# High-Speed Underwater Optical Wireless Communication with Advanced Signal Processing Methods Survey
## 3 Non-Machine Learning Equalization
### Nonlinear Equalizer  
Compared with the linear equalizer, the nonlinear equalizer has a more complex structure but superior ISI mitigation performance. It is also widely used in the recent UOWC systems, which are summarized in Table 5.  
Earlier, many UOWC experiments used an analog equalizer to improve the system frequency response. In [26], a physical tunable passive gain equalizer (TPGE) combined with the two-stage-injection-locked technique was employed to improve the frequency response, as shown in Figure 7. The frequency response of the signal is compensated by around 10 dB after TPGE, where the electrical spectrum of the data signal after TPGE is flatter, improving the system transmission performance. Results show that BER can be improved from \(2\times 10^{-2}\) to \(4\times 10^{-2}\) in an 8 m tap water channel under a transmission speed of 9.6 Gbps. Similarly, in [124], an analog post-equalizer(APE) was demonstrated to increase the 3 dB frequency response of the system from 4 MHz (LED) and 100 MHz (detector) to 124.2 MHz end-to-end. Due to the broader and flatter 3 dB bandwidth of the system, high spectral efficiency modulation formats such as OFDM can be applied. Results show that the SNR increased from 8.75 dB to 22.6 dB after employing the APE. Moreover, the BER improved from \(1.2\times 10^{-1}\) to \(3.9\times 10^{-4}\) in a UOWC link at 621.1 Mbps with 2 m tap water. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Year**} & **Bit Rate** & \multirow{2}{*}{**Distance**} & **Optical Source** & **Receiver** & **Transmission Power** & **Modulation Scheme** & **Equalizer** & **Refs.** \\ \cline{1-1}  & (**pps**) & & & & & & & \\ \hline
2016 & 9.6 G & 8 m Tap & 405 nm LD & PD & \(\sim\)30 mW & 16-QAM-OFDM & TGE & [26] \\
2016 & 745 M & 2 m Tap & 448 nm LED & APD & \(\sim\)184.5 mW & OFDM-QAM & APE & [124] \\
2017 & 16 G & 10 m Tap & 488 nm LD & PD & \(\sim\)20 mW & PAM4 & DFE & [27] \\
2018 & 16.6 G & 55 m Tap & 450 nm LD & PIN PD & \(\sim\)120 mW & OFDM-QAM & VE & [62] \\
2018 & 7.33 G & 15 m Tap & 450 nm LD & APD & \(\sim\)20 mW & DMT & VE & [64] \\
2019 & 2.5 G & 60 m Tap & 450 nm LD & APD & \(\sim\)50.2 mW & NRZ-OOK & VE & [28] \\
2019 & 500 M & 100 nm Tsp & 520 nm LD & APD & \(\sim\)7.25 mW & NRZ-OOK & VE & [38] \\
2019 & 500 M & 1 m Bubble & 520 nm LD & APD & \(\sim\)25 mW & 16 PM & VE & [76] \\
2021 & 200 M & 100 nm Tsp & 450 nm LD 520 nm LD & PMT & \(\sim\)700 mW & RRC-OK & MPE & [30] \\
2022 & 4.12 G & 2 m Tap & 484 nm LED & APD & \(\sim\) 1 mW & PAM4 & VE & [125] \\
2022 & 200 M & 1.5 m Tap & Blue LED & PD & \(\sim\)0.4 mW & CAP OFDM & VPDF & [126] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Recent research progress in UOWC systems based on NML nonlinear equalization. Figure 6: The receiver structure of the (**a**) FDE-DFE, (**b**) FDE-NP [63]. Compared with the previous nonlinear analog equalizers, digital nonlinear equalizers are more widely studied and utilized to process received signals. The most common one is the nonlinear Volterra series-based equalizer (VE), which has great advantages against non-linear effects to further improve system performance. In recent years, some works compared the nonlinear VE with conventional linear equalizers. For instance, a nonlinear VE combined with adaptive bit-power loading discrete multi-tone (DMT) was employed in [62], and results show that the VE can bring more than 2 dB gain compared with linear equalization since the nonlinear VE is more effective against non-linear effects. Up to 16.6 Gbps data rate through 55 m tap water wireless optical transmission was achieved. The nonlinear VE has also been compared with the conventional linear feed-forward equalizer (FFE), where the nonlinear VE is shown to effectively reduce the impact of device nonlinearity [125]. Results show that a significant BER reduction (from \(1\times 10^{-2}\) to \(3\times 10^{-3}\)) is observed after changing linear FFE to nonlinear VE at 4.2 Gbps with 2 m transmission.