**Underwater Optical Wireless Communication Systems: A Concise Review**

Lydia K. Gkoura, George D. Roumelas, Hector E. Nistazakis, Harilaos G. Sandalidis, Alexander Vavoulas, Andreas D. Tsigopoulos and George S. Tombras

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/67915

#### Abstract

Underwater optical wireless communications (UOWC) have gained a considerable interest during the last years as an alternative means for broadband inexpensive submarine communications. UOWC present numerous similarities compared to free space optical (FSO) communications or laser satellite links mainly due to the fact that they employ optical wavelengths to transfer secure information between dedicated point-to-point links. By using suitable wavelengths, high data rates can be attained. Some recent works showed that broadband links can be achieved over moderate ranges. Transmissions of several Mbps have been realized in laboratory experiments by employing a simulated aquatic medium with scattering characteristics similar to oceanic waters. It was also demonstrated that UOWC networks are feasible to operate at high data rates for medium distances up to a hundred meters. However, it is not currently available as an industrial product and mainly test-bed measurements in water test tanks have been reported so far. Therefore, extensive research is expected in the near future, which is necessary in order to further reveal the "hidden" abilities of optical spectrum to transfer broadband signals at higher distances. The present work summarizes the recent advances in channel modeling and system analysis and design in the area of UOWC.

Keywords: underwater optical wireless communications (UOWC), channel modeling, propagation phenomena, oceanic turbulence, experimental studies

## 1. Introduction

The present work summarizes the recent advances in channel modeling and system analysis and design in the area of underwater optical wireless communications (UOWC). UOWC have

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

gained a considerable interest during the last years as an alternative means for broadband inexpensive submarine communications.

The technology that is mostly used nowadays among divers, ships, etc. is mainly based on acoustic wave transmission. However, it is restricted to several hundreds of kbps at ranges of a few kilometers, supports slow data rates, and distresses marine mammals such as dolphins and whales. On the other hand, traditional electromagnetic (EM) waves are highly attenuated in water due to both absorption and scattering. Therefore, they can be used only for relatively short-range real-time applications in the order of a few centimeters to a few meters.

EM waves in the visible spectrum, for example, optical signals between 400 and 700nm, propagate faster in water than acoustic ones. However, the optical transmitters and receivers must be located at a short distance, since turbulence and multiscattering effects significantly deteriorate the performance. Chromatic dispersion also causes temporal broadening of the optical pulses. In contrast to the above impairments, seawater shows a decreased absorption in the blue/green region of the visible spectrum. Hence, using suitable wavelengths, high data rates can be attained. Moreover, some recent works showed that broadband links can be achieved over moderate ranges. Transmissions of several Mbps have been realized in laboratory experiments by employing a simulated aquatic medium with scattering characteristics similar to oceanic waters. It was also demonstrated that UOWC networks are feasible to operate at high data rates for medium distances up to a hundred meters.

UOWC present numerous similarities compared to free space optical (FSO) communications or laser satellite links mainly due to the fact that they employ optical wavelengths to transfer secure information between dedicated point-to-point links. It constitutes an alternate and effective transmission technique for underwater communications, instead of the traditional acoustic one. However, it is not currently available as an industrial product and mainly testbed measurements in water test tanks have been reported so far. Therefore, extensive research is expected in the near future which is necessary in order to further reveal the "hidden" abilities of optical spectrum to transfer broadband signals at higher distances.

In the current chapter, we outline the main characteristics of UOWC channel models based on theoretical and experimental results, the phenomena limiting their performance, and the key research trials reported so far for this novel branch of optical wireless systems. A brief review of acoustic and EM communication techniques is also presented, which helps the readers better understand the different ways UOWC operates.

