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Abstract
In this work, we propose an underwater wireless optical communication (UWOC) system using an arrayed transmitter/receiver and optical superimposition-based pulse amplitude modulation with 4 levels (PAM-4). At the transmitter side, we design a spatial summing scheme using a light emitting diode (LED) array, which is divided into two groups in a uniformly interleaved manner. With on-off keying (OOK) modulation for each group, optical superimposition-based PAM-4 can be realized. It has enhanced tolerance to the modulation nonlinearities of LEDs. We numerically investigate the feasibility of the proposed spatial summing scheme in various underwater channels via Monte Carlo simulation. With the increase of divergence angle of LEDs and link distance, the optical power distribution tends to be more uniform at the reception plane. It can significantly relax the requirement on the link alignment. Furthermore, we conduct a proof-of-concept experiment employing two blue LEDs. A multi-pixel photon counter (MPPC), containing an array of single-photon avalanche diodes (SPADs), is used as the detector. It has a much higher sensitivity and can further relax the requirement for pointing. Over a 2-m tap water channel, data rates of 6.144 Mb/s, 8.192 Mb/s, and 12.288 Mb/s were achieved by using the PAM-4 signal generated by optical superimposition, within a 2.5-MHz system bandwidth. With 0.570-mg/L Mg(OH)2, the measured optical power is just 12.890 µW after a 2-m underwater channel. The corresponding bit error rate (BER) of the 12.288-Mbs PAM-4 signal is 2.9 × 10−3, which is still below the forward error correction (FEC) limit of 3.8 × 10−3. It implies that the UWOC system based on the high-sensitivity MPPC with array structure has superior power efficiency and robustness.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Oceans, the most valuable resource and wealth of mankind, are being competitively developed and exploited with continuing scientific and technological advances. Underwater wireless optical communication (UWOC) technology [1–5] emerging as an exciting new frontier shows prominent technical superiority and potentiality for ocean exploration, underwater sensor network and submarine communication. Laser diodes (LDs) with the merits of high modulation bandwidth and high power density have been extensively studied for high-speed and long-distance UWOC in recent years [1–3]. However, their extremely small divergence angles and thus strong directionality have restrictive requirements for link alignment in realistic underwater environment. Extra beam expansion or other solutions may be required to relax the requirements for link alignment at expense of power density and thus transmission distance. Alternately, using light emitting diodes (LEDs) [4,5] as the light sources of UWOC systems provides many distinctive advantages, such as guaranteed eye safety, long lifetime, low power consumption, and potential of simultaneous illumination and communication. In addition, LEDs with large divergence angles can naturally relax the alignment issue, which offers simpler and compact UWOC systems. Due to the large divergence angles and small modulation bandwidth, LEDs are only applicable to short-range UWOC with moderate data rates. For example, data transmission between underwater vehicles and nodes of underwater wireless sensor networks may require transmission distances of several meters and data rates in the Mb/s level. To fully utilize the LED bandwidth, a spectrally efficient modulation technique, namely orthogonal frequency division multiplexing (OFDM) [6, 7], has been popularly investigated, although it may increase system complexity to a certain extent. Multi-level pulse amplitude modulation (PAM) also enjoys high spectral efficiency but features simpler structure, more flexible implementation and lower computational complexity [8]. It has attracted great interest of researchers in the areas of short range optical networks and visible light communication (VLC) in the past few years [8–12]. It is worthwhile to mention that in a VLC system, the LED is a major source inducing system nonlinearity, as both the voltage-current and current-light intensity relationships are nonlinear in an LED [13–15]. Traditional PAM signals generated in the electrical domain complicate the transmitter and require LEDs with good linearity [16]. To obtain better eye diagram, the modulation amplitudes of the PAM signal should be optimized within the linear operation range of LEDs. For this reason, intensive studies have been carried out in the VLC community to solve the dilemma imposed by the LED nonlinearities, especially when advanced modulation formats are employed [17, 18]. One straightforward approach is to choose a two-level modulation format that is inherently immune to system nonlinearities at the expense of reduced spectral efficiency [19]. On the other hand, with an LED array, multi-level modulation can be realized by optical superimposition to increase spectral efficiency, and at the same time to resist the modulation nonlinearities of an LED [20–25]. The effective solution in VLC bring us enormous enlightenment on future UWOC using LED arrays as light sources. LED arrays, with increased optical power [26], can effectively enhance the underwater transmission distance. Besides, considering realistic underwater channel may suffer from perturbations like waves and turbulence, LED arrays with relatively large light spot at the reception plane are expected to solve the problem of link alignment. In recent years, to enhance the robustness of UWOC systems, multiple-input multiple-output (MIMO) technology based on multiple transmitters and receivers has been preliminarily investigated in simulation [27, 28] and experiment [29]. However, some underwater platforms are subject to very stringent constraints on power consumption, which limit the application of MIMO-based UWOC system with complex transceiver and digital signal processing. In terms of the facts above, novel schemes need to be put forward and studied to realize robust UWOC.
