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Experimental Demonstration of High-Sensitivity Underwater Optical Wireless Communication Based on Photocounting Receiver

Experimental Demonstration of High-Sensitivity Underwater Optical Wireless Communication Based on... hv photonics Article Experimental Demonstration of High-Sensitivity Underwater Optical Wireless Communication Based on Photocounting Receiver 1 , 2 3 4 5 1 1 Chao Li * , Zichen Liu , Daomin Chen , Xiong Deng , Fulong Yan , Siqi Li and Zhijia Hu Information Materials and Intelligent Sensing Laboratory of Anhui Province, Anhui University, Hefei 230601, China; sqli@ahu.edu.cn (S.L.); zhijiahu@ahu.edu.cn (Z.H.) Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China; lzc8888@hust.edu.cn Shanghai Huawei Technology Co., Ltd., Shanghai 200001, China; chendaomin@huawei.com Center for Information Photonics and Communications, School of Information Science and Technology, Southwest Jiaotong University, Chengdu 611756, China; xiongdeng@swjtu.edu.cn Alibaba Cloud, Alibaba Group, Beijing 100102, China; yanfulong.yfl@alibabainc.com * Correspondence: chao.li@ahu.edu.cn Abstract: In this paper, we propose a high-sensitivity long-reach underwater optical wireless commu- nication (UOWC) system with an Mbps-scale data rate. Using a commercial blue light-emitting diode (LED) source, a photon counting receiver, and return-to-zero on–off keying modulation, a receiver sensitivity of 70 dBm at 7% FEC limit is successfully achieved for a 5 Mbps intensity modulation direct detection UOWC system over 10 m underwater channel. For 1 Mbps and 2 Mbps data rates, the receiver sensitivity is enhanced to 76 dBm and 74 dBm, respectively. We further investigate the system performance under different water conditions: first type of seawater (c = 0.056 m ), 1 1 second type (c = 0.151 m ), and third type (c = 0.398 m ). The maximum distance of the 2 Mbps signal can be extended up to 100 m in the first type of seawater. Citation: Li, C.; Liu, Z.; Chen, D.; Deng, X.; Yan, F.; Li, S.; Hu, Z. Keywords: underwater optical wireless communication (UOWC); long-reach; photon counting Experimental Demonstration of High-Sensitivity Underwater Optical Wireless Communication Based on Photocounting Receiver. Photonics 2021, 8, 467. https://doi.org/ 1. Introduction 10.3390/photonics8110467 With the expanding area explored by human beings, the observation and utilization of the underwater world is growing increasingly important. Various underwater sensors, Received: 8 September 2021 unmanned vehicles, and nodes are deployed underwater to transfer and collect information. Accepted: 21 October 2021 To build an underwater transmission link, both cable- and wireless-based methods are Published: 22 October 2021 utilized. Cables or fibers can offer a stable communication link with high transmission speed but limit the freedom of the communication terminal for a long-reach link. Publisher’s Note: MDPI stays neutral The traditional method for underwater communication is to use acoustics, which is a with regard to jurisdictional claims in medium of sound. The attenuation of the sound wave in water is acceptable, which is com- published maps and institutional affil- petent for ultralong-reach communication up to tens of kilometers. However, underwater iations. acoustic communication is limited by the huge transmitted power, low data rate, and large latency [1]. Due to the skin effect, electromagnetic waves suffer from huge attenuation when propagating in water. Thus, it is hard to realize long-reach underwater communi- cation using electromagnetic waves. Studies have shown that the visible spectrum from Copyright: © 2021 by the authors. blue–green wavelengths suffers less attenuation caused by underwater absorption and Licensee MDPI, Basel, Switzerland. scattering than electromagnetic waves [2]. Benefiting from the rich bandwidth resource of a This article is an open access article laser diode (LD), a Gbps-scale underwater optical wireless communication (UOWC) system distributed under the terms and within tens of meters is feasible [3]. However, a strict tracking and alignment system is conditions of the Creative Commons required after long-distance transmission due to the narrow beam and small divergence Attribution (CC BY) license (https:// angle of the LD source. Moreover, most of the reported UOWC links are conducted in creativecommons.org/licenses/by/ tap water with avalanche photodetectors (APDs) for optical signal detection, which may 4.0/). Photonics 2021, 8, 467. https://doi.org/10.3390/photonics8110467 https://www.mdpi.com/journal/photonics Photonics 2021, 8, 467 2 of 13 not be so attractive and available for some long-distance transmission scenarios requiring a large optical power budget and photon-scale detection, e.g., internal communications with Mbps data rates between autonomous underwater vehicles or underwater sensor nodes in underwater dynamic conditions [4]. Thus, a high-sensitivity detector combined with a large-coverage-area light source is indispensable to build a reliable communication link with respect to unpredictable channel obstructions and the various conditions of the sea. Photomultiplier tubes (PMTs), possessing the capability of single-photon detection, are the most widespread vacuum electronic devices in every field of experimental studies including optical communication, biology, space research, and chemistry. Compared with silicon photomultipliers, PMT needs high voltage to drive the device. However, the PMTs are not sensitive to temperature and have a lower noise level. Due to the sensitivity of PMT to background noise and magnetic fields, it is more suitable to build a PMT-based long-range UOWC link for deep-sea implementation. Before building a long-range experimental UOWC system, the underwater channel conditions need to be investigated to establish the system parameters such as the optimal transmitted optical wavelength, modulation scheme, signal baud rate, and beam aperture. Because underwater data transmission using a light beam is not an easy mission in the presence of high water absorption and scattering, characterizing the underwater optical channel property to achieve appropriate system parameters is of crucial importance to enable a high-reliability and high-quality UOWC link. In this paper, we consider a comprehensive underwater channel model to simulate the property of an underwater optical communication link by taking the practical system parameters into account. Under the guidance of the simulation results, we propose and experimentally demonstrate a long-reach Mbps-scale UOWC scheme with high receiver sensitivity based on a light-emitting diode (LED) transmitter and a PMT receiver. The proposed system can significantly relax the alignment requirement especially after long- distance transmission. Bit-error-ratio (BER) performance enhancements for 1 Mbps, 2 Mbps, and 5 Mbps after 10 m transmission are experimentally investigated under different water turbidities with an adaptive decision threshold (DT). The receiver adapts to the changing of signal level. With added attenuation, the maximum link loss at an attenuation coefficient of 1.33 m is up to 99 dB at l = 448 nm. The achievable maximum distances for a 2 Mbps data rate in the first type of seawater (c = 0.056 m ) are up to 100 m and 134 m at 1 W and 10 W transmitted electrical power, respectively. 2. Operation Principle Compared with free-space atmospheric laser communication, the UOWC system faces some unique challenges. (i) Spectrum for communication: blue or green wavelengths should be dedicated to the UOWC link due to the water absorption effect, rather than infrared wavelengths (C-band 1530–1565 nm and L-band 1565–1625 nm) for an atmospheric free-space link enabled by well-established fiber-optic technologies and optoelectronic devices and components. (ii) Channel condition: affected by seawater, the underwater optical transmission channel is quite complicated. When the modulated light propagates through seawater, it suffers from absorption and scattering. Seawater absorption means that part of the photon energy launched into the seawater is converted into other forms of energy, such as thermal and chemical. Scattering refers to the interaction between light and seawater, which changes the optical transmission path. Both absorption and scattering cause the loss of optical signal energy at the receiver, resulting in a reduction in signal-to-noise ratio and communication distance. As illustrated in [5], the link loss for a realistic 10 m green-light UOWC system can vary from 6.6 dB to 95.5 dB due to dynamic underwater channel conditions from a clean ocean to turbid harbor seawater. Due to the variability of underwater channels, a robust long-reach UOWC link must be designed against a link loss of roughly up to 100 dB. Meanwhile, the link must be able to tolerate the dynamic changing underwater channels without breaking off. Although Photonics 2021, 8, x FOR PEER REVIEW 3 of 13 Photonics 2021, 8, 467 3 of 13 to tolerate the dynamic changing underwater channels without breaking off. Although linear detectors including APDs have shown their abilities to detect multi-Gbps optical linear detectors including APDs have shown their abilities to detect multi-Gbps optical signals transmitted by LD sources, their sensitivities are typically limited by thermal noise signals transmitted by LD sources, their sensitivities are typically limited by thermal [6]. On the other hand, photon-counting detectors can achieve very high sensitivities with noise [6]. On the other hand, photon-counting detectors can achieve very high sensitivities moderate data rates on the Mbps scale. In this paper, we propose a reliable long-reach with moderate data rates on the Mbps scale. In this paper, we propose a reliable long- UOWC scheme using LED and PMT, whose concept is illustrated in Figure 1. Due to the reach UOWC scheme using LED and PMT, whose concept is illustrated in Figure 1. Due advantages of its large light beam, compact structure, low cost, and low power consump- to the advantages of its large light beam, compact structure, low cost, and low power tion, LEDs are proposed as viable candidates to provide a transmission data rate of several consumption, LEDs are proposed as viable candidates to provide a transmission data Mbps or even up to hundreds of Mbps for implementing an alignment-released UOWC rate of several Mbps or even up to hundreds of Mbps for implementing an alignment- system. In the demonstration, a commercial LED transmitter is modulated by a prede- released UOWC system. In the demonstration, a commercial LED transmitter is modulated signed return-to-zero on–off keying (RZ-OOK) with half power semi-angle of 1.25° [7]. by a predesigned return-to-zero on–off keying (RZ-OOK) with half power semi-angle of With increasing transmission distance z, the receiving radius 𝐷 at the detection area in- 1.25 [7]. With increasing transmission distance z, the receiving radius D at the detection creases, which significantly relaxes the alignment requirement. To achieve high receiver area increases, which significantly relaxes the alignment requirement. To achieve high sensitivity and long distance, a typical and practically implemented photocounting re- receiver sensitivity and long distance, a typical and practically implemented photocounting ceiver is used, which is the PMT combined with a pulse-holding circuit to detect photo- receiver is used, which is the PMT combined with a pulse-holding circuit to detect photo- level signals. The received photoelectric current is characterized by a series of discrete level signals. The received photoelectric current is characterized by a series of discrete rectangular pulses with certain width, whose number satisfies a Poisson distribution. In rectangular pulses with certain width, whose number satisfies a Poisson distribution. In the demonstration, we propose a digital adaptive DT algorithm for signal recovery. The the demonstration, we propose a digital adaptive DT algorithm for signal recovery. The value of DT is adjusted as a function of the received signal level to achieve the minimum value of DT is adjusted as a function of the received signal level to achieve the minimum BER value. BER value. TSS DC PMT Rx * * * * RSS * * z * * * * * * * * ** * * * * * ** * * * * ** ** * * DT * * ** LED Tx Photons DA Figure 1. Proposed concept of long-reach UOWC using LED and PMT. DC: direct current, TSS: trans- Figure 1. Proposed concept of long-reach UOWC using LED and PMT. DC: direct current, TSS: mitted signal sequence, DA: detection area, RSS: received signal sequence, DT: decision threshold. d transmitted signal sequence, DA: detection area, RSS: received signal sequence, DT: decision threshold. 𝛿 is the divergence half-angle. z is the transmission distance. 𝐷 is the radius at the is the divergence half-angle. z is the transmission distance. D is the radius at the detection area. detection area. 3. System Model 3.1. LED Transmitter 3. System Model In our experiment, a commercial low-cost LED at a peak wavelength of 448 nm 3.1. LED Transmitter was employed as the transmitter. The path loss of light caused by water absorption and In our experiment, a commercial low-cost LED at a peak wavelength of 448 nm was scattering can be dominated by the Beer–Lambert law. employed as the transmitter. The path loss of light caused by water absorption and scat- tering can be dominated by the Beer–Lambert law. cz (a+b)z P = h P L = h P e = h P e , (1) r t ch t t −− cz () a+b z PP== ηη L Pe =ηPe (1) rt ch t t where h is electrical-to-optical conversion efficiency of LED, a and b represent the coeffi- cients of absorption and scattering, respectively, c is the total loss due to both effects, and z where 𝜂 is electrical-to-optical conversion efficiency of LED, 𝑎 and 𝑏 represent the co- is the underwater transmission distance. L is the channel loss, given by exp(cz). P and efficients of absorption and scattering, respecti ch vely, 𝑐 is the total loss due to both eftfects, P are the transmitted electrical power and received optical power (ROP), respectively. and 𝑧 is the underwater transmission distance. 𝐿 is the channel loss, given by exp(−cz). The radiation pattern I f of the LED obeys the Lambertian model, defined as ( ) 𝑃 and 𝑃 are the transmitted electrical power and received optical power (ROP), respec- tively. (m + 1) The radiation pattern 𝐼(𝜙) of the LED obeys the Lambertian model, defined as I(f) = h P cos (f), (2) 2p (1 m +) where f is the angle of irradiance, and f = 0 is the maximum , radiation power angle, i.e., IP () φ = η cos (φ) (2) 2π the direct state. m is expressed as the Lambertian emission order of the beam directivity, which is related to the half-power angle f of the LED, written as 1/2 where 𝜙 is the angle of irradiance, and 𝜙 = 0 is the maximum radiation power angle, i.e., the direct state. 