underwater optical wireless communications

6th International Conference from “Scientific Computing to Computational Engineering” 6th IC-SCCE Athens, 9-12 July, 2014 © IC-SCCE

UNDERWATER OPTICAL WIRELESS COMMUNICATIONS: POSSIBILITIES DISADVANTAGES AND POSSIBLE SOLUTIONS L.K. Gkoura1, H.E. Nistazakis1*, A. Vavoulas2, A.D. Tsigopoulos3 and G.S. Tombras1 1

: Department of Electronics, Computers, Telecommunications and Control, Faculty of Physics, National and Kapodistrian University of Athens, Athens, 15784, Greece e-mails: {lgkoura; enistaz; gtombras}@phys.uoa.gr;

2

: Department of Computer Science and Biomedical Informatics, University of Thessaly, Lamia GR-35100, Greece, e-mail: [email protected]

3

: Department of Battle Systems, Naval Operations, Sea Studies, Navigation, Electronics and Telecommunications, Hellenic Naval Academy, Hadjikyriakou ave, Piraeus 18539, Greece, e-mail: [email protected]

*

Department of Electronics, Computers, Telecommunications and Control, Faculty of Physics, National and Kapodistrian University of Athens, 15784, Greece phone no: +30-210-7276710; fax no: +30-210-7276801; e-mail: [email protected] Keywords: Wireless Optical Communications, Underwater Optical Communications

ABSTRACT The growing need for secure and high speed underwater telecommunication systems has stimulated very considerable interest. Thus, the underwater optical wireless communications (UOWC) attract significant research attention due to the fact that they provide a cost-effective and low energy consumption solution that can achieve high data-rates transmission, strong anti-jamming ability and security between the transmitter and the receiver. The technology that is mostly used nowadays, among divers, ships etc, is the one with acoustic waves but this technology supports low baud rates and does not ensure the link’s security while the information signal’s delay is very big. On the other hand, the UOWC’s effective range is lower, due to the higher attenuation in these frequencies, but the communications are very fast and secure, the delay is practically minimal and many multiplexing schemes can be used in order to achieve higher capacities (i.e. WDM, TDM, etc) and thus greater performance characteristics. The main disadvantage of the scientific area of UOWC is the relatively low propagation distances and the main goal is to find the ways to minimize the influence of the signal’s mitigation factors. This work is a tutorial one which is trying to collect and present some of the important and recent developments in the UOWC research area that have been already presented. More specifically, we make an introduction to this significant new research area and technology and we present the main factors which affect the systems’ performance. Additionally, we show the ways and the solutions which have been proposed, in order to minimize their impact. 1

INTRODUCTION The growing need for secure and high speed underwater telecommunication systems that has stimulated very considerable interest nowadays, aims to investigate the ways and means of achieving efficient underwater optical wireless communications (UOWC) and develop underwater optical communication systems to serve as a broadband (10-100 Mbps), safe (non interceptable) and reliable (resistant to jamming) complement to legacy acoustic underwater communications systems. These communication means, along with the well known and very efficient, free space optical (FSO) communication links for tropospheric optical signal propagation, could create a very dense network of optical detectors which can be used either for detection and tracking of moving targets, either detection

L.K. Gkoura, H.E. Nistazakis, A. Vavoulas et al

of marine incidents such as pollution in a specific surveyed maritime area. It takes advantage of recent advances in optical wireless communications in the atmosphere, [1]-[8], along with those in underwater wireless optical schemes. It will constitute an enabling technology for true very fast broadband inexpensive submarine communications that will be used by underwater vessels [9]. The technology that is mostly used nowadays, among divers, ships etc, is the one with acoustic waves but this technology supports, relatively, low data rates and does not ensure the link’s security while the information signal’s delay is very significant. This technology of acoustic underwater communication is a legacy technology that provides low-data-rate transmissions for medium-long range communication. Thus, acoustic waves cannot satisfy the needs of new demanding technologies because of their inability to achieve high-data-rate communications in real time operations. In contrast, electromagnetic (EM) waves can be used in order to achieve much faster wireless communications. They have several advantages over acoustic waves, namely faster velocity, higher operating frequency and they are also unaffected by salinity, temperature and depth. Unfortunately all electromagnetic waves are highly attenuated in water, due to both absorption and scattering [9]-[22]. 2