In this paper, we numerically and experimentally investigate an UWOC system using an arrayed transmitter/receiver and PAM-4 modulation generated by superimposing two streams of on-off keying (OOK)-modulated signals in optical domain. At the transmitter side, we design a spatial summing scheme based on a dense LED array for UWOC, as shown in Fig. 1. LED chips in the LED array are divided into two groups, as marked with two different colors. The two groups of LED chips are uniformly interleaved and are respectively modulated by two independent streams of electrical OOK signals with properly assigned amplitudes. Thus, the generated two streams of optical OOK signals are also approximately uniformly interleaved to assure the overlapped optical power is uniformly distributed at the receiver. The spatial summing of two OOK signals in optical domain can be regarded as an optical PAM-4 signal. As a two-level modulation format is seen by each LED chip, the PAM-4 signal generated by the proposed scheme is immune to LED nonlinearities. Monte Carlo simulation is first adopted to validate the feasibility of our proposed spatial summing scheme in various underwater channels. The optical power distribution at the reception plane tends to be more uniform with the increase of the divergence angle of LEDs and link distance. Thus, the requirement for pointing can be greatly reduced. Then, we further conduct a proof-of-concept experiment, employing two commercially available blue LEDs. At the receiver side, we put forward to use a multi-pixel photon counter (MPPC) containing an array of single-photon avalanche diodes (SPADs) as the detector. In [30], a positive-intrinsic-negative (PIN) diode-based VLC using PAM-4 signals generated by optical superimposition was preliminarily verified. Compared with the commonly used PIN diodes or avalanche photo diodes (APDs), an MPPC has a much higher sensitivity and relaxed requirement on the alignment between the transmitter and receiver. Thanks to the relatively short transmission distance of an UWOC system and the huge speed of light, signal synchronization between the two OOK streams are not necessary at the receiver considering a practical transmission bit rate. Within a 2.5-MHz system bandwidth, we achieve 6.144-Mb/s, 8.192-Mb/s, and 12.288-Mb/s underwater transmission by using the PAM-4 signal generated by optical superimposition, over a 2-m tap water tank. With as much as 0.570-mg/L Mg(OH)2, 12.288-Mbs PAM-4 signal can still be successfully transmitted through a 2-m underwater channel with the bit error rate (BER) of 2.9 × 10−3. The corresponding optical power at the receiver is merely 12.890 µW. It indicates that the high-sensitivity MPPC-based UWOC system with superior power efficiency has good robustness.
2. Numerical study on the spatial summing scheme
We numerically studied the impact of divergence angle of LEDs, propagation distance and water type on the optical power distribution at the reception plane. Monte Carlo method was used to simulate the trajectories of emitted photons [31]. In the simulation, we use an LED array with 16 LED chips, which are divided into two uniformly interleaved groups A and B, as shown in Fig. 2(a). The spacing of every two adjacent LEDs in the array is assumed to be 2 cm. The number of emitted photons from each LED is assumed to be 1 × 106. The ratio of photons’ weights from group A over group B is 2: 1 such that PAM-4 signals can be generated at the receiver via optical superimposition. Lambertian radiation pattern was used to model the LED radiant irradiance [32],
where is the emission zenith angle, denotes the uniform distribution between 0 and 1, is the order of Lambertian emission defined by the LED’s half power angle of . The area of the received plane is set to be 2 m × 2 m. The field of view of the detector is assumed to be 180 degrees. Three typical water types, including clear ocean water, coastal ocean water, and turbid harbor water were considered [33]. Two main factors affecting light propagation in water are absorption and scattering, which can cause the loss of optical power and the deflection of light from its original direction, respectively. We used the particle phase function in [34] to model scattering.
