1. Introduction

The ongoing expansion of human activities in ocean, such as oceanographic research, underwater resource exploration, tactical surveillance and so on, have boosted the demand for high-speed underwater communication [1–3]. Underwater wireless optical communication (UWOC) is a revolutionary technology with merits of large bandwidth, low latency, low energy consumption, flexibility of deployment, high security, etc., as compared to underwater acoustic or radio frequency (RF) communication counterparts, which shows either low bandwidth or heavy aquatic attenuation. Development of UWOC will enhance infrastructures for scientific research, commercial, and military use by offering solutions to efficiently communicate among surface vessels, underwater vehicles, and seafloor infrastructures. However, the hostile underwater environment to UWOC makes its progress far behind the terrestrial and space communication counterparts [4]. Long range and high-speed UWOC has always been an intriguing topic and the research is just unfolding. Till now, long range and high-speed UWOC demonstrated by experiments or commercial products lags far behind the theoretical bound predicted by Monte Carlo numerical simulations [5], in which the results show that the communication distance can be extended to 500 m in pure seawater.

A wealth of studies has been conducted to enhance the figure of merit of UWOC in terms of transmission distance, data rate, and robustness to link misalignment [6–33]. In 2017, Liu et al. experimentally demonstrated 34.5-m / 2.7-Gbps UWOC in tap water based on on-off keying (OOK) modulation and a 520-nm laser diode (LD) [6]. In 2018, Shen et al. carried out 46-m UWOC utilizing power-efficient pulse position modulation (PPM) and an ultra-sensitive multi-pixel photon counter (MPPC) [7]. Hu et al. reported 120-m UWOC in Jerlov II water using 256-PPM with a bandwidth of 13.7 MHz, in which the attenuation length (AL) reached 35.88 [8]. In [9], multi-LED parallel transmission for long distance UWOC systems with one single photon avalanche diode (SPAD) receiver was designed, which could improve the bit-error-rate (BER) and anti-nonlinearity performance. In 2019, 100-m / 500-Mbps UWOC was realized using OOK and nonlinear equalization with a 520-nm LD [10]. In [11], the authors introduced multiband discrete-Fourier transform spread (DFT-S) to discrete multi-tone (DMT)-based UWOC systems, which could improve the BER performance of long range UWOC. In 2020, employing an off-the-shelf silicon photomultiplier (SiPM), Zhang et al. experimentally demonstrated a 40-m / 1-Gbps UWOC system [12]. Yang et al. experimentally demonstrated a high-power 100-m / 100-Mbps UWOC system using a 532-nm source, which is wavelength converted from a 1064-nm continuous-wave laser [13]. In [14], optical combination and arrayed MPPCs are utilized to extend the transmission distance and relax the strict alignment requirement of UWOC. In 2021, 150-m / 500-Mbps UWOC was achieved enabled by sensitive detection in combination with receiver-side partial response shaping and Trellis coded modulation (TCM) technology [15]. Later, this group successfully conducted a 200-m / 500-Mbps UWOC experiment using a sparse nonlinear equalizer [16]. The Japan Agency for Marine-Earth Science and Technology (JAMSTEC) reported a UWOC sea trial of 20-Mbps over 120-m communication range in 700-m deep ocean water [17].

Long range UWOC suffers from heavy aquatic attenuation and resultant weak received optical power (ROP), which poses serious challenges to the sensitivity of photodetectors. SPAD and MPPC (i.e., SiPM, an integrated dense array of small independent SPAD) can offer excellent low-light detection capabilities and nice feature of data rate, are studied in some pioneering UWOC works like [5,9] and [7,12,14], respectively. As a mature and unfailing module, PMT is also able to support highly sensitive photon detection, and thus has already been applied in commercially available UWOC products [32]. Additionally, due to a relatively larger effective area, PMT is competitive in terms of misalignment tolerance in long range UWOC systems. Recently, a contrastive study introduced a commercial wideband PMT, showing a 1-Gbps / 1-m UWOC transmission using cost-effective OOK modulation [33]. Together with a peak sensitivity wavelength of 420 nm, compactness, and user-friendliness, this PMT (includes a magnetic shield tube) perfectly adapts to deep ocean UWOC use, foreseeing broad prospect. Table 1 summarizes the recent research progress of long distance and high-speed UWOC in terms of transmission distance (>30 meters), data rate, adopted digital signal processing (DSP) techniques, and AL (product of attenuation coefficient and transmission distance), in which AL is considered as a fair and critical indicator since water types may greatly influence the system performance.

