## 5 Results
### Experimental Results
Thus, these groups are more likely to travel in a transverse direction. However, the HOM groups couple with LOM groups because of their wider electric field distribution. The mode MUX and mode demultiplexer (DMUX) have 45% power-splitting ratio with \(\approx\)3 dB insertion loss. The optical signal, containing the LOM groups and HOM groups, is propagated through the OM4 MMF channel with a length of 1.4 km. The transmitted signal suffers from degradation due to ISI and ICI due to a greater amount of interference present in an MMF compared to an SMF. The measured channel impulse response is demonstrated in Figure 7. The channel state information is obtained by estimating the influence on the appended pilot symbols in the data streams. A least-square pilot estimator algorithm is developed to measure the channel. The significant amount of interference is evident from Figure 7. The challenge of recovering the transmitted data is dealt with by the MIMO receiver. Figure 10: Experimental setup for the joint-PPE scheme using an optical MIMO system with a 1.4 km long MMF channel. After propagating through the MMF channel, the degraded signal is received by the PIN photo-detector on each layer. These diodes act as optical-to-electrical converters. An inherent increment in capacitance is observed due to the presence of a large detection area. Consequently, the sensitivity of the receiver suffers from this property. An internal trans-impedance amplifier is present, which amplifies the received electrical signals. A digital storage oscilloscope (DSO) is utilized to capture the electrical signals using a resolution of 40 GSa/s at a bandwidth of 13.6 GHz. The stored signals undergo an offline signal-processing chain with one sample per symbol. The first step includes receive filtering, where a rectangular filter similar to the transmit filter response is applied. Afterward, the symbol clock is recovered from the down-sampled filter signal. The next step involves the estimation of the frequency-selective channel. Most importantly, a post-equalizer is used to mitigate all the interference due to the channel. In the end, hard decision decoding is employed to retrieve the original data and subsequently, the performance is evaluated in terms of the BER performance. To obtain reliable and repetitive results, 74 frames are calculated on each MIMO layer for every instance, which adds up to five million bits approximately. The symbol clock recovery is conducted using an open loop timing recovery method for estimating the exact sampling time. Additionally, the beginning of the data frame is computed using the fine-timing acquisition algorithm. In this acquisition process, the cross-correlation between a segment of the received signal and the pilot sequence provides an aid to determine the exact starting of the data frame. Moreover, the forward error correcting decoding is not deployed at the receiver. Using the experimental setup of a \((2\times 2)\) MIMO system with a 1.4 km long MMF channel, the average optical received power \(P_{\mathrm{r}}\) dependent on the overall BER system is illustrated in Figure 12 and in Table 3. The performance comparison is conducted between the PE-MMSE, the ZF-PPE and the joint-PPE schemes. Moreover, the results are also obtained for two different scenarios, which includes the use of PAM-2 and PAM-4 formats. From the BER performances shown in Figure 12, the proposed joint-PPE clearly outperforms the ZF-PPE and the PE-MMSE schemes. When PAM-2 is utilized on both MIMO layers, the joint-PPE scheme achieves the maximum \(P_{\mathrm{r}}\) gain of \(\approx\)2.58 dB. Moreover, an improvement of \(\approx\)1.74 dB in \(P_{\mathrm{r}}\) gain is observed by the joint-PPE compared to the ZF-PPE. Similarly, the highest performance improvements of \(\approx\)2.68 dB are indicated by the joint-PPE using the PAM-4 format. The \(P_{\mathrm{r}}\) gain \(\approx\)1.73 dB of the joint-PPE over the conventional ZF-PPE scheme proves the effectiveness of the proposed joint-PPE.