## 5 Conclusions  
To alleviate bottleneck problems of high-speed underwater VLC systems, we construct and optimize a DNN-based waveform-to-symbol converter to replace conventional demodulation, down-sampling and post-equalization at the receiving end in 64 APSK and 64 QAM UVLC systems based on CAP modulation. The DNN converter optimizes the receiver as a whole rather than separately. It is regarded as a benchmark that could increase signal Vpp dynamic range by 104% (from 250 mV to 511 mV) for 64 APSK and 181% (from 180 mV to 506 mV) for 64 QAM with 7% FEC of 3.8 \(\times\) 10\({}^{-3}\) as a BER threshold, compared with traditional CAP decoder. The highest bit rate is 3.23 Gb/s in 64 APSK systems utilizing the DNN converter we optimize and 3.09 Gb/s in 64 QAM systems, which is 125 Mb/s \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Modulation** & **Network Structure** & \begin{tabular}{c} **Trainable** \\ **Parameters** \\ **(DNN Converter)** \\ \end{tabular} & \begin{tabular}{c} **Trainable** \\ **Parameters** \\ **(DD-LMS)** \\ \end{tabular} & \begin{tabular}{c} **Total** \\ **Trainable** \\ **Parameters** \\ **Rate** \\ \end{tabular} & \begin{tabular}{c} **Trainable** \\ **Parameters** \\ **(mV)** \\ \end{tabular} & \
\begin{tabular}{c} **Dynamic** \\ **Range** \\ **Rate** \\ \end{tabular} &
\begin{tabular}{c} **Ratio \({}^{*}\)** \\ **(102 mV)** \\ \end{tabular} \\ \hline \multirow{6}{*}{64 APSK} & Taps = 19, DNN & & & & & & & \\  & (96, 96, 96) & 26,210 & / & 26,210 & 100\% & 511 & 100\% & 1.95 \\  & w/oNN DD-LMS & & & & & & & \\  & (96, 96, 96) & 23,138 & 84 & 23,222 & 88.6\% & 497 & 97.3\% & 2.14 \\  & w/NN DD-LMS & & & & & & & \\  & (64, 64, 64) & 11,330 & 84 & 11,414 & 43.5\% & 481 & 94.1\% & 4.21 \\  & Taps = 11, DNN & & & & & & & \\  & (32, 32, 32) & 3618 & 84 & 3702 & 14.1\% & 458 & 89.6\% & 12.4 \\  & w/NN DD-LMS & & & & & & & \\ \hline \hline \end{tabular}  
Ratio \({}^{*}\) represents the ratio of dynamic range and trainable parameters.  
\end{table} 
Table 1: Comparison of different receivers in 64 APSK UVLC system. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Modulation** & **Network Structure** & \begin{tabular}{c} **Trainable** \\ **Parameters** \\ **(DNN Converter)** \\ \end{tabular} & \begin{tabular}{c} **Trainable** \\ **Parameters** \\ **(DD-LMS)** \\ \end{tabular} & \begin{tabular}{c} **Total** \\ **Parameters** \\ **Rate** \\ \end{tabular} & \begin{tabular}{c} **Trainable** \\ **Parameters** \\ **Rate** \\ \end{tabular} & \
\begin{tabular}{c} **Dynamic** \\ **Range** \\ **Rate** \\ \end{tabular} &
\begin{tabular}{c} **Dynamic** \\ **Rate** \\ \end{tabular} \\ \hline \multirow{6}{*}{64 QAM} & Taps = 19, DNN & & & & & & & \\  & (96, 96, 96) & 26,210 & / & 26,210 & 100\% & 506 & 100\% & 1.93 \\  & w/oNN DD-LMS & & & & & & & \\  & Taps = 11, DNN & & & & & & & \\  & (96, 96, 96) & 23,138 & 84 & 23,222 & 88.6\% & 451 & 89.1\% & 1.94 \\  & Taps = 11, DNN & & & & & & & \\  & (64, 64, 64) & 11,330 & 84 & 11,414 & 43.5\% & 420 & 83.0\% & 3.68 \\  & w/NN DD-LMS & & & & & & & \\  & (32, 32, 32) & 3618 & 84 & 3702 & 14.1\% & 382 & 75.5\% & 10.3 \\  & w/NN DD-LMS & & & & & & & \\ \hline \hline \end{tabular}  
Ratio \({}^{*}\) represents the ratio of dynamic range and trainable parameters.  
\end{table} 
Table 2: Comparison of different receivers in 64 QAM UVLC system. and 50 Mb/s faster than the traditional CAP decoder, respectively. However, it comes at the cost of high computation complexity of 26,210 total trainable parameters. To make a better tradeoff between communication performance and computation complexity, a cascaded receiver consisting of a DNN-based waveform-to-symbol converter and a modified NN-based DD-LMS algorithm is innovatively proposed. With fewer taps and nodes of hidden layers than the benchmark converter, the front-stage DNN converter could mitigate the majority of ISI and signal nonlinear distortions.