ACOUSTIC WAVES IN WATER The technology that is mostly used nowadays, among divers, ships etc, is the one with acoustic waves but this technology supports, relatively, low data rates and does not ensure the link’s security while the information signal’s delay is very significant. This technology of acoustic underwater communication is a legacy technology that provides low-data-rate transmissions for medium-long range communication. Thus, acoustic waves cannot satisfy the needs of new demanding technologies because of their inability to achieve high-data-rate communications in real time operations. The three main propagation characteristics for the acoustic waves are the following: Propagation velocity: Sound waves travel faster in water (1500 m/sec typical speed of sound in water near the ocean surface) than in air (340 m/sec) receiving very little attenuation but even if this speed is more than 4 times faster than the speed of sound in air, it is five orders of magnitude smaller than the speed of [9]. Absorption: While the sound wave travels through water, the energy of the wave is absorbed by the medium and it can be transformed to other formats. The material imperfection regulates the energy loss caused by absorption for each type of wave travelling through it. For sound waves this imperfection is inelasticity and it converts the lost energy into heat[9]. The attenuation or path loss in an underwater channel over a distance l for a signal of frequency f is frequency dependent and it can be expressed as [23] 𝐴𝐴(𝑙𝑙, 𝑓𝑓) = 𝑙𝑙 𝑘𝑘 𝛼𝛼(𝑓𝑓)𝑙𝑙

(1)

where k is the propagation constant, whose values are usually between 1-2, and a(f) is the absorption coefficient, which is an increasing function of the frequency. The cause for the frequency dependence is the energy absorption of the pressure waves and the spreading loss that increases with distance. The equation for the seawater absorption coefficient at frequency f (kHz), can be written as the sum of chemical relaxation processes and absorption from pure water [13] 𝛢𝛢 1 𝛲𝛲1 𝑓𝑓1 𝑓𝑓 2

𝛢𝛢 2 𝛲𝛲2 𝑓𝑓2 𝑓𝑓 2

+ 𝐴𝐴3 𝑃𝑃3 𝑓𝑓 2

(2)

𝑐𝑐(𝜏𝜏, 𝑡𝑡) = ∑𝑃𝑃 𝐴𝐴𝑃𝑃 (𝑡𝑡)𝛿𝛿(𝜏𝜏 − 𝜏𝜏𝑝𝑝 (𝑡𝑡))

(3)

𝛼𝛼 =

𝑓𝑓12 +𝑓𝑓 2

+

𝑓𝑓22 +𝑓𝑓 2

where A1, A2, and A3 are constants; the pressure dependencies are given by parameters P1, P2 and P3; and the relaxation frequencies f1 and f2 are for the relaxation process in boric acid and magnesium sulphate, respectively. Multipath:The multipath propagation is a common ploblem for underwater acoustic links which causes the acoustic signal to reach the receiver by multiple paths. It arises from wave reflections from the surface, bottom and other objects in the sea or wave refraction caused by sound speed variations with depth. Acoustic waves always prefer to follow paths where the propagation speed is lower.[16],[17]. As a result the receiver detects more than one pulse and each one with a different amplitude phase and instant of arrival[24]. One expression that has been reported and can express the channel impulse response for a time-varying multipath underwater acoustic channel is the following [15]:

where 𝐴𝐴𝑃𝑃 (𝑡𝑡)and 𝜏𝜏𝑝𝑝 (𝑡𝑡) denote time-varying path amplitude and time-varying path delay respectively. When a signal is transmitted underwater the fundamental mechanisms of multipath propagation that affect the light beam is the


reflection at the boundaries and the refraction. The range of transmission, the depth, the geometry of the channel, the frequency and the sound speed profile are the main factors that form the multipath effect. As a result vertical channels typically have little time dispersion, while horizontal channels may show long multipath spreads (acoustic links are classified as vertical and horizontal according to the direction of the sound with respect to the ocean bottom)[18]. Multipath propagation can severely deteriorate the acoustic signal, as it generates inter-symbol interference (ISI)[19]. The acoustic link performance for various ranges is not very promising. As such, even at short ranges, the acoustic channel is limited to sub-Mbps data rates. For medium ranges (1-10 km) the data rate drops to approximately 10 kbps and finally at very long ranges (>100 km) the data rate is lower than 1 kbps [10]-[12]. 3

