Single-photon detection for MIMO underwater wireless optical communication enabled by arrayed LEDs and SiPMs

Jinjia Li; Jinjia Li; Jinjia Li; Demao Ye; Kang Fu; Linning Wang; Jinlong Piao; Yongjin Wang; Yongjin Wang

doi:10.1364/OE.433798

1. Introduction

The ocean is the granary of the future, yet more than 95% of the underwater world remains unexplored. Obviously, the exploitation and utilization of the ocean requires the use of information technology. In this context, the rapidly increasing attention to marine informatization has made underwater wireless optical communication (UWOC) or underwater visible light communication (UVLC) very popular in recent years [1,2]. UWOC is an emerging wireless communication technology that utilizes typical blue-green (450-570 nm) optical waves as a carrier to realize information transmission underwater. UWOC has become an alternative or complementary to classical underwater wireless acoustic communication (UWAC) due to the characteristics of a tremendous bandwidth, lower latency, and better security [3]. UWOC has contributed to underwater wireless sensor networks (UWSNs), the Internet of Underwater Things (IoUT), underwater millimeter wave (mm-wave) communication, etc [4].

Compared with the achievable long-distance (dozens of km) transmission of UWAC, the short to moderate (less than 100 m) [5,6] optical link of UWOC is a shortcoming that restricts certain applications. This shortcoming mainly depends on the heavy attenuation coefficient (0.39-11 dB/m) of optical waves due to the severe impairments of underwater absorption, scattering, and oceanic turbulence, whereas the corresponding value for acoustic waves is as small as 0.1-4 dB/km [1]. Unusually, in [7] and [8], optical links of 120 m and 150 m were realized, respectively, and both systems used a photomultiplier tube (PMT) as a photodetector. Owing to its internal multiplication system, a PMT has a higher sensitivity or gain (10⁶) than an avalanche photodiode (APD) (10²). In addition, the PMT-based photon-counting system achieves a 249.2 m link distance in the Jerlov IB water type [9]. Therefore, a PMT can detect weaker light intensity and can achieve a longer-distance attenuated optical link than an APD. Imperfectly, PMTs have the shortcomings of being bulky, having a high voltage (kilovolts), fear of vibration and shock, being sensitive to magnetic interference, etc [19].

Surprisingly, a silicon photomultiplier (SiPM) (also called a multipixel photon counter, MPPC) seems to be a perfect photodetector with extremely high gain (10⁶) or sensitivity similar to a PMT. Moreover, it also has the advantages of compactness, mechanical robustness, and low bias voltage. It is a solid-state photodetector composed of an integrated matrix of single-photon avalanche diodes (SPADs) [10]. Unlike an APD, which operates in the linear region, a SPAD works in the so-called Geiger region, i.e., the reverse bias voltage is equal to or up to several volts above the breakdown voltage. Because of the high electric field intensity (10⁵ V/cm) in the Geiger region, even a single photon with extremely low energy (10⁻¹⁹ J) can obtain sufficient kinetic energy to induce both electron and hole impact ionization and sustain the avalanche, while for an APD, only electrons can generate secondary electron-hole pairs. Regardless of the number of incident photons, a SPAD is only sensitive to a single photon, while a SiPM can detect a single photon or several photons simultaneously and superimpose the response of each SPAD element. According to the wave-particle duality, low-flux light shows an obvious particle property (the wave property is not significant), i.e., optical power is transmitted in the form of distinguishable photons, and the optical power is proportional to the number of incident photons or the photon rate of arrival [11]. Therefore, a SiPM can detect optical signals in phonon-counting mode. In addition, if sufficient photons overlap, then the SiPM can be operated in analog mode similar to an APD [10]. SiPMs have entered many fields, such as positron emission tomography (PET), high-energy physics (HEP), and light detection and ranging (LiDAR). Recently, with their unique advantages, SiPMs have been gradually applied in the field of UWOC.

Table 1 lists the studies on SPAD/MPPC/SiPM-based UWOC systems. Among them, the SPAD-based system shows high sensitivity but can only operate in photon-counting mode. The author in [12] designed a system with only 40 µW (2.127 pJ per pulse), equivalent to 1.13 Mbps/mW, transmitted optical power, showing the high energy efficiency of SPAD-based UWOC. According to the optimum photon-counting threshold, SPAD-based UWOC can be predicted to have a link of 500 m through Monte Carlo simulation, while APD-based UWOC can only reach a transmission of 73 m [13]. In [14], Q. Yan et al., utilizing an innovative recovering clock method, realized that the optical signal can be recovered even with less than 10 photons on average per time slot. The application of the generalized likelihood block detection method effectively improved the system performance in [15]. In [16], Tian’s group realized that a SPAD detects average photocounts of 8.12 and 3.41 for bits “1” and “0”, respectively, under a 117 m/2 Mbps rate. However, an MPPC and a SiPM are the same devices with different names and can work not only in photon-counting mode but also in analog mode. J. Xu et al. in [17] and [18] verified the two types of modes for MPPC-based UWOC. For example, in [17], each PPM pulse contains tens of photons on average, and the receiver can make a correct decision. The MPPC-based system operates in analog mode and has lower noise equivalent power (NEP) (0.15 fW/Hz^1/2) than an APD (0.04 pW/Hz^1/2) [18]. Recently, SiPM-based UWOC has aroused considerable research interest. In [20,21,23], the transmitted or received optical powers were 185 mW, -40.2 dBm, and -41.2 dBm, and the results showed the extremely high sensitivity of and low minimum received optical power required by the analog mode SiPM. In [22], equivalent techniques were applied, and a 1 Gbps rate was achieved. The results showed that the analog mode of a SiPM is suitable for high-speed transmission. Imperfectly, a SiPM is still inferior to a PMT in terms of transmission link, e.g., 126 m for PMTs and only 66 m for SiPMs, which is mainly due to the small sensitive area of a SiPM compared with a PMT [19]. Although much valuable research has been performed, there are still relatively few detailed theoretical and experimental studies on SiPM-based UWOC.

Table 1. Literature on SPAD/MPPC/SiPM-based UWOC Systems.

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Oceanic optical turbulence and link alignment are inevitable issues in UWOC. Turbulence is mainly caused by inhomogeneous distributions of temperature, salinity, or bubbles and leads to spatial-temporal fluctuations in the refractive index, which leads to scintillation or fluctuations in the optical intensity and degrades the system performance. Multiple-input multiple-output (MIMO), i.e., spatial diversity, can reduce the impairment effect of oceanic turbulence through diversity gains [24]. In addition, a larger field of view (FOV) can be obtained through receiver diversity, thereby relaxing the link alignment. Table 2 lists some MIMO-UWOC systems and reflects the advantages of MIMO over single-input single-output (SISO). In addition, multiple-input single-output (MISO) schemes are simpler and have higher performance than single-input multiple-output (SIMO) schemes [28]. However, these studies are mostly PD/APD-based, and there are few discussions on SPAD/SiPM/MPPC-based MIMO systems. In [32] and [33], the MPPC-based MIMO hardware structure was established, but mainly, the link alignment and power efficiency of an MPPC were investigated; the studies did not focus on the issues of turbulence and MIMO performance. To the best of our knowledge, the first SiPM-based MIMO prototype system was discussed in [34]. The receiver of this system was composed of eight SiPMs and realized a 60 m sea trial at 3 Mbps. However, only one SiPM was used for signal detection in the actual test.

