## 4 Proposed System Design  
A schematic of the 10-channel (Ch) DP-QPSK-based FSO link with hybrid MDM-WDM multiplexing is shown in Figure 5. Ten spatial lasers (SL) have been employed, generating LG00 or LG 01 mode with an input power of 0 dBm at wavelengths of 1550, 1551, 1552, 1553, and 1554 nm. The transverse spatial profile of LG mode in the source plane, z = 0, is described as [24]:  
\[\Psi m,n(r,\ 0,\theta)=\left(\frac{r}{w}\right)^{m}L_{n}^{m}\left(\frac{r^{2}}{w^{ 2}}\right)exp(jm\theta) \tag{7}\]  
where \(r=(x^{2}+y^{2}))^{1/2}\) is the radius of the curvature, \(w\) is the beamwidth of fundamental Gaussian mode, \(\theta=tan-1(y/x)\), \(L_{n}^{m}\) is the associated Laguerre polynomial, and \(n\) and \(m\) represent azimuthal and radial mode numbers. The SL outputs are fed to DP-QPSK transmitters, and power combiners (PCs) combine the output of two different modes at the same wavelength. Power combiner outputs representing 10 transmission channels have been multiplexed, and the resultant signal propagates through the FSO link impaired with fog, haze, or cloud weather conditions. \begin{table}
\begin{tabular}{c c c c} \hline
**Weather Condition** & **Month** & **Visibility** & **Attenuation** \\ \hline Fog & February 2023 & 4 km & 3.077 dB/km \\ Clouds & December 2022 & 13.74 km & 0.643 dB/km \\ Clouds & January 2023 & 11.2 km & 0.789 dB/km \\ Clouds & February 2023 & 12.26 km & 0.721 dB/km \\ \hline \end{tabular}
\end{table} 
Table 4: Attenuation and visibility: Cape Town region. Figure 5: Schematic diagram of the DP-QPSK-based FSO link with hybrid MDM-WDM multiplexing. A 1 \(\times\) 5 demultiplexer at the receiving end splits the different channels, and power splitters (PSs) direct the corresponding channels to the mode selector (MS) switches to select LG00 or LG01 mode at the receiver. The detailed schematics of the DP-QPSK transmitter and receiver are shown in Figures 6 and 7, respectively. The light emitted by the laser splits into two components for horizontal polarization and two components for vertical polarization. Each light beam is modulated by Mach-Zehnder modulator (MZM), which converts the data into a sequence of light pulses. Within each polarization, the \(\Pi\)/2 phase shifter is used to generate the quadrature component. The polarization rotator (PR) rotates the incoming signal with respect to another, and the resultant signals are combined by the beam combiner (BC) to generate the 100 Gbps DP-QPSK signal, as shown in Figure 6.  
Figure 6: Schematic diagram of DPQPSK transmitter. Figure 7: Schematic diagram of DP-QPSK receiver. The DP-QPSK signal may be described by using Jacobi-Anger expansion as [25]:  
\[ \begin{split} E_{Q}(t)=\frac{E(t)}{4}\{\sum_{n=-\infty}^{n=\infty} \left[expjV_{ax}+(-1)^{n}\right]\}_{n}(m_{x})expjn\omega_{m}t+\\ \sum_{n=-\infty}^{n=\infty}\left[expjV_{ay}+(-1)^{n}\right]\,J_{n} \big{(}m_{y}\big{)}expjn\omega_{m}t+expj(V_{bx}+V_{cx})+\\ expj(V_{cx})+expj\Big{(}V_{by}+V_{cy}\Big{)}+expj\big{(}V_{cy} \Big{)}\Big{\}}\end{split}  \tag{8}\]  
where \(E(t)=Ecexp(ivct)\) represents the continuous wave laser output signal with \(Ec\) and wm representing the amplitude of light beam and the angular frequency, respectively. \(m_{x}=\pi V_{mx}/2V_{x}\) and \(m_{y}=\pi Vm_{x}/2V_{y}\) represent the modulation indexes of MZM\({}_{\text{x}}\) and MZM\({}_{\text{y}}\), respectively. \(V_{ax}=\pi V_{biasX1}/\pi\), \(Vbx=\pi V_{biasX2}/V_{\pi}\), \(V_{cx}\)= \(\pi V_{biasX3}/V_{\pi}\), \(V_{ay}\)= \(\pi V_{bias1}/V_{\pi}\), \(V_{by}=\pi V_{bias2}\) /\(V_{\pi}\), and \(V_{cy}=\pi V_{bias9}\) /\(V_{\pi}\) represent the rf amplitudes of MZM\({}_{\text{x}}\) and MZM\({}_{\text{y}}\), respectively. The power received at the receiver side is given as [21]:  
\[P_{recieved}=P_{transmitted}\frac{d_{R}^{2}}{(d_{T}+\theta R)^{2}}10^{-\frac{ \theta R}{10}} \tag{9}\]  
where \(d_{T}\) and \(d_{R}\) are aperture diameters of transmitting and receiving antenna, respectively. \(\theta\), \(R\), and \(a\) represent the beam divergence, propagation range, and attenuation coefficient, respectively.