## 5 Experimental Results  
The performance benefits of the joint-PPE scheme are evaluated using an IM/DD based (\(2\times 2\)) optical MIMO system using an MMF channel. A picture of the experimental measurement setup is demonstrated in Figure 6, where the design of the PFS configuration is shown with the delay line. The experimental setup is constructed with the aid of the provided system model, and it is illustrated in Figure 7. The procedure for the performance evaluation of the joint-PPE schemes starts by applying PE-only using an MMSE post-equalizer. Simultaneously, the pilot symbols are appended to the transmitted data intending to estimate the channel state information. Afterwards, the joint-PPE filter coefficients are computed and optimized using the abovementioned constrained optimization algorithm. Finally, the comparison between the joint-PPE and PE-only in terms of the BER is conducted. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Scenario** & **Modulation** & **Equalization** & \(L_{\text{P}}\) & \(L_{\text{f}}\) & **SNR (in dB)** & **SNR Gain** \\  & **Format** & & & & **at BER of \(10^{-4}\)** & **(in dB)** \\ \hline First scenario & PAM-2 & PE-only & - & 25 & 15.95 & - \\  & & Joint-PPE & 2 & 23 & 15.05 & 0.90 \\  & & & 4 & 21 & 13.70 & 2.25 \\ \hline Second scenario & PAM-4 & PE-only & - & 25 & 48.50 & - \\  & & Joint-PPE & 2 & 23 & 47.20 & 1.30 \\  & & & 4 & 21 & 46.60 & 1.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulated SNR gain of the \((2\times 2)\) optical MIMO system at \(10^{-4}\) BER using a \(100\,\mathrm{m}\) long MMF channel. Figure 6: Experimental measurement setup with the PFS configuration using a \(167.27\,\mathrm{m}\) delay line and an MMF channel. The design of the post-equalizer is based on the concept of the MMSE equalizer. It implies that the counterbalance between noise enhancement and ISI mitigation is taken into account. It is worth noting that the sum of pre- and post-equalizer taps remains constant while comparing the joint-PPE with the PE-only. While considering the cost-effectiveness and complexity of the experimental setup, a PFS configuration using the delay lines is employed. The structure of this setup includes the concatenation of the two different data frames. By using a coupler and a delay line on one input, the concatenated data frames are segregated simply by delaying one of the input equivalent to the length of the data frame. The length of the delay line \(L_{\text{d}}\) is calculated as  
\[L_{\text{d}}=\frac{\text{c}\cdot L_{\text{m}}}{\eta_{\text{core}}\cdot f_{ \text{T}}}\enspace, \tag{9}\]  
where c is the speed of light, and \(L_{\text{m}}\) represents the data frame length. The refractive index of the core is \(\eta_{\text{core}}\) and \(f_{\text{T}}\) is the symbol rate. The analysis of delay lines with different pseudo-random binary sequence (PRBS) sequence lengths is provided in Table 2. In Figure 7, the transmitter includes the signal generation unit, where the two sequences are mapped either to the PAM-2 or to the PAM-4 constellations on all the layers. Additionally, the pilot symbols are appended with these sequences. The channel state information is computed using the least-square pilot estimator algorithm. The measured channel impulse response of an MMF channel at a symbol rate of \(2.5\,\mathrm{GHz}\) on each layer is illustrated in Figure 3. It is clear from the plot of the estimated channel that a significant amount of cross-talk is present between \(h_{12}[k]\) and \(h_{21}[k]\). Moreover, the ISI is considerably high at \(h_{11}[k]\) compared to \(h_{22}[k]\). Therefore, the joint-PPE scheme aims to completely mitigate the ISI and ICI with a minimal increase in noise amplification. Using the pre-equalizer, the multi-level signals with the calculated amplitudes are generated with the aid of the optimization algorithm. Afterwards, the data frames are concatenated with the help of an arbitrary wave generator, which operates at a symbol rate of \(2.5\,\mathrm{GHz}\) on each layer.