𝑚 is expressed as the Lambertian emission order of the beam di- ln 2 m = . (3) rectivity, which is related to the half-power angle 𝜙 of the LED, written as ln(cos f ) 1/2 * Photonics 2021, 8, 467 4 of 13 The detected optical power by the photon counting receiver at the receiving plane A through the distance z is defined as follows [8]: e f f I(f)L A ch e f f P = . (4) 3.2. Underwater Channel In an underwater environment, the transmitted light is greatly influenced by the opti- cal properties of water. Underwater particles can cause energy attenuation and divergence of the beam. In this section, Kopelevich channel modeling is used as a volume scattering function (VSF) to investigate the extinction coefficient of natural water by simulation [9,10]. The specific form of this model is presented in [9]. Absorption coefficient a and scattering coefficient b denote the spectral absorption and scattering rate of unit interval, respectively. In this paper, we consider fulvic acid, humic acid and chlorophyll as the main absorption components of water [11,12], which can be expressed as follows: a(l) = a (l) + a (l) + a (l) + a (l), (5) w c f h 0.602 0 0 a (l) = a (l)(C /C ) , (6) c c c c a (l) = a C exp(k l), (7) f f f a (l) = a C exp(k l), (8) h h h where l indicates the light wavelength, and a (l), a (l), a (l), and a (l) are the absorp- w c f h tion coefficients caused by pure water, chlorophyll, fulvic acid, and humic acid, respectively. 0 0 0 The variables of a , a , and a represent the chlorophyll, fulvic acid, and humic acid charac- f h teristic absorption coefficients, respectively [13–15]. The two constant parameters k and k f h 1 1 are 0.0189 m and 0.0111 m . C , C , and C indicate the concentrations of chlorophyll, c f h 0 3 fulvic acid, and humic acid in water (C = 1 mg/m ). The values of C are given in Table 1. C and C are expressed as follows: f h C = 1.74098C exp(0.12327C /C ), (9) c c f c C = 0.19334C exp(0.12327C /C ). (10) c c h c Table 1. Chlorophyll concentration in four types of water (mg/m ). Pure Clean Ocean Coastal Turbid Harbor C 0 0.31 0.83 5.99 We adopt a small and large particle scattering model to get the scattering coeffi- cient of different types of water, which is a weighted summation with a pure water scattering coefficient [16]. 0 0 b(l) = b (l) + b (l)C + b (l)C , (11) w s s l 0 0 where b (l) indicates the scattering coefficient of pure water, b (l) and b (l) denote the scattering coefficients caused by small and large suspended particles, respectively [16,17], and C and C are the concentrations of both types of particles in water. The extinction coefficient c(l) is the sum of the absorption coefficient and scattering coefficient. VSF is a very important parameter in underwater channel modeling. It indicates the ratio of scattered intensity (solid angle DW centered on q) to total incident light intensity at a specific scattering angle. q indicates the scattering angle. In our model, we adopt the Kopelevich model as the VSF. Compared with the traditional Henyey–Greenstein model, Photonics 2021, 8, x FOR PEER REVIEW 5 of 13 The extinction coefficient 𝑐(𝜆) is the sum of the absorption coefficient and scattering coefficient. VSF is a very important parameter in underwater channel modeling. It indi- cates the ratio of scattered intensity (solid angle ΔΩ centered on 𝜃 ) to total incident light Photonics 2021, 8, 467 5 of 13 intensity at a specific scattering angle. 𝜃 indicates the scattering angle. In our model, we adopt the Kopelevich model as the VSF. Compared with the traditional Henyey–Green- stein model, the Kopelevich model not only covers small and large particles, but also can the be more Kopelevic accura h tel model y app not lied to hi only covers gh turbsmall id water and [9lar ]. ge particles, but also can be more accurately VSF for applied underwa to high ter a turbid pplicat water ion ca[n be expressed by t 9]. he combination of pure water, VSF for underwater application can be expressed by the combination of pure water, small particles, and large particles [16]. small particles, and large particles [16]. 0 0 p(λ,θ) = b (λ) p (θ) + b (λ) p (θ)C + b (λ) p (θ)C , (12) w R s s s l l l 0 0 p(l, q) = b (l) p (q) + b (l) p (q)C + b (l) p (q)C , (12) w s s R s l l where 𝑝 (𝜃) , 𝑝 (𝜃) , and 𝑝 (𝜃) indicate the probability density functions for pure water, small particles, and large particles, respectively. where p (q), p (q), and p (q) indicate the probability density functions for pure water, R l For the Kopelevich model, the total seawater scattering coefficient can be modeled as small particles, and large particles, respectively. follows [9]: For the Kopelevich model, the total seawater scattering coefficient can be modeled as follows [9]: 4.3 550 550 550  1.7 0.3 b λ=× 0.0017 +1.34CC ( ) +0.312 ( ) , (13) () 4.3  sl 1.7 0.3 550 550 550 λλ λ  b(l) = 0.0017 + 1.34C ( ) + 0.312C ( ) , (13) l l l where 𝐶 and 𝐶 are the concentrations of small and large particles, respectively. where C and C are the concentrations of small and large particles, respectively. We set the w s eight (unit energy) for each photon, and the energy attenuation of the We set the weight (unit energy) for each photon, and the energy attenuation of the transmitted light beam is equivalent to the change in weight. We define four main param- transmitted light beam is equivalent to the change in weight. We define four main param- eters at the transmitter: the wavelength λ, the maximum half-divergence angle 𝜃 , the eters at the transmitter: the wavelength l, the maximum half-divergence angle q , the zenith angle 𝜃 , and the azimuth angle 𝜑 . Initially, each photo is launched into wa m ta ex r with zenith angle q, and the azimuth angle j. Initially, each photo is launched into water with the given maximum half-divergence angle 𝜃 and unit weight. The initial departure the given maximum half-divergence angle q and unit weight. The initial departure max direction of the photon is determined on the basis of random variables 𝜃 and 𝜑 . The di- direction of the photon is determined on the basis of random variables q and j. The direc- rection is generated according to [−𝜃 , 𝜃 ] for 𝜃 and [0, 2π] for 𝜑 . The direction vec- tion is generated according to [q , q ] for q and [0, 2p] for j. The direction vector max max tor of emitted photons is (sin𝜃cos𝜑 , sin𝜃sin𝜑 , cos𝜃 ). After traveling at a certain distance of emitted photons is (sin q cos j, sin q sin j, cos q). After traveling at a certain distance called the free path, emitted photons might lose their energy and change their transmis- called the free path, emitted photons might lose their energy and change their transmission sion direction due to collision with particles in the underwater medium. Using a proba- direction due to collision with particles in the underwater medium. Using a probability bility model, the free path can be expressed as follows [18]: model, the free path can be expressed as follows [18]: d =−ln( ξ)/c, (14) d = ln(x)/c, (14) where 𝜉 is a random variable which obeys a uniform distribution within (0, 1]. whereDue t x is aorandom the collivariable sion with which partic obeys les in t ah uniform e underw distribution ater medium, emitted photons lose within (0, 1]. Due to the collision with particles in the underwater medium, emitted photons lose their energy and change their transmission direction. It is assumed that the weights of their energy and change their transmission direction. It is assumed that the weights of emit- emitted photons before and after collision are 𝑊 and 𝑊 , which satisfy Equation ted photons before and after collision are W and W , which satisfy Equation (15) [18]. (15) [18]. pre post W = W (1 − a/ c) . W = W (1 a/c). (15) (15) postpost prepre Once scattering occurs, the transmission direction of emitted photons is changed. The Once scattering occurs, the transmission direction of emitted photons is changed. new direction vector P2 after collision is dependent on the old direction vector P1, scatter- The new direction vector P after collision is dependent on the old direction vector P , 2 1 ing angle 𝜃 , and azimuth angle 𝜑 , as shown in Figure 2. Random variable 𝜑 satisfies a scattering angle q, and azimuth angle j, as shown in Figure 2. Random variable j satisfies uniform distribution within [0, 2π]. a uniform distribution within [0, 2]. Figure 2. Scattering pattern of emitted photons. Figure 2. Scattering pattern of emitted photons. For a single photon, VSF can be considered as the probability density function of the scattering angle. The generating methods of scattering angle for different VSFs are definitely different. As for the Kopelevich model, we use the acceptance–rejection sampling method to get the random scattering angle. According to the old transmission direction Photonics 2021, 8, 467 6 of 13 i i i vector (ux , uy , uz ), the scattering angle q, and the azimuth angle j, the transmission i+1 i+1 i+1 direction vector after scattering is represented by (ux , uy , uz ) [19]. i+1 i i u = u sin q cos f + u (cos q + sin q sin f) x y x i+1 i i u = u sin q cos f + u (cos q + sin q sin f) (16) y x y i+1 i 2 i 2 i i u = (u + u ) sin q sin f/u + u cos q z x y z z 3.3. Photocounting Receiver After several scattering events, the photons have a chance to be detected by the receiver. Since the solid angle DW of the photon scattering space is small enough, it can be assumed that the VSF among DW is constant. The variable p q of the scattering direction satisfies ( ) Z Z p 2p 1/2p p(q)dqdf = 1. (17) 0 0 By changing it into the integral of the solid angle, we get Z Z p(q) p(q) sin qdqdf = dW = 1. (18) 2p sin q 2p sin q Thus, the reception probability of the emitted photon is p(q) P = DW. (19) 2p sin q Considering the conditional probability of free path, the final reception probability becomes p(q) P = DW exp(k jr r j), (20) s r i 2p sin q where r is the position of receive window, and r is the position where the final scattering before detection happens. In our model, the threshold setting of the photon weight is 10 , as shown in Table 2. Path loss and impulse response are crucial. We can calculate the path loss by summation of all products of reception probability and receiving photon weights. As for each scattering event, the position prior to scattering is available; thus, the entire path of the photon before detection is recorded. The channel response can be calculated so long as we count the receiving intensity in a given time slot. In summary, we can get the flow chart of the Monte Carlo model as shown in Figure 3. The channel responses of different wavelengths in four types of water are shown in Figure 4. It can be seen from Figure 4a–d that the optimum transmission wavelength is switched from 450 nm (blue) to 595 nm (red) when the water condition is changed from pure to turbid harbor. Moreover, a clear multipath channel characteristic is observed due to heavy scattering as illustrated Figure 4d, which is consistent with the results in [17]. The theoretical analysis and impulse response results under different water conditions guide the design of the experimental system. We can select the optimal wavelength according to the different water conditions to achieve the maximum data rate and the maximum transmission distance. Table 2. Simulation parameters. Symbol Physical Meaning Value l Incident optical wavelength (unit: nm) 400, 450, 500, 550, and 595 Initial maximum half-divergence angle (random q 8.2 0,max generation within [0, 2p]) Statistical random variable for free path (random x 0.6 generation within (0, 1]) W Decision weight at the receiver >10 Photonics 2021, 8, x FOR PEER REVIEW 7 of 13 Photonics 2021, 8, x FOR PEER REVIEW 7 of 13 Table 2. Simulation parameters. Table 2. Simulation parameters. Symbol Physical Meaning Value Symbol Physical Meaning Value 𝜆 Incident optical wavelength (unit: nm) 400, 450, 500, 550, and 595 𝜆 Incident optical wavelength (unit: nm) 400, 450, 500, 550, and 595 Initial maximum half-divergence angle Initial maximum half-divergence angle 𝜃 8.2° , 8.2° (( rr aa n n dom genera dom genera ti ti on on wi wi thin [0 thin [0 , , 22 π π ]) ]) St St at at ist ist ii ca ca l r l r aa n n d d om var om var ii ab ab le le for for free p free p aa tt h h Photonics 2021, 8, 467 7 of 13 𝜉 0.6 𝜉 0.6 (random generation within (0, 1]) (random generation within (0, 1]) −− 44 𝑊 Decision weight at the receiver >10 𝑊 Decision weight at the receiver >10 -4 -4 Free path d W=(1-a/c)>10 Free path d W=(1-a/c)>10 1st scattering point Receiving probability 1st scattering point Receiving probability 2 -4 2 -4 Free path d WW=(=(1-1-a/a/cc))>1>100 Free path d 2nd scattering point Receiving probability 2nd scattering point Receiving probability Y N N Cycle the above Cycle the above End End process Save scattering position process Save scattering position Figure 3. Flow chart of Monte Carlo model for photocounting receiver. Figure 3. Flow chart of Monte Carlo model for photocounting receiver. Figure 3. Flow chart of Monte Carlo model for photocounting receiver. 0.014 0.1 0.014 0.1 400nm 400nm 400nm 400nm 450nm 450nm 450nm 0.09 450nm 0.09 500nm 500nm 0. 0. 012 012 500nm 500nm 550nm 0.08 550nm 550nm 0.08 550nm 595nm 595nm 595nm 595nm 0.01 0.01 0.07 0.07 0.06 0.06 0.008 0.008 0. 0. 05 05 00 .006 .006 0.04 0.04 0.03 0.03 0.004 0.004 0.02 0.02 (b) clean ocean water (a) pure water (b) clean ocean water (a) pure water 0. 0. 002 002 0.01 0.01 @150m @50m @150m @50m 00 0 461 10 12 146 18 20 0 2 4 6 8 10 12 14 16 16 18 20 20 02 02 461 88 10 12 146 18 20 0 2 4 6 8 10 12 14 18 t(ns) t(ns) t(ns) t(ns) -1-1 ×10 ×10 0.035 0.035 0.018 0.018 400nm 400nm 400nm 400nm 450nm 450nm 450nm 450nm 0.016 0.016 500nm 500nm 0.03 500nm 500nm 0.03 550nm 550 550 nm nm 550nm 0.014 0.014 595 595 nm nm 595 595 nm nm 0.025 0.025 0.012 0.012 (d) turbid harbor water (d) turbid harbor water 0.02 0.01 0.02 0.01 @8m @8m 0.00 0.00 88 0.015 0.015 0.006 0.006 0.0 0.0 11 0.004 0.004 (c) coastal water (c) coastal water 0.002 0.005 0.002 0.005 @30m @30m 0 6 12 14 16 18 20 0 10 15 20 25 30 35 40 0 2 4 6 88 10 10 12 14 16 18 20 0 55 10 15 20 25 30 35 40 2 4 t(ns) t(ns) t(ns) t(ns) Figure 4. Channel response of different wavelengths in four types of water. The launched wave- Figure 4. Channel response of different wavelengths in four types of water. The launched wave- Figure 4. Channel response of different wavelengths in four types of water. The launched wave- lengths were set to 400 nm, 450 nm, 500 nm, 550 nm, and 595 nm, respectively. (a) pure water (𝑐 = lengths were set to 400 nm, 450 nm, 500 nm, 550 nm, and 595 nm, respectively. (a) pure water (𝑐 = lengths were set to 400 nm, 450 nm, 500 nm, 550 nm, and 595 nm, respectively. (a) pure water −1 −1 −1 −1 −1 −1 0.056 m ), (b) clean ocean water (𝑐 = 0.151 m ); (c) coastal water (𝑐 = 0.398 m ); (d) turbid harbor 0.056 m ), ( b1 ) clean ocean water (𝑐 = 0.151 m ); (c) coastal wa 1 ter (𝑐 = 0.398 m ); (d) turbid harbor 1 (c = 0.056 m ), (b) clean ocean water (c = 0.151 m ); (c) coastal water (c = 0.398 m ); (d) turbid −1 −1 water ( 𝑐 = 2.17 m ). water ( 𝑐 = 2.17 m ). harbor water ( c = 2.17 m ). 4. Experiment and Results 4. 