ELECTROMAGNETIC WAVES IN WATER The use of electromagnetic waves in the radio frequency band, has several advantages over acoustic waves and they can be used in order to achieve much faster wireless communications underwater. High operating frequency hence higher bandwidth and faster velocity are the most important ones. They are also unaffected by salinity, temperature and depth [9], [20]-[29] . Unfortunately all electromagnetic waves are highly attenuated in water, due to both absorption and scattering Electromagnetic waves behavior in freshwater and seawater are quite different and that’s because seawater is a high-loss medium. Both the propagation velocity and the absorptive loss of EM waves can be described as functions of carrier frequency. The propagation speed in seawater and the absorption can be approximated as [20] 4πf

c≈�

μσ

α ≈ �π f μ σ

(4) (5)

where μ is the magnetic permeability (4π⋅10-7 H/m), σ is the electric conductivity of water (σ∼4 Siemens/m for seawater) and f stands for the frequency. From the diagrams in Ref [9] between absorption coefficient and velocity versus frequency in seawater we can see that electromagnetic waves are highly frequency dependent and proportional to the square root of frequency. This explains the main reason for using low frequencies. But for such low frequencies of the order of several Hz to several kHz, the main limitation of electromagnetic waves is the big antenna size needed in freshwater and for seawater is the high attenuation. RF modem (model S1510 from Wireless Fibre Systems) is a commercially available product for underwater use in RadioFrequency band and it achieves a bit rate of 100 bps for a range of several tens of meters. Also, 1-10 Mbps within 1 meter range has been reported (model S5510 from Wireless Fibre Systems). 4 OPTICAL WAVES IN WATER It seems therefore, that acoustic waves cannot satisfy the needs of new demanding technologies because of their inability to achieve high-data-rate communications in real time operations. The use of Radio Frequency waves which are EM waves in the frequency band below 300GHz, is very difficult, due to large attenuations of the electric and magnetic field which limits it range and effectiveness to transmit data. Electromagnetic waves in the visible spectrum like optical signals between 400-700nm are propagating faster in water than the acoustic ones and that is the reason why they have gained considerable interest during the last years to serve as a broadband (10-100 Mbps), safe (non interceptable) and reliable complement to legacy acoustic underwater communications systems. They present yet another alternative for establishing wireless underwater links. Optical technologies have proven their ability to provide large information bandwidths with the success of fiber optic communications and the growing applications and success of free space optical links. The main disadvantages for optical communication in water are first, optical signals are rapidly absorbed in water and secondly, optical scattering caused by suspending particles and planktons which is significant. Also high level of ambient light in the upper part of the water is another adverse effect for using optical communications especially in shallow water communications [4], [9]. In contrast to these limitations, seawater exhibits a “window” of decreased absorption in the blue/green region of the visible spectrum where a number of laser sources are available. From figures of attenuation of electromagnetic radiation in Ref. [10], we can see that RF waves suffer severe attenuation which allows them to propagate only a few feet underwater. Infrared wavelengths, also suffer greater attenuation. Only visible wavelengths between 400nm and 700nm seem to be useful range for underwater communications. The preferred wavelength for superior


transmission of an optic signal ranges between 400nm-550nm depending on the precise water composition. Due to their very short wavelength, the optical waves offer the potential for very high data rate underwater optical communication links. Thus, using a suitable wavelength, i.e. in the blue/green spectrum range, they can attain high data rates depending on the water conditions and the transmitter and receiver parameters. Light propagation in seawater is highly wavelength sensitive, with transmittance falling from nearly 100% over several meters in clear ocean water for light of wavelengths 400–500 nm to near zero for turbid waters and wavelength values below 300 nm and above 700 nm. This is due to the spectral dependence of scattering and absorption caused by aquatic molecules and suspended particles. This transmission window is centered near 0.460 μm, in clear waters. Even though, the minimum attenuation of the window shifts to higher wavelengths as the water becomes murkier (see Figure in Ref [30]), approaching 0.540μm for coastal waters [30]. Attenuation Underwater Jerlov in 1968, proposed a classification system for the clarity of water bodies based on their spectral optical attenuation depth 𝑧𝑧𝑘𝑘 = 1�𝑘𝑘 and divides them into five specific classes from Type I – the clearest till Type III – the 𝑑𝑑

