## 3 Results and Discussion
For the back-to-back case, we observe that the four levels are already visible before any equalization, in contrast with the back-to-back case of Figure 2, indicating the impact of the improved signal generation in that scheme. For this scheme, distinguishable seven-level eye diagrams can be observed at the output of the FIR for links up to 20-km. However, the eye diagram gets degraded as the transmission distance increases due to the strong ISI imposed by CD as the reach is increased. This can be confirmed by observing the total system's transfer function for all transmission scenarios, shown in Figure 5. Note here that the results of Figure 5 were obtained by sending a multi-tone signal from the AWG and measuring the frequency response using a real-time oscilloscope. The black line at Figure 5a represents the back-to-back case, and as we can see, the 3-dB bandwidth of the system is 28-GHz in that case. Comparing Figure 5a-e, we infer that the system's transfer function (TF) entails a dip at 15-GHz, 13-GHz, 11-GHz, 10-GHz, and 9-GHz after transmission over 10-km, 15-km, 20-km, 25-km, and 30-km, respectively, as expected due to chromatic dispersion that dominates after transmission. In particular, Figure 5f shows in detail that the 3-dB bandwidth gets reduced down to 10-GHz, 8-GHz, 7-GHz, 6.5-GHz, and 6-GHz after transmission over 10-km, 15-km, 20-km, 25-km, and 30-km, respectively. BER results for the back-to-back case for the scheme shown in Figure 1a are shown in Figure 6a, in black. For the discussion of the results, we will consider the 7% hard decision (HD) forward error correction code (FEC) threshold [20] (i.e., BER = 4.5 \(\times\) 10\({}^{-3}\)), and the 20% soft decision FEC threshold [23] (i.e., BER = 2 \(\times\) 10\({}^{-2}\)). As we can see, there is a 1 dB sensitivity improvement at the 7% HD-FEC BER threshold which approaches higher (i.e., \(\sim\)2 dB) sensitivity improvement for lower BER values (BER in the order of 10\({}^{-5}\)) compared with the results of the second scheme (Figure 1b, in grey) [15]. The 7% HD-FEC BER threshold can be achieved at \(-\)9 dBm received optical power using only a FIR filter for equalization. MLSE employment after the FIR is also investigated, however there is no impact on the performance of the system when employing the latter, as the FIR alone can compensate for any signal distortion in that case. The results for the 56 Gb/s PAM-4 transmission over 10 km for the scheme shown in Figure 1a are presented in Figure 6b, in black. The 7% HD-FEC threshold in that case can be achieved at \(-\)7.5 dBm received optical power only by employing an 81-taps FIR filter in the receiver's DSP. Implementing  
Figure 3: 56 Gb/s four-level pulse amplitude modulation (PAM-4) BER vs. received optical power for the back-to-back case when no equalization is employed (dashed line), when only an FIR filter is employed (triangles), and when an FIR followed by an 16-, 64-, 256-, and 1024 states MLSE equalizer is employed at the receiver (crosses, circles, squares, and diamonds, respectively). (**a**) When a four-level MMA and (**b**) when a seven-level MMA is used for FIR taps convergence (conditions: Experimental setup of Figure 1b). the MLSE equalizer at the output of the FIR would result in further BER improvement by \(\sim\)0.5 dB. Increasing the complexity of the MLSE up to 64, 256, or 1024 states does not bring further benefit to the overall BER performance. The BER results are improved by 1.5 dB compared to the results of the second scheme (Figure 1b, in grey) [15] when only an FIR is employed, and by 2 dB when an MLSE with 16 states (MLSE-16) is employed after the FIR. Higher complexity MLSE implementations are not justified, since the improvement in the performance is negligible, and it appears at lower BER values. The results for 56 Gb/s PAM-4 transmission over 15 km for the scheme shown in Figure 1a are presented in Figure 6c, in black. The 7% HD-FEC threshold in that case can be achieved at \(-\)7 dBm received optical using an 81-taps FIR filter in the receiver's DSP.