Over 10 Attenuation Length Gigabits Per Second Underwater Wireless Optical Communication Using A Silicon Photomultiplier (SiPM) Based Receiver

Underwater wireless optical communication (UWOC) will play an important role in the underwater environment exploration and marine resource development due to its advantages of high data rate and good mobility. However, the significant signal power attenuation in the underwater channel limits the transmission distance of UWOC. Attenuation length (AL) is widely used as an indicator for evaluating the UWOC system's long-distance transmission capability. At present, Gbps UWOC is limited within 7AL. Using a SiPM based receiver can dramatically increase the AL that UWOC can support. In this paper, a novel UWOC receiver built from an off-the-shelf SiPM has been demonstrated. The finite pulse width and limited bandwidth of SiPM limit the SiPM based UWOC system's data rate. To boost the system's data rate, an optimum method to process the SiPM's signal has therefore been investigated. Based on these methods, the communication capabilities of the SiPM based UWOC have been investigated experimentally. Results show that the SiPM based receiver can support 11.6AL without turbulence and 9.28AL within weak turbulence (scintillation index = 0.0447) at 1 Gbps.

bandwidth of SiPM, the data rate of the SiPM based UWOC is limited to 100Mbps.
The significant power attenuation from the underwater channel limits UWOC's transmission distance. Using a SiPM based receiver can address this challenge. However, the sensitivity of a SiPM based receiver is limited by the non-idealities within SiPM [17] .
Results in [17] suggest that a receiver containing a SiPM with a photon detection efficiency (PDE) higher than 14% is more sensitive than APD. Thanks to the continuing improvements in manufacturing processes, SiPM with a PDE higher than 14% is available. In this paper, an off the shelf SiPM SensL J series 30035 which contains an array of 5676 SPADs with a 30% 2.Method to Increase SiPM's Data Rate of detected photons per bit N p required by an ideal photon-counting receiver to a target BER is given by [23] Based on the analogue mode and DFE, the sensitivity of the tested SiPM at different data rates where S out (k)refers to received signal and S in (k) is the estimated symbol. To find the optimum filter coefficients F and B, the least mean square (LMS) algorithm [26,27] has been applied. Figure 2(d) shows the eye-diagram after DFE. This result suggests that DFE effectively mitigates the impact of ISI. In (2  ) p N BER = − × According to Eq. (2), 6.2 detected photons per bit are required by an ideal photon-counting receiver to achieve a BER of 10 −3 in the dark. The BER of 10 −3 is below the level at which a standard Forward Error Correction (FEC) code can operate (BER of 3.8×10 −3 ) [24] . Consequently, the upper bond of the maximum OOK data rate using this tested SiPM in the photon-counting mode is 7.9 Mbps. However, in practice, SiPM suffers from the background noise (dark counts and photon counts generated by ambient light). More number of photons per bit are required to compensate for the background noise. Therefore, the maximum OOK data rate that the photon counting mode can support with this tested SiPM is less than 7.9Mbps. This data rate is far from the Gbps target.
Analogue mode is an alternative operation method recommended by the manufacturer to process SiPM's output signal [25] . Instead of counting pulses, the analogue mode directly measures the amplitude of SiPM's output signal. In analogue mode, the frequency response of the SiPM based receiver can be effected by the incident optical power, bias voltage and etc.
At the optimum bias voltage (28.5V), the maximum 3dB bandwidth of the tested SiPM is ~107MHz and the corresponding incident optical power is 128nW.
The detailed investigation of the influencing factors on SiPM 3 dB bandwidth is beyond the scope of this paper. To release the tested SiPM's potential for supporting a data rate of Gbps, analogue mode has to be used. Additionally, when the OOK data rate is higher than the bandwidth of the SiPM, inter-symbol interference (ISI) is generated. Hence, equalization (EQ) is required to mitigate the impact of ISI [26,27] .
