## 4 Results of the Water Tank Experiment  
We investigated the communication performance of the proposed underwater photon-counting communication system. In this communication system, the 32-PPM modulation was used, and the slot frequency of the system was set as 12.5 MHz. The received optical power was attenuated from \(-76\) dBm to \(-86\) dBm by improving the input voltage of the variable attenuator. Figure 11 only shows the output signal by oscilloscope that for sampling rate was 250 MS/s at received optical was \(-76\) Bm and \(-84\) dBm, respectively. By comparing Figure 12a,c, we intuitively find that the average number of photons at the signal time slots is higher at the received optical power of \(-76\) dBm than at \(-84\) dBm, but the maximum photon counts per slot do not exceed four photons. Moreover, the photon counts at the empty time slots increase as received optical power increases.  
To further analyze the performance of the photon-counting communication system proposed in this study, the frequency histogram of photocounts per symbol times under the differently received optical powers was calculated. As shown in Figure 13, the horizontal coordinate of the picture indicates the number of counted photons per the signal slot of 32-PPM symbols, and the vertical coordinate indicates the probability of the number of counted photons of each symbol. The frequency of photon counts at the signal slots is represented by the light red histogram, the frequency of photon counts at the empty time slots is represented by the blue histogram, and the dark red histogram shows the overlapping part. As shown in the frequency histogram of \(k_{s}\), for 12.5 Mslot/s, the probability that the number of counted photons is equal to 3 or 4 increases with the received optical power. However, the number of counted photons never exceeds 4. The mean photon counts in signal slots, \(k_{s}\), and the mean number of counted photons in the empty slots, \(k_{n}\) are labeled in Figure 13.  
Figure 12: The signal sampled by the oscilloscope at the sampling rate was 250 MS/s: the display resolution of the oscilloscope is 2.0 μs/div (**a**) and the display resolution of the oscilloscope is 800.0 μs/div (**b**) at a received optical power of \(-76\) dBm; the display resolution of the oscilloscope is 2.0 μs/div (**c**) and the display resolution of the oscilloscope is 800.0 μs/div (**d**) at a received optical power of \(-84\) dBm.  
Figure 14 shows that for 12.5 Mslot/s, \(k_{\rm s}\), \(k_{\rm b}\), and the signal-to-noise ratio (SNR) are a function of received optical power. The measured kb increases with the received optical power. However, because the PCM's saturation is dependent on the dead time, the measured \(k_{\rm s}\) increases with the received optical power with nearly constant proportionality below \(-\)78 dBm. In this case, the SNR of the receiver decreases with received light power until it falls to a negative value above \(-\)82 dBm.  
Figure 15 shows the measured maximum likelihood decision BER as a function of optical power \(P_{r}\) and the number of counted photons \(k_{\rm s}\). As shown in Figure 15a, the corresponding BER is 3.6 \(\times\) 10\({}^{-3}\) when the received optical power is \(-\)84 dBm, which is below the FEC limit (BER of 3.8 \(\times\) 10\({}^{-3}\)). At this received optical power, as shown in Figure 14, the mean number of counted photons in a signal slot is 1.72 photons where SNR is 0.1 dB. Therefore, we can conclude that the tested photon-counting-based UWOC system has achieved 80.72 dB link loss with S.I. equal to 0.02 under a communication rate of about 1.9 Mbps.  
Figure 14: The mean number of photons, \(k_{\rm s}\), \(k_{\rm n}\), and SNR as a function of received optical power.  
Figure 13: The frequency histogram of photocounts per symbol times for 32-PPM photon-counting communication system vs. received optical power: (**a**) \(-\)86 dBm, (**b**) \(-\)84 dBm, (**c**) \(-\)82 dBm, (**d**) \(-\)80 dBm, (**e**) \(-\)78 dBm, (**f**) \(-\)76 dBm.