4. Ex Experiment periment and and Re Results sults 4.1. Experimental Setup and Paraeters 4.1. Experimental Setup and Paraeters 4.1. Experimental Setup and Paraeters Figure 5 shows a schematic diagram of our experimental UOWC system using a blue Figure 5 shows a schematic diagram of our experimental UOWC system using a blue Figure 5 shows a schematic diagram of our experimental UOWC system using a blue LED source and PMT receiver (Hamamatsu, model CR315). An inclination angle of 5 is LED source and PMT receiver (Hamamatsu, model CR315). An inclination angle of 5° is LED source and PMT receiver (Hamamatsu, model CR315). An inclination angle of 5° is introduced to the transceiver, which causes huge attenuation to build a non-line-of-sight iin ntroduced to the tra troduced to the tran nscei sceiver, ver, wh which ich causes huge causes huge attenuatio attenuation to n to bui builld d aa n no on- n-li lin nee--o of- f-ssiig gh htt link. All the signal processing modules are implemented offline by MATLAB. At the link. All the signal processing modules are implemented offline by MATLAB. At the trans- link. All the signal processing modules are implemented offline by MATLAB. At the trans- transmitter, a pseudo-random bit sequence (PRBS) is generated and then sampled by an mitter, a pseudo-random bit sequence (PRBS) is generated and then sampled by an arbi- mitter, a pseudo-random bit sequence (PRBS) is generated and then sampled by an arbi- arbitrary signal generator (AWG) running at 10 MSa/s (1 Mbps), 20 MSa/s (2 Mbps), trary signal generator (AWG) running at 10 MSa/s (1 Mbps), 20 MSa/s (2 Mbps), 50 MSa/s trary signal generator (AWG) running at 10 MSa/s (1 Mbps), 20 MSa/s (2 Mbps), 50 MSa/s 50 MSa/s (5 Mbps), and 100 MSa/s (10 Mbps). Then, the baseband signals combined (5 Mbps), and 100 MSa/s (10 Mbps). Then, the baseband signals combined with a DC bias (5 Mbps), and 100 MSa/s (10 Mbps). Then, the baseband signals combined with a DC bias with a DC bias are injected into the LED. Compared with LD, the LED-based transmitter are are injected injected into the LED. into the LED. Compared w Compared w iith LD, the th LD, the LE LED-based tr D-based tran ansmitter has n smitter has no o need of need of has no need of strict alignment or high emission power. A real-time oscilloscope is used to convert the analog signal into the digital domain. Simple digital signal processing (DSP) algorithms are applied at the receiving end, such as synchronization, decision, and BER calculation. The data length of each frame is 1151 bits, of which 127 bits are used for synchronization. We use multiple frames of information to increase the number of calculated bits. The number of effective bits used to calculate the BER was 20,718. To avoid synchronization problems, we increased the number of synchronization header bits. Unlike the conventional waveform sampling amplitude demodulation method, the photon- counting pulse signals need to be judged. When the amplitude of the sampled pulse is above the decision threshold voltage (DTV) V , one photon is counted. Final decisions on h(t) h(t) Generation of photon h(t) h(t) Generation of photon (θ , , , W) (θ 0,max, , , W) 0,max h(t) h(t) h(t) h(t) Photonics 2021, 8, x FOR PEER REVIEW 8 of 13 strict alignment or high emission power. A real-time oscilloscope is used to convert the analog signal into the digital domain. Simple digital signal processing (DSP) algorithms are applied at the receiving end, such as synchronization, decision, and BER calculation. The data length of each frame is 1151 bits, of which 127 bits are used for synchronization. We use multiple frames of information to increase the number of calculated bits. The num- ber of effective bits used to calculate the BER was 20,718. To avoid synchronization prob- lems, we increased the number of synchronization header bits. Unlike the conventional Photonics 2021, 8, 467 8 of 13 waveform sampling amplitude demodulation method, the photon-counting pulse signals need to be judged. When the amplitude of the sampled pulse is above the decision thresh- old voltage (DTV) VD, one photon is counted. Final decisions on symbol “1” or “0” are made by the counted average values in each symbol. Thus, the BER value can be calcu- symbol “1” or “0” are made by the counted average values in each symbol. Thus, the BER lated according to the hard threshold 𝑛 . Some key parameters of the proposed UOWC value can be calculated according to the hard threshold n . Some key parameters of the th system are summarized an proposed UOWC system ar d elisted in summarized Table and 3. listed in Table 3. DC PC generated 5° BER Cacul. OOK PMT Water tank AWG PRBS modulation Sync 10 m Bias-T Scope &Decision Offline processing Figure 5. Figure 5. Exper Experimental imental setup of LED– setup of LED–PMT PMT U UOWC OWC sy system stem with 5° m with 5 misalignment isalignment between transm between transmitter itter a and nd rece receiver iver.. PR PRBS: BS: pseudo-random bit sequence, AWG: arbitrary signal generator. pseudo-random bit sequence, AWG: arbitrary signal generator. Table 3. Key parameters of the proposed UOWC system. Table 3. Key parameters of the proposed UOWC system. Symbol Physical Meaning Value/Unit Symbol Physical Meaning Value/Unit m1 Lambertian order 2.9 × 10 m Lambertian order 2.9  10 f𝜙 Angle Angle of irradiance of irradiance 5 5° f Half-power semi-angle of LED 1.25 𝜙 1/2 Half-power semi-angle of LED 1.25° z Transmission distance 10 m z Transmission distance 10 m h E/O conversion efficiency 0.1289 𝜂 E/O conversion efficiency 0.1289 P Transmitted electrical power 1 W RPt Transm Transmitted itted data elect rate rical power 1/2/5 Mbps 1 W Rb Transmitted data rate 1/2/5 Mbps 4.2. Attenuation Coefficient Measurement 4.2. Attenuation Coefficient Measurement Water quality significantly impacts the BER performance. The PMT receiver is more Water quality significantly impacts the BER performance. The PMT receiver is more sensitive to optical power than other light-sensitive devices such as an APD. Ambient light sensitive to optical power than other light-sensitive devices such as an APD. Ambient light may annihilate signals. Thus, the experimental system should be thoroughly shaded with may annihilate signals. Thus, the experimental system should be thoroughly shaded with black nonreflective material. Our experimental channel was a 10 m long water tank with b alack volume nonre of fl3 ect m iv.e m Light ateri absorption al. Our expand erimscattering ental chann in el w seawater as a 10 m are lon caused g watby er t inor ankganic with a volume of 3 m . Light absorption and scattering in seawater are caused by inorganic salts and planktonic plants. Some previous studies have shown that a similar effect of salts and planktonic plants. Some previous studies have shown that a similar effect of aluminum hydroxide or magnesium hydroxide to seawater is observed on the light of alumin particles um hydroxide or m [20]. In the experiment, agnesium hydroxide to we added different concentrations seawater is observed on the light of of aluminum hydroxide part to picle ures water [20]. In t to simulate he experiseawater ment, we ad with dedif d di fer fferent c ent degr oncentrations ees of turbidity of al , i.e., uminum pure seawater hydrox-, clean seawater, coastal seawater, and harbor seawater, characterized by the parameters of ide to pure water to simulate seawater with different degrees of turbidity, i.e., pure sea- wat attenuation er, clean s coef eaw ficients. ater, coastal seawater, and harbor seawater, characterized by the param- P 1 eters of attenuation coefficients. c = ln . + c . (21) P z P 1 In the experiment, we could not directly measure the relationship between the at- cc =+ ln . (21) tenuation coefficient and the aluminum hydroxide concentration due to the presence of Pz an off-angle at the transmitter. A preliminary experiment was carried out using an LD In the experiment, we could not directly measure the relationship between the atten- with very narrow divergence angle and a high-sensitivity optical power meter. Because of uation coefficient and the aluminum hydroxide concentration due to the presence of an the reflection and absorption caused by the glass wall, we used Equation (21) to measure off-angle at the transmitter. A preliminary experiment was carried out using an LD with the relative attenuation coefficient. The results are shown in Figure 6a. We can see an very approximate narrow divergenc linear relationship e angle an between d a high-sen the alumin sitivity opti um hydr cal power meter. Because of th oxide concentration and the e attenuation coefficient. The parameter c is the measured attenuation coefficient, and c is the attenuation coefficient of pure seawater with a value of 0.056 m . The shaded tank was filled with pure water. Then, we added aluminum hydroxide powder to the water at a mass of 3 g each time and measured the ROP as P . Figure 6b shows the measured curve of the ROP as a function of the attenuation coefficient varying from 0.2 m to 1.3 m for different data rates. It can be seen from Figure 3b that the ROP was about 78 dBm for a 2 Mbps data rate at c = 1.3 m , which means that a total loss of 99 dB was introduced (launched optical power was 21 dBm). The values of ROP were calculated using the average number of experimentally counted photons according to Equation (22). Photonics 2021, 8, x FOR PEER REVIEW 9 of 13 reflection and absorption caused by the glass wall, we used Equation (21) to measure the relative attenuation coefficient. The results are shown in Figure 6a. We can see an approx- imate linear relationship between the aluminum hydroxide concentration and the attenu- ation coefficient. The parameter c is the measured attenuation coefficient, and 𝑐 is the −1 attenuation coefficient of pure seawater with a value of 0.056 m . The shaded tank was filled with pure water. Then, we added aluminum hydroxide powder to the water at a mass of 3 g each time and measured the ROP as Pc. Figure 6b shows the measured curve −1 −1 of the ROP as a function of the attenuation coefficient varying from 0.2 m to 1.3 m for different data rates. It can be seen from Figure 3b that the ROP was about −78 dBm for a 2 −1 Mbps data rate at c = 1.3 m , which means that a total loss of 99 dB was introduced Photonics 2021, 8, 467 9 of 13 (launched optical power was 21 dBm). The values of ROP were calculated using the aver- age number of experimentally counted photons according to Equation (22). 2.00 −65 1Mb/s 2Mb/s (a) (b) 1.60 5Mb/s 10Mb/s −70 1.20 0.80 −75 Fitting 0.40 Measured −80 0.00 0.2 0.4 0.6 0.8 1 1.2 1.4 02468 10 -1 c(m ) C (g/m ) Figure 6. (a) Attenuation coefficient as a function of aluminum hydroxide concentration and (b) Figure 6. (a) Attenuation coefficient as a function of aluminum hydroxide concentration and (b) re- received optical power (ROP) under different water turbidities after 10 m underwater channel. ceived optical power (ROP) under different water turbidities after 10 m underwater channel. 4.3. Measured BER Performance 4.3. Measured BER Performance In our experiment, we used a Hamamatsu PMT with a spectral response range from In our experiment, we used a Hamamatsu PMT with a spectral response range from 300 nm to 650 nm as the receiver. The quantum efficiency of the PMT was 5%, and the 300 nm to 650 nm as the receiver. The quantum efficiency of the PMT was 5%, and the typical dark count was 20 counts/sec. The number of photons counted in symbol “1” was typical dark count was 20 counts/sec. The number of photons counted in symbol “1” was contributed by the signal and the background light, while the photons counted in symbol contributed by the signal and the background light, while the photons counted in symbol “0” were caused by the background light and inter-symbol interference. An RZ code with a “0” were caused by the background light and inter-symbol interference. An RZ code with duty cycle of 0.7 was designed according to Equation (22), since the ROP can be maximized a duty cycle of 0.7 was designed according to Equation (22), since the ROP can be maxim- and a clock frequency component is included [21], where x is the quantum efficiency of ized and a clock frequency component is included [21], where 𝜉 is the quantum efficiency PMT, h is Planck’s constant, n is the frequency of light, T is the symbol duration, and n b 1 of PMT, h is Planck’s constant, ν is the frequency of light, Tb is the symbol duration, and and n are the average numbers of photons contained in symbols “1” and “0”. n1 and 𝑛 are the average numbers of photons contained in symbols “1” and “0”. 1 7 hn(n n ) 1 0 17 hn ν() −n P = . . 10. (22) r,P MT P = .. (22) x 20 T rP, MT ξ 20 T According to the measured results shown in Figure 7, when the number of received According to the measured results shown in Figure 7, when the number of received photons was less than 20, the measured data followed a relatively strict Poisson distribution photons was less than 20, the measured data followed a relatively strict Poisson distribu- since the PMT worked in the linear region. Upon increasing the number of photos to 40, the tion since the PMT worked in the linear region. Upon increasing the number of photos to PMT was subjected to overexposure and worked in the nonlinear region, thus experiencing 40, the PMT was subjected to overexposure and worked in the nonlinear region, thus ex- signal distortion [21]. In this condition, the distribution of the counted photons does not periencing signal distortion [21]. In this condition, the distribution of the counted photons obey a strict Poisson distribution, as shown in Figure 7. The BER value can be calculated does not obey a strict Poisson distribution, as shown in Figure 7. The BER value can be using Equation (23), where n is the hard-decision threshold [5]. th calculated using Equation (23), where 𝑛 is the hard-decision threshold [5]. n 1 th n k n k 1 k 1 0 k n n 1 0 n n n 0 n n −1 1 th k! 1 ∞ k!0 BER = e + e , n = . (23) å −−nn å th 11 nn − Photonics 2021, 8, x FOR PEER REVIEW 2 kk!! 2 ln n ln n 10 of 13 1 0 BER== k=0 e + k=n e ,n . (23)  th th 22 lnnn −ln kk == 0 n  10 th 0.16 0.12 Poisson Poisson (a) (b) Measured Measured 0.12 0.08 0.08 0.04 0.04 0 0.00 0 5 10 15 20 25 30 35 40 45 50 55 60 Number of photons Number of photons Figure 7. Distribution of the received photons: (a) seven photons; (b) 40 photons. Figure 7. Distribution of the received photons: (a) seven photons; (b) 40 photons. We present the measured BER performance under different water conditions in We present the measured BER performance under different water conditions in Fig- Figure 8. As discussed before, when the number of received photons is increased to around ure 8. As discussed before, when the number of received photons is increased to around 20 (~73 dBm), the number of the received photons no longer obeys a Poisson distribution. 20 (~−73 dBm), the number of the received photons no longer obeys a Poisson distribution. At this moment, the values of V should also be adjusted. In our experiment, the optimal At this moment, the values of 𝑉 D should also be adjusted. In our experiment, the optimal values of 𝑉 were obtained according to the rule of minimizing the BER. As illustrated in Figure 6b, an ROP of −73 dBm corresponded to a 10 m underwater transmission with an −1 attenuation coefficient of 0.8 m . When the PMT worked in photon-counting mode (𝑐 > −1 0.8 m ), the number of photons in symbol “1” obeyed a strict Poisson distribution. Thus, the value of DTV 𝑉 was set to 2.5 mV. However, the measured BER performance wors- ened, especially for 1 Mbps and 2 Mbps data rates, when the attenuation coefficients var- −1 −1 ied from 0.2 m to 0.8 m (saturation region of PMT). With the adapted optimal value of 𝑉 = 4.5 mV, error-free transmissions of 1 Mbps and 2 Mbps data rates were successfully achieved. The BER performance enhancement at the 5 Mbps data rate was not significant, because, when increasing the signal baud rate, severe inter-symbol interference was in- troduced due to the limited bandwidth of LED. Moreover, conclusions can be made ac- cording to Figure 8 that the receiver sensitivities of our proposed LED–UOWC systems at −1 −1 1 Mbps, 2 Mbps, and 5 Mbps data rates were −76 dBm (1.08 m ), −74 dBm (0.92 m ), and −1 −3 −70 dBm (0.24 m ) at the 7% FEC limit of 3.8 × 10 , respectively. 