## 2. Wave transmission in the aquatic medium

#### 2.1. Acoustic waves

Until today, underwater transmission is attained by employing acoustic waves. This technology supports, relatively, low data rates for medium distances and does not ensure the link security. Furthermore, the information signal delay is quite increased. It is a legacy technology, and even it works at long distances, it can only establish low speed transmissions. Therefore, it is inappropriate for broadband transmission driven by the current and ongoing communication demands.

gained a considerable interest during the last years as an alternative means for broadband

The technology that is mostly used nowadays among divers, ships, etc. is mainly based on acoustic wave transmission. However, it is restricted to several hundreds of kbps at ranges of a few kilometers, supports slow data rates, and distresses marine mammals such as dolphins and whales. On the other hand, traditional electromagnetic (EM) waves are highly attenuated in water due to both absorption and scattering. Therefore, they can be used only for relatively

EM waves in the visible spectrum, for example, optical signals between 400 and 700nm, propagate faster in water than acoustic ones. However, the optical transmitters and receivers must be located at a short distance, since turbulence and multiscattering effects significantly deteriorate the performance. Chromatic dispersion also causes temporal broadening of the optical pulses. In contrast to the above impairments, seawater shows a decreased absorption in the blue/green region of the visible spectrum. Hence, using suitable wavelengths, high data rates can be attained. Moreover, some recent works showed that broadband links can be achieved over moderate ranges. Transmissions of several Mbps have been realized in laboratory experiments by employing a simulated aquatic medium with scattering characteristics similar to oceanic waters. It was also demonstrated that UOWC networks are feasible to

UOWC present numerous similarities compared to free space optical (FSO) communications or laser satellite links mainly due to the fact that they employ optical wavelengths to transfer secure information between dedicated point-to-point links. It constitutes an alternate and effective transmission technique for underwater communications, instead of the traditional acoustic one. However, it is not currently available as an industrial product and mainly testbed measurements in water test tanks have been reported so far. Therefore, extensive research is expected in the near future which is necessary in order to further reveal the "hidden"

In the current chapter, we outline the main characteristics of UOWC channel models based on theoretical and experimental results, the phenomena limiting their performance, and the key research trials reported so far for this novel branch of optical wireless systems. A brief review of acoustic and EM communication techniques is also presented, which helps the readers

Until today, underwater transmission is attained by employing acoustic waves. This technology supports, relatively, low data rates for medium distances and does not ensure the link security. Furthermore, the information signal delay is quite increased. It is a legacy technology, and even it works at long distances, it can only establish low speed transmissions. Therefore, it

short-range real-time applications in the order of a few centimeters to a few meters.

operate at high data rates for medium distances up to a hundred meters.

abilities of optical spectrum to transfer broadband signals at higher distances.

better understand the different ways UOWC operates.

2. Wave transmission in the aquatic medium

2.1. Acoustic waves

inexpensive submarine communications.

220 Turbulence Modelling Approaches - Current State, Development Prospects, Applications

Although sound travels decently through air, it travels much better through water. The speed of sound in clear air is 340m/s, which is almost four times smaller than the speed of sound in water, which is 1500m/s. However, it is much smaller than the speed of light and EM waves.

The speed at which sound travels through water is highly dependent on the temperature, pressure, and salinity of the water. While the sound waves travel through water, the energy is absorbed by the aquatic medium and can be transformed to other forms, such as heat [1]. Roughly speaking, the main impairments of underwater acoustic transmission are presented in the sequel.

Path Loss: The attenuation or path loss in an underwater channel is frequency dependent and expressed as [2]

$$A(l,f) = l^k a(f)^l \tag{1}$$

where l is the distance between the transmitter and the receiver, f is the frequency of the signal, k is the propagation constant with values usually between 1 and 2, and a(f) is the absorption coefficient, which depends on frequency. The cause for the frequency dependence is the energy absorption of the pressure waves and the spreading loss that increases by the distance. The seawater absorption coefficient is expressed by the sum of chemical relaxation processes and absorption from pure water [3]

$$\alpha = \frac{A\_1 P\_1 f\_1 f^2}{f\_1^2 + f^2} + \frac{A\_2 P\_2 f\_2 f^2}{f\_2^2 + f^2} + A\_3 P\_3 f^2 \tag{2}$$

where f<sup>1</sup> and f<sup>2</sup> are for the relaxation process in boric acid and magnesium sulfate parameters, P<sup>1</sup> and P<sup>2</sup> are parameters for pressure, and A1, A2, and A<sup>3</sup> are constants.

