# High-Speed Underwater Optical Wireless Communication with Advanced Signal Processing Methods Survey
## 4 Machine Learning Applications in UOWC  
### Supervised Learning in UOWC Systems  
Table 6 lists key studies in recent years on the application of ML algorithms in UOWC systems. Most ML algorithms are applied to the equalization at the receiver side to improve the BER performance and the transmission data rate. For instance, a novel Gaussian kernel-aided deep neural network (GK-DNN) equalizer shown in Figure 9 was employed for compensating the high nonlinear distortion of PAM8 UOWC channels in [50]. Because the GK-DNN treats the equalization problem as a classification problem, it has the advantage of performing both equalization and de-mapping at the same time. After being combined with the scalar-modified cascaded multi-modulus algorithm (S-MCMMA), the GK-DNN equalizer can perform linear equalization, nonlinear equalization, and de-mapping at the same time. Moreover, compared with the conventional DNN equalizer, the GK-DNN equalizer can reduce required training iterations by 47.06%. Results show that the BER can be significantly reduced by 1.78 dB in the LED-based UOWC system employing the GK-DNN equalizer. Figure 8: BER vs. received optical power for different data rates with hard-decision detection and nonlinear VE detection [38]. Moreover, in [111], a dual-branch multilayer perceptron (DBMLP)-based equalizer was employed in UOWC systems. Due to the limitation on the order of the Volterra series, the nonlinear distortion in the received signal cannot be compensated accurately in conventional NML VE. Unlike NML VE, the deep neural network-based equalizer has a better capability to compensate for nonlinear distortions as it can model arbitrary mappings at arbitrary progress. Results show that the UOWC system succeeded in achieving 3.2 Gbps data transmission. Compared with the conventional VE, 63.5% BER performance enhancement and 33.8% better space complexity are achieved with the proposed DBMLP scheme. In [112; 128; 129], a nonlinear ML post equalizer based on the time-frequency domains deep neural network (TFDNet) was proposed in UOWC systems, as shown in Figure 10. The short-time Fourier transformation (STFT) was employed to combine the signal from two one-dimension (time domain and frequency domain) images to a two-dimension (time-frequency domain) image. Then, the signal 2D time-frequency image is fed into the DNN, which learns the mapping relations to equalize the signal to match the labeled 2D time-frequency image. Unlike the conventional DNN-based equalizers that consider only the time domain, the additional frequency domain information enables the DNN to learn complementary signal characteristics. The proposed TFDNet-based equalizers can improve the BER from \(2\times 10^{-2}\) (VE) and \(7\times 10^{-3}\) (DNN-based equalizer) to \(2\times 10^{-3}\) at a valid operating Vpp of 0.8 V in a 2.85 Gbps UOWC system to achieve FEC limits. Furthermore, in [113], an adaptive constellation-partitioned equalizer based on a complex-valued neural network (PCVNN) was employed to reduce the computational complexity in typical ML algorithms in UOWC systems. Experimental results show that compared with conventional ML equalizers, the computation cost can be reduced by 56.1% in the proposed PCVNN scheme in a 2.85 Gbps UOWC system. Two transfer learning-based (TL) DBMLPs were demonstrated in [114]. Unlike the conventional DBMLPs, the TL-DBMLP is more robust to the jitter of LED transmitter bias current and also requires a