## 5 Results
### Experimental Results  
A \((2\times 2)\) optical MIMO experimental setup is developed, which is shown in Figures 10 and 11. Similar to the provided system model, this measurement setup is also divided into three parts: MIMO transmitter, MMF channel and MIMO receiver. Starting from the transmitter side, a S/P converter is applied to convert a serial data stream into two pseudo-random binary sequences (PRBSs). Afterward, these sequences are mapped on the Gray coded symbols in accordance with the chosen PAM-2 or PAM-4 modulation formats. Additionally, the pilot symbols are also appended to the data symbols for the purpose of channel estimation. By using the above-mentioned optimization statement, the optimal pre-equalizer coefficients are computed using channel information. Consequently, multi-level signals are enabled by applying pre-equalization to the input data streams. In case no channel state information is available, the pre-equalizer acts as a Dirac delta function, and the results for the PE-only are obtained. The signal-generation process is concluded by generating the electrical signals from the input symbols using an arbitrary waveform generator (AWG). The channels of the AWG are operated on the symbol rate of 5 GBaud per MIMO layer. The electrical signals are converted into the optical signals using chirp-free external Mach-Zehnder modulators (MZMs). A lithium-niobate (LiNbO\({}_{3}\)) substrate is used in the optical circuit of the MZM. The bias of the MZM is manually adjusted, and the quadrature points are stabilized using a temperature controller. The carrier laser sources work on the operating wavelength \(\lambda=1550\,\mathrm{nm}\). Using variable optical attenuators (VOAs), the overall BER performance is calculated over a distinct range of the average received optical power (\(P_{\mathrm{r}}\)). Thereafter, the MMF splice boxes are utilized \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Scenario** & **Modulation Format** & **Equalization** & \(L_{\mathrm{P}}\) & \(L_{\mathrm{f}}\) & \
\begin{tabular}{c} \(P_{\mathrm{r}}\) **(in dBm)** \\ **at a BER of \(10^{-4}\)** \\ \end{tabular} &
\begin{tabular}{c} \(P_{\mathrm{r}}\) **(in dBm)** \\ **(in dB)** \\ \end{tabular} \\ \hline First & PAM-2 & PE-only & - & 30 & \(-21.37\) & - \\ scenario & & ZF-PPE & 4 & 26 & \(-22.19\) & 0.82 \\  & & Joint-PPE & 4 & 26 & \(-23.91\) & 2.54 \\  & & SVD-PPE & 4 & 26 & \(-24.89\) & 3.52 \\ Second & PAM-4 & PE-only & - & 30 & \(-16.23\) & \(-\) \\ scenario & & ZF-PPE & 4 & 26 & \(-17.27\) & 1.04 \\  & & Joint-PPE & 4 & 26 & \(-18.96\) & 2.73 \\  & & SVD-PPE & 4 & 26 & \(-20.09\) & 3.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Overall simulated \(P_{\mathrm{r}}\) gains of the \((2\times 2)\) optical MIMO system at \(10^{-4}\) BER using a \(1.4\,\mathrm{km}\) long MMF channel at \(f_{\mathrm{T}}=5\,\mathrm{GHz}\). Figure 9: BER dependent on simulated received power \(P_{\mathrm{r}}\) for PAM-2 and PAM-4 transmissions for SVD-based optical MIMO system. for the excitation of the selective mode groups by launching the light with a certain offset. In this provided experimental setup, the SDM scheme is enabled by utilizing centric and eccentric launching conditions into a 1.4 km long MMF with the offsets of 0 \(\upmu\)m and 15 \(\upmu\)m, respectively. The offset light-launching conditions are demonstrated in Figures 2 and 10. Centric launching of the light into the MMF results in the excitation of the fundamental mode group or lower-order mode (LOM) group. Similarly, the high-order mode (HOM) groups are excited with the 15 \(\upmu\)m offset launching condition. The last part of the transmitter includes an optical fusion coupler, which is useful in multiplexing the mode groups. In this setup, custom-made fusion couplers are utilized with a slight asymmetric power split ratio as these are well suited for mode multiplexing (MUX) applications [31; 32]. The function of a mode MUX is to combine the LOM groups with HOM groups using an x-shaped structure. The LOM groups travel from the center of the fiber core.