Multipath: The multipath propagation is a common problem for underwater acoustic links and causes the acoustic signals to reach the receiver following different multiple paths. In general, reflected waves from the bottom, from the surface, or from other objects are received from the transmitter. Moreover, sound speed variations with depth create wave refraction [4, 5]. As a result, the receiver detects more than one pulses with a different amplitude phase and instant of arrival [6]. An efficient expression for the channel impulse response is the following [7]

$$\mathcal{L}(\boldsymbol{\pi},t) = \sum\_{P} A\_P(t)\delta(\boldsymbol{\pi} - \boldsymbol{\pi}\_p(t))\tag{3}$$

where APðtÞ is the path amplitude and τpðtÞ is the path delay, both time dependent.

The transmission range, the depth, the geometry of the channel, the frequency, and the sound speed profile are the main factors that create multipath effects. As a result, horizontal channels (according to the direction of the wave with respect of the ocean bottom) exhibit longer multipath spreads, whereas vertical channels have little time dispersion [8]. Multipath propagation can severely deteriorate the acoustic signal as it generates intersymbol interference (ISI) [9].

Noise: Noise is created by machines which are in use or by shipping activities usually in high traffic areas. Another kind of noise is ambient noise, which is mostly related to hydrodynamics caused by the movement of water from one place to another like currents or tides. Weather effects on the sea like winds, rains, storms, atmospheric turbulence, thermal noise, seismic, and biological phenomena can also induce noise [2, 8]. The primary sources of noise in shallow waters seem to be created by ships and snapping shrimps [10].

Doppler spread: Doppler frequency spread is caused by the relative motion between the transmitter and the receiver. ISI is also related to Doppler spread mostly in high data rate transmissions where adjacent symbols interfere at the receiver. The Doppler effect can be estimated by the ratio a¼Ur/c where Ur is the relative velocity between the transmitter and the receiver, and c is the signal propagation speed. The Doppler factor is about a¼10�<sup>4</sup> due to the relatively low frequency of the acoustic signals inside water (1500m/s) [2, 8, 11].

Even at short ranges, the acoustic channel is limited to low data rates under Mbps. For medium ranges (1–10km), the data rate drops to approximately 10kbps, and eventually at very long ranges (>100km), the data rate is less than 1kbps [9, 12, 13]. Therefore, the acoustic wave transmission cannot satisfy the needs of new demanding technologies because of the inability to achieve high data rate communications in real-time operation.

#### 2.2. EM waves

EM waves in the RF band can be used in order to achieve faster wireless transmission. They are also unaffected by temperature and depth. Attenuation is the main effect of water in all EM waves, due to both absorption and scattering. EM wave behavior in freshwater and seawater is quite different and that is due to the fact that sea water is a high-loss medium. Propagation velocity and the absorptive loss of EM waves can be described as functions of carrier frequency [14, 15].

EM waves inside water are highly frequency dependent and proportional to the square root of frequency. This is the main reason for using low frequencies VLF and ELF. VLF band consists of radio waves between 3 and 30kHz, can achieve data rates of 300bit/s, and is able to penetrate seawater at a depth of 20m. ELF band (3–300Hz) can penetrate seawater at depths of hundreds of meters, something quite useful for communications between submarines.

To sum up, the main limitations of EM waves are the big antenna size needed in freshwater and the high attenuation for seawater [16]. Available commercial products for underwater in RF band can achieve bit rates of 100bps for a range of several decades of meters. 1–10Mbps within 1m range has been reported, as well [17].

#### 2.3. Optical waves

Optical wireless communications are a relatively new technology providing many serious advantages, such as the very high rates of data transmission, secure links, very small and light size of the transceiver components, including apertures, low installation and operational cost, and no need of licensing fees and tariffs, since the optical band is not included in the telecommunications regulations [18]. Optical wireless uses modulated optical beams in order to establish short, medium or long communications. Unfortunately, because the propagation medium is the free space, the performance and the reliability of these systems depend mainly on the weather conditions between the receiver and the transmitter [19, 20].

multipath spreads, whereas vertical channels have little time dispersion [8]. Multipath propagation can severely deteriorate the acoustic signal as it generates intersymbol interference

