## 5 Assessment of Algorithms Against Prior Research Results  
The performance of the proposed DFE, MLD, and RDE algorithms is compared against the least mean square (LMS) [52] algorithm, the constant modulus algorithm (CMA) [53; 54; 55], and the adaptive median filtering (AMF) [56] algorithm, as reported in our previously published work [31; 32]. Although the LMS is simpler and more efficient for linear channels, it is inadequate for severely dispersive channels. At the same time, AMF, primarily intended for reducing noise, is less appropriate for equalization tasks in high-frequency, high-data-rate situations. For QPSK modulation across all OFDM subcarriers, specifically, when comparing MLD, DFE, and RDE with LMS, CMA, and AMF for an SSMF of length 120 km, as shown in Table 5 and Figure 8a, the LMS, CMA, and AMF algorithms do not provide an EVM value for QPSK, indicating that they failed to perform effectively under the given conditions or configuration. This suggests that LMS, CMA, and AMF may struggle to adapt to QPSK modulation over long fiber distances, making it unsuitable for this particular setup. For QPSK, the MLD algorithm achieves an EVM of 17.06% over a fiber length of 120 km, while the DFE algorithm slightly outperforms MLD in terms of EVM, with a value of 16.6%. However, both MLD and DFE can manage fiber lengths up to 120 km, indicating that both algorithms can maintain signal quality over similar transmission distances. The small improvement in EVM for DFE suggests that this algorithm may be better suited for \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & \multicolumn{2}{c}{**QPSK**} & \multicolumn{2}{c}{**16-QAM**} \\ \hline  & **EVM (\%)** & **Fiber Length (km)** & **EVM (\%)** & **Fiber Length (km)** \\ \hline
**MLD** & 17.06 & 120 & 12.4 & 100 \\ \hline
**DFE** & 16.6 & 120 & 12.32 & 100 \\ \hline
**LMS** & - & 120 & 23.75 & 100 \\ \hline
**CMA** & - & 120 & - & 100 \\ \hline
**AMF** & - & 120 & 23.00 & 100 \\ \hline
**RDE** & 11.35 & 120 & 9.41 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: EVM and fiber length comparisons for the different equalization algorithms. Figure 7: EVM results obtained before and after equalization vs. the fiber lengths for (**a**) 64 QAM constellations after MLD and DFE equalization and (**b**) 128-QAM constellations after MLD and DFE equalization. compensating for distortion in the dispersive channel compared to the MLD. Moreover, RDE surpasses MLD and DFE in EVM values for both QPSK and 16-QAM modulation formats, indicating that it is a suitable algorithm for specific formats. For 16-QAM modulation, implementing MLD and DFE algorithms allows for an extended transmission distance of up to 50 km beyond what is achievable with LMS and AMF algorithms while maintaining EVM values below the 3 GPP threshold, as shown in Figure 8b. Specifically, when comparing MLD with LMS and AMF after equalization for 16-QAM modulation, as shown in Figure 8b, MLD achieves an EVM improvement of 11.35% over LMS and a 10.60% improvement over AMF at a fixed fiber length of 100 km. The CMA algorithm is not employed in this scenario due to its limitations with multiple radii in the constellation points, rendering it ineffective for 16-QAM modulation [57]. Further analysis reveals that DFE slightly outperforms MLD and outperforms LMS and AMF for 16-QAM modulation in OFDM subcarriers, demonstrating an EVM improvement of 0.80% over MLD, 11.43% over LMS, and 10.68% over AMF for the same fixed fiber length of 100 km. For 16-QAM modulation over a transmission distance of 50 km, a comparative analysis reveals significant improvements in EVM when using MLD and DFE algorithms. In the context of QPSK and 16-QAM modulation across all OFDM subcarriers, a comparison of RDE with MLD, DFE, LMS, CMA, and AMF reveals that RDE attains an EVM of 11.35% for a fiber length of 120 km in the case of QPSK and an EVM of 9.41% for a fiber length of 100 km for 16-QAM, as illustrated in Table 5 and Figure 8a,b.