1Mb/s, 2.5mV 1Mb/s, 4.5mV 2Mb/s, 2.5mV 2Mb/s, 4.5mV 1 × 10 5Mb/s, 2.5mV 5Mb/s, 4.5mV 7% FEC limit −1 1 × 10 −2 1 × 10 −3 1 × 10 −4 1 × 10 −5 1 × 10 0.2 0.4 0.6 0.8 1 1.2 1.4 -1 c(m ) Figure 8. Experimental BER performance under different water turbidities after 10 m. 4.4. The Predicted Performance Based on the Proposed System As illustrated in Figure 9, we further investigated the proposed system performance −1 under conditions of the first type of seawater (pure, c = 0.056 m ), the second type (clean, −1 −1 c = 0.151 m ), and the third type (coastal, c = 0.398 m ). According to the experimental results illustrated in Figure 4, the required ROP for 2 Mbps at the 7% FEC limit is −74 dBm. Using Equation (4) and the parameters in Table 1, the optical power distribution at the receiving plane within the receiver sensitivity of −74 dBm was established using Lamber- tian model. Within the receiving radii of 1.28 m, 0.62 m, and 0.29 m, the achievable dis- tances were 83.5 m, 40.5 m, and 19.2 m for the first, second, and third types of seawater, -1 c(m ) Rate BER ROP(dBm) Rate Photonics 2021, 8, x FOR PEER REVIEW 10 of 13 0.16 0.12 Poisson Poisson (a) (b) Measured Measured 0.12 0.08 0.08 0.04 0.04 0 0.00 0 5 10 15 20 25 30 35 40 45 50 55 60 Number of photons Number of photons Figure 7. Distribution of the received photons: (a) seven photons; (b) 40 photons. We present the measured BER performance under different water conditions in Fig- Photonics 2021, 8, 467 10 of 13 ure 8. As discussed before, when the number of received photons is increased to around 20 (~−73 dBm), the number of the received photons no longer obeys a Poisson distribution. At this moment, the values of 𝑉 should also be adjusted. In our experiment, the optimal values of V were obtained according to the rule of minimizing the BER. As illustrated values of 𝑉 were obtained according to the rule of minimizing the BER. As illustrated in in Figure 6b, an ROP of 73 dBm corresponded to a 10 m underwater transmission with Figure 6b, an ROP of −73 dBm corresponded to a 10 m underwater transmission with an −1 an attenuation coefficient of 0.8 m . When the PMT worked in photon-counting mode attenuation coefficient of 0.8 m . When the PMT worked in photon-counting mode (𝑐 > −1 (c > 0.8 m ), the number of photons in symbol “1” obeyed a strict Poisson distribution. 0.8 m ), the number of photons in symbol “1” obeyed a strict Poisson distribution. Thus, Thus, the value of DTV V was set to 2.5 mV. However, the measured BER performance the value of DTV 𝑉 was set to D 2.5 mV. However, the measured BER performance wors- worsened, especially for 1 Mbps and 2 Mbps data rates, when the attenuation coefficients ened, especially for 1 Mbps and 2 Mbps data rates, when the attenuation coefficients var- 1 1 varied from 0.2 m to 0.8 m (saturation region of PMT). With the adapted optimal −1 −1 ied from 0.2 m to 0.8 m (saturation region of PMT). With the adapted optimal value of value of V = 4.5 mV, error-free transmissions of 1 Mbps and 2 Mbps data rates were 𝑉 = 4.5 mV, error-free transmissions of 1 Mbps and 2 Mbps data rates were successfully successfully achieved. The BER performance enhancement at the 5 Mbps data rate was not achieved. The BER performance enhancement at the 5 Mbps data rate was not significant, significant, because, when increasing the signal baud rate, severe inter-symbol interference because, when increasing the signal baud rate, severe inter-symbol interference was in- was introduced due to the limited bandwidth of LED. Moreover, conclusions can be made troduced due to the limited bandwidth of LED. Moreover, conclusions can be made ac- according to Figure 8 that the receiver sensitivities of our proposed LED–UOWC systems cording to Figure 8 that the receiver sensitivities of our proposed LED–UOWC systems at 1 1 at 1 Mbps, 2 Mbps, and 5 Mbps data rates were 76 dBm (1.08 m ), 74 dBm (0.92 m ), −1 −1 1 Mbps, 2 Mbps, and 5 Mbps data rates were −76 dBm (1.08 m ), −74 dBm (0.92 m ), and 1 3 and 70 dBm (0.24 m ) at the 7% FEC limit of 3.8  10 , respectively. −1 −3 −70 dBm (0.24 m ) at the 7% FEC limit of 3.8 × 10 , respectively. 1Mb/s, 2.5mV 1Mb/s, 4.5mV 2Mb/s, 2.5mV 2Mb/s, 4.5mV 1 × 10 5Mb/s, 2.5mV 5Mb/s, 4.5mV 7% FEC limit −1 1 × 10 −2 1 × 10 −3 1 × 10 −4 1 × 10 −5 1 × 10 0.2 0.4 0.6 0.8 1 1.2 1.4 -1 c(m ) Figure 8. Figure 8. Ex Experimental perimental BER BER pe performance rformance u under nder di dif fferent water turbidities after 10 m. ferent water turbidities after 10 m. 4.4. The Predicted Performance Based on the Proposed System 4.4. The Predicted Performance Based on the Proposed System As illustrated in Figure 9, we further investigated the proposed system performance As illustrated in Figure 9, we further investigated the proposed system performance under conditions of the first type of seawater (pure, c = 0.056 m ), the second type (clean, −1 under conditions of the first type of seawater (pure, c = 0.056 m ), the second type (clean, 1 1 c = 0.151 m ), and the third type (coastal, c = 0.398 m ). According to the experimental −1 −1 c = 0.151 m ), and the third type (coastal, c = 0.398 m ). According to the experimental results illustrated in Figure 4, the required ROP for 2 Mbps at the 7% FEC limit is74 dBm. results illustrated in Figure 4, the required ROP for 2 Mbps at the 7% FEC limit is −74 dBm. Using Equation (4) and the parameters in Table 1, the optical power distribution at the re- Using Equation (4) and the parameters in Table 1, the optical power distribution at the ceiving plane within the receiver sensitivity of74 dBm was established using Lambertian receiving plane within the receiver sensitivity of −74 dBm was established using Lamber- model. Within the receiving radii of 1.28 m, 0.62 m, and 0.29 m, the achievable distances tian model. Within the receiving radii of 1.28 m, 0.62 m, and 0.29 m, the achievable dis- were 83.5 m, 40.5 m, and 19.2 m for the first, second, and third types of seawater, respec- tances were 83.5 m, 40.5 m, and 19.2 m for the first, second, and third types of seawater, tively. The maximum transmission distances could be extended to 100 m, 46 m, and 21 m when the receiver was located in the center of the receiving plane, as depicted in Figure 10. With a transmitted electrical power of 10 W, the maximum distances were further increased to 134 m, 60 m, and 27 m. When c exceeded the value of 0.92 m (ROP = 74 dBm), as shown in Figure 8, the BER performance for the 2 Mbps signal became worse than the 7% FEC limit. The calculated optical power based on Equation (22) was 74.37 dBm in this condition, which is consistent with the optical power distribution obtained by the Lambertian model, as shown in Figure 9. The experimental 2 Mbps data rate after 10 2 2 m could achieve a receiving area of p  0.15 = 0.07 m . Thus, it is believed that our proposed long-reach UOWC system is capable of achieving an Mbps-scale data rate with an alignment-released configuration. Rate BER Rate Photonics 2021, 8, x FOR PEER REVIEW 11 of 13 Photonics 2021, 8, x FOR PEER REVIEW 11 of 13 respectively. The maximum transmission distances could be extended to 100 m, 46 m, and respectively. The maximum transmission distances could be extended to 100 m, 46 m, and 21 m when the receiver was located in the center of the receiving plane, as depicted in Figure 21 m when the receiver was located in the center of the receiving plane, as depicted in Figure 10. With a transmitted electrical power of 10 W, the maximum distances were further in- 10. With a transmitted electrical power of 10 W, the maximum distances were further in- −1 creased to 134 m, 60 m, and 27 m. When c exceeded the value of 0.92 m (ROP = −74 dBm), −1 creased to 134 m, 60 m, and 27 m. When c exceeded the value of 0.92 m (ROP = −74 dBm), as shown in Figure 8, the BER performance for the 2 Mbps signal became worse than the 7% as shown in Figure 8, the BER performance for the 2 Mbps signal became worse than the 7% FEC limit. The calculated optical power based on Equation (22) was −74.37 dBm in this con- FEC limit. The calculated optical power based on Equation (22) was −74.37 dBm in this con- dition, which is consistent with the optical power distribution obtained by the Lambertian dition, which is consistent with the optical power distribution obtained by the Lambertian model, as shown in Figure 9. The experimental 2 Mbps data rate after 10 m could achieve a model, as shown in Figure 9. The experimental 2 Mbps data rate after 10 m could achieve a receiving area of π × 0.15 = 0.07 m . Thus, it is believed that our proposed long-reach Photonics 2021, 8, 467 11 of 13 receiving area of π × 0.15 = 0.07 m . Thus, it is believed that our proposed long-reach UOWC system is capable of achieving an Mbps-scale data rate with an alignment-released UOWC system is capable of achieving an Mbps-scale data rate with an alignment-released configuration. configuration. Figure 9. Optical power distribution at the receiving plane within the receiver sensitivity of Figure 9. Optical power distribution at the receiving plane within the receiver sensitivity of −74 Figure 9. Optical power distribution at the receiving plane within the receiver sensitivity of −74 1 1 −1 −1 dBm: (a) c = 0.056 m , z = 83.5 m, 𝐷 = 1.28 m; (b) c = 0.151 m , z = 40.5 m, 𝐷 = 0.62 m; (c) c = 74 dBm: (a) c = 0.056 −1 m , z = 83.5 m, D = 1.28 m; (b) c =−1 0.151 m , z = 40.5 m, D = 0.62 m; r r dBm: (a) c = 0.056 m , z = 83.5 m, 𝐷 = 1.28 m; (b) c = 0.151 m , z = 40.5 m, 𝐷 = 0.62 m; (c) c = −1 −1 1 1 0.398 m , z = 19.2 m, 𝐷 = 0.29 m; (d) c = 0.92 m , z = 10 m,. 𝐷 = 0.15 m. −1 −1 (c) c = 0.398 m , z = 19.2 m, D = 0.29 m; (d) c = 0.92 m , z = 10 m,. D = 0.15 m. r r 0.398 m , z = 19.2 m, 𝐷 = 0.29 m; (d) c = 0.92 m , z = 10 m,. 𝐷 = 0.15 m. pure, 1W pure, 10W pure, 1W pure, 10W clean, 1W clean, 10W clean, 1W clean, 10W coastal, 1W coastal, 10W coastal, 1W coastal, 10W -74dBm receiver sensitivity -74dBm receiver sensitivity −50 −50 −100 −100 −150 −150 −200 −200 21m 27m 46m 60m 100m 134m 21m 27m 46m 60m 100m 134m −250 −250 −300 −300 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140 Distance(m) Distance(m) Figure 10. The predicted maximum distances using the proposed system. Figure Figure 10. 10. The The pr predicte edicted d maxi maximum mum distances using the prop distances using the proposed osed system. system. 5. Discussion 5. Discussion 5. Discussion To build To build a lon a long-range g-range UO UOWC WC link o link or r tto o propagat propagate e li light ght th thr rough rel ough relative ative tturbid urbid wat water er, , To build a long-range UOWC link or to propagate light through relative turbid water, two factors n two factors need eed to be con to be consider sider ed: ed: (i) (i) p pointing ointing and and alignment, alignment, an and (ii) d (imultipath i) multipath interfer interference - . two factors need to be considered: (i) pointing and alignment, and (ii) multipath interfer- ence. ence. 5.1. Pointing and Alignment To maintain a reliable line-of-sight UOWC link using an LD source after long-distance transmission is very difficult, since the optical beam is quite narrow. At this moment, pointing errors usually occur because of the link misalignment. Using a beam spread function, the link misalignment model for a UOWC system can be expressed as follows [3]: 8 9 2 3 ¥ L Z Z < = cL cL 4 5 BSF(L, r) = E(L, r)e + E(L, J)e  exp bb(J(L z))dz 1 J (Jr)JdJ, (24) : ; 0 0 ROP(dBm) ROP(dBm) Photonics 2021, 8, 467 12 of 13 where BSF(L, r) is the irradiance distribution at the receiver plane. Employing a LED source with a large beam size corresponds to a large receiving range. Thus, we can get the irradiance distribution more accessibly at the receiver plane. 5.2. Multipath Interference As illustrated in Figure 4d, a multipath interference effect is produced in an optical turbid harbor underwater channel after 8 m transmission. For a certain data rate, the effect of multipath interference eventually leads to time spreading and waveform distortion, thus decreasing the BER performance due to the inter-symbol interference. Thus, when designing a UOWC system, this issue should be taken into consideration. Fortunately, technologies such as channel equalization [22], adaptive optics, and spatial diversity [23] are capable of suppressing the interference. 6. Conclusions In this paper, we demonstrated a high-sensitivity long-reach UOWC system using LED and PMT. An experiment was conducted to investigate the BER performance under different water turbidities. Several key factors were taken into consideration during the system design, such as symbol rates, symbol duty cycles, water conditions, PMT characteristics, and decision criteria. With the help of RZ-OOK modulation and a PMT receiver, we experimentally achieved receiver sensitivities of 76 dBm, 74 dBm, and 70 dBm for 1 Mbps, 2 Mbps, and 5 Mbps data rates over a 10 m underwater channel, respectively. More than 100 m distance is achievable for a 2 Mbps data rate in pure seawater at 1 W transmitted power. Author Contributions: C.L. and Z.L. contributed equally; C.L. and Z.L. performed the investiga- tion and experiment; C.L. performed the analytical calculations and wrote the original draft; D.C. conducted the underwater channel simulation; X.D., F.Y., S.L., and Z.H. discussed the experimen- tal results and revised the manuscript. All authors read and agreed to the published version of the manuscript. Funding: This work was supported by the National Natural Science Foundation of China (12174002, 11874012), the Anhui Provincial Natural Science Foundation of China (1808085MF186), the China Postdoctoral Science Foundation (2021M690179), the Beijing Postdoctoral research Foundation (2021- ZZ-093), the Innovation project for the Returned Overseas Scholars of Anhui Province (2021LCX011), the Key Research and Development Plan of Anhui Province (202104a05020059), the University Synergy Innovation Program of Anhui Province (GXXT-2020-052), and the Project of State Key Labo- ratory of Environment-Friendly Energy Materials, Southwest University of Science and Technology (19FKSY0111). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. References 1. Stojanovic, M. Recent advances in high-speed underwater acoustic communications. IEEE J. 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In Proceedings of the Ocean Optics XIV CD-ROM, Kailua-Kona, HI, USA, 10–13 November 1998; pp. 1–7. 17. Gabriel, C.; Khalighi, M.-A.; Bourennane, S.; Léon, P.; Rigaud, V. Monte-Carlo-based channel characterization for underwater optical communication systems. J. Opt. Commun. Netw. 2013, 5, 1–12. [CrossRef] 18. Ishimaru, A. Wave Propagation and Scattering in Random Media; IEEE Press: Piscataway, NJ, USA, 1997. 19. Bohren, C.-F.; Huffman, D.-R. Absorption and Scattering of Light by Small Particles; Wiley: Hoboken, NJ, USA, 1988. 20. Pontbriand, C.; Farr, N.; Ware, J.; Preisig, J.; Popenoe, H. Diffuse high-bandwidth optical communications. In Proceedings of the IEEE OCEANS, Quebec City, QC, Canada, 15–18 September 2008; pp. 15–18. 21. Ning, J.; Gao, G.; Zhang, J.; Peng, H.; Guo, Y. Adaptive receiver control for reliable high-speed underwater wireless optical communication with photomultiplier tube receiver. IEEE Photonics J. 2021, 13, 1–7. [CrossRef] 22. Jaruwatanadilok, S. Underwater wireless optical communication channel modeling and performance evaluation using vector radiative transfer theory. IEEE J. Sel. Areas Commun. 2008, 26, 1620–1627. [CrossRef] 23. Jamali, M.-V.; Salehi, J.-A.; Akhoundi, F. Performance studies of underwater wireless optical communication systems with spatial diversity: MIMO scheme. IEEE Trans. Commun. 2016, 65, 1176–1192. [CrossRef] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Photonics Multidisciplinary Digital Publishing Institute