Noise: Noise is created by machines which are in use or by shipping activities usually in high traffic areas. Another kind of noise is ambient noise, which is mostly related to hydrodynamics caused by the movement of water from one place to another like currents or tides. Weather effects on the sea like winds, rains, storms, atmospheric turbulence, thermal noise, seismic, and biological phenomena can also induce noise [2, 8]. The primary sources of noise in shallow

Doppler spread: Doppler frequency spread is caused by the relative motion between the transmitter and the receiver. ISI is also related to Doppler spread mostly in high data rate transmissions where adjacent symbols interfere at the receiver. The Doppler effect can be estimated by the ratio a¼Ur/c where Ur is the relative velocity between the transmitter and the receiver, and c is the signal propagation speed. The Doppler factor is about a¼10�<sup>4</sup> due to

Even at short ranges, the acoustic channel is limited to low data rates under Mbps. For medium ranges (1–10km), the data rate drops to approximately 10kbps, and eventually at very long ranges (>100km), the data rate is less than 1kbps [9, 12, 13]. Therefore, the acoustic wave transmission cannot satisfy the needs of new demanding technologies because of the

EM waves in the RF band can be used in order to achieve faster wireless transmission. They are also unaffected by temperature and depth. Attenuation is the main effect of water in all EM waves, due to both absorption and scattering. EM wave behavior in freshwater and seawater is quite different and that is due to the fact that sea water is a high-loss medium. Propagation velocity and the absorptive loss of EM waves can be described as functions of carrier frequency [14, 15].

EM waves inside water are highly frequency dependent and proportional to the square root of frequency. This is the main reason for using low frequencies VLF and ELF. VLF band consists of radio waves between 3 and 30kHz, can achieve data rates of 300bit/s, and is able to penetrate seawater at a depth of 20m. ELF band (3–300Hz) can penetrate seawater at depths of hundreds of meters, something quite useful for communications between submarines.

To sum up, the main limitations of EM waves are the big antenna size needed in freshwater and the high attenuation for seawater [16]. Available commercial products for underwater in RF band can achieve bit rates of 100bps for a range of several decades of meters. 1–10Mbps

Optical wireless communications are a relatively new technology providing many serious advantages, such as the very high rates of data transmission, secure links, very small and light

the relatively low frequency of the acoustic signals inside water (1500m/s) [2, 8, 11].

inability to achieve high data rate communications in real-time operation.

within 1m range has been reported, as well [17].

waters seem to be created by ships and snapping shrimps [10].

222 Turbulence Modelling Approaches - Current State, Development Prospects, Applications

(ISI) [9].

2.2. EM waves

2.3. Optical waves

EM waves in the visible spectrum (400–700nm) present an alternative way to provide broadband communications in the water. They propagate faster in water (300,000,000m/s) than the acoustic ones (∼340m/s in air–∼1500m/s in water), which is about 200,000 times faster than sound travels through water. That is the main reason why they have gained a considerable interest during the last years to serve as a broadband (10–100Mbps), safe (non-interceptable), and reliable complement to legacy acoustic underwater communications systems [6].

In general, optical signals are highly absorbed in water, and this is one of the main disadvantages; the other one is the optical scattering by all the particles existing inside the sea. However, seawater shows a decreased absorption in the blue/green region of the visible spectrum. Thus, using suitable wavelengths, for instance in the blue/green region, high speed connections can be attained according to the type of water (400–500nm for clear to 300–700nm for turbid water conditions). Minimum attenuation is centered near 0.460μm in clear waters and shifts to higher values for dirty waters approaching 0.540μm for coastal waters [21, 22].

Roughly speaking, the power received P(z), given initial power P0, propagating through a medium of thickness z is estimated by the Beer's Law as follows

$$P(z) = \,\_0P\_0 e^{-c(\lambda)z} \tag{4}$$

c(λ)(m�<sup>1</sup> ) is the extinction coefficient expressing the total attenuation occurred by the propagation through the water. According to the Haltrin's model in Ref. [23], the total attenuation can be described as the sum of absorption and scattering. For a completely absorbing or completely scattering medium, the total attenuation coefficient in Eq. (4) can be replaced with the absorption coefficient, that is, a, or scattering coefficient, that is, b, respectively. The product cz is also referred as attenuation length, and it contributes on the reduction of the received power by a factor of exp(�1), or ~63% [24]. Based on the above, we have

$$\mathfrak{c}(\lambda) = \mathfrak{a}(\lambda) + \beta(\lambda) \tag{5}$$

where a(λ) is the absorption coefficient, b(λ) is the scattering coefficient, and λ is the wavelength.

