## 3 Experimental Setup  
Figure 3 shows the experimental setup for the underwater visible light communication system. The original binary data are generated from an offline MATLAB program. First, the binary data are mapped into 16-QAM symbols. After a 4-time up-sampling, the in-phase and quadrature parts of the complex-valued QAM symbols are separated. Then, a pair of orthogonal shaping filters (roll-off factor = 0.205) are used for CAP modulation. Afterward, the real-valued signal is loaded into an arbitrary waveform generator (Tektronix AWG710B, 4.2 GSa/s). As the typical \(-3\) dB modulation bandwidth of large-scale LED is limited to a dozen of MHz or lower, a hardware pre-equalization circuit is used to increase the power of high-frequency component and decrease the power of low-frequency component [20]. The hardware pre-equalization circuit is a single constant-resistance symmetrical bridged-T amplitude equalizer [20] with the resonant frequency at 500 MHz and low-frequency attenuation 28 dB. Afterward, the signal is sent to an amplifier (ZHL-2-8-5+), followed by a Bias Tee (ZFBT-4R2 GW-FT+) which couples the signal and direct current to drive a blue LED (\(-3\) dB bandwidth is 17 MHz) [7]. After transmission through a 1.2 m water tank, the signal is focused by a lens (\(\mathcal{O}\)75 mm, f = 60 mm) and detected by a PIN (Hamamatsu, 510784). Tap water is used in this experiment. The system is line-of-sight point-to-point transmission and turbulence can be ignored, so that the UVLC channel is approximately deterministic. The PIN outputs two opposite signals which are subtracted after the amplifier, oscilloscope (DSO9404A, 20 GSa/s) and synchronization to suppress the common mode noise of the system.  
Then, the received signal is sent into the offline digital signal processing (DSP) block for data recovery. First, two matched filters are employed for CAP demodulation. Since the zero-forcing (ZF) pre-equalization to obtain a flat spectrum is not suitable in UVLC system [25], the hardware pre-equalization circuit merely provides the rough power allocation and a more balanced SNR distribution. After down-sampling, LMS-based linear adaptive post-equalization is used to mitigate the ISI. The tap-number of the LMS-based linear equalizer is 21, and the step-size is optimized at every operating condition in this experiment. Next, the proposed SVM-based soft decision for 4-D constellation is used to determine the 4-D decision boundary. We use radial basis function (RBF) as the kernel  
Figure 2: Schematic of SVM-based soft decision. (**a**) SVM training phase with data preprocessing. (**b**) SVM testing phase.  
function. The detail implementation about the scheme has been introduced in Section 2.2. Finally, the original data are recovered after QAM de-mapping.  
The inset (i) shows the normalized input amplitude-output amplitude (AM-AM) of the UVLC system at 1.1V and 1.6 Gbps. The red line is the linear reference. The black points are the average value in a small grid of input amplitude. Obviously, the AM-AM curve displays nonlinear effect. The inset (ii) is the spectrum of the received signal which is obtained by fast Fourier transform (FFT). The baud rate of the signal is 400 MBaud. Although hardware pre-equalization circuit is applied, the high frequency component still displays great attenuation. In summary, the system is working at nonlinear and bandwidth-limited condition. It is difficult to remove the correlation between adjacent symbols thoroughly. Independent of the equalization method, the proposed method is used for soft decision, which enhances the decoder.