## 3 Results and Discussion  
For both schemes, in the receiver DSP we investigated two cases: (i) when the multi-modulus algorithm (MMA) used for the FIR taps convergence is set to deliver a four level signal at its output;  
Figure 1: **(a)**: Experimental setup using a 30-GHz arbitrary waveform generator (AWG); **(b)** Experimental setup using a 15-GHz digital–analog converter (DAC) [15]; **(c)**: Digital signal processing (DSP) algorithms used for offline processing for both implementations. and (ii) when the MMA is modified so as its output corresponds to a seven-level poly-binary signal instead of a four-level one due to strong filtering imposed by the CD dominating the link. For qualitative comparison, the 56 Gb/s received eye-diagrams for the implementation depicted in Figure 1b are shown in Figure 2 for the back-to-back case, and after 10-km, 15-km, and 20-km transmission. Here, we chose to illustrate the eye-diagrams for the scheme of Figure 1b, considering that it is a worst case scenario between the two implementations. As we can see in the first row, the received signal gets significantly degraded after all transmission scenarios compared to the back-to-back due to the chromatic dispersion that dominates in the link. For the back-to-back case when a four-level MMA is used, performance is superior compared to the case of a seven-level MMA employment, as indicated both by the eye-diagrams of the first column and the BER results shown in Figure 3; thus, it is used throughout this paper to obtain the BER performance for the back-to-back case for both schemes in Figure 1a,b. In particular, as we can see in Figure 3a, transmission is not feasible when no equalization is employed at the receiver. Making use of an FIR filter with 81 taps optimizes the BER by orders of magnitude, and brings the BER below the HD-FEC (hard decision forward error correction code) threshold; i.e., 4.5 \(\times\) 10\({}^{-3}\)[20], for \(-\)8 dBm. Employing an MLSE of either complexity (i.e., 16-, 64-, 256-, or 1024 state) at the output of the FIR filter does not further improve the performance. Results employing a seven-level MMA are shown in Figure 3b for comparison. As it is shown, this approach performs worse than a four-level MMA, since the bandwidth limitations are not so severe in the back-to-back case; however, they become critical for transmission over SSMF, making the seven-level MMA outperform the four-level one for links longer than 10-km for both schemes of Figure 1 (not shown here for the sake of brevity). So, to obtain all of the BER results presented in this paper for transmission over 10-km, 15-km, 20-km, 25-km, and 30-km, the MMA used for FIR taps convergence is modified so its output corresponds to a seven-level poly-binary signal instead of a four-level, due to strong filtering imposed by chromatic dispersion. This can be seen in Figure 2 in the second row, where we can observe that the eye-diagram becomes heavily distorted when the four-level MMA is employed for links longer than 10-km SMF, making the transmission unfeasible. The seven-level signal that is obtained at the output of the FIR will subsequently be fed to the input of the MLSE, operating in training mode. The latter is then able to decode the duo-binary signal and re-construct the original four-levels acting as a Viterbi decoder [21; 22]. However, even if the employment of a seven-level MMA--depicted in the third row in Figure 2--improves the quality of the signal at the output of the FIR, the eye-opening becomes narrower for 15-km transmission, and finally the signal is severely degraded for 20-km such that the signal levels are no longer distinguishable. Figure 2: Eye-diagrams before and after finite impulse response (FIR) for back-to-back, 10-km, 15-km, and 20-km for Figure 1b. Next, the results obtained using the experimental setup of Figure 1a are presented. The received eye-diagrams as well the eye-diagrams after the FIR are shown in Figure 4 for the back-to-back, and after transmission over 10-km, 15-km, 20-km, 25-km, and 30-km.