Beer's Law provides a limited applicability as it describes only the attenuation due to absorption and single scattering events. In reality, however, many cases of multiple scattering may occur. Also it presumes that the source and receiver are in exact alignment with each other, and it can be applied only in Line-of-Sight (LOS) communication scenarios. Moreover, Beer's Law ignores temporal dispersion [25].

More accurate expressions have to take the link geometry into account. For instance, assuming that the transmitter and receiver are positioned in a LOS configuration, the received power can be estimated by [24]

$$P\_R(\mathbf{t}, \mathbf{r}, \mathbf{z}) = \,^P P\_T(\mathbf{t}) D\_T L\_w(\mathbf{t}, \mathbf{r}, \mathbf{z}) D\_R \tag{6}$$

where PR(t, r, z) is the received power dependent on time t, lateral displacement from the beam axis r, and range z, PT (t) represents the transmitted power, DT is the aperture and divergence of the optical source, and D<sup>R</sup> is the photoreceiver aperture and field of view. The channel loss term, L<sup>W</sup> (t, r, z), characterizes the spatial and temporal characteristics of light propagation in seawater.

## 3. UOWC propagation phenomena

## 3.1. Aquatic medium characteristics

The aquatic medium contains almost 80 different elements, dissolved or suspended in pure water, with different concentrations. Some of them are listed below [26, 27]


Since chlorophyll absorbs the blue and red wavelengths and the particles strongly contribute to the scattering coefficient, we can use its concentration C (in mg/m<sup>3</sup> ) as the free parameter to calculate the absorption and scattering coefficients [23, 28].

The exact type of water plays a significant role in the estimation of the amount of chlorophyll concentration and consequently the amount of absorption and scattering for a specific geographic location. A classification system for the clarity of water types based on their spectral optical attenuation depth zk ¼ <sup>1</sup> kd = was proposed by Jerlov in 1968. This classification was made in the upper portions of the ocean, and it was based on spectral irradiance transmittance measurements [29]. The four major water types that are usually referred in the literature are the following [30, 31]

• Pure deep ocean waters cobalt blue where the absorption is high and the scattering coefficient is low.


#### 3.2. Absorption

More accurate expressions have to take the link geometry into account. For instance, assuming that the transmitter and receiver are positioned in a LOS configuration, the received power can

224 Turbulence Modelling Approaches - Current State, Development Prospects, Applications

where PR(t, r, z) is the received power dependent on time t, lateral displacement from the beam axis r, and range z, PT (t) represents the transmitted power, DT is the aperture and divergence of the optical source, and D<sup>R</sup> is the photoreceiver aperture and field of view. The channel loss term, L<sup>W</sup> (t, r, z), characterizes the spatial and temporal characteristics of light propagation in

The aquatic medium contains almost 80 different elements, dissolved or suspended in pure

• Various dissolved salts such as NaCl, MgCl2, etc, which absorb light at specific wavelengths

• Detrital and mineral components, for example, sand, metal oxides, which contribute to both

• Colored dissolved organic matters such as fulvic and humic acids which affect absorption,

• Organic matters such as viruses, bacteria, and organic detritus which add backscattering,

• Phytoplankton with chlorophyll-A which strongly absorbs in the blue-red region and scat-

Since chlorophyll absorbs the blue and red wavelengths and the particles strongly contribute

The exact type of water plays a significant role in the estimation of the amount of chlorophyll concentration and consequently the amount of absorption and scattering for a specific geographic location. A classification system for the clarity of water types based on their spectral optical attenuation depth zk ¼ <sup>1</sup> kd = was proposed by Jerlov in 1968. This classification was made in the upper portions of the ocean, and it was based on spectral irradiance transmittance measurements [29]. The four major water types that are usually referred in the literature are

• Pure deep ocean waters cobalt blue where the absorption is high and the scattering coeffi-

) as the free parameter to

water, with different concentrations. Some of them are listed below [26, 27]

to the scattering coefficient, we can use its concentration C (in mg/m<sup>3</sup>

calculate the absorption and scattering coefficients [23, 28].