dirtiest. This classification was made in the upper portions of the ocean and it was based on spectral irradiance transmittance measurements. This system is still widely used and by using Jerlov water type maps, we can estimate the performance of an underwater platform in different locations, since the exact type of water can be useful in the estimation of the amount of chlorophyll concentration and consequently the amount of absorption and scattering in a specific geographic location [1]. The water types are the following: Pure deep ocean waters cobalt blue: absorption is the main limiting factor. The low scattering coefficient and the forward angle scattering make the beam propagate approximately in a straight line. Clear sea waters: higher concentration of dissolved particles that affect scattering. Near Coasts ocean waters: much higher concentration of planktonic matters, detritus and mineral components that affect absorption and scattering. Harbor murky waters: very high concentration of dissolved and in-suspension matters that make them especially constraining for optical propagation The two main processes that affect light propagation in water, as mentioned above, are absorption and scattering, which are both wavelength depended. When encountering a particle in water the light scatters and part of the incident light flux is absorbed by the particle and the remaining flux is scattered through an angle Ψ. The scattering direction Ψ is within a solid angle ΔΩ around Ψ. Absorption: the irreversible loss of intensity, depends on the water’s index of refraction. It is an irreversible thermal process where photon energy is lost due to interaction of light with water molecules and other particulates. Optical signals are rapidly absorbed in water Absorption coefficient 𝛼𝛼(𝜆𝜆) is the ratio of the absorbed energy from an incident power per unit distance [25]. 𝛼𝛼(𝜆𝜆) =

𝛷𝛷 (𝜆𝜆 ) 𝑑𝑑( 𝛼𝛼(𝜆𝜆 ) ) 𝛷𝛷 𝑖𝑖

(6)

𝑑𝑑𝑑𝑑

We have to quantify the value of the absorption and estimate the light absorbed by water and any particle in it. The absorption by pure water is already known so we have to calculate the absorption due to various dissolved particles such as phytoplankton, detritus etc [31] 𝛼𝛼(𝜆𝜆) = 𝛼𝛼𝑤𝑤 (𝜆𝜆) + 𝛼𝛼𝑐𝑐0 (𝜆𝜆)(𝐶𝐶𝑐𝑐 /𝐶𝐶𝑐𝑐0 )0.602 + 𝛼𝛼𝑓𝑓0 𝐶𝐶𝑓𝑓 𝑒𝑒 −𝑘𝑘 𝑓𝑓 𝜆𝜆 + 𝛼𝛼ℎ0 𝐶𝐶ℎ 𝑒𝑒 −𝑘𝑘 ℎ 𝜆𝜆

(7)

Where 𝛼𝛼𝑤𝑤 (𝜆𝜆) is the absorption by the pure water in m-1, λ is the wavelength in nm, 𝛼𝛼𝑐𝑐0 (𝜆𝜆) is the absorption coefficient in m-1 of chlorophyll, Cc is the total concentration of chlorophyll per cubic meter (Cc0 =1mg/m3)[31] 𝛼𝛼𝑓𝑓0 = 35.959 m2/mg absorption coefficient of fulvic acid kf =0.0189nm-1

𝛼𝛼ℎ0 = 18.828 m2/mg absorption coefficient of humic acid kh =0.01105 nm-1 𝐶𝐶𝑓𝑓 = 1.74098 𝐶𝐶𝑐𝑐 𝑒𝑒

𝐶𝐶 0.12327 � 0𝑐𝑐 �

concentration of fulvic acid

(8)

𝐶𝐶 0.12343 � 0𝑐𝑐 �

concentration of humic acid

(9)

𝐶𝐶ℎ = 0.19334 𝐶𝐶𝑐𝑐 𝑒𝑒

𝐶𝐶 𝑐𝑐

𝐶𝐶 𝑐𝑐


Scattering: the deflection of light from the original path which can be caused by particles of size comparable to λ (diffraction) or by particulate matters with refraction index different from that of the water (refraction). Optical scattering caused by suspending particles and planktons is significant. Scattering coefficient 𝑏𝑏(𝜆𝜆) is the ratio of energy scattered from an incident power per unit distance and it is also referred to as total scattering coefficient and is the sum of backward scattering 𝑏𝑏𝑏𝑏 (𝜆𝜆) and forward scattering coefficient 𝑏𝑏𝑓𝑓 (𝜆𝜆) [25] 𝑏𝑏(𝜆𝜆) =

𝛷𝛷 (𝜆𝜆 ) 𝑑𝑑( 𝑠𝑠(𝜆𝜆 ) ) 𝛷𝛷 𝑖𝑖

(10)

