# Optical OFDM for SiPM-Based Underwater Optical Wireless Communication Links
## 6 Performance Study of the UWOC Link
### Comparison with OOK  
First of all, in order to elucidate the real interest of O-OFDM signaling, let us compare the performances of DCO-OFDM and OOK modulation schemes for a typical scenario. In Figure 5 BER plots as a function of link distance are presented, considering an electrical transmit power of \(P_{\rm Tx,e}=125\) mW. For OOK, the transmitted electrical power corresponding to \"Off\" symbols is set to 2.75 mW (given \(V_{\rm min}=2.75\) V and \(I_{\rm min}=1\) mA). The transmit power for \"On\" symbols is set so as to result in an average transmit electrical power of 125 mW. At the Rx side, signal demodulation is based on optimal thresholding, as considered in [9].  
First, notice a high BER for very short link ranges (e.g., \(Z\lesssim 8\) m for OOK), which is due to SiPM saturation [6; 9]. For relatively large link ranges (e.g., \(Z\gtrsim 45\) m for OOK at \(R_{b}=10\) Mbps), the BER reasonably increases due to decreased SNR as a result of channel attenuation.  
Similar to [7], we define the low BER interval (LBI, in units of meter) for a given transmission scheme, indicating the interval of link range satisfying a target BER. The LBI can be considered as a measure of link operation flexibility, i.e., the range interval in which the system can function with a low BER. In other words, the larger the LBI, the more flexible is the designed system with respect to the actual link distance. For instance, considering OOK modulation with \(R_{b}=10\) Mbps and a target BER of \(10^{-3}\), the LBI is around 41.4 m, as indicated in the figure.  
As expected, for increased \(R_{b}\), the BER performance degrades due to the decreased SNR as a result of shorter symbol duration, and also (for the case of OOK) due to increased ISI. For instance, for BER \(=10^{-3}\), the maximum transmission distance \(Z_{\rm max}\) is around 73.7, 59.2, and 49.5 m for OOK with \(R_{b}=1\), 5, and 10 Mbps, respectively. For \(R_{b}=20\) Mbps that is much higher than the aggregate channel BW, the link with OOK effectively becomes nonoperational. Obviously, DCO-OFDM is robust against channel frequency selectivity, and even for \(R_{b}=20\) Mbps we obtain a relatively large \(Z_{\rm max}\). On the other hand, the BER performance is affected more by SiPM saturation due to the higher PAPR and the more complex waveform compared to OOK, which explains the saturation limit at slightly larger distances (i.e., around 12 m at BER \(=10^{-3}\)). Nevertheless, DCO remains quite advantageous  
\begin{table}
\begin{tabular}{l c c} \hline \hline  & Wavelength \(\lambda\) & 470 nm \\ Tx (LED) & 3 dB cut-off frequency & 10 MHz \\  & Lambertian order \(m\) & 45 \\  & I-V parameters (\(V_{min}\), \(V_{max}\); \(I_{init}\), \(I_{max}\)) & (2.75 V, 4.03 V; 1 mA, 110 mA) \\ \hline Channel & Diffuse attenuation coefficient \(K\) & 0.08 m\({}^{-1}\) \\ \hline  & Photon Detection Efficiency, Y\({}_{\rm PDE}\) & 40\% \\  & Surface Area, \(A_{\rm PD}\) & 9 mm\({}^{2}\) \\  & Dark Current Rate, \(f_{\rm DCR}\) & 25 kHz \\ Rx (SiPM) & Dead Time, \(\tau_{d}\) & 68.1 ns \\  & No. of SPADs, \(N_{\rm SPAD}\) & 3600 \\  & Cross-Talk Prob., \(P_{\rm CT}\) & 3\% \\  & After-Pulsing Prob., \(P_{\rm AP}\) & 0.1\% \\  & 3 dB Cut-Off Frequency & 4 MHz \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of the Tx, channel, and the Hamamatsu C13366 3050 GA SiPM.  
in terms of LBI. For instance, for \(R_{b}=1\,\)Mbps, the LBI is \(\sim 107\,\)m, in contrast to \(\sim 65.5\,\)m for OOK. LBI and \(Z_{\text{max}}\) for the different \(R_{b}\) values are summarized in Table 2.