Table 1. Comparison of long distance and high-speed UWOC in recent works.

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In long range and low-light detection UWOC, complicated modulation schemes may bring high data rates but at the expense of complex DSP techniques and increased cost. With outstanding anti-noise ability, the cost-effective OOK modulation is more practical in such UWOC settings, while a data rate of Gbps transmission is already sufficient to most UWOC applications. In this paper, a commercially available wideband PMT is utilized as the receiver in the proposed UWOC system and a comprehensive experimental study is conducted, in which the transmission range, data rate, and AL is pushed to 100.6 meters, 3 Gbps, and 6.62, respectively. The ROP at 100.6-meter transmission is as low as -40 dBm for the OOK signal (@1.5 Gbps). To the best of our knowledge, this is the first Gbps-class UWOC experimental demonstration in >100-meter transmission that has ever been reported. To further simplify the equalization process, a sparsity-aware channel equalizer is also adopted to reduce the number of filter coefficients due to the sparsity of coefficient distribution of the UWOC channel while keeping only slight performance penalty.

2. Experimental setup and DSP techniques

Figure 1 shows the experimental setup of the proposed PMT-based UWOC system, in which the UWOC system is firstly evaluated in indoor environment, then moved to outdoor 100.6-m field test. In the indoor test as depicted in Fig. 1(a)-(d), an OOK modulated pseudo-random binary sequence (PRBS) is generated, 2-times up-sampled, and pulse-shaped using a root-raised cosine (RRC) filter with a roll-off coefficient of 0.05 and a length of 100. Then the shape-filtered signal is loaded into an arbitrary waveform generator (AWG) for digital-to-analog (D/A) conversion. The output analog signal is boosted by an electrical amplifier (26 dB, 10-1200 MHz) followed by a variable electrical attenuator (VEA) to find the optimal RF output power. Coupled with a direct current (DC) bias via a bias-T, the resulting RF + DC signal is injected into a 450-nm LD (Thorlabs LP450-SF15). The emitted laser beam is collimated and power optimized by a neutral density (ND) filter before entering a 5 m × 0.6 m × 0.3 m glass water tank. After traversing a 5-m aquatic channel, the output beam from the water tank passes through an iris and is fed into a commercial PMT (Hamamatsu H14447), which has a large effective area of Φ25 mm and frequency response up to 1 GHz. To reduce the dark current, this PMT is refrigerated to ∼4℃, which is the water temperature in deep ocean. To minimize the ambient light noise, the receiver side is shielded using a black curtain and the ambient light power is around 0.1 nW (-70 dBm). The signal output of the PMT is connected to a trans-impedance amplifier (TIA) (36 dB, 50 KHz - 1.5 GHz). The control voltage input of the PMT is used to adjust the sensitivity. The detected electrical signal from the PMT is captured by a digital serial analyzer (Tektronix, DSA72004C). Finally, the received signal is synchronized, resampled, and reshaped by the same RRC filter as in the transmitter side. The resulting discrete sequence is equalized to mitigate inter-symbol interference (ISI) then recovered for BER performance evaluation. In the outdoor 100.6-m field test as shown in Fig. 1(e)-(h), the output beam from the polyvinyl chloride (PVC) water pipe (one 15-cm diameter glass window installed at either end) is converged by a coated lens to collect light (a spot light of ∼12 cm) in front of the iris. All the experiments are conducted in the nighttime to minimize the impact of ambient light noise.