PRðt, r, zÞ ¼ PTðtÞDTLwðt, r, zÞDR ð6Þ

be estimated by [24]

3. UOWC propagation phenomena

3.1. Aquatic medium characteristics

and induce scattering effects.

absorption and scattering.

ters green light.

the following [30, 31]

cient is low.

mainly in blue and ultraviolet wavelengths.

especially in the blue spectral range.

seawater.

The absorption coefficient, αðλÞ, is the ratio of the absorbed energy from an incident power per unit distance due to various dissolved particles such as phytoplankton, detritus, etc. [19, 23]

$$a(\lambda) = \left(a\_w(\lambda) + a\_c^0(\lambda)(\mathbb{C}\_c/\mathbb{C}\_c^0)^{0.602} + a\_f^0 \mathbb{C}\_f e^{-k\_f \lambda} + a\_h^0 \mathbb{C}\_h e^{-k\_h \lambda} \tag{7}$$

where <sup>α</sup>wðλ<sup>Þ</sup> is the absorption by the pure water in m�<sup>1</sup> , λ is the wavelength in nm, α<sup>0</sup> <sup>c</sup> ðλÞ is the absorption coefficient of chlorophyllin m�<sup>1</sup> , Cc is the total concentration of chlorophyll per cubic meter (C<sup>0</sup> <sup>C</sup> <sup>¼</sup> 1mg/m<sup>3</sup> ), α<sup>0</sup> <sup>f</sup> <sup>¼</sup> 35.959 m2 /mg is the absorption coefficient of fulvic acid, kf <sup>¼</sup> 0.0189 nm�<sup>1</sup> , α<sup>0</sup> <sup>h</sup> <sup>¼</sup> 18.828 m2 /mg is the absorption coefficient of humic acid, and kh <sup>¼</sup> 0.01105 nm�<sup>1</sup> . The concentrations Cf and Cc, are expressed through Cc as follows

$$\mathbf{C}\_{f} = 1.74098 \ \mathbf{C}\_{c} e^{0.12327 \begin{pmatrix} \frac{C\_c}{C\_c} \\ \frac{C\_c}{C\_c} \end{pmatrix}} \tag{8}$$

$$\mathbf{C}\_{\hbar} = 0.19334 \ \mathbf{C}\_{c} \mathbf{e}^{0.12343\left(\frac{c\_c}{C\_c}\right)}\tag{9}$$

#### 3.3. Scattering

Scattering coefficient, bðλÞ, is the ratio of energy scattered from an incident power per unit distance. It is the sum of backward scattering, bbðλÞ, and forward scattering coefficient, bfðλÞ.

Scattering is caused by small and large particles. Small particles are the particles with refractive index equal to 1.15, whereas large particles have a refractive index of 1.03.

The scattering and backscattering coefficients are calculated as follows [23]

$$b(\lambda) = b\_w(\lambda) + b\_s^0(\lambda)\mathbb{C}\_s + b\_l^0(\lambda)\mathbb{C}\_l \tag{10}$$

$$b\_B(\lambda) = 0.5b\_w(\lambda) + B\_s b\_s^0(\lambda)\mathbb{C}\_s + B\_l b\_l^0(\lambda)\mathbb{C}\_l \tag{11}$$

For small and large particulate matter, b0 <sup>s</sup> and b0 <sup>l</sup> are given as follows

$$b\_s^0(\lambda) = 1.151302 \ (m^2/g) \left(\frac{400}{\lambda}\right)^{1.7} \tag{12}$$

$$b\_l^0(\lambda) = 0.341074 \ (m^2/\text{g}) \left(\frac{400}{\lambda}\right)^{0.3} \tag{13}$$

and the concentrations are expressed through the chlorophyll concentration as follows

$$\mathbf{C}\_{s} = 0.01739 \, (\text{g/mg}) \, \mathbf{C}\_{c} \mathbf{e}^{0.11631 \begin{pmatrix} \frac{\mathbf{C}\_{c}}{\mathbf{C}\_{c}}\\\end{pmatrix}} \tag{14}$$

$$\text{C}\_{l} = 0.76284 \text{(g/mg)} \text{ C}\_{c} e^{0.03092 \left(\frac{\text{C}\_{c}}{\text{C}\_{c}}\right)} \tag{15}$$

#### 3.4. Oceanic turbulence

Optical wireless communications are greatly affected by optical turbulence, which refers to random fluctuations of the refraction index. In the case of underwater systems, these fluctuations are mainly caused by variations in temperature and salinity of the oceanic water.