Table 2. Literature on MIMO-UWOC Systems.

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In this work, for the first time, we analytically and experimentally study the performance of a SiPM-based MIMO-UWOC system under weak turbulence. We aim to extend the method of the photon-counting mode and analog mode of SiPMs in UWOC. This paper is organized as follows. In Section 2, a brief description of the experimental setup is proposed. Section 3 describes the oceanic turbulence model and analysis of the performance of the MIMO scheme. The results and discussion are presented in Section 4. Lastly, Section 5 concludes the paper.

2. Experimental setup

Figure 1 presents the block diagram or experimental setup of the proposed SiPM-based 6×3 MIMO-UWOC system. The system is divided into three parts: LED array-based transmitter, SiPM array-based receiver, and attenuated and turbulent underwater channel, which are briefly introduced below.

Fig. 1. Structure of the proposed SiPM-based 6×3 MIMO-UWOC system.

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2.1 LED array and transmitter

As shown in Fig. 1, for the transmitter, six identical blue LEDs (Cree T6) are equidistant and form a circular array with a radius of 40 mm. As shown in Fig. 2(a), for the purpose of increasing the light intensity, we adopt reflective cones and a plano-convex lens (Rayan optics) to reduce the divergence angle. Figure 2(b) shows that the central wavelength of the LEDs is 445 nm with a full width at half maximum (FWHM) of 50 nm. The 3-dB bandwidth of the LEDs is 15.85 MHz, as shown in Fig. 2(c). An arbitrary waveform generator (AWG) generates an on-off-keying (OOK) modulated pseudorandom binary sequence (PRBS) signal that can be amplified by a power amplifier and superimposed with the DC bias by a bias tee. The bias current of the LEDs is set by a constant current source (UNI-T UTP1306S).

Fig. 2. Transmitter blue LED array: (a) configuration of the LED array, (b) electroluminescence (EL) spectra of the LEDs, (c) 3-dB bandwidth of the LEDs.

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2.2 Silicon photomultiplier (SiPM)

An off-the-shelf SiPM module is selected as the receiver device. This module integrates a 1 mm² SiPM and only needs an external +5 V DC voltage, as shown in Fig. 3 [35]. Figure 4 demonstrates the internal structure of the module. The analog SiPM contains 324 SPAD elements connected in parallel. Unlike an APD, which can stop the avalanche by itself, a SPAD needs a quench resistor to drop the bias voltage below the breakdown voltage to end the self-sustaining avalanche and wait for the next detection or counting of a photon [36]. This internal SiPM chip is refrigerated by a thermoelectric cooler (TEC), which uses the Peltier effect to transfer the heat to a heat sink and significantly reduces the dark current of the SiPM. The external DC 5 V is converted to 28-30 V and used as the bias voltage. Since it works in Geiger mode, the SiPM can output a measurable voltage without transimpedance amplification (TIA), so the influence of thermal noise can be ignored. In addition, secondary amplification, signal acquisition and digitization, and temperature control are needed to keep the operation stable.

Fig. 3. Appearance of the SiPM module: (a) dimensions of the module, (b) front view of the module, (c) side view of the module.

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Fig. 4. Internal structure of the SiPM module.

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The SiPM has excellent single-photon sensitivity or counting capability. A single photon is responded to or counted by the module with a probability corresponding to the photon detection efficiency (PDE) (35%@420 nm, 33%@445 nm). As shown in Fig. 5, the single-photon photoelectron (p.e.) voltage amplitude can reach 55-60 mV, and the rise time τ_r and dead time τ_d are 3.7 ns and 72.8 ns, respectively. The p.e. rising edge marks the incident time of the detected photon, followed by an exponential voltage drop. Obviously, the SiPM can respond to several detected photons simultaneously and overlap each single-photon response as the output. However, other mechanisms produce the same response as photon signals, such as dark noise, after-pulse, and cross-talk [10]. In total darkness, thermally generated carriers or the dark current can cause the same response, and the average count per second is the so-called dark count rate (DCR). The release of trapped carriers causing a secondary response is called after-pulse, and the response of a neighboring SPAD caused by the photon signal is called cross-talk. These two phenomena are inevitable but have a low probability of occurrence. For example, Fig. 6 shows the multiple p.e., after-pulse with a lower amplitude, and delayed cross-talk with an equal amplitude [11]. This module was made by Joinbon in China, and the main parameters are listed in Table 3. These parameters are strongly related to the breakdown voltage. Other similar SiPM products are listed in Table 4.

Fig. 5. Single-photoelectron waveform.

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Fig. 6. Multiple p.e., after-pulse, and cross-talk.

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Table 3. Detailed Parameters of the SiPM Module.

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Table 4. Similar SPAD/MPPC/SiPM products.

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2.3 Photocount distribution and counting system

The photocount of a SiPM is the sum of the corresponding values of each SPAD [37]:

(1)$$Y = \sum\limits_{i = 1}^{{N_{SPAD}}} {{K_i}} ,$$

Here, N_SPAD is the number of SPADs and K_i represents the photocount of the ith SPAD element. Ideally, the photocount of a SPAD is modeled as a Poisson distribution [37]:

(2)$${P_K}(k) = \frac{{{{(\lambda {T_s})}^k}}}{{k!}}\exp ({ - \lambda {T_s}} ),k = 0,1,2, \cdots ,$$

Here, T_s is the symbol period, and λ (photons/s) is the average detected photon arrival rate given by $\lambda = {\eta _{PDE}}{P_r}/h\nu$, with η_PDE being the PDE of the SPAD, P_r is the received optical power, h is the Planck’s constant, and ν is the optical frequency. Therefore, the mean and variance of K are expressed as [19]:

(3)$${\mu _K} = \sigma _K^2 = \lambda {T_s} = \left( {\frac{{{\eta_{PDE}}{P_r}}}{{{E_{ph}}}} + {f_{DCR}} + {f_B}} \right)({1 + {f_{AP}} + {f_{CT}}} ){T_s},$$

where f_DCR is the DCR, f_B is the count rate of the background or ambient light noise, f_AP is the after-pulse probability, f_CT is the cross-talk probability, and the single-photon energy E_ph is:

(4)$${E_{ph}}({eV} )= \frac{{1240}}{\lambda },\; \; {E_{ph}} = \frac{{hc}}{\lambda } \approx 4.46 \times {10^{ - 19}}J,$$

where h is Planck’s constant, 6.626×10⁻³⁴ J·s; c is the velocity of light, 3×10⁸ m/s; λ is the wavelength, 445 nm; and 1 electron volt (eV) is 1.6×10⁻¹⁹ J. However, due to the influence of the SPAD dead time after being fired, the photocount distribution of a passive quenching (PQ) SPAD changes to [37]:

(5)$${p_K}(k) = \left\{ \begin{array}{l} \sum\limits_{i = k}^{{k_{\max }} - 1} {{{( - 1)}^{i - k}}\left( {\begin{array}{c} i\\ k \end{array}} \right)\frac{{{\lambda^i}{{({T_s} - i{\tau_d})}^i}}}{{i!}}{e^{ - i\lambda {\tau_d}}},k < {k_{\max }}} \\ 0,k \ge {k_{\max }} \end{array} \right.,$$

where τ_d is the dead time and k_max = [T_s/τ_d] + 1, with [x] denoting the largest integer that is smaller than x. The mean and variance of K are no longer equal and are derived as [38]:

(6)$${\mu _K} \approx \lambda {e^{ - \lambda {\tau _d}}}({T_s} - {\tau _d})\; ,$$

(7)$$\sigma _K^2 \approx {\lambda ^2}{e^{ - 2\lambda {\tau _d}}}(3\tau _d^2 - 2{T_s}{\tau _d}) + \lambda {e^{ - \lambda {\tau _d}}}({T_s} - {\tau _d}),$$

In addition, we designed a photon-counting system, as shown in Fig. 7. The p.e. sequence is digitized by a comparator and counted by the MCU built-in counter. The photocount is displayed on the PC in real time through the serial port. In particular, the threshold of the comparator can be adjusted online through the PC terminal. For example, if counting 2 p.e. and 3 p.e. pulses, then the threshold should be set to a value slightly below 2×60 mV and 3×60 mV, respectively.

Fig. 7. Photon-counting system of the SiPM: (a) hardware of the system, (b) block diagram of the system.

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2.4 SiPM analog mode detection

If the received optical power or photon incidence rate is sufficiently large, the detected photon pulses will overlap, and the SiPM can be operated in analog mode similar to an APD. This analog mode does not count photons, but the waveform amplitude is proportional to the received optical power or the rate of incident photons; a SPAD cannot work in this analog mode. As shown in Fig. 8, the output analog voltage is further amplified by an automatic gain control (AGC) amplifier and digitized by the comparator.

Fig. 8. AGC and comparator circuit module.

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2.5 Underwater channel

In the experiment, a water tank with dimensions of 0.8 × 0.8 × 10 m is used to simulate an underwater channel, and optical glass with a diameter of 300 mm is installed on both sides of the tank, as shown in Fig. 9. In particular, we added magnesium hydroxide (Mg(OH)₂) powder to the water to increase the attenuation coefficient. The powder is a white amorphous powder that is almost insoluble in water, as shown in Fig. 10. In addition, air bubbles are generated by the electromagnetic air pump shown in Fig. 11 to enhance the effect of turbulence. Here, we ignored the effects of turbulence caused by the temperature or salinity gradient.

Fig. 9. The indoor water tank: (a) the appearance of the tank, (b) optical glass and underwater channel.

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Fig. 10. Mg(OH)₂ powder.

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Fig. 11. Electromagnetic air-pump.

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3. Turbulence and photon-counting MIMO scheme

3.1 Oceanic turbulence and optical link model

Tides, air-sea exchange, and marine heat flow are the main sources of energy for oceanic turbulence. The scalar fields of temperature and salinity concentration are the main factors that cause turbulence and an inhomogeneous refractive index and hence cause channel fading, optical intensity scintillation, and phase change of the received optical signal, leading to an increase in the bit error rate (BER). Different from laminar flow, turbulence refers to a flow in which the movement speed at any point in the ocean water body disorderly changes in magnitude and direction, and there is a strong mixing phenomenon between fluids in each layer [39]. In 1883, the British researcher O. Reynolds proposed the Reynolds number (Re), a dimensionless number that can be used to characterize fluid flow:

(8)$${\textrm{Re}} = \frac{{\rho vL}}{\mu },$$

where v and L are the characteristic velocity and length of the flow field, respectively, and ρ and µ are the fluid density and coefficient of kinematic viscosity, respectively. When Re increases to a certain critical value, the fluid changes from laminar flow to turbulent flow.

The turbulence-induced fading strength is often measured by the scintillation index and is defined by [24]:

(9)$$\sigma _I^2({r,L,\lambda } )= \frac{{E[{{I^2}({r,L,\lambda } )} ]- {E^2}[{I({r,L,\lambda } )} ]}}{{{E^2}[{I({r,L,\lambda } )} ]}},$$

where I(r,L,λ) is the instantaneous intensity at position vector (r, L), r is the previous position coordinates (x, y), L is the link distance, and E(I) denotes the expected value of I. Moreover, the weak turbulence scintillation index can also be obtained as [24]:

(10)$$\sigma _I^2 = 8{\pi ^2}k_0^2L\int_0^1 {\int_0^\infty \kappa } {\Phi _n}(\kappa )\left. {\left\{ {1 - \cos \left[ {\frac{{L{\kappa^2}}}{{{k_0}}}\xi ({1 - ({1 - \Theta } )\xi } )} \right]} \right.} \right\}d\kappa d\xi ,$$

where k₀ is the wavenumber, κ denotes the scalar spatial frequency, Φ_n(κ) is the power spectrum, and Θ is 1 or 0 for planar and spherical waves.

In addition, the channel line-of-sight (LOS) geometric loss is [30]:

(11)$${H_{los}}(0) = \frac{{({m + 1} ){A_{PD}}}}{{2\pi {d^2}}}\cos ({{\beta_1}} ){\cos ^m}({{\beta_2}} ),$$

where β₁ and β₂ are the incidence and irradiance angles, respectively, m is the order of the LED Lambertian emission, A_PD is the active area of the photodetector, and d is the link distance. Therefore, the optical link model or received optical power is:

(12)$${P_r} = {P_t}{H_{los}}(0)\exp ({ - c(\lambda )d} )h,$$

where P_t is the transmitted optical power, c(λ) is the attenuation coefficient related to the wavelength, and h is the channel fading coefficient and is assumed to have the lognormal probability density function (PDF) [38]:

(13)$${f_h}(h) = \frac{1}{{2h\sqrt {2\pi \sigma _X^2} }}\exp \left( { - \frac{{{{({\ln (h) - 2{\mu_X}} )}^2}}}{{8\sigma_X^2}}} \right),$$

where µ X and σ2 X are the mean and variance of X = 0.5ln(h), i.e., X∼N(µ X, σ2 X). Here, the relationship between σ2 X and scintillation index σ2 I is σ2 X = 0.25ln(1+ σ2 I). Recently, a variety of fading statistical models have been proposed, such as the Weibull distribution, Gamma-Gamma distribution, and generalized Gamma distribution. Even the two-lobe mixed distribution shows better fitting accuracy in certain cases [40,41]. Such a study is not the main purpose of this work, so we simply use the lognormal distribution as the fading statistical model.

