## 2 Modeling of MDM-OCDMA System  
Figure 1 depicts a block diagram of the proposed 8 \(\times\) 10 Gbps MDM-based FSO-OCDMA system by incorporating MNZCC code.  
The proposed OCDMA-MDM-FSO-MMF model is modeled in OptiSystem(tm) V-19 and Matlab(tm) due to their high accuracy. In the proposed OCDMA-based MDM-FSO-MMF system, there are eight channels with a group of four channels operating at four MNZCC code sequences for four users. At the transmitter side, two external continuous wave (CW) laser arrays with an input power of 10 dBm are used. Here, each CW laser array generates twelve wavelengths of 1550, 1551.6, 1552.4, 1553.2, 1554, 1554.8, 1555.6, 1556.4, 1555.6, 1557.2, 1558 and 1558.8 nm, as depicted in Figure 1a. In each transmitter, a 12:1 ideal multiplexer multiplexes all input signals and transfers them to the 1:12 wavelength-divisionmultiplexing (WDM) demultiplexer. Each encoder consists of a 3:1 WDM multiplexer to multiplex different input wavelengths as per the MNZCC code sequence, PRBS, to generate a random bit sequence, NRZ pulse generator and Mach-Zehnder modulator (MZM) to modulate the coded signals. A 4:1 ideal multiplexer is used to multiplex the outputs of distinct coded signals representing four transmission channels. The output of the multiplexer is fed to a donut mode generator which generates the Donut mode 0. Similarly, in another transmitter, the next four transmission channels are fed to a donut mode generator which generates the Donut mode 1. The generated donut modes are shown in Figure 2. A 2:1 power combiner is used to combine the incoming signals operating at two different modes for propagation through the FSO link, followed by a multimode fiber, as shown in Figure 1b.  
At the receiver side, a splitter is used to split the optical signal into two parts; each one is followed by the mode selector, which selects the desired mode transmitted on the transmitter side. The output of the mode selector is fed to the relevant receiver side which consists of four decoders to decode the output for four end users. A decoder consists of a 3:1 WDM multiplexer followed by a spatial optical receiver to recover the original baseband signal, followed by a low-pass filter (LPF). Tables 1 and 2 present the MNZCC code design used in the system for four users at Donut mode 0 and 1, respectively. Table 3 shows the various parameters used in the modeling of the proposed system.  
Figure 1: Proposed 8 \(\times\) 10 Gbps OCDMA based MDM-FSO-MMF system of (a) transmitter, (b) receiver.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Wavelength** & **1550** & **1550.8** & **1551.6** & **1552.4** & **1553.2** & **1554** & **1554.8** & **1555.6** & **1556.4** & **1557.2** & **1558** & **1558.8** \\ \hline User 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ User 2 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ User 3 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 \\ User 4 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: MNZCC code design for four users at Donut mode 0.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Laser input power & 10 dBm \\ Wavelength & 1550–1558.8 nm \\ Data rate & 10 Gbps \\ Tx aperture diameter & 15 cm \\ Rx aperture diameter & 20 cm \\ Reference wavelength & 1550 nm \\ Dark current & 10 nA \\ FSO range & 1500–2200 m \\ Measured index multimode fiber length & 320–420 m \\ Mux/De-mux bandwidth & 10 GHz \\ Mux/De-mux filter type & Bessel \\ Mux/De-mux filter order & 2 \\ MZM extinction ratio & 30 dB \\ NRZ rectangle shape & Exponential \\ NRZ amplitude & 1 a.u. \\ Turbulence condition & Weak (\(10^{-17}\) m\({}^{-2/3}\)) and strong (\(10^{-13}\) m\({}^{-2/3}\)) \\ Turbulence model & Gamma-Gamma and log-normal \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameter values for MDM-based FSO-OCDMA system.  
Figure 2: Generated donut modes. (a) Donut mode 0, (b) Donut mode 1.