## 3 Communication Performance and Analysis  
To assess the effectiveness of the NN equaliser in handling PAM-\(M\), this section presents the BER results from the SM-VCSEL-based OWC experiment setups (Setup-I and Setup-II) discussed in Section 2. The bit rates range from 2 Gbps to 40 Gbps in order to explore multigigabit communication over the SM-VCSEL-based OWC link. For comparison purposes, the link is evaluated (1) without equalisation (unequalised), (2) with the transversal DFE (TRDFE), and (3) with the MLPDFE. The parameters for both the TRDFE and the MLPDFE are summarised in Table 2.  
The BER results are presented across various bit rates for the equalisers employing PAM-2 and PAM-4 schemes for the SM-VCSEL and the MM-VCSEL in Figure 4. A BER of \(\sim\)3.8 \(\times\) 10\({}^{-3}\), which is the second-generation super forward error correction (S-FEC) limit and has a 7% overhead and \(\sim\)6 dB coding gain [28], is used to estimate the system's bit rate performance. For PAM-2, the MLPDFE output layer uses the sigmoid activation function due to its \"binary\" nature and superior performance compared to the linear activation function [16]. However, the linear activation function is better for PAM at four or more levels. Without equalisation at this FEC limit, the PAM-2 scheme with the SM-VCSEL achieves bit rates of \(\sim\)8 Gbps and \(\sim\)9 Gbps for Setup-I and Setup-II, respectively. Conversely, the bit rates achieved with PAM-4 are \(\sim\)5 Gbps and \(\sim\)4.5 Gbps for Setup-I and Setup-II, respectively. A notable observation is that Setup-II demonstrates superior performance with PAM-2, while Setup-II showcases better results with PAM-4. This discrepancy arises due to PAM-2's lower susceptibility to non-linearity than PAM-4, leveraging the high SNR specifically achievable in Setup-II. With PAM-2, the MLPDFE demonstrates a marginal BER performance improvement compared to the TRDFE across all bit rates. Both equalisers significantly enhance the OWC link, enabling bit rates of \(\sim\)23 Gbps and \(\sim\)28 Gbps at the 7% S-FEC limit for Setup-I and Setup-II, respectively. With PAM-4, the MLPDFE and TRDFE exhibit similar BER performances for bit rates exceeding 25 Gbps, achieving \(\sim\)27 Gbps and \(\sim\)29 Gbps at the 7% S-FEC limit for Setup-I and Setup-II, respectively. However, the MLPDFE notably outperforms the TRDFE for bit rates below 25 Gbps, i.e., at low BER values. For instance, at a BER of 10\({}^{-6}\) with Setup-I, the MLPDFE achieves bit rates of \(\sim\)11 Gbps, while the TRDFE offers \(\sim\)6 Gbps. This is because non-linearity is the dominant performance-limiting factor at lower bit rates, while SNR becomes the limiting factor at higher bit rates. Hence, this result clearly demonstrates the effectiveness of the NN in compensating for non-linearity, which is further evident at higher modulation levels. It is worth mentioning that both \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Number of Forward Taps & \(N_{ft}\) & 32 \\ Number of Feedback Taps & \(N_{ht}\) & 8 \\ Number of Hidden-Layer Neurons & \(N_{ht}\) & 6 \\ Number of Training Symbols & \(N_{tr}\) & 4000 \\ Number of Bits for BER Testing & & 10\({}^{6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Equaliser parameters. equalisers exhibit better performance with PAM-4 on Setup-I than in Setup-II at bit rates below 25 Gbps. Specifically, the MLPDFE achieves \(\sim\)7 Gbps and \(\sim\)10 Gbps at a BER of \(10^{-6}\) for Setup-I and Setup-II, respectively. Additionally, both equalisers showcase enhanced performance with PAM-2 on Setup-II relative to Setup-I at lower bit rates, as the MLPDFE attains \(\sim\)10 Gbps and \(\sim\)15 Gbps for Setup-I and Setup-II, respectively, at a BER of \(10^{-6}\). As with SM-VCSEL, equalisation significantly improves the performance of MM-VCSEL links.