3.2 Photon-counting MIMO scheme

If the number of SPADs N_SPAD is sufficiently large, then according to the central limit theorem, the photocount distribution of the SiPM can be approximated by a Gaussian distribution [37]:

(14)$$Y = \sum\limits_{i = 1}^{{N_{SPAD}}} {{K_i}} ,\; \; {p_Y}(y) \sim N({\mu _Y},\sigma _Y^2),$$

(15)$${\mu _Y} = \sum\limits_{i = 1}^{{N_{SPAD}}} {{\mu _{{K_i}}}} ,\sigma _Y^2 = \sum\limits_{i = 1}^{{N_{SPAD}}} {\sigma _{{K_i}}^2} ,$$

where µ Y and σ2 Y are the mean and variance, respectively. Therefore, the probability distributions of the photocount when sending “1” and “0” are:

(16)$$p_Y^1(y)\sim N({\mu _1},\sigma _1^2),\; \; p_Y^0(y)\sim N({\mu _0},\sigma _0^2),$$

where µ₁, σ₁, µ₀, and σ₀ are the mean and standard deviation for “1”and “0”. Therefore, the SISO BER is [37]:

(17)$$\begin{aligned} p_e^{SISO} &= \frac{1}{2}\sum\limits_{y = \lfloor{{y_{th}}} \rfloor + 1}^\infty {p_Y^0} (y) + \frac{1}{2}\sum\limits_{y = 0}^{{y_t}_h} {p_Y^1} (y) \approx \frac{1}{2}\int\limits_{{y_{th}}}^\infty {p_Y^0({y^{\prime}})d} {y^{\prime}} + \frac{1}{2}\int\limits_0^{{y_t}_h} {p_Y^1({y^{\prime}})d} {y^{\prime}}\\ & = \frac{1}{2}Q\left( {\frac{{{y_{th}} - {\mu_0}}}{{{\sigma_0}}}} \right) + \frac{1}{2}Q\left( {\frac{{{\mu_1} - {y_{th}}}}{{{\sigma_1}}}} \right) = Q\left( {\frac{{{\mu_1} - {\mu_0}}}{{{\sigma_1} + {\sigma_0}}}} \right), \end{aligned}$$

where Q(x) is the Q-function and y_th is the optimum threshold value and approximated as [37]:

(18)$${y_{th}} = \frac{{{\mu _1}{\sigma _0} + {\mu _0}{\sigma _1}}}{{{\sigma _0} + {\sigma _1}}},$$

Furthermore, under the condition of $\sigma _{0,1}^2 \approx {\mu _{0,1}}$ and the influence of noise-dependent small values µ₀ and σ₀ being neglected, the BER can be simplified to:

(19)$$p_e^{SISO} \approx Q\left( {\frac{{{\mu_1} - {\mu_0}}}{{\sqrt {{\mu_1}} + \sqrt {{\mu_0}} }}} \right) \approx Q\left( {\sqrt {{\mu_1}} } \right),$$

Because the received optical power P_r or µ₁ is a function of the fading coefficient h, the average BER can be evaluated as:

(20)$$\overline {p_e^{SISO}} \approx \int_0^{\textrm{ + }\infty } {Q\left( {\frac{{{\mu_1}(h) - {\mu_0}}}{{{\sigma_1}(h) + {\sigma_0}}}} \right)} {f_h}(h)dh,$$

where f_h(h) is the lognormal PDF of the channel fading coefficient in formula (13).

Similarly, the photocount distribution in the MIMO scheme is:

(21)$$p_Y^{1,MIMO}(y)\sim N({\mu_1^{MIMO},{{({\sigma_1^{MIMO}} )}^2}} ),$$

(22)$$\mu _1^{MIMO} \approx {({\sigma_1^{MIMO}} )^2} = \sum\limits_{i = 1}^M {\sum\limits_{j = 1}^N {({h_{ij}^{}\mu_{1s}^{ij} + \mu_b^j + \mu_d^j} )} } ,$$

(23)$$p_Y^{0,MIMO}(y)\sim N({\mu_0^{MIMO},{{({\sigma_0^{MIMO}} )}^2}} ),$$

(24)$$\mu _0^{MIMO} \approx {({\sigma_0^{MIMO}} )^2} = \sum\limits_{j = 1}^N {({\mu_b^j + \mu_d^j} )} ,$$

where h_ij is the channel fading coefficient of the subchannel from the ith transmitter to the jth receiver, µij 1s is the optical signal photocount on the i,jth subchannel, and µj b and µj d are the background light average photocount and the dark photocount on the jth receiver, respectively. Therefore, the BER can be expressed as:

(25)$$\begin{aligned} p_e^{MIMO} &\approx Q\left( {\frac{{\mu_1^{MIMO} - \mu_0^{MIMO}}}{{\sigma_1^{MIMO} + \sigma_0^{MIMO}}}} \right) = Q\left( {\frac{{\sum\limits_{i = 1}^M {\sum\limits_{j = 1}^N {({h_{ij}^{}\mu_{1s}^{ij} + \mu_b^j + \mu_d^j} )} } - \sum\limits_{j = 1}^N {({\mu_b^j + \mu_d^j} )} }}{{\sqrt {\sum\limits_{i = 1}^M {\sum\limits_{j = 1}^N {({h_{ij}^{}\mu_{1s}^{ij} + \mu_b^j + \mu_d^j} )} } } + \sqrt {\sum\limits_{j = 1}^N {({\mu_b^j + \mu_d^j} )} } }}} \right)\\ & \approx Q\left( {\sqrt {\sum\limits_{i = 1}^M {\sum\limits_{j = 1}^N {({h_{ij}^{}\mu_{1s}^{ij} + \mu_b^j + \mu_d^j} )} } } } \right), \end{aligned}$$

The average BER can be obtained as [24]:

(26)$$\overline {p_e^{MIMO}} \approx \int_0^\infty {p_e^{MIMO}} (\overrightarrow {\boldsymbol h} ){f_{\overrightarrow {\boldsymbol h} }}(\overrightarrow {\boldsymbol h} )d\overrightarrow {\boldsymbol h} ,$$

where f$\vec{{\boldsymbol h}}$($\vec{{\boldsymbol h}}$) is the joint PDF of i×j dimensional fading coefficients vector $\vec{{\boldsymbol h}}$.