Experimental Demonstration of High-Sensitivity Underwater Optical Wireless Communication Based on Photocounting Receiver

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hv photonics Article Experimental Demonstration of High-Sensitivity Underwater Optical Wireless Communication Based on Photocounting Receiver 1 , 2 3 4 5 1 1 Chao Li * , Zichen Liu , Daomin Chen , Xiong Deng , Fulong Yan , Siqi Li and Zhijia Hu Information Materials and Intelligent Sensing Laboratory of Anhui Province, Anhui University, Hefei 230601, China; sqli@ahu.edu.cn (S.L.); zhijiahu@ahu.edu.cn (Z.H.) Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China; lzc8888@hust.edu.cn Shanghai Huawei Technology Co., Ltd., Shanghai 200001, China; chendaomin@huawei.com Center for Information Photonics and Communications, School of Information Science and Technology, Southwest Jiaotong University, Chengdu 611756, China; xiongdeng@swjtu.edu.cn Alibaba Cloud, Alibaba Group, Beijing 100102, China; yanfulong.yfl@alibabainc.com * Correspondence: chao.li@ahu.edu.cn Abstract: In this paper, we propose a high-sensitivity long-reach underwater optical wireless commu- nication (UOWC) system with an Mbps-scale data rate. Using a commercial blue light-emitting diode (LED) source, a photon counting receiver, and return-to-zero on–off keying modulation, a receiver sensitivity of 70 dBm at 7% FEC limit is successfully achieved for a 5 Mbps intensity modulation direct detection UOWC system over 10 m underwater channel. For 1 Mbps and 2 Mbps data rates, the receiver sensitivity is enhanced to 76 dBm and 74 dBm, respectively. We further investigate the system performance under different water conditions: first type of seawater (c = 0.056 m ), 1 1 second type (c = 0.151 m ), and third type (c = 0.398 m ). The maximum distance of the 2 Mbps signal can be extended up to 100 m in the first type of seawater. Citation: Li, C.; Liu, Z.; Chen, D.; Deng, X.; Yan, F.; Li, S.; Hu, Z. Keywords: underwater optical wireless communication (UOWC); long-reach; photon counting Experimental Demonstration of High-Sensitivity Underwater Optical Wireless Communication Based on Photocounting Receiver. Photonics 2021, 8, 467. https://doi.org/ 1. Introduction 10.3390/photonics8110467 With the expanding area explored by human beings, the observation and utilization of the underwater world is growing increasingly important. Various underwater sensors, Received: 8 September 2021 unmanned vehicles, and nodes are deployed underwater to transfer and collect information. Accepted: 21 October 2021 To build an underwater transmission link, both cable- and wireless-based methods are Published: 22 October 2021 utilized. Cables or fibers can offer a stable communication link with high transmission speed but limit the freedom of the communication terminal for a long-reach link. Publisher’s Note: MDPI stays neutral The traditional method for underwater communication is to use acoustics, which is a with regard to jurisdictional claims in medium of sound. The attenuation of the sound wave in water is acceptable, which is com- published maps and institutional affil- petent for ultralong-reach communication up to tens of kilometers. However, underwater iations. acoustic communication is limited by the huge transmitted power, low data rate, and large latency [1]. Due to the skin effect, electromagnetic waves suffer from huge attenuation when propagating in water. Thus, it is hard to realize long-reach underwater communi- cation using electromagnetic waves. Studies have shown that the visible spectrum from Copyright: © 2021 by the authors. blue–green wavelengths suffers less attenuation caused by underwater absorption and Licensee MDPI, Basel, Switzerland. scattering than electromagnetic waves [2]. Benefiting from the rich bandwidth resource of a This article is an open access article laser diode (LD), a Gbps-scale underwater optical wireless communication (UOWC) system distributed under the terms and within tens of meters is feasible [3]. However, a strict tracking and alignment system is conditions of the Creative Commons required after long-distance transmission due to the narrow beam and small divergence Attribution (CC BY) license (https:// angle of the LD source. Moreover, most of the reported UOWC links are conducted in creativecommons.org/licenses/by/ tap water with avalanche photodetectors (APDs) for optical signal detection, which may 4.0/). Photonics 2021, 8, 467. https://doi.org/10.3390/photonics8110467 https://www.mdpi.com/journal/photonics Photonics 2021, 8, 467 2 of 13 not be so attractive and available for some long-distance transmission scenarios requiring a large optical power budget and photon-scale detection, e.g., internal communications with Mbps data rates between autonomous underwater vehicles or underwater sensor nodes in underwater dynamic conditions [4]. Thus, a high-sensitivity detector combined with a large-coverage-area light source is indispensable to build a reliable communication link with respect to unpredictable channel obstructions and the various conditions of the sea. Photomultiplier tubes (PMTs), possessing the capability of single-photon detection, are the most widespread vacuum electronic devices in every field of experimental studies including optical communication, biology, space research, and chemistry. Compared with silicon photomultipliers, PMT needs high voltage to drive the device. However, the PMTs are not sensitive to temperature and have a lower noise level. Due to the sensitivity of PMT to background noise and magnetic fields, it is more suitable to build a PMT-based long-range UOWC link for deep-sea implementation. Before building a long-range experimental UOWC system, the underwater channel conditions need to be investigated to establish the system parameters such as the optimal transmitted optical wavelength, modulation scheme, signal baud rate, and beam aperture. Because underwater data transmission using a light beam is not an easy mission in the presence of high water absorption and scattering, characterizing the underwater optical channel property to achieve appropriate system parameters is of crucial importance to enable a high-reliability and high-quality UOWC link. In this paper, we consider a comprehensive underwater channel model to simulate the property of an underwater optical communication link by taking the practical system parameters into account. Under the guidance of the simulation results, we propose and experimentally demonstrate a long-reach Mbps-scale UOWC scheme with high receiver sensitivity based on a light-emitting diode (LED) transmitter and a PMT receiver. The proposed system can significantly relax the alignment requirement especially after long- distance transmission. Bit-error-ratio (BER) performance enhancements for 1 Mbps, 2 Mbps, and 5 Mbps after 10 m transmission are experimentally investigated under different water turbidities with an adaptive decision threshold (DT). The receiver adapts to the changing of signal level. With added attenuation, the maximum link loss at an attenuation coefficient of 1.33 m is up to 99 dB at l = 448 nm. The achievable maximum distances for a 2 Mbps data rate in the first type of seawater (c = 0.056 m ) are up to 100 m and 134 m at 1 W and 10 W transmitted electrical power, respectively. 2. Operation Principle Compared with free-space atmospheric laser communication, the UOWC system faces some unique challenges. (i) Spectrum for communication: blue or green wavelengths should be dedicated to the UOWC link due to the water absorption effect, rather than infrared wavelengths (C-band 1530–1565 nm and L-band 1565–1625 nm) for an atmospheric free-space link enabled by well-established fiber-optic technologies and optoelectronic devices and components. (ii) Channel condition: affected by seawater, the underwater optical transmission channel is quite complicated. When the modulated light propagates through seawater, it suffers from absorption and scattering. Seawater absorption means that part of the photon energy launched into the seawater is converted into other forms of energy, such as thermal and chemical. Scattering refers to the interaction between light and seawater, which changes the optical transmission path. Both absorption and scattering cause the loss of optical signal energy at the receiver, resulting in a reduction in signal-to-noise ratio and communication distance. As illustrated in [5], the link loss for a realistic 10 m green-light UOWC system can vary from 6.6 dB to 95.5 dB due to dynamic underwater channel conditions from a clean ocean to turbid harbor seawater. Due to the variability of underwater channels, a robust long-reach UOWC link must be designed against a link loss of roughly up to 100 dB. Meanwhile, the link must be able to tolerate the dynamic changing underwater channels without breaking off. Although Photonics 2021, 8, x FOR PEER REVIEW 3 of 13 Photonics 2021, 8, 467 3 of 13 to tolerate the dynamic changing underwater channels without breaking off. Although linear detectors including APDs have shown their abilities to detect multi-Gbps optical linear detectors including APDs have shown their abilities to detect multi-Gbps optical signals transmitted by LD sources, their sensitivities are typically limited by thermal noise signals transmitted by LD sources, their sensitivities are typically limited by thermal [6]. On the other hand, photon-counting detectors can achieve very high sensitivities with noise [6]. On the other hand, photon-counting detectors can achieve very high sensitivities moderate data rates on the Mbps scale. In this paper, we propose a reliable long-reach with moderate data rates on the Mbps scale. In this paper, we propose a reliable long- UOWC scheme using LED and PMT, whose concept is illustrated in Figure 1. Due to the reach UOWC scheme using LED and PMT, whose concept is illustrated in Figure 1. Due advantages of its large light beam, compact structure, low cost, and low power consump- to the advantages of its large light beam, compact structure, low cost, and low power tion, LEDs are proposed as viable candidates to provide a transmission data rate of several consumption, LEDs are proposed as viable candidates to provide a transmission data Mbps or even up to hundreds of Mbps for implementing an alignment-released UOWC rate of several Mbps or even up to hundreds of Mbps for implementing an alignment- system. In the demonstration, a commercial LED transmitter is modulated by a prede- released UOWC system. In the demonstration, a commercial LED transmitter is modulated signed return-to-zero on–off keying (RZ-OOK) with half power semi-angle of 1.25° [7]. by a predesigned return-to-zero on–off keying (RZ-OOK) with half power semi-angle of With increasing transmission distance z, the receiving radius 𝐷 at the detection area in- 1.25 [7]. With increasing transmission distance z, the receiving radius D at the detection creases, which significantly relaxes the alignment requirement. To achieve high receiver area increases, which significantly relaxes the alignment requirement. To achieve high sensitivity and long distance, a typical and practically implemented photocounting re- receiver sensitivity and long distance, a typical and practically implemented photocounting ceiver is used, which is the PMT combined with a pulse-holding circuit to detect photo- receiver is used, which is the PMT combined with a pulse-holding circuit to detect photo- level signals. The received photoelectric current is characterized by a series of discrete level signals. The received photoelectric current is characterized by a series of discrete rectangular pulses with certain width, whose number satisfies a Poisson distribution. In rectangular pulses with certain width, whose number satisfies a Poisson distribution. In the demonstration, we propose a digital adaptive DT algorithm for signal recovery. The the demonstration, we propose a digital adaptive DT algorithm for signal recovery. The value of DT is adjusted as a function of the received signal level to achieve the minimum value of DT is adjusted as a function of the received signal level to achieve the minimum BER value. BER value. TSS DC PMT Rx * * * * RSS * * z * * * * * * * * ** * * * * * ** * * * * ** ** * * DT * * ** LED Tx Photons DA Figure 1. Proposed concept of long-reach UOWC using LED and PMT. DC: direct current, TSS: trans- Figure 1. Proposed concept of long-reach UOWC using LED and PMT. DC: direct current, TSS: mitted signal sequence, DA: detection area, RSS: received signal sequence, DT: decision threshold. d transmitted signal sequence, DA: detection area, RSS: received signal sequence, DT: decision threshold. 𝛿 is the divergence half-angle. z is the transmission distance. 𝐷 is the radius at the is the divergence half-angle. z is the transmission distance. D is the radius at the detection area. detection area. 3. System Model 3.1. LED Transmitter 3. System Model In our experiment, a commercial low-cost LED at a peak wavelength of 448 nm 3.1. LED Transmitter was employed as the transmitter. The path loss of light caused by water absorption and In our experiment, a commercial low-cost LED at a peak wavelength of 448 nm was scattering can be dominated by the Beer–Lambert law. employed as the transmitter. The path loss of light caused by water absorption and scat- tering can be dominated by the Beer–Lambert law. cz (a+b)z P = h P L = h P e = h P e , (1) r t ch t t −− cz () a+b z PP== ηη L Pe =ηPe (1) rt ch t t where h is electrical-to-optical conversion efficiency of LED, a and b represent the coeffi- cients of absorption and scattering, respectively, c is the total loss due to both effects, and z where 𝜂 is electrical-to-optical conversion efficiency of LED, 𝑎 and 𝑏 represent the co- is the underwater transmission distance. L is the channel loss, given by exp(cz). P and efficients of absorption and scattering, respecti ch vely, 𝑐 is the total loss due to both eftfects, P are the transmitted electrical power and received optical power (ROP), respectively. and 𝑧 is the underwater transmission distance. 𝐿 is the channel loss, given by exp(−cz). The radiation pattern I f of the LED obeys the Lambertian model, defined as ( ) 𝑃 and 𝑃 are the transmitted electrical power and received optical power (ROP), respec- tively. (m + 1) The radiation pattern 𝐼(𝜙) of the LED obeys the Lambertian model, defined as I(f) = h P cos (f), (2) 2p (1 m +) where f is the angle of irradiance, and f = 0 is the maximum , radiation power angle, i.e., IP () φ = η cos (φ) (2) 2π the direct state. m is expressed as the Lambertian emission order of the beam directivity, which is related to the half-power angle f of the LED, written as 1/2 where 𝜙 is the angle of irradiance, and 𝜙 = 0 is the maximum radiation power angle, i.e., the direct state. 