# High-Speed Underwater Optical Wireless Communication with Advanced Signal Processing Methods Survey
## 3 Non-Machine Learning Equalization  
### Linear Equalizer  
UOWC has developed rapidly in recent years and made remarkable achievements. Table 4 lists the recent studies of NML linear equalization in UOWC systems. Due to simplicity and efficiency, the linear ZF-LE and feedforward equalizer (FFE) have been studied in UOWC systems to enhance data transmission performance. In [37], to reduce the effect of ISI and improve the BER, the ZF-LE based on the double Gamma model was employed in a UOWC system with coastal water. MC results show that to achieve the forward error correction (FEC) threshold (\(3.8\times 10^{-3}\)), the ZF-LE can reduce the transmission power by around 2 dBm and 1.5 dBm in the 1 Gbps 40 m coastal water link and the 500 Mbps 10 m harbor water link, respectively. In addition, the ZF-LE combined with the dual-wavelength UOWC transmission was demonstrated in [104] to improve the BER simultaneously in two wavelength channels. Results in Figure 5 show that the ZF-LE can restore eye opening in the corresponding eye diagram of both blue and green channels and improve the BER performance. Furthermore, a linear T/2-spaced feedforward equalizer (FFE) combined with the high-bandwidth GaN-based mini-LEDs was demonstrated in [25]. Due to mitigating the ISI by simple and efficient FFE, the net \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Year**} & **Bit Rate** & \multirow{2}{*}{**Distance**} & **Optical** & \multirow{2}{*}{**Receiver**} & **Transmission** & **Modulation** & \multirow{2}{*}{**Sceheme**} & **Equalizer** & **Refs.** \\  & **(bps)** & & & **Source** & & & & & \\ \hline
2013 & 1 G & 40 m Coastal & 532 nm LED & PD & \(\sim\)50 W & OOK & ZF-LE & [37] \\
2017 & 1 M & 3 m Tap & 532 nm LED & SPAD & N/A & OFDM-QAM & MMSE-FDE & [31] \\
2019 & 256 G & 50 m Air 5 m & \multirow{2}{*}{Red LD} & APD & \(\sim\)500 W & PAM4 & FDE & [79] \\  & & 125 m Tap & & & & & & \\
2019 & 30 G & 2.5 m Harb & 488 nm LD & APD & \(\sim\)20 mW & PAM4 & FDE & [35] \\
2020 & 20 M & 28 m Tap & 470 nm LED & SPM & \(\sim\)600 mW & PAM & FDE & [123] \\
2020 & 50 M & 10 m Tap & 520 nm LD & APD & \(\sim\)50 mW & OFDM & FDE-NP & [63] \\
2020 & 3.31 G & 56 m Tap & 377 nm LD & 2 APDs & \(\sim\)70 mW to & NRZ-OOK & ZF-LE & [104] \\
2021 & 1 G & 1 m Tap & 405 nm LD & 120 mW & NRZ-OOK & ZF-LE & [104] \\
2022 & 4 G & 2 m Tap & 484 nm LED & APD & \(\sim\)1 mW & PAM4 & FFE & [25] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Research progress in the UOWC system based on NML linear equalization. data rate can reach up to 4.08 Gbps (the highest for UOWC systems using a single-pixel mini-LED) with a BER below the FEC threshold in short-distance transmission. In addition to the simple ZF-LE, low-complexity linear frequency domain equalizers (FDE) were also employed to mitigate the ISI effect. In [123], the FDE combined with high sensitive silicon photo-multipliers (SiPMs) receiver was employed to overcome the limited bandwidth of components at a high data rate. Results show that the FDE can significantly improve BER from \(1\times 10^{-1}\) to \(0.9\times 10^{-4}\) in a 10 Mbps UOWC system with a 40 m tap water channel. Moreover, the FDE can improve the data rate to achieve 20 Mbps and 50 Mbps transmission under 28 m and 10 m tap water channels, respectively. In addition, linear FDE has also been studied in the free-space optical underwater optical wireless communication (FSO-UOWC) convergent system to optimize the modulation frequency response and enhance the transmission capacity [79]. Together with the two-stage injection locking technique, a 256 Gb/s four-channel FSO-UOWC convergent system with 50 m free space and 5 m turbid underwater transmission is successfully demonstrated. Furthermore, in another work [35], a red LD is used as the transmitter, and both an injection-locking optoelectronic feedback and a linear FDE at the receiving end are applied. Results show that the 3 dB bandwidth can be increased from 8.4 GHz to 10.8 GHz using the linear FDE.