4. Results and discussion

4.1 Dark count rate of SiPM

As shown in Fig. 12, we applied the photon-counting system mentioned above to test the DCR of the SiPM. The counting time is set to 1 s and the threshold voltages to 40 mV, 96 mV, 160 mV, and 216 mV to count 1 p.e., 2 p.e., 3 p.e., and 4 p.e. pulses, respectively. In particular, the TEC needs a cooling stabilization time of approximately 30 s (30 times) to reach a steady state. Therefore, the average count is calculated 30-60 times to obtain an approximate DCR of the SiPM. Here, the DCRs of 3 p.e. and 4 p.e. pulses are very low and can be ignored. Finally, the average DCR can be estimated:

(27)$${f_{DCR}} \approx \frac{{2.8 + 0.19 + 0.0127}}{{1 + {f_{CT}} + {f_{AP}}}} \approx 2.76\; \; KHz/m{m^2},$$

where f_AP (0.2%) and f_CT (0.7%) are the after-pulse and cross-talk probabilities, respectively. Obviously, this DCR counting method is also suitable for optical signals and ambient or background optical.

Fig. 12. Measured dark count rate of SiPM: (a) 1 p.e. threshold, (b) 2 p.e. threshold, (c) 3 p.e. threshold, (d) 4 p.e. threshold.

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4.2 Distribution of photocounts for SiPM

According to formulas (6), (7), and (15), we can obtain the moments of SiPM photocounts as illustrated in Fig. 13. At low photon incidence rate λ_SPAD, the mean and variance are approximately equal, i.e., µ_Y≈σ2 Y, but after the λ_SPAD reaches approximately 10⁶ photons/s, the difference between µ_Y and σ2 Y is obvious; even when it reaches 10⁸ photons/s, the counting will not be completed, showing obvious nonlinear distortion [42,43]. The abovementioned difference and distortion are mainly due to the influence of the dead time t_d; for the Poisson distribution without dead time, the mean and variance are always equal.

Fig. 13. Moments of photocounts with T_s = 1 µs, t_d = 72.8 ns.

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Figure 14(a) and (b) shows two low-flux 1 Mbps OOK optical signals detected by the SiPM, and the measured photon incidence rates λ_SiPM are 7.9×10⁷ and 5.2×10⁷ photons/s during the “1” symbol period, respectively. These results indicate that a higher optical power has been received in (a) than in (b). Therefore, the SPAD average photon arrival rate λ_SPAD is given as:

(28)$${\lambda _{SPAD}} = \frac{{{\lambda _{SiPM}}}}{{{N_{array}}}} = \frac{{{\lambda _{SiPM}}}}{{324}},$$

where λ_SiPM is the average photon arrival rate for the SiPM during the “1” symbol measured by the photon-counting system and N_array is the number of SPAD elements. According to Fig. 15, the approximate Gaussian distributions of the photocounts in (a) and (b) are obtained as N(71.1, 68.9) and N(48.2, 46.9). In the “0” symbol period, there are low photocounts caused by the DCR or ambient light, and λ_SiPM = 3×10⁵ photons/s. Then, the Gaussian distribution of the SiPM optical signal and the dark noise and ambient light photocounts N_s(µ_Y,σ2 Y) and N_b(µ_Y,σ2 Y) can be determined, as shown in Fig. 15 [37]. Figure 16 presents the probability mass function (PMF) of the SPAD photocounts according to formula (5), and the dead time t_d has a significant effect on the photocount distribution.

Fig. 14. The 1 Mbps OOK with different λ_SiPM.

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Fig. 15. Gaussian PDF of SiPM photocounts.

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Fig. 16. PMF of SPAD photocounts.

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4.3 Received optical power

Figure 17 depicts the transmitter LED array equipped with reflective cups and a plano-convex lens. Figure 18 illustrates the receiver SiPM array equipped with an optical bandpass filter (OBPF) to reduce the influence of ambient light. The center wavelength of this filter (Rayan optics BP445-50) is 445 nm with an FWHM of 50 nm, an optical density (OD) of 4, and a blocking range of 200-800 nm. In addition, to collimate the received optical beam or use the aperture averaging effect to reduce the optical turbulence, a plano-convex lens with an effect focal length (EFL) of 50 mm and a diameter of 25.4 mm can be used. Figure 19 shows the transmitted optical signal from LED. And in the Fig. 20, the water tank lid is used to reduce the ambient light interference.

Fig. 17. The transmitter LED array.

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Fig. 18. The receiver SiPM array.

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Fig. 19. The transmitted optical signal.

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Fig. 20. The water tank lid and underwater channel.

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According to formula (3), the received optical power P_r can be calculated as:

(29)$${P_r} = \left( {\frac{{{\mu_K}}}{{({1 + {f_{AP}} + {f_{CT}}} ){T_s}}} - {f_{DCR}} - {f_B}} \right) \cdot \frac{{{E_{ph}}}}{{{\eta _{PDE}}}},$$

where µ_K is the photocount during symbol period T_s. The relationship between P_r and µ_K at T_s = 1 µs is shown in Fig. 21. This figure shows that if there are dozens of detected photons within a symbol period, then the received optical power is on the order of pW. For example, as shown in Fig. 15, for a 1 Mbps signal, the average photocounts are 71.1 and 48.2, so the received optical power can be estimated to be 48.1 and 94.8 pW, respectively.

Fig. 21. Estimate received optical power based on the photocounts.

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Fig. 22. The BER of photon-counting system.

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4.4 Bit error rate

In this subsection, the BER performance is discussed. Using the photon-counting system, the total photon count rate for ambient light and dark noise is approximately 300 kHz; therefore, at a rate of 1 Mbps, the average count value in the “0” symbol period is:

(30)$${\mu _0} \approx \sigma _0^2 = {\mu _b} + {\mu _d} \approx 300\; KHz\; \; \times \; \; 1\; \mu s = 0.3,$$

where µ_b and µ_d are the average background light photocount and dark count, respectively. Therefore, the SISO BER can be estimated according to formula (19):

(31)$$p_e^{SISO} \approx Q\left( {\frac{{{\mu_1} - {\mu_0}}}{{\sqrt {{\mu_1}} + \sqrt {{\mu_0}} }}} \right) \approx Q\left( {\frac{{{\mu_1} - 0.3}}{{\sqrt {{\mu_1}} + \sqrt {0.3} }}} \right),$$

As shown in Fig. 22, in theory, only a photocount of 13.3 is needed in the “1” symbol period to achieve a BER of 10⁻³ at µ₀ = 0.3. Furthermore, if the influence of ambient light and dark noise µ₀ is ignored, only a photocount of 9.5 is needed. The 13.3 photons are equivalent to the energy provided by 5.93 pW in 1 µs, i.e., the bit energy is 5.93×10⁻¹⁸ J, which reflects the extremely high energy efficiency of the photon-counting system.