𝑚 is expressed as the Lambertian emission order of the beam di- ln 2 m = . (3) rectivity, which is related to the half-power angle 𝜙 of the LED, written as ln(cos f ) 1/2 * Photonics 2021, 8, 467 4 of 13 The detected optical power by the photon counting receiver at the receiving plane A through the distance z is defined as follows [8]: e f f I(f)L A ch e f f P = . (4) 3.2. Underwater Channel In an underwater environment, the transmitted light is greatly influenced by the opti- cal properties of water. Underwater particles can cause energy attenuation and divergence of the beam. In this section, Kopelevich channel modeling is used as a volume scattering function (VSF) to investigate the extinction coefficient of natural water by simulation [9,10]. The specific form of this model is presented in [9]. Absorption coefficient a and scattering coefficient b denote the spectral absorption and scattering rate of unit interval, respectively. In this paper, we consider fulvic acid, humic acid and chlorophyll as the main absorption components of water [11,12], which can be expressed as follows: a(l) = a (l) + a (l) + a (l) + a (l), (5) w c f h 0.602 0 0 a (l) = a (l)(C /C ) , (6) c c c c a (l) = a C exp(k l), (7) f f f a (l) = a C exp(k l), (8) h h h where l indicates the light wavelength, and a (l), a (l), a (l), and a (l) are the absorp- w c f h tion coefficients caused by pure water, chlorophyll, fulvic acid, and humic acid, respectively. 0 0 0 The variables of a , a , and a represent the chlorophyll, fulvic acid, and humic acid charac- f h teristic absorption coefficients, respectively [13–15]. The two constant parameters k and k f h 1 1 are 0.0189 m and 0.0111 m . C , C , and C indicate the concentrations of chlorophyll, c f h 0 3 fulvic acid, and humic acid in water (C = 1 mg/m ). The values of C are given in Table 1. C and C are expressed as follows: f h C = 1.74098C exp(0.12327C /C ), (9) c c f c C = 0.19334C exp(0.12327C /C ). (10) c c h c Table 1. Chlorophyll concentration in four types of water (mg/m ). Pure Clean Ocean Coastal Turbid Harbor C 0 0.31 0.83 5.99 We adopt a small and large particle scattering model to get the scattering coeffi- cient of different types of water, which is a weighted summation with a pure water scattering coefficient [16]. 0 0 b(l) = b (l) + b (l)C + b (l)C , (11) w s s l 0 0 where b (l) indicates the scattering coefficient of pure water, b (l) and b (l) denote the scattering coefficients caused by small and large suspended particles, respectively [16,17], and C and C are the concentrations of both types of particles in water. The extinction coefficient c(l) is the sum of the absorption coefficient and scattering coefficient. VSF is a very important parameter in underwater channel modeling. It indicates the ratio of scattered intensity (solid angle DW centered on q) to total incident light intensity at a specific scattering angle. q indicates the scattering angle. In our model, we adopt the Kopelevich model as the VSF. Compared with the traditional Henyey–Greenstein model, Photonics 2021, 8, x FOR PEER REVIEW 5 of 13 The extinction coefficient 𝑐(𝜆) is the sum of the absorption coefficient and scattering coefficient. VSF is a very important parameter in underwater channel modeling. It indi- cates the ratio of scattered intensity (solid angle ΔΩ centered on 𝜃 ) to total incident light Photonics 2021, 8, 467 5 of 13 intensity at a specific scattering angle. 𝜃 indicates the scattering angle. In our model, we adopt the Kopelevich model as the VSF. Compared with the traditional Henyey–Green- stein model, the Kopelevich model not only covers small and large particles, but also can the be more Kopelevic accura h tel model y app not lied to hi only covers gh turbsmall id water and [9lar ]. ge particles, but also can be more accurately VSF for applied underwa to high ter a turbid pplicat water ion ca[n be expressed by t 9]. he combination of pure water, VSF for underwater application can be expressed by the combination of pure water, small particles, and large particles [16]. small particles, and large particles [16]. 0 0 p(λ,θ) = b (λ) p (θ) + b (λ) p (θ)C + b (λ) p (θ)C , (12) w R s s s l l l 0 0 p(l, q) = b (l) p (q) + b (l) p (q)C + b (l) p (q)C , (12) w s s R s l l where 𝑝 (𝜃) , 𝑝 (𝜃) , and 𝑝 (𝜃) indicate the probability density functions for pure water, small particles, and large particles, respectively. where p (q), p (q), and p (q) indicate the probability density functions for pure water, R l For the Kopelevich model, the total seawater scattering coefficient can be modeled as small particles, and large particles, respectively. follows [9]: For the Kopelevich model, the total seawater scattering coefficient can be modeled as follows [9]: 4.3 550 550 550  1.7 0.3 b λ=× 0.0017 +1.34CC ( ) +0.312 ( ) , (13) () 4.3  sl 1.7 0.3 550 550 550 λλ λ  b(l) = 0.0017 + 1.34C ( ) + 0.312C ( ) , (13) l l l where 𝐶 and 𝐶 are the concentrations of small and large particles, respectively. where C and C are the concentrations of small and large particles, respectively. We set the w s eight (unit energy) for each photon, and the energy attenuation of the We set the weight (unit energy) for each photon, and the energy attenuation of the transmitted light beam is equivalent to the change in weight. We define four main param- transmitted light beam is equivalent to the change in weight. We define four main param- eters at the transmitter: the wavelength λ, the maximum half-divergence angle 𝜃 , the eters at the transmitter: the wavelength l, the maximum half-divergence angle q , the zenith angle 𝜃 , and the azimuth angle 𝜑 . Initially, each photo is launched into wa m ta ex r with zenith angle q, and the azimuth angle j. Initially, each photo is launched into water with the given maximum half-divergence angle 𝜃 and unit weight. The initial departure the given maximum half-divergence angle q and unit weight. The initial departure max direction of the photon is determined on the basis of random variables 𝜃 and 𝜑 . The di- direction of the photon is determined on the basis of random variables q and j. The direc- rection is generated according to [−𝜃 , 𝜃 ] for 𝜃 and [0, 2π] for 𝜑 . The direction vec- tion is generated according to [q , q ] for q and [0, 2p] for j. The direction vector max max tor of emitted photons is (sin𝜃cos𝜑 , sin𝜃sin𝜑 , cos𝜃 ). After traveling at a certain distance of emitted photons is (sin q cos j, sin q sin j, cos q). After traveling at a certain distance called the free path, emitted photons might lose their energy and change their transmis- called the free path, emitted photons might lose their energy and change their transmission sion direction due to collision with particles in the underwater medium. Using a proba- direction due to collision with particles in the underwater medium. Using a probability bility model, the free path can be expressed as follows [18]: model, the free path can be expressed as follows [18]: d =−ln( ξ)/c, (14) d = ln(x)/c, (14) where 𝜉 is a random variable which obeys a uniform distribution within (0, 1]. whereDue t x is aorandom the collivariable sion with which partic obeys les in t ah uniform e underw distribution ater medium, emitted photons lose within (0, 1]. Due to the collision with particles in the underwater medium, emitted photons lose their energy and change their transmission direction. It is assumed that the weights of their energy and change their transmission direction. It is assumed that the weights of emit- emitted photons before and after collision are 𝑊 and 𝑊 , which satisfy Equation ted photons before and after collision are W and W , which satisfy Equation (15) [18]. (15) [18]. pre post W = W (1 − a/ c) . W = W (1 a/c). (15) (15) postpost prepre Once scattering occurs, the transmission direction of emitted photons is changed. The Once scattering occurs, the transmission direction of emitted photons is changed. new direction vector P2 after collision is dependent on the old direction vector P1, scatter- The new direction vector P after collision is dependent on the old direction vector P , 2 1 ing angle 𝜃 , and azimuth angle 𝜑 , as shown in Figure 2. Random variable 𝜑 satisfies a scattering angle q, and azimuth angle j, as shown in Figure 2. Random variable j satisfies uniform distribution within [0, 2π]. a uniform distribution within [0, 2]. Figure 2. Scattering pattern of emitted photons. Figure 2. Scattering pattern of emitted photons. For a single photon, VSF can be considered as the probability density function of the scattering angle. The generating methods of scattering angle for different VSFs are definitely different. As for the Kopelevich model, we use the acceptance–rejection sampling method to get the random scattering angle. According to the old transmission direction Photonics 2021, 8, 467 6 of 13 i i i vector (ux , uy , uz ), the scattering angle q, and the azimuth angle j, the transmission i+1 i+1 i+1 direction vector after scattering is represented by (ux , uy , uz ) [19]. i+1 i i u = u sin q cos f + u (cos q + sin q sin f) x y x i+1 i i u = u sin q cos f + u (cos q + sin q sin f) (16) y x y i+1 i 2 i 2 i i u = (u + u ) sin q sin f/u + u cos q z x y z z 3.3. Photocounting Receiver After several scattering events, the photons have a chance to be detected by the receiver. Since the solid angle DW of the photon scattering space is small enough, it can be assumed that the VSF among DW is constant. The variable p q of the scattering direction satisfies ( ) Z Z p 2p 1/2p p(q)dqdf = 1. (17) 0 0 By changing it into the integral of the solid angle, we get Z Z p(q) p(q) sin qdqdf = dW = 1. (18) 2p sin q 2p sin q Thus, the reception probability of the emitted photon is p(q) P = DW. (19) 2p sin q Considering the conditional probability of free path, the final reception probability becomes p(q) P = DW exp(k jr r j), (20) s r i 2p sin q where r is the position of receive window, and r is the position where the final scattering before detection happens. In our model, the threshold setting of the photon weight is 10 , as shown in Table 2. Path loss and impulse response are crucial. We can calculate the path loss by summation of all products of reception probability and receiving photon weights. As for each scattering event, the position prior to scattering is available; thus, the entire path of the photon before detection is recorded. The channel response can be calculated so long as we count the receiving intensity in a given time slot. In summary, we can get the flow chart of the Monte Carlo model as shown in Figure 3. The channel responses of different wavelengths in four types of water are shown in Figure 4. It can be seen from Figure 4a–d that the optimum transmission wavelength is switched from 450 nm (blue) to 595 nm (red) when the water condition is changed from pure to turbid harbor. Moreover, a clear multipath channel characteristic is observed due to heavy scattering as illustrated Figure 4d, which is consistent with the results in [17]. The theoretical analysis and impulse response results under different water conditions guide the design of the experimental system. We can select the optimal wavelength according to the different water conditions to achieve the maximum data rate and the maximum transmission distance. Table 2. Simulation parameters. Symbol Physical Meaning Value l Incident optical wavelength (unit: nm) 400, 450, 500, 550, and 595 Initial maximum half-divergence angle (random q 8.2 0,max generation within [0, 2p]) Statistical random variable for free path (random x 0.6 generation within (0, 1]) W Decision weight at the receiver >10 Photonics 2021, 8, x FOR PEER REVIEW 7 of 13 Photonics 2021, 8, x FOR PEER REVIEW 7 of 13 Table 2. Simulation parameters. Table 2. Simulation parameters. Symbol Physical Meaning Value Symbol Physical Meaning Value 𝜆 Incident optical wavelength (unit: nm) 400, 450, 500, 550, and 595 𝜆 Incident optical wavelength (unit: nm) 400, 450, 500, 550, and 595 Initial maximum half-divergence angle Initial maximum half-divergence angle 𝜃 8.2° , 8.2° (( rr aa n n dom genera dom genera ti ti on on wi wi thin [0 thin [0 , , 22 π π ]) ]) St St at at ist ist ii ca ca l r l r aa n n d d om var om var ii ab ab le le for for free p free p aa tt h h Photonics 2021, 8, 467 7 of 13 𝜉 0.6 𝜉 0.6 (random generation within (0, 1]) (random generation within (0, 1]) −− 44 𝑊 Decision weight at the receiver >10 𝑊 Decision weight at the receiver >10 -4 -4 Free path d W=(1-a/c)>10 Free path d W=(1-a/c)>10 1st scattering point Receiving probability 1st scattering point Receiving probability 2 -4 2 -4 Free path d WW=(=(1-1-a/a/cc))>1>100 Free path d 2nd scattering point Receiving probability 2nd scattering point Receiving probability Y N N Cycle the above Cycle the above End End process Save scattering position process Save scattering position Figure 3. Flow chart of Monte Carlo model for photocounting receiver. Figure 3. Flow chart of Monte Carlo model for photocounting receiver. Figure 3. Flow chart of Monte Carlo model for photocounting receiver. 0.014 0.1 0.014 0.1 400nm 400nm 400nm 400nm 450nm 450nm 450nm 0.09 450nm 0.09 500nm 500nm 0. 0. 012 012 500nm 500nm 550nm 0.08 550nm 550nm 0.08 550nm 595nm 595nm 595nm 595nm 0.01 0.01 0.07 0.07 0.06 0.06 0.008 0.008 0. 0. 05 05 00 .006 .006 0.04 0.04 0.03 0.03 0.004 0.004 0.02 0.02 (b) clean ocean water (a) pure water (b) clean ocean water (a) pure water 0. 0. 002 002 0.01 0.01 @150m @50m @150m @50m 00 0 461 10 12 146 18 20 0 2 4 6 8 10 12 14 16 16 18 20 20 02 02 461 88 10 12 146 18 20 0 2 4 6 8 10 12 14 18 t(ns) t(ns) t(ns) t(ns) -1-1 ×10 ×10 0.035 0.035 0.018 0.018 400nm 400nm 400nm 400nm 450nm 450nm 450nm 450nm 0.016 0.016 500nm 500nm 0.03 500nm 500nm 0.03 550nm 550 550 nm nm 550nm 0.014 0.014 595 595 nm nm 595 595 nm nm 0.025 0.025 0.012 0.012 (d) turbid harbor water (d) turbid harbor water 0.02 0.01 0.02 0.01 @8m @8m 0.00 0.00 88 0.015 0.015 0.006 0.006 0.0 0.0 11 0.004 0.004 (c) coastal water (c) coastal water 0.002 0.005 0.002 0.005 @30m @30m 0 6 12 14 16 18 20 0 10 15 20 25 30 35 40 0 2 4 6 88 10 10 12 14 16 18 20 0 55 10 15 20 25 30 35 40 2 4 t(ns) t(ns) t(ns) t(ns) Figure 4. Channel response of different wavelengths in four types of water. The launched wave- Figure 4. Channel response of different wavelengths in four types of water. The launched wave- Figure 4. Channel response of different wavelengths in four types of water. The launched wave- lengths were set to 400 nm, 450 nm, 500 nm, 550 nm, and 595 nm, respectively. (a) pure water (𝑐 = lengths were set to 400 nm, 450 nm, 500 nm, 550 nm, and 595 nm, respectively. (a) pure water (𝑐 = lengths were set to 400 nm, 450 nm, 500 nm, 550 nm, and 595 nm, respectively. (a) pure water −1 −1 −1 −1 −1 −1 0.056 m ), (b) clean ocean water (𝑐 = 0.151 m ); (c) coastal water (𝑐 = 0.398 m ); (d) turbid harbor 0.056 m ), ( b1 ) clean ocean water (𝑐 = 0.151 m ); (c) coastal wa 1 ter (𝑐 = 0.398 m ); (d) turbid harbor 1 (c = 0.056 m ), (b) clean ocean water (c = 0.151 m ); (c) coastal water (c = 0.398 m ); (d) turbid −1 −1 water ( 𝑐 = 2.17 m ). water ( 𝑐 = 2.17 m ). harbor water ( c = 2.17 m ). 4. Experiment and Results 4. 