 

Fig. 1. Experimental setup of the indoor (a)-(d) and outdoor 100.6-m (e)-(h) PMT-based UWOC system. (a) and (e): The schematic of the experimental setup; (b) and (f): Transmitter side; (c) Water tank; (d) and (g): Receiver side; (h) 100.6-m PVC water pipe. AWG: arbitrary waveform generator; EA: electrical amplifier; VEA: variable electrical attenuator; LD: laser diode; ND filter: neutral density filter; TIA: trans-impedance amplifier; PMT: photomultiplier tube; CV: control voltage; DSA: digital serial analyzer.

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In the channel equalization stage, the feed-forward equalization (FFE) is used to reduce ISI. The n-th sample of the output equalized signal can be expressed as:

Assuming that the UWOC channel is sparse, the complexity of channel equalization can be further reduced by only selecting the dominant values while discarding the unimportant ones without large performance penalty, which is relevant to the problem of sparse reconstruction, i.e., searching for a good approximation of the transmitted vector ${\mathbf y}$ in terms of linear combination of only a small number of columns from the measurement matrix ${\mathbf B}$. Several sparse recovery algorithms have been studied to restore sparse or compressed signal from random measurements, such as image/video estimation, speech recognition, and data acquisition [34–37]. By virtue of low computational complexity, no reselection occurrence, and ease of implementation, sparse orthogonal matching pursuit (OMP) is performed in this paper to adaptively search for non-trivial coefficients before sparse equalization. The key step in OMP is the orthogonal procedure, which results in the following residual vector [38,39]:

Step 1: Initialize the residual vector ${{\mathbf c}_0} = {\mathbf y}$, the index set ${{\mathbf{T}}_0} = \phi$ (i.e., an empty matrix), the matrix of chosen atoms ${{\mathbf R}_0} = \phi$, the iteration counter m = 1, and the sparsity level M.

Step 2: Correlate all columns of ${\mathbf B}$ with the residual vector and find the index ${k_m}$ that solves the optimization problem ${k_m} = \mathop {\arg \max }\limits_q |{\boldsymbol{\mathrm{\beta}}_q^H{{\mathbf c}_{m - 1}}} |$, where $q = 1,2, \cdots ,Q,\;\;q \notin {{\mathbf{T}}_{m - 1}}$.

Step 3: Augment the range of index set ${{\mathbf{T}}_m} = {{\mathbf{T}}_{m - 1}} \cup {k_m}$ and the matrix of chosen atoms ${{\mathbf R}_m} = \;\;[{{\mathbf R}_{m - 1}},{\boldsymbol{\mathrm{\beta}}_{{k_m}}}]$.

Step 4: Solve the LS problem of the equation ${\mathbf y} = {{\mathbf R}_m}{\boldsymbol{\mathrm{\lambda}}_m},$ i.e., ${\hat{{\mathbf w}}_m}\textrm{ = }\;\mathop {\arg \max }\limits_{{\boldsymbol{\mathrm{\lambda}}_m}} |{{\mathbf y} - {{\mathbf R}_m}{\boldsymbol{\mathrm{\lambda}}_m}} |\textrm{ = }$ ${\textrm{(}{\mathbf R}_m^H{{\mathbf R}_m}\textrm{)}^{ - 1}}{\mathbf R}_m^H{\mathbf y}$ and update the new residual vector ${{\mathbf c}_m} = {\mathbf y} - {{\mathbf R}_m}{\hat{{\mathbf w}}_m}$.

Step 5: Increase the value of m, i.e., m = m+1 and return to Step 2 if m < M.

Step 6: After obtaining the index set ${\mathbf{T}} = {{\mathbf{T}}_m}$ and the coefficients of M-sparse coefficients ${\hat{{\mathbf w}}_{sparse}}({\mathbf{T}}) = {\hat{{\mathbf w}}_m}$, the M-sparse FFE filter is employed to equalize the received signal by using ${\mathbf y} = {\mathbf B}{\hat{{\mathbf w}}_{sparse}}({\mathbf{T}})$.