4.5 Photon-counting MIMO performance

For the results in Fig. 23, the transmitter sends a 1 Mbps PRBS7 signal, and three SiPMs at the receiver receive the single-photon pulse sequence. The green curve in Fig. 23(a) is the combination of the sequences of the three branches. Occasionally, no photon is detected in a branch during the “1” symbol period, but the combination of the branches can greatly reduce this probability. In addition, if multiple photons are detected during the “0” period, then this will cause errors. Similarly, Fig. 23(b) shows the transmission of 2 Mbps signals. However, due to the limited bandwidth, short symbol period, and DCR, realizing a much lower data BER is still a challenge.

Fig. 23. The performance of SiPM-based MIMO-UWOC system: (a) 1 Mbps PRBS-OOK, (b) 2 Mbps PRBS-OOK.

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The BER of the 6×3 MIMO scheme is calculated according to formula (25):

(32)$$p_e^{6 \times 3} \approx Q\left( {\frac{{\mu_1^{6 \times 3} - \mu_0^{6 \times 3}}}{{\sigma_1^{6 \times 3} + \sigma_0^{6 \times 3}}}} \right),$$

(33)$$\mu _1^{6 \times 3} = \sum\limits_{i = 1}^6 {\sum\limits_{j = 1}^3 {({h_{ij}^{}\mu_{1s}^{ij} + \mu_b^j + \mu_d^j} )} } ,\; \; \mu _0^{6 \times 3} = \sum\limits_{j = 1}^3 {({\mu_b^j + \mu_d^j} )} ,$$

where the average counts µ₁ and µ₀ are tested by the photon-counting system. In the same way, we consider other MIMO schemes, for example, transmitter diversity in Fig. 24 and single receiver of MISO schemes in Fig. 25, and obtain the corresponding BER, as shown in Fig. 23. Table 5 shows the transmitter parameters and 7.38×10⁻⁹ J/bit is achieved at 6×3 MIMO schemes. In addition, when transmitting a constant light intensity, the receiver can detect the fluctuations in the optical signal under the presence of air bubble-induced turbulence and the corresponding scintillation index is calculated, as shown in Fig. 26 [44]. Therefore, Fig. 27 shows the BER of the photon-counting MIMO-UWOC system and reflects the better performance than SISO schemes under weak turbulence.

Fig. 24. Transmitter diversity of LED array.

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Fig. 25. The single receiver of MISO schemes.

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Fig. 26. The PDF histograms and scintillation index under the presence of air bubbles.

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Fig. 27. The BER of photon-counting MIMO-UWOC system under the optical turbulence.

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Table 5. The transmitter parameters of the system.

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4.6 Analog mode detection of SiPM

When the number of photons detected in the symbol period is sufficient, the discrete photon characteristics of the received waveform are not obvious, and a continuous analog waveform is observed instead [11]. For the results in Fig. 28, the analog 1 Mbps PRBS7 signal detected by the SiPM is fed to the AGC amplifier and then to the comparator. If the PDE of the SiPM is higher than 14%, its sensitivity will exceed that of an APD [45]. For the results shown in Fig. 29, the APD module (Hamamatsu C12702-12) and SiPM module simultaneously receive 1 Mbps PRBS signals from the transmitter, and SiPM shows significantly better detection performance than APD.

Fig. 28. The analog detection mode of SiPM.

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Fig. 29. Comparison of analog detection of APD and SiPM.

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5. Conclusion

In this study, we experimentally demonstrated a SiPM-based 6×3 MIMO UWOC system. The receiver SiPM device has excellent photon-counting ability. The information bit is judged by counting the photons of the combined branch signal during the symbol period. Theories and experiments confirm that the MIMO scheme performs better under optical turbulence. In addition, because of its higher quantum efficiency, the SiPM has a more prominent analog detection mode than an APD. Furthermore, we also elucidated the statistical distribution of photocounts of the SiPM and SPAD. In future work, the link alignment performance for this MIMO-UWOC system will be investigated.

Funding

Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX20_0712).

Disclosures

The authors declare that there are no conflicts of interest related to this paper.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. Z. Zeng, S. Fu, H. Zhang, Y. Dong, and J. Cheng, “A survey of underwater optical wireless communications,” IEEE Commun. Surv. Tut. 19(1), 204–238 (2017). [CrossRef]

2. H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4, 1518–1547 (2016). [CrossRef]

3. H. M. Oubei, C. Shen, A. Kammoun, E. Zedini, K. H. Park, X. Sun, G. Liu, C. Kang, T. K. Ng, M. S. Alouini, and B. S. Ooi, “Light based underwater wireless communications,” Jpn. J. Appl. Phys. 57(8S2), 08PA06 (2018). [CrossRef]

4. M. F. Ali, D. N. K. Jayakody, Y. Chursin, S. Affes, and S. Dmitry, “Recent advances and future directions on underwater wireless communications,” Arch. Computat. Methods Eng. 27(5), 1379–1412 (2020). [CrossRef]

5. M. Doniec and D. Rus, “Bidirectional optical communication with AquaOptical II,” in Proc. IEEE Int. Conf. on Commun. Syst. (ICCS), 390–394 (2010).

6. J. Wang, C. Lu, S. Li, and Z. Xu, “100 m/500 Mbps underwater optical wireless communication using an NRZ-OOK modulated 520 nm laser diode,” Opt. Express 27(9), 12171–12181 (2019). [CrossRef]

7. S. Fasham and S. Dunn, “Bluecomm underwater optical communications,” http://www.sonardyne.com/products/all-products/instruments/1148-bluecomm-underwater-optical-modem.html.

8. T. Sawa, “Study of adaptive underwater optical wireless communication with photomultiplier tube,” http://www.godac.jamstec.go.jp/catalog/data/doc_catalog/media/KR17–11_leg2_all.pdf.

9. S. Hu, L. Mi, T. Zhou, and W. Chen, “35.88 attenuation lengths and 3.32 bits/photon underwater optical wireless communication based on photon-counting receiver with 256-PPM,” Opt. Express 26(17), 21685–21699 (2018). [CrossRef]

10. N. D’Ascenzo, V. Saveliev, L. Wang, and Q. Xie, “Analysis of photon statistics with Silicon Photomultiplier,” J. Instrum. 10(8), C08017 (2015). [CrossRef]

11. S. Gundacker and A. Heering, “The silicon photomultiplier: fundamentals and applications of a modern solid-state photon detector,” Phys. Med. Biol. 65(17), 17TR01 (2020). [CrossRef]

12. P. A. Hiskett and R. A. Lamb, “Underwater optical communications with a single photon-counting system,” Proc. SPIE 9114, 91140P (2014). [CrossRef]

13. C. Wang, H. Yu, and Y. Zhu, “A long distance underwater visible light communication system with single photon avalanche diode,” IEEE Photonics J. 8(5), 1–11 (2016). [CrossRef]

