# High-Speed Underwater Optical Wireless Communication with Advanced Signal Processing Methods Survey
## 3 Non-Machine Learning Equalization
### Nonlinear Equalizer
In addition to conventional VE, the nonlinear Volterra series-based DFE (VDFE) can further mitigate the intrinsic static and dynamic non-linearity effects in the UOWC system. In [126], a nonlinear VDFE was demonstrated in carrierless amplitude and phase (CAP) modulation and compared with the linear DFE. However, since the LED is biased in the linear region of its transfer curve, the linear DFE and nonlinear VDFE have similar BER performance. Moreover, the nonlinear VE combined with DMT was demonstrated in [64]. Due to effectively combating nonlinear effects, results show that VE can bring more than 3 dB gain on average compared with the system without VE. In a 15 m underwater channel, the system with a nonlinear equalizer can achieve 7.33 Gbps with BER lower than the 7% FEC threshold, which is 0.9 Gbps higher than the system without VE. Furthermore, the nonlinear second-order VE has been used in [28]. Results show that the VE can significantly reduce the influence of ISI, which achieved a better BER from \(1\times 10^{-1}\) to \(3.5\times 10^{-3}\) at 2.5 Gbps transmission under 60 m of tap water. In addition, nonlinear VE was also applied in [8] to compare with the direct hard-decision detection in the receiving offline DSP. Results show that the VE achieved low BER performance (\(2.5\times 10^{-3}\) compared with \(5.91\times 10^{-2}\) of hard-decision detection) in a 100 m 500 Mbps UOWC system. Moreover, in Figure 8, when the data rate reaches 400 Mbps and 500 Mbps, severe ISI makes the system impossible to reduce the BER to achieve the FEC limit by using hard decision detection. However, the nonlinear VE can bring the BER below the FEC limit with minimum optical powers required for 400 Mbps and 500 Mbps being \(-26.4\) dBm and \(-24.0\) dBm, respectively. Figure 7: Electrical spectra of the 9.6 Gbps 5 GHz 16-QAM-OFDM data signal (**a**) before TPGE and (**b**) after TPGE [26]. In addition to tap water channels, nonlinear VE has also been employed under the bubble water channel to improve the BER performance and combat ISI induced by signal light scattering from bubbles [76]. Results show that the UOWC system without the nonlinear VE can only achieve a BER below the FEC limit when the bubble size is smaller than 1.2 mm, whereas the system with VE works under bubbles with sizes up to 2.8 mm. Compared with the conventional nonlinear VE, in which the computation complexity increases with the memory length and nonlinear order, the simpler nonlinear DFE combined with the light injection and optoelectronic feedback techniques was employed, which achieved 16 Gbps (8 Gbaudps) PAM4 signal transmission in a UOWC system [27]. Moreover, the nonlinear memory polynomial model-based equalizer (MPE) has great advantages of faster convergence speed and lower error. After employing the nonlinear MPE in [30], the BER significantly increase from \(1\times 10^{-2}\) to \(5\times 10^{-5}\) at 160 Mbps under 100 m tap water. Moreover, due to the nonlinear MPE reducing the effect of ISI efficiently, a 200 Mbps data rate over 120 m and a 100 Mbps data rate over 139 m underwater transmission were achieved.