𝑑𝑑𝑑𝑑

b(λ) in units of inverse meters. On the other hand, scattering is caused by small and large particles. Small particles are the particles with refractive index equal to 1.15, while large particles have a refractive index of 1.03. The scattering coefficient is calculated from references as [31] 𝑏𝑏(𝜆𝜆) = 𝑏𝑏𝑤𝑤 (𝜆𝜆) + 𝑏𝑏𝑠𝑠0 (𝜆𝜆)𝐶𝐶𝑠𝑠 + 𝑏𝑏𝑙𝑙0 (𝜆𝜆)𝐶𝐶𝑙𝑙 (11) and backscattering coefficient is calculated as[31] 𝑏𝑏𝐵𝐵 (𝜆𝜆) = 0.5𝑏𝑏𝑤𝑤 (𝜆𝜆) + 𝛣𝛣𝑠𝑠 𝑏𝑏𝑠𝑠0 (𝜆𝜆)𝐶𝐶𝑠𝑠 + 𝐵𝐵𝑙𝑙 𝑏𝑏𝑙𝑙0 (𝜆𝜆)𝐶𝐶𝑙𝑙 For small and large particulate matter b0s and b0l is given by:

𝑏𝑏𝑠𝑠0 (𝜆𝜆) = 1.151302 (𝑚𝑚2 /𝑔𝑔)(

(12)

400 1.7 ) 𝜆𝜆

𝑏𝑏𝑙𝑙0 (𝜆𝜆) = 0.341074 (𝑚𝑚2 /𝑔𝑔)(

(13)

400 0.3 ) 𝜆𝜆

(14)

and the concentrations are expressed through the chlorophyll concentration as [31] 𝐶𝐶𝑠𝑠 = 0.01739(𝑔𝑔/𝑚𝑚𝑚𝑚) 𝐶𝐶𝑐𝑐 𝑒𝑒

𝐶𝐶 0.11631 � 0𝑐𝑐 �

(15)

𝐶𝐶 0.03092 � 0𝑐𝑐 �

(16)

𝐶𝐶𝑙𝑙 = 0.76284(𝑔𝑔/𝑚𝑚𝑚𝑚) 𝐶𝐶𝑐𝑐 𝑒𝑒

𝐶𝐶 𝑐𝑐

𝐶𝐶 𝑐𝑐

Beam attenuation coefficient is defined as the ration of energy absorbed or scattered from an incident power per unit distance and it shows the total energy loss, [24],[26]. c(λ) = α(λ) + β(λ)

(17)

where a(λ) is the absorption coefficient, b(λ) the scattering coefficient, λ the wavelength and α, b, c in units of m-1. In Table 1, typical values for α, b, c and C (Chlorophyll concentration) are shown for various types of ocean waters. Water Types

C (mg/m2)

α (m-1)

b (m-1)

c (m-1)

Deep Ocean waters

0.005

0.053

0.003

0.056

Clear waters

0.31

0.069

0.08

0.151

Near coasts

0.83

0.088

0.216

0.305

Murky waters

5.9

0.295

1.875

2.17

Table 1 Absorption Scattering and attenuation coefficients for 4 different water types [24], [26]. 5 COMMUNICATION LINK MODELS AND LINK BUDGET Line-of-Sight Communication Link An unobstructed path between the transmitter and the receiver is the most commonly used link in optical wireless communications. It is called Line of Sight (LOS) and the transmitter sends directly the light beam on the


direction of the receiver[28],[29]. 𝑑𝑑

𝑃𝑃𝑅𝑅_𝑙𝑙𝑙𝑙𝑙𝑙 = 𝑃𝑃𝑇𝑇 𝜂𝜂 𝛵𝛵 𝜂𝜂𝑅𝑅 𝐿𝐿𝑝𝑝𝑝𝑝 �𝜆𝜆,

𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

𝑃𝑃𝑅𝑅_𝑙𝑙𝑙𝑙𝑙𝑙 = 𝑃𝑃𝑇𝑇 𝜂𝜂 𝛵𝛵 𝜂𝜂𝑅𝑅 𝐿𝐿𝑝𝑝𝑝𝑝 �𝜆𝜆,


𝛢𝛢 𝑅𝑅𝑅𝑅𝑅𝑅 𝑐𝑐𝑐𝑐𝑐𝑐 𝜃𝜃

�

2𝜋𝜋𝑑𝑑 2 (1−𝑐𝑐𝑐𝑐𝑐𝑐 𝜃𝜃0 )