14. Q. Yan, Z. Li, Z. Hong, T. Zhan, and Y. Wang, “Photon-counting underwater wireless optical communication by recovering clock and data from discrete single photon pulses,” IEEE Photonics J. 11(5), 1–15 (2019). [CrossRef]

15. Y. Ji, G. Wu, and C. Wang, “Generalized likelihood block detection for SPAD-based underwater VLC system,” IEEE Photonics J. 12(1), 1–10 (2020). [CrossRef]

16. H. Chen, X. Chen, J. Lu, X. Liu, J. Shi, L. Zheng, R. Liu, X. Zhou, and P. Tian, “Toward long-distance underwater wireless optical communication based on a high-sensitivity single photon avalanche diode,” IEEE Photonics J. 12(3), 1–10 (2020). [CrossRef]

17. J. Shen, J. Wang, C. Yu, X. Chen, M. Zhao, F. Qu, Z. Xu, J. Han, and J. Xu, “Single LED-based 46-m underwater wireless optical communication enabled by a multi-pixel photon counter with digital output,” Opt. Commun. 438, 78–82 (2019). [CrossRef]

18. J. Wang, X. Yang, W. Lv, C. Yu, J. Wu, M. Zhao, F. Qu, Z. Xu, J. Han, and J. Xu, “Underwater wireless optical communication based on multi-pixel photon counter and ofdm modulation,” Opt. Commun. 451, 181–185 (2019). [CrossRef]

19. M. A. Khalighi, T. Hamza, S. Bourennane, P. Léon, and J. Opderbecke, “Underwater wireless optical communications using Silicon Photo-Multipliers,” IEEE Photonics J. 9(4), 1–10 (2017). [CrossRef]

20. T. Essalih, M. A. Khalighi, S. Hranilovic, and H. Akhouayri, “Optical OFDM for SiPM-based underwater optical wireless communication links,” Sensors 20(21), 6057 (2020). [CrossRef]

21. X. Tang, L. Zhang, C. Sun, Z. Chen, H. Wang, R. Jiang, Z. Li, W. Shi, and A. Zhang, “Underwater Wireless Optical Communication Based on DPSK Modulation and Silicon Photomultiplier,” IEEE Access 8, 204676–204683 (2020). [CrossRef]

22. L. Zhang, X. Tang, C. Sun, Z. Chen, Z. Li, H. Wang, R. Jing, W. Shi, and A. Zhang, “Towards 200 m Gigabits per second underwater wireless optical communication using Silicon Photomultiplier (SiPM) based receiver,” Opt. Express 28(17), 24968–24980 (2020). [CrossRef]

23. Z. Chen, X. Tang, C. Sun, Z. Li, W. Shi, H. Wang, L. Zhang, and A. Zhang, “Experimental demonstration of over 14 AL underwater wireless optical communication,” IEEE Photonics Technol. Lett. 33(4), 173–176 (2021). [CrossRef]

24. M. V. Jamali, J. A. Salehi, and F. Akhoundi, “Performance studies of underwater wireless optical communication systems with spatial diversity: MIMO scheme,” IEEE Trans. Commun. 65(3), 1176–1192 (2017). [CrossRef]

25. J. Li, F. Wang, M. Zhao, F. Jiang, and N. Chi, “Large-coverage underwater visible light communication system based on blue led employing equal gain combining with integrated pin array reception,” Appl. Opt. 58(2), 383–388 (2019). [CrossRef]

26. J. A. Simpson, B. Hughes, and J. Muth, “Smart transmitters and receivers for underwater free-space optical communication,” IEEE J. Sel. Areas Commun. 30(5), 964–974 (2012). [CrossRef]

27. W. Liu, Z. Xu, and L. Yang, “SIMO detection schemes for underwater optical wireless communication under turbulence,” Photonics Res. 3(3), 48–53 (2015). [CrossRef]

28. M. C. Gökçe and Y. Baykal, “Scintillation analysis of multiple-input single-output underwater optical links,” Appl. Opt. 55(22), 6130–6136 (2016). [CrossRef]

29. Y. Dong and J. Liu, “On BER performance of underwater wireless optical MISO links under weak turbulence,” in Proc. IEEE/MTS OCEANS, 1–4 (2016).

30. J. Li, B. Yang, D. Ye, L. Wang, K. Fu, J. Piao, and Y. Wang, “A real-time, full-duplex system for underwater wireless optical communication: hardware structure and optical link model,” IEEE Access 8, 109372–109387 (2020). [CrossRef]

31. C. Wang, H. Yu, Y. Zhu, T. Wang, and Y. Ji, “Multi-LED parallel transmission for long distance underwater VLC system with one SPAD receiver,” Opt. Commun. 410, 889–895 (2018). [CrossRef]

32. M. Kong, Y. Chen, R. Sarwar, B. Sun, Z. Xu, J. Han, J. Chen, H. Qin, and J. Xu, “Underwater wireless optical communication using an arrayed transmitter/receiver and optical superimposition-based PAM-4 signal,” Opt. Express 26(3), 3087–3097 (2018). [CrossRef]

33. M. Zhao, X. Li, X. Chen, Z. Tong, W. Liu, Z. Zhang, and J. Xu, “Long-reach underwater wireless optical communication with relaxed link alignment enabled by optical combination and arrayed sensitive receivers,” Opt. Express 28(23), 34450–34460 (2020). [CrossRef]

34. P. Leon, F. Roland, L. Brignone, J. Opderbecke, J. Greer, M. A. Khalighi, T. Hamza, S. Bourennane, and M. Bigand, “A new underwater optical modem based on highly sensitive Silicon Photomultipliers,” in Proc. IEEE OCEANS Conf., 1–6 (2017).

35. http://www.joinbon.com/en/index.php/pro_view-9.html.

36. A. Eisele, R. Henderson, B. Schmidtke, T. Funk, L. A. Grant, J. A. Richardson, and W. Freude, “185 MHz count rate, 139 dB dynamic range single-photon avalanche diode with active quenching circuit in 130 nm CMOS technology,” in International Image Sensor Workshop, 278–281 (2011).

37. E. Sarbazi, M. Safari, and H. Haas, “The bit error performance and information transfer rate of SPAD array optical receivers,” IEEE Trans. Commun. 68(9), 5689–5705 (2020). [CrossRef]

38. E. Sarbazi, M. Safari, and H. Haas, “Statistical modeling of single-photon avalanche diode receivers for optical wireless communications,” IEEE Trans. Commun. 66(9), 4043–4058 (2018). [CrossRef]

39. O. Korotkova, N. Farwell, and E. Shchepakina, “Light scintillation in oceanic turbulence,” Waves Random Complex Media 22(2), 260–266 (2012). [CrossRef]

40. M. V. Jamali, A. Mirani, A. Parsay, B. Abolhassani, P. Nabavi, A. Chizari, P. Khorramshali, S. Abdollahramezani, and J. A. Salehi, “Statistical studies of fading in underwater wireless optical channels in the presence of air bubble, temperature, and salinity random variations,” IEEE Trans. Commun. 66(10), 4706–4723 (2018). [CrossRef]

41. E. Zedini, H. M. Oubei, A. Kammoun, M. Hamdi, B. S. Ooi, and M. Alouini, “Unified statistical channel model for turbulence-induced fading in underwater wireless optical communication systems,” IEEE Trans. Commun. 67(4), 2893–2907 (2019). [CrossRef]

42. Y. Li, M. Safari, R. Henderson, and H. Haas, “Nonlinear distortion in SPAD-based optical OFDM systems,” in Global Commun. Conf. Workshop Opt. Wireless Commun., 1–6 (2015).

