## 3 Experiments  
The experimental setup of the 4-ASK-FOFDM transmission through a random media channel is shown in Figure 1. The picture of the experimental setup is displayed in Figure 2. At the transmitter, a 4-ASK-FOFDM time domain signal was first generated by an offline Matlab program. In the offline digital signal processing (DSP) which was marked by the dashed rectangles in Figure 1, firstly, a pseudorandom binary sequence (PRBS 215-1) was mapped into 4-ASK symbols. Then, DCT pre-coding [22] was adopted to lower the peak-to-average power ratio. Due to the restriction of the 500 MHz bandwidth of the digital oscilloscope used, the pre-coded 4-ASK symbols were just modulated onto 112 subcarriers by inverse discrete cosine transform (IDCT) with a length of 256. To avoid DC coupling, the first six subcarriers were set to be zeros. And the guard interval with the length of 16 was added to prevent inter-symbol interference (ISI). Thus, the time domain FOFDM signal was generated. After parallel-to-serial (P/S) conversion, we uploaded the sequence to an arbitrary waveform generator (AWG, Agilent 81180A), and the sampling rate was set to 2.5 GSa/s. For the baseband signal, the bandwidth was calculated as \(2.5\times(6+112)/256/2\approx 576\) MHz, the net data rate was 965.5 Mb/s and the spectral efficiency (SE) was 1.68. After AWG, an RF amplifier (SHF 100 AP) was used to amplify the baseband 4-ASK-FOFDM signal, and a Bias-tee (PE1611) was used to superimpose the amplified signal on the DC bias current. An LD outputting blue light was directly modulated by the mixed signal. A curve of optical power versus bias current for the blue LD is shown in Figure 3a. And when the DC current was set to 65 mA, we measured the optical spectra by an Andor SR-500i spectrometer, and the spectra are shown in Figure 3b. When the current was 65 mA, the optical power of 30 mW was output by the LD, and the emission wavelength was around 451 nm. The blue light from the LD was launched into a simulated turbulent air channel by a Plano-Convex lens with a focal length of 49.8 mm, and the radius of curvature was 25.8 mm. The atmospheric turbulence simulator consisted of a chamber, heater, cooler and fans. Its length was 2.5 m. When the fans and heater in the chamber work, the simulator can generate turbulent airflow. The blue light was reflected four times by mirrors mounted on the chamber side. After reflection, the transmission distance was extended to 12.5 m. If we disabled the fans and the heater, the simulator just produced a 12.5 m free-space atmospheric channel. After passing through the simulated atmospheric turbulence, the  
Figure 1: Experimental setup of 4-ASK-FOFDM transmission over a simulated turbulent air channel followed by a water channel for OWC: arbitrary waveform generator (AWG), electrical amplifier (EA), laser diode (LD), mirror (M1), avalanche photodiode (APD). blue light was reflected into a water tank with a length of 1.6 m and was filled with tap water. The estimated attenuation coefficient of the tap water was about 0.23 m\({}^{-1}\)[23]. When the blue light was propagating in the water tank, it was reflected four times by mirrors mounted on the side of the tank. The transmission distance in the water tank could be increased to 8 m after reflection. Lastly, the output blue light from the water tank was focused onto an APD (APD210, Menlo Systems) by a lens which was the same as the lens used at the transmitter side. The bandwidth of the APD210 was 1 GHz, and its active diameter was 0.5 mm. The APD converted the received light to an analog electrical signal, then the electrical signal was sampled by a digital oscilloscope (Keysight DSO-X 4054A), which had a bandwidth of 500 MHz, a sampling rate of 5 GSa/s and a resolution of 8 bits.