3. Experimental results and discussions

At first, the performance of the proposed PMT-based UWOC system is experimentally investigated in indoor environment. The power-current-voltage characteristic of the used 450-nm LD is measured, as shown in Fig. 2(a). Figure 2(b) exhibits the normalized frequency response of the back-to-back (B2B) PMT-based UWOC system, which shows the 20-dB bandwidth of the system is ∼1.5 GHz. Figure 2(c) shows the BER versus LD driving current of the proposed 5-m UWOC system, in which the ROP and data rate are fixed at 200 nW (-36.99 dBm) and 2 Gbps, respectively. The optimal working point of the LD is at 65 mA. The BER performance at LD driving current of 65 mA behaves quite close to that of 75 mA, while a larger driving current corresponds to a higher power delivery, which is beneficial to a longer distance underwater transmission. Figure 2(d) gives the BER performance relative to the control voltage input of the PMT at 5-m underwater transmission, in which the ROP and data rate are also fixed at the same condition as Fig. 2(c). Here, the optimal value of control voltage is 2 V.

 

Fig. 2. (a) The P-I-V curve of the LD; (b) Frequency response of the B2B PMT-based UWOC system; (c) BER versus LD driving current of the proposed 5-m UWOC system; (d) BER relative to the control voltage input of the PMT at 5-m underwater transmission.

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The measured BER versus length of the FFE filter of the proposed 5-m PMT-based UWOC system at different ROP and data rates is depicted in Fig. 3(a). The BER of all cases improves as the length of the FFE filter increases and then reaches saturation. To get convergent BER while reducing the complexity of channel equalization, FFE filter length of 32, 34, 40, 44, and 52 are selected in the data rates of 1-Gbps, 1.5-Gbps, 2-Gbps, 2.5-Gbps, and 3-Gbps cases, respectively. The sudden BER improvement is attributed to the sparsity of coefficient distribution in the UWOC channel. Figure 3(b) plots BER as a function of the sparsity level M of the above five cases. The BER improves with increasing sparsity level M and then levels off, indicating that OMP can automatically distinguish different contributions of the channel coefficients and select the dominant components. The sparsity level M of 14, 16, 18, 21, and 24 are selected in the data rates of 1-Gbps, 1.5-Gbps, 2-Gbps, 2.5-Gbps, and 3-Gbps cases, respectively, in the rest of the paper. By sparse channel equalization, the number of FFE filter coefficients can be further reduced by more than 50%, and thus significantly reduce the complexity of the UWOC system.

 

Fig. 3. (a) BER vs. length of the FFE filter; (b) BER as a function of the sparsity level of the proposed 5-m PMT-based UWOC system at different ROP and data rates.

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To investigate the performance of the proposed PMT-based UWOC system in different turbidity waters, Fig. 4 illustrates the BER relative to ROP of the 5-m PMT-based UWOC system at different data rates. Solid lines refer to FFE cases, while dashed lines refer to sparse equalization cases. Three different turbidity water types are created by adding the 1% diluted Maalox^R [Al(OH)₃ and Mg(OH)₂] suspension as in [40], namely tap water, “clear seawater”, and “coastal water”. In Fig. 4(a), (b), and (c), the ROP supporting a data rate of 3-Gbps transmission in the FFE and sparse equalization cases is all as low as -32 dBm with a BER all below 7% hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10⁻³. While the ROP that sustains a data rate of 1-Gbps transmission in the FFE and sparse equalization cases is all as low as -42 dBm when BER all below the FEC limit. Figure 4(d) shows the ROP (at BER of 3.8 × 10⁻³) versus different turbidity waters at different data rates, in which the data is all extracted from the cross points of BER versus ROP curves and reference line 3.8 × 10⁻³ in Fig. 4(a), (b), and (c). The attenuation coefficients, (i.e., c) shown in the horizontal axis in Fig. 4(d), are calculated as [41], i.e., tap water (c = 0.0641 m^-1), “clear seawater” (c = 0.1502 m^-1) and “coastal water” (c = 0.39 m^-1). It is manifested that the receiver sensitivity for different data rates in different turbidity waters is relatively flat as shown in Fig. 4(d). All the figures indicate that sparse equalization brings comparable performance as FFE with lower computational complexity.