Fig. 2 (a) An LED array containing two uniformly interleaved LED groups A and B, (b) superimposed optical power distribution at the reception plane after 2-m clear ocean water, and (c) ratio of the optical power emitted from LED group A over that from LED group B after 2-m clear ocean water.
At first, the divergence angle of all the LEDs were set at 20 degrees. Figure 2(b) illustrates the superimposed optical power distribution at the reception plane after 2-m clear ocean water. Figure 2(c) indicates that after 2-m clear ocean water the ratio of the optical power emitted from LED group A over that from LED group B is approximately 2, which is the same with the ratio of photons’ weights. The uniform ratio of the optical power verified the feasibility of our proposed spatial summing scheme. Furthermore, it can ensure to achieve PAM-4 signals at the reception plane using optical superimposition [21].
We then studied the impact of LEDs with different divergence angles on the optical power distribution at the reception plane after 2-m clear ocean water. As shown in Fig. 3, when the divergence angle (full angle) of LEDs increases from 40° to 120°, the optical power distribution becomes more uniform at the reception plane, which can significantly relax the requirement of link alignment.
Fig. 3 Optical power distribution at the reception plane after 2-m clear ocean water versus different divergence angles of LEDs, (a) 40 degrees, (b) 80 degrees, and (c) 120 degrees.
Over 4-m, 6-m, and 8-m clear ocean water, the optical power distributions at the reception plane are illustrated in Fig. 4. Due to the light absorption and scattering in water and initial divergence angle of LEDs (20 degrees), the overall optical power becomes weaker at the reception plane as increasing the transmission distance. However, the optical power distribution becomes more uniform.
Fig. 4 Optical power distribution at the reception plane over (a) 4-m, (b) 6-m, and (c) 8-m clear ocean water.
We further investigate the impact of water turbidity on the performance of an LED array in three water types. Over 5-m clear ocean water, coastal ocean water, and turbid harbor water, the optical power distributions at the reception plane are presented in Fig. 5. In the measurement, all the divergence angles of the LEDs are set at 20 degrees. With the water becoming more turbid, again the overall optical power gets weaker due to the light absorption and scattering. Nevertheless, the optical power at the reception plane can maintain a uniform distribution within a relatively large area in all the three cases. It can thus guarantee the feasibility of the proposed spatial summing scheme for PAM-4 signal generation using optical superimposition.
Fig. 5 Optical power distribution at the reception plane after 5-m (a) clear ocean water, (b) coastal ocean water, and (c) turbid harbor water.
3. Experimental setup
Figure 6 illustrates the experimental setup of the UWOC system based on PAM-4 signals generated by optical superimposition. In the experiment, two pseudo-random binary sequence (PRBS) signals of length 27 – 1 and 28 – 1 were generated first in MATLAB. Then these two signal sequences were loaded into an arbitrary waveform generator (AWG), SDG 5162, via a U disk, and superimposed on two blue LEDs via two output ports of the AWG. A lens was placed behind the LEDs for collimation. The two uncorrelated optical OOK signals emitted from the two LEDs were overlapped in optical domain, generating an optical PAM-4 signal. After transmitting through a water tank (length: 2 m, width: 0.3 m, height: 0.3 m), the PAM-4 signal was detected by an MPPC with a bandwidth of around 4 MHz. The MPPC consists of an array of SPADs (3 mm × 3 mm) with each SPAD unit of 50 μm × 50 μm. Note that the experiment was conducted in the dark environment, because the MPPC is very sensitive to light. A blue filter was put in front of the MPPC to further reduce the impact of background light. The water tank was fabricated with the material of ordinary polymethyl methacrylate and filled with 175.29-L fresh tap water. In the experiment, we gradually added different quantities of Mg(OH)2 powders into the water, which acted as scattering agent. At the receiver, the detected PAM-4 signal was captured by an Agilent DSO-X 74104A digital signal oscilloscope (DSO). Finally, the captured PAM-4 signal was transmitted to a computer via U disk for offline processing including bit synchronization and calculation of BERs.