�

𝜋𝜋(𝑑𝑑 𝑡𝑡𝑡𝑡𝑡𝑡 𝜃𝜃0 )2

(18)

where 𝑃𝑃𝑇𝑇 , 𝜂𝜂 𝑇𝑇 , are the average transmitter optical power and the optical efficiency of the transmitter, 𝜂𝜂𝑅𝑅 is the optical efficiency of the receiver, 𝜃𝜃 is the angle between the perpendicular to the receiver and the transmitter-receiver trajectory, 𝛢𝛢𝑅𝑅𝑅𝑅𝑅𝑅 is the receiver aperture area, 𝜃𝜃0 is the laser beam divergence angle, d is the perpendicular distance between the transmitter and the receiver. When the transmitter beam divergence angle is very narrow (18) can be approximated as [24]: 𝑑𝑑

𝛢𝛢 𝑅𝑅𝑅𝑅𝑅𝑅 𝑐𝑐𝑐𝑐𝑐𝑐 𝜃𝜃

(19)

Modulating retro-reflector communication link This communication scenario is mostly used when one party (submarine or a diver) has more resources from the other In this case the system combines an optical retro reflector and an optical modulator. For example in a submarine-diver communication, the submarine has more energy, payload and lifting capacity than the diver and thus most of the complexity and power requirement of the communication system is being placed into the submarine. In a modulating retro-reflector link, the interrogator sits at one end, (in our case on the submarine), and a small modulating optical retro-reflector sits, at the remote end. In operation, the interrogator illuminates the retroreflecting end of the link with a continuous wave beam and the retro-reflector inactively reflects this beam back to the interrogator while modulating the information on it [6]. The received power is given by [24] 𝑃𝑃𝑅𝑅_𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = 𝑃𝑃𝑇𝑇 𝜂𝜂 𝛵𝛵 𝜂𝜂𝑅𝑅𝑅𝑅𝑅𝑅 𝜂𝜂𝑅𝑅𝑅𝑅𝑅𝑅 𝑟𝑟𝑟𝑟 𝐿𝐿𝑝𝑝𝑝𝑝 �𝜆𝜆,

2𝑑𝑑


��

𝛢𝛢 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑐𝑐𝑐𝑐𝑐𝑐 𝜃𝜃

� 𝑥𝑥 �

2𝜋𝜋𝑑𝑑 2 (1−𝑐𝑐𝑐𝑐𝑐𝑐 𝜃𝜃0 )

𝛢𝛢 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑐𝑐𝑐𝑐𝑐𝑐 𝜃𝜃

𝜋𝜋(𝑑𝑑 𝑡𝑡𝑡𝑡𝑡𝑡 𝜃𝜃0𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 )2

�

(20)

where 𝜂𝜂𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 is the optical efficiency of the retroreflector, 𝛢𝛢𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 is the retroreflector’s aperture area, and 𝜃𝜃0𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 is the retroreflector’s beam divergence angle [24]. Reflective Communication Link Sometimes the line of sight is not available due to obstructions, misalignment, or random orientation of the transceivers. To address this problem a reflective communication link could be used. In this case, the laser transmitter emits a cone of light, defined by inner and outer angles θmin and θmax, in the upward direction [28]. 𝐴𝐴𝑎𝑎𝑎𝑎𝑎𝑎 = 2𝜋𝜋(ℎ + 𝑥𝑥)2 (1 − 𝑐𝑐𝑐𝑐𝑐𝑐𝜃𝜃𝑚𝑚𝑚𝑚𝑚𝑚 − 1 + 𝑐𝑐𝑐𝑐𝑐𝑐𝜃𝜃𝑚𝑚𝑚𝑚𝑚𝑚 ) = 2𝜋𝜋(ℎ + 𝑥𝑥)2 (𝑐𝑐𝑐𝑐𝑐𝑐𝜃𝜃𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑐𝑐𝑐𝑐𝑐𝑐𝜃𝜃𝑚𝑚𝑚𝑚𝑚𝑚 )

(21)