4. Ex Experiment periment and and Re Results sults 4.1. Experimental Setup and Paraeters 4.1. Experimental Setup and Paraeters 4.1. Experimental Setup and Paraeters Figure 5 shows a schematic diagram of our experimental UOWC system using a blue Figure 5 shows a schematic diagram of our experimental UOWC system using a blue Figure 5 shows a schematic diagram of our experimental UOWC system using a blue LED source and PMT receiver (Hamamatsu, model CR315). An inclination angle of 5 is LED source and PMT receiver (Hamamatsu, model CR315). An inclination angle of 5° is LED source and PMT receiver (Hamamatsu, model CR315). An inclination angle of 5° is introduced to the transceiver, which causes huge attenuation to build a non-line-of-sight iin ntroduced to the tra troduced to the tran nscei sceiver, ver, wh which ich causes huge causes huge attenuatio attenuation to n to bui builld d aa n no on- n-li lin nee--o of- f-ssiig gh htt link. All the signal processing modules are implemented offline by MATLAB. At the link. All the signal processing modules are implemented offline by MATLAB. At the trans- link. All the signal processing modules are implemented offline by MATLAB. At the trans- transmitter, a pseudo-random bit sequence (PRBS) is generated and then sampled by an mitter, a pseudo-random bit sequence (PRBS) is generated and then sampled by an arbi- mitter, a pseudo-random bit sequence (PRBS) is generated and then sampled by an arbi- arbitrary signal generator (AWG) running at 10 MSa/s (1 Mbps), 20 MSa/s (2 Mbps), trary signal generator (AWG) running at 10 MSa/s (1 Mbps), 20 MSa/s (2 Mbps), 50 MSa/s trary signal generator (AWG) running at 10 MSa/s (1 Mbps), 20 MSa/s (2 Mbps), 50 MSa/s 50 MSa/s (5 Mbps), and 100 MSa/s (10 Mbps). Then, the baseband signals combined (5 Mbps), and 100 MSa/s (10 Mbps). Then, the baseband signals combined with a DC bias (5 Mbps), and 100 MSa/s (10 Mbps). Then, the baseband signals combined with a DC bias with a DC bias are injected into the LED. Compared with LD, the LED-based transmitter are are injected injected into the LED. into the LED. Compared w Compared w iith LD, the th LD, the LE LED-based tr D-based tran ansmitter has n smitter has no o need of need of has no need of strict alignment or high emission power. A real-time oscilloscope is used to convert the analog signal into the digital domain. Simple digital signal processing (DSP) algorithms are applied at the receiving end, such as synchronization, decision, and BER calculation. The data length of each frame is 1151 bits, of which 127 bits are used for synchronization. We use multiple frames of information to increase the number of calculated bits. The number of effective bits used to calculate the BER was 20,718. To avoid synchronization problems, we increased the number of synchronization header bits. Unlike the conventional waveform sampling amplitude demodulation method, the photon- counting pulse signals need to be judged. When the amplitude of the sampled pulse is above the decision threshold voltage (DTV) V , one photon is counted. Final decisions on h(t) h(t) Generation of photon h(t) h(t) Generation of photon (θ , , , W) (θ 0,max, , , W) 0,max h(t) h(t) h(t) h(t) Photonics 2021, 8, x FOR PEER REVIEW 8 of 13 strict alignment or high emission power. A real-time oscilloscope is used to convert the analog signal into the digital domain. Simple digital signal processing (DSP) algorithms are applied at the receiving end, such as synchronization, decision, and BER calculation. The data length of each frame is 1151 bits, of which 127 bits are used for synchronization. We use multiple frames of information to increase the number of calculated bits. The num- ber of effective bits used to calculate the BER was 20,718. To avoid synchronization prob- lems, we increased the number of synchronization header bits. Unlike the conventional Photonics 2021, 8, 467 8 of 13 waveform sampling amplitude demodulation method, the photon-counting pulse signals need to be judged. When the amplitude of the sampled pulse is above the decision thresh- old voltage (DTV) VD, one photon is counted. Final decisions on symbol “1” or “0” are made by the counted average values in each symbol. Thus, the BER value can be calcu- symbol “1” or “0” are made by the counted average values in each symbol. Thus, the BER lated according to the hard threshold 𝑛 . Some key parameters of the proposed UOWC value can be calculated according to the hard threshold n . Some key parameters of the th system are summarized an proposed UOWC system ar d elisted in summarized Table and 3. listed in Table 3. DC PC generated 5° BER Cacul. OOK PMT Water tank AWG PRBS modulation Sync 10 m Bias-T Scope &Decision Offline processing Figure 5. Figure 5. Exper Experimental imental setup of LED– setup of LED–PMT PMT U UOWC OWC sy system stem with 5° m with 5 misalignment isalignment between transm between transmitter itter a and nd rece receiver iver.. PR PRBS: BS: pseudo-random bit sequence, AWG: arbitrary signal generator. pseudo-random bit sequence, AWG: arbitrary signal generator. Table 3. Key parameters of the proposed UOWC system. Table 3. Key parameters of the proposed UOWC system. Symbol Physical Meaning Value/Unit Symbol Physical Meaning Value/Unit m1 Lambertian order 2.9 × 10 m Lambertian order 2.9  10 f𝜙 Angle Angle of irradiance of irradiance 5 5° f Half-power semi-angle of LED 1.25 𝜙 1/2 Half-power semi-angle of LED 1.25° z Transmission distance 10 m z Transmission distance 10 m h E/O conversion efficiency 0.1289 𝜂 E/O conversion efficiency 0.1289 P Transmitted electrical power 1 W RPt Transm Transmitted itted data elect rate rical power 1/2/5 Mbps 1 W Rb Transmitted data rate 1/2/5 Mbps 4.2. Attenuation Coefficient Measurement 4.2. Attenuation Coefficient Measurement Water quality significantly impacts the BER performance. The PMT receiver is more Water quality significantly impacts the BER performance. The PMT receiver is more sensitive to optical power than other light-sensitive devices such as an APD. Ambient light sensitive to optical power than other light-sensitive devices such as an APD. Ambient light may annihilate signals. Thus, the experimental system should be thoroughly shaded with may annihilate signals. Thus, the experimental system should be thoroughly shaded with black nonreflective material. Our experimental channel was a 10 m long water tank with b alack volume nonre of fl3 ect m iv.e m Light ateri absorption al. Our expand erimscattering ental chann in el w seawater as a 10 m are lon caused g watby er t inor ankganic with a volume of 3 m . Light absorption and scattering in seawater are caused by inorganic salts and planktonic plants. Some previous studies have shown that a similar effect of salts and planktonic plants. Some previous studies have shown that a similar effect of aluminum hydroxide or magnesium hydroxide to seawater is observed on the light of alumin particles um hydroxide or m [20]. In the experiment, agnesium hydroxide to we added different concentrations seawater is observed on the light of of aluminum hydroxide part to picle ures water [20]. In t to simulate he experiseawater ment, we ad with dedif d di fer fferent c ent degr oncentrations ees of turbidity of al , i.e., uminum pure seawater hydrox-, clean seawater, coastal seawater, and harbor seawater, characterized by the parameters of ide to pure water to simulate seawater with different degrees of turbidity, i.e., pure sea- wat attenuation er, clean s coef eaw ficients. ater, coastal seawater, and harbor seawater, characterized by the param- P 1 eters of attenuation coefficients. c = ln . + c . (21) P z P 1 In the experiment, we could not directly measure the relationship between the at- cc =+ ln . (21) tenuation coefficient and the aluminum hydroxide concentration due to the presence of Pz an off-angle at the transmitter. A preliminary experiment was carried out using an LD In the experiment, we could not directly measure the relationship between the atten- with very narrow divergence angle and a high-sensitivity optical power meter. Because of uation coefficient and the aluminum hydroxide concentration due to the presence of an the reflection and absorption caused by the glass wall, we used Equation (21) to measure off-angle at the transmitter. A preliminary experiment was carried out using an LD with the relative attenuation coefficient. The results are shown in Figure 6a. We can see an very approximate narrow divergenc linear relationship e angle an between d a high-sen the alumin sitivity opti um hydr cal power meter. Because of th oxide concentration and the e attenuation coefficient. The parameter c is the measured attenuation coefficient, and c is the attenuation coefficient of pure seawater with a value of 0.056 m . The shaded tank was filled with pure water. Then, we added aluminum hydroxide powder to the water at a mass of 3 g each time and measured the ROP as P . Figure 6b shows the measured curve of the ROP as a function of the attenuation coefficient varying from 0.2 m to 1.3 m for different data rates. It can be seen from Figure 3b that the ROP was about 78 dBm for a 2 Mbps data rate at c = 1.3 m , which means that a total loss of 99 dB was introduced (launched optical power was 21 dBm). The values of ROP were calculated using the average number of experimentally counted photons according to Equation (22). Photonics 2021, 8, x FOR PEER REVIEW 9 of 13 reflection and absorption caused by the glass wall, we used Equation (21) to measure the relative attenuation coefficient. The results are shown in Figure 6a. We can see an approx- imate linear relationship between the aluminum hydroxide concentration and the attenu- ation coefficient. The parameter c is the measured attenuation coefficient, and 𝑐 is the −1 attenuation coefficient of pure seawater with a value of 0.056 m . The shaded tank was filled with pure water. Then, we added aluminum hydroxide powder to the water at a mass of 3 g each time and measured the ROP as Pc. Figure 6b shows the measured curve −1 −1 of the ROP as a function of the attenuation coefficient varying from 0.2 m to 1.3 m for different data rates. It can be seen from Figure 3b that the ROP was about −78 dBm for a 2 −1 Mbps data rate at c = 1.3 m , which means that a total loss of 99 dB was introduced Photonics 2021, 8, 467 9 of 13 (launched optical power was 21 dBm). The values of ROP were calculated using the aver- age number of experimentally counted photons according to Equation (22). 2.00 −65 1Mb/s 2Mb/s (a) (b) 1.60 5Mb/s 10Mb/s −70 1.20 0.80 −75 Fitting 0.40 Measured −80 0.00 0.2 0.4 0.6 0.8 1 1.2 1.4 02468 10 -1 c(m ) C (g/m ) Figure 6. (a) Attenuation coefficient as a function of aluminum hydroxide concentration and (b) Figure 6. (a) Attenuation coefficient as a function of aluminum hydroxide concentration and (b) re- received optical power (ROP) under different water turbidities after 10 m underwater channel. ceived optical power (ROP) under different water turbidities after 10 m underwater channel. 4.3. Measured BER Performance 4.3. Measured BER Performance In our experiment, we used a Hamamatsu PMT with a spectral response range from In our experiment, we used a Hamamatsu PMT with a spectral response range from 300 nm to 650 nm as the receiver. The quantum efficiency of the PMT was 5%, and the 300 nm to 650 nm as the receiver. The quantum efficiency of the PMT was 5%, and the typical dark count was 20 counts/sec. The number of photons counted in symbol “1” was typical dark count was 20 counts/sec. The number of photons counted in symbol “1” was contributed by the signal and the background light, while the photons counted in symbol contributed by the signal and the background light, while the photons counted in symbol “0” were caused by the background light and inter-symbol interference. An RZ code with a “0” were caused by the background light and inter-symbol interference. An RZ code with duty cycle of 0.7 was designed according to Equation (22), since the ROP can be maximized a duty cycle of 0.7 was designed according to Equation (22), since the ROP can be maxim- and a clock frequency component is included [21], where x is the quantum efficiency of ized and a clock frequency component is included [21], where 𝜉 is the quantum efficiency PMT, h is Planck’s constant, n is the frequency of light, T is the symbol duration, and n b 1 of PMT, h is Planck’s constant, ν is the frequency of light, Tb is the symbol duration, and and n are the average numbers of photons contained in symbols “1” and “0”. n1 and 𝑛 are the average numbers of photons contained in symbols “1” and “0”. 1 7 hn(n n ) 1 0 17 hn ν() −n P = . . 10. (22) r,P MT P = .. (22) x 20 T rP, MT ξ 20 T According to the measured results shown in Figure 7, when the number of received According to the measured results shown in Figure 7, when the number of received photons was less than 20, the measured data followed a relatively strict Poisson distribution photons was less than 20, the measured data followed a relatively strict Poisson distribu- since the PMT worked in the linear region. Upon increasing the number of photos to 40, the tion since the PMT worked in the linear region. Upon increasing the number of photos to PMT was subjected to overexposure and worked in the nonlinear region, thus experiencing 40, the PMT was subjected to overexposure and worked in the nonlinear region, thus ex- signal distortion [21]. In this condition, the distribution of the counted photons does not periencing signal distortion [21]. In this condition, the distribution of the counted photons obey a strict Poisson distribution, as shown in Figure 7. The BER value can be calculated does not obey a strict Poisson distribution, as shown in Figure 7. The BER value can be using Equation (23), where n is the hard-decision threshold [5]. th calculated using Equation (23), where 𝑛 is the hard-decision threshold [5]. n 1 th n k n k 1 k 1 0 k n n 1 0 n n n 0 n n −1 1 th k! 1 ∞ k!0 BER = e + e , n = . (23) å −−nn å th 11 nn − Photonics 2021, 8, x FOR PEER REVIEW 2 kk!! 2 ln n ln n 10 of 13 1 0 BER== k=0 e + k=n e ,n . (23)  th th 22 lnnn −ln kk == 0 n  10 th 0.16 0.12 Poisson Poisson (a) (b) Measured Measured 0.12 0.08 0.08 0.04 0.04 0 0.00 0 5 10 15 20 25 30 35 40 45 50 55 60 Number of photons Number of photons Figure 7. Distribution of the received photons: (a) seven photons; (b) 40 photons. Figure 7. Distribution of the received photons: (a) seven photons; (b) 40 photons. We present the measured BER performance under different water conditions in We present the measured BER performance under different water conditions in Fig- Figure 8. As discussed before, when the number of received photons is increased to around ure 8. As discussed before, when the number of received photons is increased to around 20 (~73 dBm), the number of the received photons no longer obeys a Poisson distribution. 