## 3 Communication Performance and Analysis
However, due to higher RIN from the MM-VCSEL, its achievable bit rates are considerably lower than those of SM-VCSEL at the 7% S-FEC limit, such as 15 Gbps with PAM-4 MLPDFE in Setup-I and \(\sim\)17.5 Gbps with PAM-2 MLPDFE with Setup-II. It is also worth noting that, unlike the SM-VCSEL, the MLPDFE offers better bit rate performance than TRDFE for PAM-2 from the MM-VCSEL because the MM-VCSEL has higher non-linearity than the SM-VCSEL. Nonetheless, we will focus only on the SM-VCSEL in the following sections due to its superior bit rate performance compared to the MM-VCSEL. Figure 5 presents the BER results for bit rates with PAM-8 and PAM-16 using Setup-I (Figure 5a) and Setup-II (Figure 5b). Significant BER challenges are evident across different modulation schemes and setups without equalisation. Firstly, with PAM-8 modulation on Setup-I, the BER surpasses 0.07 for bit rates starting from 2 Gbps and beyond. Similarly, using PAM-16 on Setup-I exacerbates the situation, with the BER exceeding 0.15 for bit rates of 2 Gbps and higher. Conversely, with Setup-II, employing PAM-8 modulation results in a BER of \(\sim\)0.02 at a bit rate of 2 Gbps, suggesting relatively improved performance compared to Setup-I. However, with PAM-16 on Setup-II, the BER exceeds 0.09 for bit rates starting from 2 Gbps. These results underscore the critical importance of effective equalisation strategies in mitigating ISI and non-linearity for OWC links utilising PAM-8 and PAM-16. Figure 4: BER vs. bit rate plots comparing the equalisers’ performance with PAM-2 and PAM-4 for: (**a**) SM-VCSEL with Setup-I, (**b**) SM-VCSEL with Setup-II, (**c**) MM-VCSEL with Setup-I, and (**d**) MM-VCSEL with Setup-II. The comparison between the TRDFE and the MLPDFE underscores the latter's superior performance, particularly in Setup-II. With the TRDFE on Setup-I, the BER surpasses 0.03 for bit rates of 2 Gbps and beyond with PAM-8, escalating to over 0.09 with PAM-16. In contrast, Setup-II exhibits improved performance with the TRDFE but still encounters BER issues exceeding 0.07 for bit rates beyond 2 Gbps with PAM-16. These results demonstrate the ineffectiveness of the TRDFE to mitigate the ISI in the presence of non-linearity. The MLPDFE, however, showcases remarkable improvements in both setups. In Setup-I, it achieves an impressive bit rate of about 22.5 Gbps at the 7% S-FEC limit with PAM-8, alongside a low BER of about \(3.5\times 10^{-4}\) at a bit rate of 3 Gbps with the same modulation scheme. Similarly, in Setup-II, the MLPDFE achieves a substantial bit rate of about 17.5 Gbps with PAM-8 at the 7% S-FEC limit, coupled with an exceptionally low BER of about \(10^{-6}\) at a bit rate of 5 Gbps. These results signify the MLPDFE's effectiveness in significantly improving transmission rates and minimising errors, which is particularly notable in Setup-II compared to the TRDFE, highlighting its superiority in optimising OWC systems with high non-linearities. To highlight the effectiveness of the NN equaliser, eye diagrams for the output of each equaliser using PAM-8 and PAM-16 modulation schemes are presented in Figure 6. These diagrams are computed by upsampling the received PAM symbols by eight and filtering the result with a raised cosine filter with a 0.35 roll-off factor. The diagrams are presented at 12 Gbps for PAM-8 and 6 Gbps for PAM-16 in Figures 6a and 6b, respectively. Without equalisation, the PAM-8 and PAM-16 waveforms exhibit severe distortion due to ISI and non-linearities, resulting in closed eye diagrams. Implementing the TRDFE improves the situation by opening the eye diagrams; however, the levels remain unequally spaced due to incomplete mitigation of system non-linearity. In contrast, the eye diagrams with the MLPDFE show more uniform spacing between levels. This uniformity is attributed to the MLPDFE's ability to compensate for the inherent  
Figure 5: BER vs. bit rate plots comparing the equalisers’ performance for the SM-VCSEL with PAM-8 and PAM-16 for: (**a**) Setup-I and (**b**) Setup-II.