4. Experimental results
We first measured the optical spectra of the two LEDs. As shown in Fig. 7(a), both of the emission wavelengths are around 460 nm. As is known to all, LEDs are incoherent light sources. Thus, although most of the spectra of the two LEDs overlap, no beating noise will be generated when optical signals from the two LEDs are combined at the detector. Then we set up an experimental system employing a single LED as the transmitter and a low-cost PIN photodiode (THORLABS PDA10A-EC) as the detector to measure the frequency response of the system. Figure 7(b) shows the back-to-back frequency response of this system, indicating that the 3 dB bandwidth is approximately 2.5 MHz. Because the PIN photodiode had a bandwidth of 150 MHz, the small bandwidth of the system was attributed to the limited bandwidth of the LED [30].
Fig. 7 (a) Optical spectra of the two LEDs, (b) back-to-back frequency response of the system employing a single LED as the transmitter and the PIN as the detector.
Using the MPPC as the detector, we conducted the experiment of UWOC based on PAM-4 signals generated by optical superimposition. The two electrical driving signals generated in MATLAB were separately output from the two ports of the AWG. In the experiment, bias voltages and peak to peak amplitudes of the two electrical driving signals were preliminarily optimized at the AWG to fully utilize the linear modulation region of the LEDs. Both the bias voltages were set at 3 V and the peak to peak amplitudes of the two electrical driving signals were set at 1.6 V and 800 mV respectively. Thus, four symbol levels were obtained at the receiver side by superimposing the two signal sequences in optical domain. In the decoding procedure, eye diagram was first plotted via a straightforward Matlab program. Then, according to the eye diagram, we could obtain three optimal decision thresholds, which rested in the middle of every two adjacent horizontal levels of the PAM-4 signal, to achieve the minimum BER [9]. We did not use any adaptive decision threshold control schemes and no equalization was applied to the received PAM-4 signals. The PAM-4 signals generated by optical superimposition with gross data rates of 6.144 Mb/s, 8.192 Mb/s, and 12.288 Mb/s were successfully transmitted through the 2-m tap water channel with the BERs of 0, 0, and 2.4414 × 10−4, respectively. Figure 8 illustrates the corresponding eye diagrams. The eye diagrams degraded with the increase of the transmission rate.
Fig. 8 Eye diagrams of the (a) 6.144-Mbps, (b) 8.192-Mbps, and (c) 12.288-Mbs PAM-4 signal generated by optical superimposition after propagating through a 2-m tap water channel using the MPPC as the detector.
Because the received waveform of the PAM-4 signal generated by optical superimposition is especially vulnerable to the position of the receiver. To study the potential advantages of the high-sensitivity MPPC in the proposed scheme, it is deliberately placed at different distances from the center of the overlapping region of the two light spots, as shown in Fig. 9(a). Figure 9(b) illustrates that at the distances of 0 cm, 0.5 cm, 1.5 cm and 3.5 cm, the BERs of the 12.288-Mbs PAM-4 signal generated by optical superimposition were 2.4414 × 10−4, 4.8828 × 10−4, 9.7656 × 10−4 and 1.2 × 10−3, respectively, over a 2-m tap water channel. Figures 10(a)-10(d) present the corresponding eye diagrams. As expected, the MPPC-based UWOC system has good robustness due to the high sensitivity and arrayed structure of the MPPC. In addition, the link performance can be further enhanced if a dense LED or micro-LED array is used as the transmitter, where the light-emitting elements are driven by two OOK signals in an interleaved manner to assure the overlapped optical power is uniformly distributed at the reception side.
Fig. 9 (a) Diagram of two light spots and (b) BERs of the 12.288-Mbs PAM-4 signal over a 2-m tap water channel, when the MPPC is located at different distances from the center of the overlap region of the two light spots.
Fig. 10 Eye diagrams of the 12.288-Mbs PAM-4 signal over a 2-m tap water channel, when the MPPC is put at (a) 0 cm, (b) 0.5 cm, (c) 1.5 cm and (d) 3.5 cm away from the center of the overlap region of the two light spots.