This equation describes an annular area taken from a sphere of radius h+x, which would have uniform power density in free space. If we model the ocean-air surface as smooth, then θ = θi and we can derive the link budget by using the variables defined in equation of line of sight scenario. Then we can define the auxiliary function and calculate the received power as [28]: 𝑓𝑓𝑅𝑅𝑟𝑟𝑟𝑟𝑟𝑟 (𝜃𝜃) =

𝑃𝑃 𝑇𝑇 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝛢𝛢 𝑎𝑎𝑎𝑎𝑎𝑎

2

2

⎧ 𝜂𝜂 𝛵𝛵 𝜂𝜂𝑅𝑅 𝐿𝐿𝑝𝑝𝑝𝑝 �𝜆𝜆, ℎ +𝑥𝑥 � 1 ��tan (𝜃𝜃𝑡𝑡 −𝜃𝜃 )� + �sin (𝜃𝜃𝑡𝑡 −𝜃𝜃 )� � , 𝜃𝜃𝑚𝑚𝑚𝑚𝑚𝑚 ≤ 𝜃𝜃 ≤ 𝜃𝜃𝑐𝑐 ⎫ 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 2 tan (𝜃𝜃𝑡𝑡 +𝜃𝜃 ) sin (𝜃𝜃𝑡𝑡 +𝜃𝜃 ) � ⎨ 𝜂𝜂 𝜂𝜂 𝐿𝐿 �𝜆𝜆, ℎ +𝑥𝑥 � , 𝜃𝜃𝑐𝑐 ≤ 𝜃𝜃 ≤ 𝜃𝜃𝑚𝑚𝑚𝑚𝑚𝑚 ⎬ 𝛵𝛵 𝑅𝑅 𝑝𝑝𝑝𝑝 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 ⎩ ⎭

(22)

At the plane of the receiving sensor, node coverage is provided within an annular area bounded by radii (h + x) tan(θmin) and (h + x)tan(θmax). Equation (7) can be further simplified on the assumption that the receiver aperture is small relative to (h+ x) yielding the approximate received power as [28]: 𝑃𝑃𝑅𝑅_𝑟𝑟𝑟𝑟𝑟𝑟 (𝜃𝜃) ≈ 𝛢𝛢𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑓𝑓𝑅𝑅𝑟𝑟𝑟𝑟𝑟𝑟 (𝜃𝜃)

(23)

Among the scenarios we discussed, the line of sight scenario is most effective than the other two. A hybrid communication system which would include both an optical and an acoustical transceiver could improve the availability of the network by using the optical transceiver for high data rate transmissions, when the water turbidity is low and when it increases it can be switched to the acoustic transceiver and in low data rates. Additional improvements to the availability of the network could be achieved by a hybrid communication system that would include an optical transceiver and an acoustical transceiver. A hybrid communication system can provide high data rate transmission by using optical transceiver. When the water turbidity is high or the distance between the terminals


is large, the system can be switch to low data rate using the acoustic transceiver, thereby increase in the average data rate and availability [29]. 6 BIT ERROR RATE The simplest and most widespread modulation technique in FSO is intensity modulation in the form of On–Off keying (OOK). The detection method is direct detection. In this technique, the receiver is based on the emerging technology of silicon photomultipliers _SiPMs_ [15], [24], [28]. These photodetector devices are fabricated in the form of arrays of photodiodes that are operated in Geiger mode to create a photon-counting device [24],[28]. If we assume that a large number of photons are received, then according to the central limit theorem, the Poisson distribution can be approximated by a Gaussian distribution and the BER is given by [24] 1

𝐵𝐵𝐵𝐵𝐵𝐵 = 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 � 2

𝑟𝑟1 𝑇𝑇−𝑟𝑟0 𝑇𝑇 � 1 1 √2�(𝑟𝑟1 𝑇𝑇) �2 +(𝑟𝑟2 𝑇𝑇) �2 �

(24)

Here r1=rd+rbg+rs and r0=rd+rbg, where rd and rbg represent the sources of additive noise due to dark counts and background illumination, respectively, [24]: 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒(𝜓𝜓) =

2 ∞ ∫ √𝜋𝜋 𝜓𝜓

exp(−𝛾𝛾 2 ) 𝑑𝑑𝛾𝛾

(25)

7 CONCLUSIONS There has been a dramatic increase in the use of optical techniques underwater over the past few years. Optical links are a viable option for high bandwidth wireless links underwater. Because of the challenging underwater environment, laser links will have the most utility in short range scenarios (