20 (~−73 dBm), the number of the received photons no longer obeys a Poisson distribution. At this moment, the values of V should also be adjusted. In our experiment, the optimal At this moment, the values of 𝑉 D should also be adjusted. In our experiment, the optimal values of 𝑉 were obtained according to the rule of minimizing the BER. As illustrated in Figure 6b, an ROP of −73 dBm corresponded to a 10 m underwater transmission with an −1 attenuation coefficient of 0.8 m . When the PMT worked in photon-counting mode (𝑐 > −1 0.8 m ), the number of photons in symbol “1” obeyed a strict Poisson distribution. Thus, the value of DTV 𝑉 was set to 2.5 mV. However, the measured BER performance wors- ened, especially for 1 Mbps and 2 Mbps data rates, when the attenuation coefficients var- −1 −1 ied from 0.2 m to 0.8 m (saturation region of PMT). With the adapted optimal value of 𝑉 = 4.5 mV, error-free transmissions of 1 Mbps and 2 Mbps data rates were successfully achieved. The BER performance enhancement at the 5 Mbps data rate was not significant, because, when increasing the signal baud rate, severe inter-symbol interference was in- troduced due to the limited bandwidth of LED. Moreover, conclusions can be made ac- cording to Figure 8 that the receiver sensitivities of our proposed LED–UOWC systems at −1 −1 1 Mbps, 2 Mbps, and 5 Mbps data rates were −76 dBm (1.08 m ), −74 dBm (0.92 m ), and −1 −3 −70 dBm (0.24 m ) at the 7% FEC limit of 3.8 × 10 , respectively. 1Mb/s, 2.5mV 1Mb/s, 4.5mV 2Mb/s, 2.5mV 2Mb/s, 4.5mV 1 × 10 5Mb/s, 2.5mV 5Mb/s, 4.5mV 7% FEC limit −1 1 × 10 −2 1 × 10 −3 1 × 10 −4 1 × 10 −5 1 × 10 0.2 0.4 0.6 0.8 1 1.2 1.4 -1 c(m ) Figure 8. Experimental BER performance under different water turbidities after 10 m. 4.4. The Predicted Performance Based on the Proposed System As illustrated in Figure 9, we further investigated the proposed system performance −1 under conditions of the first type of seawater (pure, c = 0.056 m ), the second type (clean, −1 −1 c = 0.151 m ), and the third type (coastal, c = 0.398 m ). According to the experimental results illustrated in Figure 4, the required ROP for 2 Mbps at the 7% FEC limit is −74 dBm. Using Equation (4) and the parameters in Table 1, the optical power distribution at the receiving plane within the receiver sensitivity of −74 dBm was established using Lamber- tian model. Within the receiving radii of 1.28 m, 0.62 m, and 0.29 m, the achievable dis- tances were 83.5 m, 40.5 m, and 19.2 m for the first, second, and third types of seawater, -1 c(m ) Rate BER ROP(dBm) Rate Photonics 2021, 8, x FOR PEER REVIEW 10 of 13 0.16 0.12 Poisson Poisson (a) (b) Measured Measured 0.12 0.08 0.08 0.04 0.04 0 0.00 0 5 10 15 20 25 30 35 40 45 50 55 60 Number of photons Number of photons Figure 7. Distribution of the received photons: (a) seven photons; (b) 40 photons. We present the measured BER performance under different water conditions in Fig- Photonics 2021, 8, 467 10 of 13 ure 8. As discussed before, when the number of received photons is increased to around 20 (~−73 dBm), the number of the received photons no longer obeys a Poisson distribution. At this moment, the values of 𝑉 should also be adjusted. In our experiment, the optimal values of V were obtained according to the rule of minimizing the BER. As illustrated values of 𝑉 were obtained according to the rule of minimizing the BER. As illustrated in in Figure 6b, an ROP of 73 dBm corresponded to a 10 m underwater transmission with Figure 6b, an ROP of −73 dBm corresponded to a 10 m underwater transmission with an −1 an attenuation coefficient of 0.8 m . When the PMT worked in photon-counting mode attenuation coefficient of 0.8 m . When the PMT worked in photon-counting mode (𝑐 > −1 (c > 0.8 m ), the number of photons in symbol “1” obeyed a strict Poisson distribution. 0.8 m ), the number of photons in symbol “1” obeyed a strict Poisson distribution. Thus, Thus, the value of DTV V was set to 2.5 mV. However, the measured BER performance the value of DTV 𝑉 was set to D 2.5 mV. However, the measured BER performance wors- worsened, especially for 1 Mbps and 2 Mbps data rates, when the attenuation coefficients ened, especially for 1 Mbps and 2 Mbps data rates, when the attenuation coefficients var- 1 1 varied from 0.2 m to 0.8 m (saturation region of PMT). With the adapted optimal −1 −1 ied from 0.2 m to 0.8 m (saturation region of PMT). With the adapted optimal value of value of V = 4.5 mV, error-free transmissions of 1 Mbps and 2 Mbps data rates were 𝑉 = 4.5 mV, error-free transmissions of 1 Mbps and 2 Mbps data rates were successfully successfully achieved. The BER performance enhancement at the 5 Mbps data rate was not achieved. The BER performance enhancement at the 5 Mbps data rate was not significant, significant, because, when increasing the signal baud rate, severe inter-symbol interference because, when increasing the signal baud rate, severe inter-symbol interference was in- was introduced due to the limited bandwidth of LED. Moreover, conclusions can be made troduced due to the limited bandwidth of LED. Moreover, conclusions can be made ac- according to Figure 8 that the receiver sensitivities of our proposed LED–UOWC systems cording to Figure 8 that the receiver sensitivities of our proposed LED–UOWC systems at 1 1 at 1 Mbps, 2 Mbps, and 5 Mbps data rates were 76 dBm (1.08 m ), 74 dBm (0.92 m ), −1 −1 1 Mbps, 2 Mbps, and 5 Mbps data rates were −76 dBm (1.08 m ), −74 dBm (0.92 m ), and 1 3 and 70 dBm (0.24 m ) at the 7% FEC limit of 3.8  10 , respectively. −1 −3 −70 dBm (0.24 m ) at the 7% FEC limit of 3.8 × 10 , respectively. 1Mb/s, 2.5mV 1Mb/s, 4.5mV 2Mb/s, 2.5mV 2Mb/s, 4.5mV 1 × 10 5Mb/s, 2.5mV 5Mb/s, 4.5mV 7% FEC limit −1 1 × 10 −2 1 × 10 −3 1 × 10 −4 1 × 10 −5 1 × 10 0.2 0.4 0.6 0.8 1 1.2 1.4 -1 c(m ) Figure 8. Figure 8. Ex Experimental perimental BER BER pe performance rformance u under nder di dif fferent water turbidities after 10 m. ferent water turbidities after 10 m. 4.4. The Predicted Performance Based on the Proposed System 4.4. The Predicted Performance Based on the Proposed System As illustrated in Figure 9, we further investigated the proposed system performance As illustrated in Figure 9, we further investigated the proposed system performance under conditions of the first type of seawater (pure, c = 0.056 m ), the second type (clean, −1 under conditions of the first type of seawater (pure, c = 0.056 m ), the second type (clean, 1 1 c = 0.151 m ), and the third type (coastal, c = 0.398 m ). According to the experimental −1 −1 c = 0.151 m ), and the third type (coastal, c = 0.398 m ). According to the experimental results illustrated in Figure 4, the required ROP for 2 Mbps at the 7% FEC limit is74 dBm. results illustrated in Figure 4, the required ROP for 2 Mbps at the 7% FEC limit is −74 dBm. Using Equation (4) and the parameters in Table 1, the optical power distribution at the re- Using Equation (4) and the parameters in Table 1, the optical power distribution at the ceiving plane within the receiver sensitivity of74 dBm was established using Lambertian receiving plane within the receiver sensitivity of −74 dBm was established using Lamber- model. Within the receiving radii of 1.28 m, 0.62 m, and 0.29 m, the achievable distances tian model. Within the receiving radii of 1.28 m, 0.62 m, and 0.29 m, the achievable dis- were 83.5 m, 40.5 m, and 19.2 m for the first, second, and third types of seawater, respec- tances were 83.5 m, 40.5 m, and 19.2 m for the first, second, and third types of seawater, tively. The maximum transmission distances could be extended to 100 m, 46 m, and 21 m when the receiver was located in the center of the receiving plane, as depicted in Figure 10. With a transmitted electrical power of 10 W, the maximum distances were further increased to 134 m, 60 m, and 27 m. When c exceeded the value of 0.92 m (ROP = 74 dBm), as shown in Figure 8, the BER performance for the 2 Mbps signal became worse than the 7% FEC limit. The calculated optical power based on Equation (22) was 74.37 dBm in this condition, which is consistent with the optical power distribution obtained by the Lambertian model, as shown in Figure 9. The experimental 2 Mbps data rate after 10 2 2 m could achieve a receiving area of p  0.15 = 0.07 m . Thus, it is believed that our proposed long-reach UOWC system is capable of achieving an Mbps-scale data rate with an alignment-released configuration. Rate BER Rate Photonics 2021, 8, x FOR PEER REVIEW 11 of 13 Photonics 2021, 8, x FOR PEER REVIEW 11 of 13 respectively. The maximum transmission distances could be extended to 100 m, 46 m, and respectively. The maximum transmission distances could be extended to 100 m, 46 m, and 21 m when the receiver was located in the center of the receiving plane, as depicted in Figure 21 m when the receiver was located in the center of the receiving plane, as depicted in Figure 10. With a transmitted electrical power of 10 W, the maximum distances were further in- 10. With a transmitted electrical power of 10 W, the maximum distances were further in- −1 creased to 134 m, 60 m, and 27 m. When c exceeded the value of 0.92 m (ROP = −74 dBm), −1 creased to 134 m, 60 m, and 27 m. When c exceeded the value of 0.92 m (ROP = −74 dBm), as shown in Figure 8, the BER performance for the 2 Mbps signal became worse than the 7% as shown in Figure 8, the BER performance for the 2 Mbps signal became worse than the 7% FEC limit. The calculated optical power based on Equation (22) was −74.37 dBm in this con- FEC limit. The calculated optical power based on Equation (22) was −74.37 dBm in this con- dition, which is consistent with the optical power distribution obtained by the Lambertian dition, which is consistent with the optical power distribution obtained by the Lambertian model, as shown in Figure 9. The experimental 2 Mbps data rate after 10 m could achieve a model, as shown in Figure 9. The experimental 2 Mbps data rate after 10 m could achieve a receiving area of π × 0.15 = 0.07 m . Thus, it is believed that our proposed long-reach Photonics 2021, 8, 467 11 of 13 receiving area of π × 0.15 = 0.07 m . Thus, it is believed that our proposed long-reach UOWC system is capable of achieving an Mbps-scale data rate with an alignment-released UOWC system is capable of achieving an Mbps-scale data rate with an alignment-released configuration. configuration. Figure 9. Optical power distribution at the receiving plane within the receiver sensitivity of Figure 9. Optical power distribution at the receiving plane within the receiver sensitivity of −74 Figure 9. Optical power distribution at the receiving plane within the receiver sensitivity of −74 1 1 −1 −1 dBm: (a) c = 0.056 m , z = 83.5 m, 𝐷 = 1.28 m; (b) c = 0.151 m , z = 40.5 m, 𝐷 = 0.62 m; (c) c = 74 dBm: (a) c = 0.056 −1 m , z = 83.5 m, D = 1.28 m; (b) c =−1 0.151 m , z = 40.5 m, D = 0.62 m; r r dBm: (a) c = 0.056 m , z = 83.5 m, 𝐷 = 1.28 m; (b) c = 0.151 m , z = 40.5 m, 𝐷 = 0.62 m; (c) c = −1 −1 1 1 0.398 m , z = 19.2 m, 𝐷 = 0.29 m; (d) c = 0.92 m , z = 10 m,. 𝐷 = 0.15 m. −1 −1 (c) c = 0.398 m , z = 19.2 m, D = 0.29 m; (d) c = 0.92 m , z = 10 m,. D = 0.15 m. r r 0.398 m , z = 19.2 m, 𝐷 = 0.29 m; (d) c = 0.92 m , z = 10 m,. 𝐷 = 0.15 m. pure, 1W pure, 10W pure, 1W pure, 10W clean, 1W clean, 10W clean, 1W clean, 10W coastal, 1W coastal, 10W coastal, 1W coastal, 10W -74dBm receiver sensitivity -74dBm receiver sensitivity −50 −50 −100 −100 −150 −150 −200 −200 21m 27m 46m 60m 100m 134m 21m 27m 46m 60m 100m 134m −250 −250 −300 −300 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140 Distance(m) Distance(m) Figure 10. The predicted maximum distances using the proposed system. Figure Figure 10. 10. The The pr predicte edicted d maxi maximum mum distances using the prop distances using the proposed osed system. system. 5. Discussion 5. Discussion 5. Discussion To build To build a lon a long-range g-range UO UOWC WC link o link or r tto o propagat propagate e li light ght th thr rough rel ough relative ative tturbid urbid wat water er, , To build a long-range UOWC link or to propagate light through relative turbid water, two factors n two factors need eed to be con to be consider sider ed: ed: (i) (i) p pointing ointing and and alignment, alignment, an and (ii) d (imultipath i) multipath interfer interference - . two factors need to be considered: (i) pointing and alignment, and (ii) multipath interfer- ence. ence. 5.1. Pointing and Alignment To maintain a reliable line-of-sight UOWC link using an LD source after long-distance transmission is very difficult, since the optical beam is quite narrow. At this moment, pointing errors usually occur because of the link misalignment. Using a beam spread function, the link misalignment model for a UOWC system can be expressed as follows [3]: 8 9 2 3 ¥ L Z Z < = cL cL 4 5 BSF(L, r) = E(L, r)e + E(L, J)e  exp bb(J(L z))dz 1 J (Jr)JdJ, (24) : ; 0 0 ROP(dBm) ROP(dBm) Photonics 2021, 8, 467 12 of 13 where BSF(L, r) is the irradiance distribution at the receiver plane. Employing a LED source with a large beam size corresponds to a large receiving range. Thus, we can get the irradiance distribution more accessibly at the receiver plane. 5.2. Multipath Interference As illustrated in Figure 4d, a multipath interference effect is produced in an optical turbid harbor underwater channel after 8 m transmission. For a certain data rate, the effect of multipath interference eventually leads to time spreading and waveform distortion, thus decreasing the BER performance due to the inter-symbol interference. Thus, when designing a UOWC system, this issue should be taken into consideration. Fortunately, technologies such as channel equalization [22], adaptive optics, and spatial diversity [23] are capable of suppressing the interference. 6. Conclusions In this paper, we demonstrated a high-sensitivity long-reach UOWC system using LED and PMT. An experiment was conducted to investigate the BER performance under different water turbidities. Several key factors were taken into consideration during the system design, such as symbol rates, symbol duty cycles, water conditions, PMT characteristics, and decision criteria. With the help of RZ-OOK modulation and a PMT receiver, we experimentally achieved receiver sensitivities of 76 dBm, 74 dBm, and 70 dBm for 1 Mbps, 2 Mbps, and 5 Mbps data rates over a 10 m underwater channel, respectively. More than 100 m distance is achievable for a 2 Mbps data rate in pure seawater at 1 W transmitted power. Author Contributions: C.L. and Z.L. contributed equally; C.L. and Z.L. performed the investiga- tion and experiment; C.L. performed the analytical calculations and wrote the original draft; D.C. conducted the underwater channel simulation; X.D., F.Y., S.L., and Z.H. discussed the experimen- tal results and revised the manuscript. All authors read and agreed to the published version of the manuscript. Funding: This work was supported by the National Natural Science Foundation of China (12174002, 11874012), the Anhui Provincial Natural Science Foundation of China (1808085MF186), the China Postdoctoral Science Foundation (2021M690179), the Beijing Postdoctoral research Foundation (2021- ZZ-093), the Innovation project for the Returned Overseas Scholars of Anhui Province (2021LCX011), the Key Research and Development Plan of Anhui Province (202104a05020059), the University Synergy Innovation Program of Anhui Province (GXXT-2020-052), and the Project of State Key Labo- ratory of Environment-Friendly Energy Materials, Southwest University of Science and Technology (19FKSY0111). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. References 1. Stojanovic, M. Recent advances in high-speed underwater acoustic communications. IEEE J. 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Journal

Photonics – Multidisciplinary Digital Publishing Institute

Published: Oct 22, 2021

Keywords: underwater optical wireless communication (UOWC); long-reach; photon counting

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