To study the influence of turbidity on link performance, Mg(OH)2 powders was added into the tap water step by step. When the added Mg(OH)2 was 0.057 mg/L, 0.285 mg/L, 0.570 mg/L, 0.856 mg/L, 1.141 mg/L and 1.426 mg/L, the received optical powers measured by an optical power meter were 18.742 µW, 15.870 µW, 12.890 µW, 10.800 µW, 8.750 µW and 6.800µW, respectively. The corresponding BERs of the 12.288-Mbs PAM-4 signal over a 2-m underwater channel are presented in Fig. 11. With as much as 0.570-mg/L Mg(OH)2, the BER was 2.9 × 10−3, which is just below the forward error correction (FEC) limit of 3.8 × 10−3 [10]. The corresponding eye diagram is shown in the inset. The high-sensitivity MPPC-based UWOC system shows superior power efficiency and the experimental results can be further improved by increasing the LED number.
Fig. 11 BERs of the 12.288-Mbs PAM-4 signal over a 2-m underwater channel with different Mg(OH)2 concentration.
5. Conclusion
In this paper, we have demonstrated the feasibility of generating PAM-4 signals by a new optical superimposition scheme for UWOC employing an arrayed transmitter/receiver. Compared with the conventional approach for PAM-4 signals generation in the electrical domain, the generation of PAM-4 signals by optical superimposition can reduce transmitter complexity and enhance the tolerance to the modulation nonlinearities of LEDs. We first use Monte Carlo simulation to numerically study the validity of our proposed spatial summing scheme in various underwater channels. With the increased divergence angle of LEDs and link distance, the optical power at the reception plane tends to a uniform distribution, which can significantly solve the problem of link alignment. Furthermore, a proof-of-concept experiment is conducted using two blue LEDs and an MPPC. In the experiment, two blue LEDs, each with a modulation bandwidth of around 2.5 MHz, generate 6.144-Mb/s, 8.192-Mb/s, and 12.288-Mb/s PAM-4 signals by optical superimposition, which are successfully transmitted through a 2-m tap water tank. Even with 0.570-mg/L Mg(OH)2, the BER of 2.9 × 10−3 can be reached for the 12.288-Mbs PAM-4 signal after transmitting through a 2-m underwater channel. The corresponding optical power measured at the receiver side is only 12.890 µW. The MPPC with high sensitivity and array structure shows competitive advantages in power efficiency. Meanwhile, it can significantly reduce the requirement of link alignment and ensure the reliability of the proposed UWOC system. In the future, a dense LED array will be used to further improve the system reliability and enhance the underwater transmission distance.
Funding
Natural National Science Foundation of China (NSFC) (61671409, 61301141); National Key Research and Development Program of China (2016YFC1401202, 2017YFC0306100); Conservation Science and Technology Program of Administration of Cultural Heritage, Zhejiang Province (2016010).
Acknowledgments
The authors would like to thank Mr. Jiongliang Wang and Mr. Chao Zhang for the assistance in the simulation work.
References and links
1. J. Baghdady, K. Miller, K. Morgan, M. Byrd, S. Osler, R. Ragusa, W. Li, B. M. Cochenour, and E. G. Johnson, “Multi-gigabit/s underwater optical communication link using orbital angular momentum multiplexing,” Opt. Express 24(9), 9794–9805 (2016). [CrossRef] [PubMed]
2. A. Al-Halafi, H. M. Oubei, B. S. Ooi, and B. Shihada, “Real-time video transmission over different underwater wireless optical channels using a directly modulated 520 nm laser diode,” J. Opt. Commun. Netw. 9(10), 826–832 (2017). [CrossRef]
3. X. Liu, S. Yi, X. Zhou, Z. Fang, Z. J. Qiu, L. Hu, C. Cong, L. Zheng, R. Liu, and P. Tian, “34.5 m underwater optical wireless communication with 2.70 Gbps data rate based on a green laser diode with NRZ-OOK modulation,” Opt. Express 25(22), 27937–27947 (2017). [CrossRef] [PubMed]
4. H. Brundage, “Designing a wireless underwater optical communication system,” Massachusetts Institute of Technology (2010).