The blue curve in Fig. 2 [26,27] : The blue curve in Fig. 4 shows the optical power required by the tested SiPM at different data rates to get a target BER of 10 −3 . For SiPM, when no background counts present, the number of signal photons per bit required to get a specific BER, Ns, at different data rates are fixed according to the Poisson statistics [18] . Therefore, the optical power needed by the SiPM linearly increases with the data rate. When background counts present, to compensate the impact of background counts, N s has to be increased with the background counts per bit Nb [18] . For a given ambient light level, the background counts rate (background counts per second) is fixed. Therefore, at a given ambient light condition, N b decrease with the increase of data rate and hence N s . Consequently, the increasing rate of the required optical power is getting decreased when the data rate is getting increased. Therefore, the increasing rate of the blue curve is getting reduced with the increase of data rate. Moreover, results in Fig. 4 suggest that the tested SiPM achieves 1Gbps at a BER of 10 −3 using analogue mode with DFE which only requires a received power of 80nW (-40.9 dBm).
The red curve is the estimated result of the achievable AL at a 10 mW transmitted power assuming the channel bandwidth is limited by the tested SiPM and all the power at the receiver plane can be collected.
This estimated result suggests that the tested SiPM can support ∼11.6AL with a BER of 10 −3 at 1Gbps. has been measured. Figure 3  The overall optical power loss LP against propagation distance z can be expressed by Beer lambert model which is given by [1,2] where c (λ) is called the attenuation coefficient which is determined by the turbidity of water. The product of c (λ) and z is AL. To create a 11.6AL underwater channel within the 40 m link, c(λ)= 0.29 m/s is required which is close to Jerlov II water type (c(λ)= 0.303/m) [28,29] . The suspensions of AL (OH) 3 and Mg(OH) 2 , Maalox, which has been widely used for varying the turbidity of water [7] , is used in the experiment for increasing the turbidity of tap water from c(λ)= 0.15/m to c(λ)=0.29/m. Figure   The frequency responses of the tested SiPM based UWOC system within the tested underwater channel against different distances have been measured using the transmitter and receiver shown in Fig. 6 and VNA E5063A. In these measurements, the received power over the SiPM is set to 80nW which is consistent with the 1Gbps result in Fig. 4. The measurement results are shown in Fig. 9. The red curve in Fig. 9 suggests that the bandwidth of this tested SiPM is only 90MHz at this condition. Simulation results in Fig. 8 suggest that the 3dB bandwidth of the underwater channel using the transmitter and receiver shown in Fig. 6 within the coastal water is 170MHz when distance is 40m.
Since the turbidity of Jerlov II water is clearer than the coastal water, the 3 dB bandwidth of the tested water is higher than 170 MHz. Moreover, the measured bandwidth of the transmitter is 1GHz. Therefore, the channel bandwidth is limited by the tested SiPM.
Consequently, the measured frequency responses in Fig. 9 overlap together. Therefore, the assumption of channel bandwidth is determined by the tested SiPM for the 11.6AL 1 Gbps UWOC estimation is valid using the transmitter and receiver shown in Fig. 6 within the Jerlov II water at a transmission distance of 40 m.
Results in previous sections indicate that the tested SiPM based UWOC system has the potential to support 11.6AL 1Gbps UWOC. This performance has then been experimentally demonstrated. Figure   10 shows the experimental set-up for SiPM based UWOC demonstration. In this experiment, the tested water (c(λ)= 0.29/m) has been filled within the water The ultimate performance of this SiPM based UWOC system has been measured without turbulence. Figure 11 shows the measured BERs at 40 m transmission distance with a data rate of 1Gbps at different transmitted powers. This result suggests that this tested system requires 10dBm (10 mW) transmitted power to achieve 11.6AL 1Gbps UWOC at a BER of 10−3 which validates the 1Gbps estimation result in Fig. 4 When turbulence is generated, the received signal fluctuates. Figure 12(b) shows the eye-diagram in the 40 m link with the lowest turbulence that has been generated. The corresponding BER is 8×10 −3 which is over the FEC limit (BER of 3.8×10 −3 ).
With turbulence, reducing the transmission distance can improve the received optical power and hence improving the BER performance of this SiPM based UWOC system. Figure 13 shows the measured BERs at 32 m transmission distance within the four turbulence levels. Based on the method proposed in [31,32] , the corresponding scintillation indexes (SI) of the generated turbulence have been measured, which are listed in Table 3. The inset histogram in Fig. 13 illustrates the fluctuation of the received power at SI equals to 0.0447, and the red curve is the lognormal model for estimating the power distribution of turbulence [31,32] . The inset eye-diagram in Fig.   13 shows that eye-opening has been achieved in the turbulence with SI equal to 0.0447. The corresponding BER is 2×10 −3 which bellows the FEC limit.
Therefore, this tested SiPM based UWOC system has achieved 32 m (9.28AL) UWOC in the weak turbulence with SI equal to 0.0447.

Conclusion
Using analogue mode and DFE, the sensitivity of the [ 2 ] H . K a u s h a l a n d G