43. S. Huang and M. Safari, “Hybrid SPAD/PD receiver for reliable free-space optical communication,” IEEE Open J. Commun. Soc. 1, 1364–1373 (2020). [CrossRef]

44. D. Chen, J. Wang, S. Li, and Z. Xu, “Effects of air bubbles on underwater optical wireless communication,” Chin. Opt. Lett. 17(10), 48–53 (2019). [CrossRef]

45. L. Zhang, H. Chun, Z. Ahmed, G. Faulkner, D. O’Brien, and S. Collins, “The Future Prospects for SiPM-Based Receivers for Visible Light Communications,” J. Lightwave Technol. 37(17), 4367–4374 (2019). [CrossRef]

Light source	Photodetector	Modulation	Water tape	Data rate	Link	Ref./Year
LD 450 nm	SPAD	OOK	Maalox	45.3 kbps	1 m	[12] 2014
LED blue/green	SPAD	OOK	Pure/Clear	100 Mbps	500 m	[13] 2016
LED Cree Q5	SPAD	NRZ-OOK	Pure seawater	1 Mbps	1.5 m	[14] 2019
LD 450 nm	SPAD	OOK	0.12/m	2 Mbps	117 m	[16] 2020
LED 532 nm	SPAD	NRZ-OOK	turbulence	1 Mbps	-	[15] 2020
LED blue	MPPC	8-PPM	Tap water	5 Mbps	46 m	[17] 2019
LD 520 nm	MPPC	OFDM	Tap water	312Mbps	21 m	[18] 2019
LED 470 nm	SiPM	OOK	Clear water	1 Mbps	66 m	[19] 2017
LED 470 nm	SiPM	OFDM	0.08/m	20 Mbps	81 m	[20] 2020
LD 532 nm	SiPM	DPSK	0.15/m	200Mbps	1.6 m	[21] 2020
LD 520nm	SiPM	OOK/DFE	0.29/m	1 Gbps	40 m	[22] 2020
LD 520 nm	SiPM	NRZ-OOK	Coastal	20 Mbps	24 m	[23] 2021
LED 445 nm	SiPM	NRZ-OOK	Mg(OH)₂	1 Mbps	10 m	This work

Light source/Photodetector	Modulation	Data rate/Link	Water type	MIMO Schemes	Methods	Ref./Year
LED/PIN	QAM	1.8 Gbps/1.2 m	Tap water	1 × 4 SIMO	Experimental	[25] 2019
LED/PD	OOK	/3.66 m	Maalox	7 × 7 MIMO	Experimental	[26] 2012
LED/APD	OOK	/30 m	Clear ocean	1 × 5 SIMO	Theoretical	[27] 2015
LD/PD		10-70 m	Turbulence	3 × 1 MISO	Theoretical	[28] 2016
LED/PD	OOK		Turbulence	6 × 1 MISO	Theoretical	[29] 2016
LED/APD	2FSK	1 Mbps/10 m	Tap water	6 × 1 MISO	-	[30] 2020
LED/SPAD	OOK	50 Mbps/220 m	0.0561/m	M × 1 MISO	Theoretical	[31] 2018
LD/MPPC	4-PPM	2.5 Mbps/46 m	Mg(OH)₂	M × 1 MISO	-	[32] 2018
LD/MPPC	NRZ-OOK	16.8 Mbps/50 m	0.24/m	1 × 2 SIMO	-	[33] 2020
LED/SiPM	OOK	3 Mbps/60 m	Jerlov I	M × 8 MIMO	-	[34] 2017
LED/SiPM	NRZ-OOK	1 Mbps/10 m	Mg(OH)₂	6 × 3 MIMO	Experimental	This work

Metrics	Values	Metrics	Values
Active area	1 mm×1 mm	Dead time	72 ns
Spectral response range	250-950 nm	Dark count rate, f_DCR	3.3 KHz/mm²
Peak sensitivity wavelength	420 nm	Number of SPADs	324
Photon detection efficiency	35% @420 nm	No. of Pixels	50 µm
Probability of cross-talk f_CT	0.7%	Single photon amplitude	55-60 mV
Probability of after-pulse f_AP	0.2%	Fill factor	81%
Operating voltage	5 ± 0.1 V	Type of the quenching	Passive quenching

Products/Applications	Company/Country
SPAD/MPPC/optical sensors	Hamamatsu/Japan
SPAD/SiPM/low light sensors	SensL/Ireland
SPAD/photonics detectors	Excelitas/USA
SPAD/SiPM/quantum sensing	ID Quantique/Switzerland
SiPM/low-flux-light imaging	Joinbon/China

MIMO schemes	Current/Voltage	Transmitted optical power	Energy per bit at 1 Mbps
SISO 1×1	6 mA/7.56 V	7.56 mW	7.56×10⁻⁹ J/bit
SIMO 1×3	6 mA/7.56 V	7.56 mW	7.56×10⁻⁹ J/bit
MISO 3×1	2 mA/7.45 V	7.45 mW	7.45×10⁻⁹ J/bit
MIMO 3×3	2 mA/7.45 V	7.45 mW	7.45×10⁻⁹ J/bit
MISO 6×1	1 mA/7.38 V	7.38 mW	7.38×10⁻⁹ J/bit
MIMO 6×3	1 mA/7.38 V	7.38 mW	7.38×10⁻⁹ J/bit

Single-photon detection for MIMO underwater wireless optical communication enabled by arrayed LEDs and SiPMs

Abstract

1. Introduction

2. Experimental setup

2.1 LED array and transmitter

2.2 Silicon photomultiplier (SiPM)

2.3 Photocount distribution and counting system

2.4 SiPM analog mode detection

2.5 Underwater channel

3. Turbulence and photon-counting MIMO scheme

3.1 Oceanic turbulence and optical link model

3.2 Photon-counting MIMO scheme

4. Results and discussion

4.1 Dark count rate of SiPM

4.2 Distribution of photocounts for SiPM

4.3 Received optical power

4.4 Bit error rate

4.5 Photon-counting MIMO performance

4.6 Analog mode detection of SiPM

5. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (29)

Tables (5)

Equations (33)

Optics Express