5. J. Xu, M. Kong, A. Lin, Y. Song, X. Yu, F. Qu, J. Han, and N. Deng, “OFDM-based broadband underwater wireless optical communication system using a compact blue LED,” Opt. Commun. 369, 100–105 (2016). [CrossRef]
6. H. M. Oubei, J. R. Duran, B. Janjua, H. Y. Wang, C. T. Tsai, Y. C. Chi, T. K. Ng, H. C. Kuo, J. H. He, M. S. Alouini, G. R. Lin, and B. S. Ooi, “4.8 Gbit/s 16-QAM-OFDM transmission based on compact 450-nm laser for underwater wireless optical communication,” Opt. Express 23(18), 23302–23309 (2015). [CrossRef] [PubMed]
7. J. Xu, Y. Song, X. Yu, A. Lin, M. Kong, J. Han, and N. Deng, “Underwater wireless transmission of high-speed QAM-OFDM signals using a compact red-light laser,” Opt. Express 24(8), 8097–8109 (2016). [CrossRef] [PubMed]
8. K. Szczerba, P. Westbergh, J. Karout, J. Gustavsson, Å. Haglund, M. Karlsson, P. Andrekson, E. Agrell, and A. Larsson, “30 Gbps 4-PAM transmission over 200 m of MMF using an 850 nm VCSEL,” Opt. Express 19(26), B203–B208 (2011). [CrossRef] [PubMed]
9. H. K. Shim, H. Kim, and C. C. Yun, “20-Gb/s polar RZ 4-PAM transmission over 20-km SSMF using RSOA and direct detection,” IEEE Photonics Technol. Lett. 27(10), 1116–1119 (2015). [CrossRef]
10. C. Xie, “Transmission of 128-Gb/s PDM-4PAM Generated with Electroabsoption Modulators over 960-km Standard Single-Mode Fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper Th4F.5. [CrossRef]
11. G. Stepniak, L. Maksymiuk, and J. Siuzdak, “1.1 Gbit/s white lighting LED-based visible light link with pulse amplitude modulation and Volterra DFE equalization,” Microw. Opt. Technol. Lett. 57(7), 1620–1622 (2015). [CrossRef]
12. N. Chi, M. Zhang, Y. Zhou, and J. Zhao, “3.375-Gb/s RGB-LED based WDM visible light communication system employing PAM-8 modulation with phase shifted Manchester coding,” Opt. Express 24(19), 21663–21673 (2016). [CrossRef] [PubMed]
13. K. Ying, Z. Yu, R. J. Baxley, H. Qian, G.-K. Chang, and G. T. Zhou, “Nonlinear distortion mitigation in visible light communications,” IEEE Wirel. Commun. 22(2), 36–45 (2014). [CrossRef]
14. A. M. J. Koonen, B. Inan, I. Neokosmidis, J. W. Walewski, S. C. J. Lee, and S. Randel, “Impact of led nonlinearity on discrete multitone modulation,” J. Opt. Commun. Netw. 1(5), 439–451 (2009). [CrossRef]
15. D. Tsonev, S. Sinanovic, and H. Haas, “Complete modeling of nonlinear distortion in OFDM-based optical wireless communication,” J. Lightwave Technol. 31(18), 3064–3076 (2013). [CrossRef]
16. O. Ozolins, X. Pang, M. I. Olmedo, A. Kakkar, A. Udalcovs, S. Gaiarin, J. R. Navarro, K. M. Engenhardt, T. Asyngier, R. Schatz, J. Li, F. Nordwall, U. Westergren, D. Zibar, S. Popov, and G. Jacobs, “100 GHz Externally modulated laser for optical interconnects,” J. Lightwave Technol. 99, 1 (2017).
