# Optical OFDM for SiPM-Based Underwater Optical Wireless Communication Links
## 6 Performance Study of the UWOC Link
### Clipping Effect on the Link Performance  
Let us now study the impact of signal clipping on the performance of DCO-, ACO-, and LACO-OFDM schemes. For this, the spectral efficiency for the three schemes is fixed by setting accordingly the QAM modulation orders, as explained previously in Section 6.1. Figure 6 contrasts the BER performances of these schemes as a function of \(P_{\text{Tx,e}}\). The link data rate is fixed to 20 Mbps with \(T_{s}=5.165\times 10^{-5}\) s, and the link distance is fixed to \(Z=20\) and \(70\,\)m, corresponding to relatively moderate and high channel attenuations, respectively. From Figure 6, for relatively low transmit powers, i.e., \(P_{\text{Tx,e}}\lesssim 25\,\)mW, notice the close performances of the three techniques, in particular for the relatively short range of \(Z=20\,\)m. For \(Z=70\,\)m, ACO and LACO outperform DCO, with a slight advantage for ACO. For instance, at a target BER of \(10^{-3}\), the required \(P_{\text{Tx,e}}\) is around 9.7, 13.2, and 19.1 mW for ACO, LACO, and DCO schemes, respectively. Meanwhile, the performances of these schemes are affected differently for relatively large transmit powers. For instance, for \(Z=20\,\)m, upper signal clipping limits the link performance for \(P_{\text{Tx,e}}\) larger \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(R_{b}\) (Mbps) & LBI (m) & \(Z_{\text{max}}\) (m) \\ \hline \multirow{4}{*}{DCO} & 1 & 106.6 & 118.8 \\  & 5 & 92.8 & 105 \\  & 10 & 86.4 & 98.8 \\  & 15 & 82.2 & 94.4 \\  & 20 & 78.9 & 91.3 \\ \hline \multirow{4}{*}{OOK} & 1 & 65.6 & 73.7 \\  & 5 & 51.15 & 59.2 \\ \cline{1-1}  & 10 & 41.4 & 49.5 \\ \cline{1-1}  & 15 & 5.1 & 13.2 \\ \cline{1-1}  & 20 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: LBI and maximum attainable range for OOK and 4-QAM DCO-OFDM transmission schemes according to Figure 5; \(P_{\text{Tx,e}}=125\,\)mW, BER \(=10^{-3}\). Figure 5: BER comparison of OOK and 4-QAM DCO-OFDM for \(P_{\text{Tx,e}}=125\,\)mW. \(N=1024\). \(N_{\text{CP}}=2\), 3, 5, 7, and 9, for \(R_{b}=1\), 5, 10, 15, and 20 Mbps, respectively. that about 90.4, 125.6, and 310 mW for ACO, LACO, and DCO cases, respectively. The advantage of DCO can be explained by the smaller modulation size used, which results in a lower signal PAPR, and hence a less detrimental effect of the clipping noise. For LACO, which has a lower PAPR than ACO, the clipping effect appears for a smaller \(P_{\text{Tx,e}}\); yet, we again notice a neat advantage of DCO. Notice that, as explained previously, here a non-zero bias is considered for ACO and LACO due to the LED characteristics. The presented results show how these schemes are compared in practice. In particular, for relatively low \(P_{\text{Tx,e}}\), there is evidence of higher energy efficiency of ACO and LACO over DCO: this latter suffers from the higher DC-bias used. Meanwhile, benefiting from a lower PAPR, DCO is more robust than the two other schemes with respect to increasing the transmit power. Note that, in addition to having a lower PAPR, DCO uses a smaller \(\alpha\). For instance, for \(P_{\text{Tx,e}}=25\) mW, \(\alpha\) is set to 0.0455, 0.153, and 0.092, for DCO, ACO, and LACO-OFDM schemes, respectively. It is worth focusing on the difference between the upper limits of \(P_{\text{Tx,e}}\) for \(Z=20\) and 70 m in Figure 6. One would expect the same limit irrespective of \(Z\), since clipping affects the signal at the Tx side. However, the SiPM saturation at the Rx also affects the link performance for relatively high \(P_{\text{Tx,e}}\). Consequently, we notice a lower limit for \(P_{\text{Tx,e}}\) for a smaller \(Z\), where the Rx saturation becomes increasingly important. In order to better contrast the performances of the three signaling schemes, while taking into account the effects of signal clipping, channel attenuation, and Rx saturation, we have presented color maps of BER versus \(P_{\text{Tx,e}}\) and \(Z\) in Figure 7 for \(R_{b}=20\), 50, and 100 Mbps.