# Optical OFDM for SiPM-Based Underwater Optical Wireless Communication Links
## 6 Performance Study of the UWOC Link
### Impact of QAM Constellation Size  
Up to now, the spectral efficiency of \(\sim 1\,\mathrm{bps}/\mathrm{Hz}\) was considered, corresponding to the signal constellations of 4-QAM for DCO, 16-QAM for ACO, and 8-QAM and 4-QAM for layers 1 and 2 for LACO. Let us now consider larger signal constellations to see how these schemes are affected by a consequently increased PAPR. Accordingly, the constellation is set to 16-QAM for DCO and 256-QAM for ACO, resulting in a spectral efficiency of \(\sim 2\,\mathrm{bps}/\mathrm{Hz}\). For LACO, 64-QAM is considered for the first layer and 16-QAM for the second layer. Note that using larger constellation sizes allows us to increase the data rate, while keeping the same OFDM symbol duration \(T_{s}\). Nevertheless, in order to make a fair comparison with the previous case (i.e., \(\eta\approx 1\,\mathrm{bps}/\mathrm{Hz}\)), the same \(R_{b}\) values as before are considered, i.e., 20, 50, and 100 Mbps, and accordingly \(T_{s}\) is multiplied by 2. The BER performances versus \(Z\) are compared in Figure 10 for \(P_{\mathrm{Tx},e}=20\) and 50 mW. First, notice from Figure 10a that (as it was the case in Figure 8) for relatively short \(Z\) where the performance is limited by SiPM saturation, we have a shorter saturation range for DCO. This is due to the high PAPR of ACO and LACO because of using a larger signal constellation. As expected, the best LBI is obtained with DCO for a given target BER. For relatively large \(Z\), the lower power efficiency of DCO becomes penalizing. Interestingly, LACO offers the best performance. For \(P_{\mathrm{Tx},e}=50\,\mathrm{mW}\), from Figure 10b, notice the superiority of DCO compared to the two other schemes. Indeed, given the large constellation sizes used for ACO and LACO, this transmit power of 50 mW appears to be too high, resulting in considerable signal clipping. Indeed, it was already the case in Figure 10a for ACO. To better understand this limitation, we have presented in Figure 11 color maps of BER versus \(Z\) and \(P_{\mathrm{Tx},e}\) for \(R_{b}=20\), 50, and 100 Mbps, where we can notice the significant reduction of the LBI, in particular, for ACO and LACO, as compared with Figure 7. Table 5 summarizes the LBI and \(Z_{\mathrm{max}}\) for different data-rates and the target BER of \(10^{-3}\) for the three schemes. It is worth mentioning that here we have considered only two layers for LACO. In fact, using more layers, we can reduce the constellation size in the first layer but at the cost of increased computational complexity. By increasing the number of layers, the spectral efficiency of LACO approaches that of DCO. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{\(P_{\mathrm{Tx},e}=20\,\mathrm{mW}\)} & \multicolumn{3}{c}{\(P_{\mathrm{Tx},e}=50\,\mathrm{mW}\)} \\ \hline  & \(R_{b}\) (Mbps) & LBI (m) & \(Z_{\mathrm{max}}\) (m) & LBI (m) & \(Z_{\mathrm{max}}\) (m) \\ \hline  & 20 & 53.2 & 61.6 & 59.1 & 70.1 \\ DCO & 50 & 43.6 & 51.9 & 49.5 & 60.3 \\  & 100 & 33.5 & 40.9 & 38 & 48.9 \\ \hline  & 20 & 25.5 & 40.1 & 3.4 & 23.1 \\ ACO & 50 & 20.8 & 35.2 & \(-\) & \(-\)Figure 10: BER performance as a function of distance for DCO, ACO and LACO-OFDM. Spectral efficiency of \(\sim 2\,\mathrm{bps}/\mathrm{Hz}\) using, e.g., 16 QAM for DCO. \(N=1024\), \(N_{\mathrm{CP}}=5\), 11, and 20, for \(R_{b}=20\), 50, and 100 Mbps, respectively. Electrical transmit power of (**a**) 20 mW and (**b**) 50 mW. optical power [9; 53]. Consider 100 LEDs at the Tx, modulated simultaneously, and set the transmit power per LED to \(P_{\rm{Tx,e}}=50\,\)mW (this way, the total transmit electrical power is \(5\,\)W). We assume that we have almost the same radiation pattern (i.e., Lambertian with \(m\approx 45\)) as for a single LED. Figure 12 shows the BER plots for the three considered data rates and for spectral efficiencies of \(\eta\approx 1\,\)bps\(/\,\)Hz (i.e., with 4-QAM for DCO-OFDM) and \(\eta\approx 2\,\)bps\(/\,\)Hz (i.e., with 16-QAM for DCO-OFDM).