}\) & \(50\) cm \\ \hline Transmitted wavelength & \(\lambda\) & \(1550\) nm \\ \hline Transmitter Power & \(P_{t}\) & \(15\) dBm \\ \hline Maximum RIS constant & \(C_{n}^{2}\) & \(1\times 10^{-15}\) m\({}^{-2/3}\) \\ \hline Maximum Rytov constant & \(\sigma^{2}\) & \(3.98\) \\ \hline Number of subcarriers & \(f_{sc}\) & \(65615\) \\ \hline Minimum subcarrier & \(f_{sc}\) & \(30\) GHz \\ frequency & \(f_{sc}\) & \(30\) GHz \\ \hline Subcarrier interval & \(\Delta f\) & \(1\) KHz \\ \hline Gaussian beam size & \(\omega_{0}\) & \(30\) cm \\ \hline Maximum FSO link distance & \(z\) & \(2\) km \\ \hline Receiver losses & \(L_{rx}\) & \(0\) dB \\ \hline Photo-detector responsivity & \(R\) & \(1\) A/W \\ \hline Detector dark current & \(I_{0}\) & \(10\) nA \\ \hline Thermal noise power density & \(\eta\) & \(10^{-22}\) W/Hz \\ \hline \end{tabular}
\end{table} 
Table 1: Physical parameters for the proposed system.