17. Z. Yu, R. J. Baxley, and G. T. Zhou, “Distributions of upper PAPR and lower PAPR of OFDM signals in visible light communications,” in IEEE International Conference on Acoustics, Speech and Signal Processing (2014), pp. 355–359. [CrossRef]
18. C. H. Yeh, H. Y. Chen, C. W. Chow, and Y. L. Liu, “Utilization of multi-band OFDM modulation to increase traffic rate of phosphor-LED wireless VLC,” Opt. Express 23(2), 1133–1138 (2015). [CrossRef] [PubMed]
19. B. Fahs, J. Chellis, M. J. Senneca, A. Chowdhury, S. Ray, A. Mirvakili, B. Mazzara, Y. Zhang, J. Ghasemi, Y. Miao, P. Zarkesh-Ha, V. J. Koomson, and M. M. Hella, “A 6-m OOK VLC link using CMOS-compatible p-n photodiode and red LED,” IEEE Photonics Technol. Lett. 28(24), 2846–2849 (2016). [CrossRef]
20. J. Du, W. Xu, H. Zhang, and C. Zhao, “Visible light communications using spatial summing PAM with LED array,” in Wireless Communications and NETWORKING Conference (IEEE, 2017), pp. 1–6. [CrossRef]
21. A. Yang, Y. Wu, M. Kavehrad, and G. Ni, “Grouped modulation scheme for led array module in a visible light communication system,” IEEE Wirel. Commun. 22(2), 24–28 (2015). [CrossRef]
22. X. Li, N. Bamiedakis, J. Wei, J. Mckendry, E. Xie, R. Ferreira, E. Gu, M. Dawson, R. V. Penty, and I. H. White, “6.25 Gb/s POF link using GaN μLED arrays and optically generated pulse amplitude modulation,” in CLEO:2015, OSA Technical Digest (online) (Optical Society of America, 2015), paper STu4F.7.
23. T. Fath, C. Heller, and H. Haas, “Optical wireless transmitter employing discrete power level stepping,” J. Lightwave Technol. 31(11), 1734–1743 (2013). [CrossRef]
24. J. Yew, S. D. Dissanayake, and J. Armstrong, “Performance of an experimental optical DAC used in a visible light communication system,” in IEEE GLOBECOM Workshops (2014), pp. 1110–1115.
25. C. Xi, A. Mirvakili, and V. J. Koomson, “A visible light communication system demonstration based on 16-level pulse amplitude modulation of an LED array,” in IEEE Photonics and Optoelectronics (2012), pp. 1–4.
26. M. Doniec, I. Vasilescu, M. Chitre, C. Detweiler, M. Hoffmann-Kuhnt, and D. Rus, “AquaOptical: A lightweight device for high-rate long-range underwater point-to-point communication,” Mar. Technol. Soc. J. 44(4), 55–65 (2010). [CrossRef]
27. H. Zhang and Y. Dong, “Impulse response modeling for general underwater wireless optical MIMO links,” IEEE Commun. Mag. 54(2), 56–61 (2016). [CrossRef]
28. M. V. Jamali, J. A. Salehi, and F. Akhoundi, “Performance studies of underwater wireless optical communication systems with spatial diversity: MIMO scheme,” IEEE Trans. Commun. 65(3), 1176–1192 (2017). [CrossRef]
29. Y. Song, W. Lu, B. Sun, Y. Hong, F. Qu, J. Han, W. Zhang, and J. Xu, “Experimental demonstration of MIMO-OFDM underwater wireless optical communication,” Opt. Commun. 403, 205–210 (2017). [CrossRef]
30. M. W. Kong, Y. F. Chen, R. Sarwar, B. Sun, B. Cong, and J. Xu, “Optical superimposition-based PAM-4 signal generation for visible light communication,” in 16th International Conference on Optical Communications and Networks (ICOCN 2017), pp. 1–3. [CrossRef]
31. B. M. Cochenour, L. J. Mullen, and A. E. Laux, “Characterization of the beam-spread function for underwater wireless optical communications links,” IEEE J. Oceanic Eng. 33(4), 513–521 (2008). [CrossRef]
32. T. Liu, H. Zhang, and J. Song, “Monte-Carlo simulation-based characteristics of underwater scattering channel,” Opt. Eng. 56(7), 070501 (2017). [CrossRef]
33. A. S. Fletcher, S. A. Hamilton, and J. D. Moores, “Undersea laser communication with narrow beams,” IEEE Commun. Mag. 53(11), 49–55 (2015). [CrossRef]
34. D. C. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).