 

Fig. 4. BER vs. ROP of the proposed 5-m PMT-based UWOC system for FFE and sparse equalization at different data rates in (a) tap water, (b) “clear seawater”, and (c) “coastal water”; (d) Receiver sensitivity vs. different turbidity waters at different data rates.

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Figure 5 exhibits the performance of outdoor 100.6-m field test of the proposed PMT-based UWOC system. The ROP of the output beam from the 100.6-m PVC water pipe (filled with tap water, attenuation coefficient is 0.0658 m^-1) is ∼20μW (-16.99 dBm) after converging by a coated lens. The measured BER versus ROP for FFE and sparse equalization at different data rates is plotted in Fig. 5(a), in which the ROP enabling data rates of 3-Gbps and 1.5-Gbps transmission is as low as -32 dBm and -40 dBm, respectively, with BER both below 3.8 × 10⁻³. It is worth mentioning that the results are comparable to that of 5-m indoor test as shown in Fig. 4, and sparse equalization declares similar performance as FFE again. The insets in Fig. 5(a) show eye diagrams of three FFE cases, implying that the lower the BER is, the clearer eye diagrams can be acquired. The laser beams and received spot lights of every extracted transmission distance from the 100.6-m PVC pipe are presented in Fig. 5(b), where the laser beams become expanded and the received light spots are diffused with the increasing transmission distance due to the inhomogeneity of refractive index of water. The result of line-of-sight optical propagation shown in Fig. 5(b) seems more intuitive than a zig-zag way of optical propagation mostly used in reported UWOC works.

 

Fig. 5. Outdoor 100.6-m field test of the proposed PMT-based UWOC system. (a) BER vs. ROP of the PMT-based UWOC system for FFE and sparse equalization at different data rates; (b) laser beams and received light spots of every extracted transmission distance from the 100.6-m underwater link.

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PMT has a relatively larger effective area, which can ease link misalignment. To explore such benefit, a proof-of-concept 5-m UWOC experiment is carried out. Employing a rotation stage, the measured BER as a function of the rotation angle of the PMT at different ROP and data rates for FFE and sparse equalization is shown in Fig. 6. Keeping the effective area of the PMT covered in the received light spot, the PMT is gradually turned clockwise (corresponding to negative angles in Fig. 6) and counterclockwise (corresponding to positive angles in Fig. 6). From the figure, with the same ROP, the larger data rate, the worse BER, while with the same data rate, the smaller ROP, the worse BER. The missing points mean BER equals to zero in these circumstances. With ROP of -40 dBm and a data rate of 1 Gbps, the PMT-based UWOC system can sustain a rotation angle of -50°to 40°with BER below 3.8 × 10⁻³, showing superiority to tolerance of link misalignment, while sparse equalization still reveals similar performance as FFE with lower complexity.

 

Fig. 6. BER vs. rotation angle of the PMT of the proposed 5-m UWOC system at different ROP and data rates.

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4. Conclusion

In this paper, we have proposed a PMT-based UWOC system and a comprehensive experimental study has been conducted, in which the transmission range, data rate, and AL is pushed to 100.6 meters, 3 Gbps, and 6.62, respectively. The ROP at 100.6-meter transmission is as low as -40 dBm for the 1.5-Gbps OOK signal. To the best of authors’ knowledge, this is the first Gbps-class UWOC experimental demonstration in >100-meter transmission that has ever been reported. To further reduce the complexity of channel equalization, a sparsity-aware equalizer with OMP has been adopted to reduce the number of filter coefficients by more than 50% with minor performance loss. Meanwhile, the performance of the proposed PMT-based UWOC system has been evaluated in different turbidity waters at 5-m transmission, showing the robustness of the equalization method. The PMT has larger effective area and allows for reduced alignment requirements between the transmitter and the receiver. A proof-of-concept UWOC experiment has also been demonstrated, which verifies the advantage of large received angle of the PMT. The research results foresee a bright future of the wideband PMT in long range and high-speed UWOC. In future work, we will explore the application of the PMT in a real underwater scenario, like swimming pool or lake.