An important parameter for the description of oceanic turbulence is the scintillation index, which expresses the variance of the wave intensity. As shown in Ref. [32], when a Gaussian beam propagates through weak turbulence and without taking into consideration the scattering phenomenon, the scintillation index is expressed as the sum of two components

$$
\sigma\_l^2(\overrightarrow{r}\,,L,\lambda) = \sigma\_{l,l}^2(0,L,\lambda) + \sigma\_{l,r}^2(\overrightarrow{r}\,,L,\lambda),
\tag{16}
$$

where

$$\sigma\_{l,l}^2(\mathbf{0}, L, \lambda) = 8\pi^2 k^2 L \left[ \int\_0^\pi \kappa \Phi\_n(\kappa) \exp\left(-\frac{\ell \Lambda \kappa^2 \xi^2}{k}\right) \times \left[1 - \cos\left(\frac{L\kappa^2}{k} \xi \left(1 - (1 - \Theta)\xi\right)\right)\right] d\kappa \, d\xi \right] \tag{17}$$

is the longitudinal component and

$$\sigma\_{l,r}^2(\overrightarrow{r}',L,\lambda) = 8\pi^2k^2L \left| \int\_0^\infty \kappa \Phi\_n(\kappa) \exp\left(-\frac{\Lambda L\kappa^2\xi^2}{k}\right) [I\_0(2\Lambda r\xi\kappa) - 1] d\kappa \,d\xi\right|\tag{18}$$

is the radial component. In the above equations, λ is the wavelength, k is the wave number, L is the direction of propagation, κ is the magnitude of spatial frequency, ξ is the normalized path length, I0ðxÞ is the zero order Bessel function, and Λ, Θ are parameters of the Gaussian beam given by

$$A = \frac{\frac{2L}{kW\_0^2}}{\left(\frac{2L}{kW\_0^2}\right)^2 + \left(1 - \frac{L}{F\_0}\right)^2} \tag{19}$$

and

$$\Theta = \frac{1 - \frac{L}{F\_0}}{\left(\frac{2L}{k\mathcal{W}\_0^2}\right)^2 + \left(1 - \frac{L}{F\_0}\right)^2} \tag{20}$$

where W<sup>0</sup> is the radius of the Gaussian beam at the 1/e amplitude at the plane of propagation and F<sup>0</sup> is the radius of curvature of the beam wavefront. The function ΦnðκÞ is the power spectrum of turbulence and for homogeneous and isotropic oceanic waters takes the form [32]

$$\Phi\_n(\kappa) = 0.38 \cdot 10^{-8} \varepsilon^{-\frac{1}{3}} \kappa^{-\frac{1}{3}} \left[ 1 + 2.35 (\kappa \eta)^{\frac{2}{3}} \right] \frac{X\_T}{w^2} (w^2 e^{-A\_T \delta} + e^{-A\_S \delta} - 2w e^{-A\_{TS} \delta}) \tag{21}$$

where <sup>η</sup> <sup>¼</sup> <sup>10</sup>�<sup>3</sup> <sup>m</sup> is the Kolmogorov microscale, <sup>ε</sup> is the rate of dissipation of turbulent kinetic energy per unit mass of fluid, χΤ is the rate of dissipation of mean-square temperature, δ ¼ 8:284ðκηÞ <sup>4</sup>=<sup>3</sup> <sup>þ</sup> <sup>12</sup>:978ðκη<sup>Þ</sup> 2 , and AT, AS, and ATS are constants with values AT <sup>¼</sup> <sup>1</sup>:<sup>863</sup> · <sup>10</sup>�<sup>2</sup> , AS <sup>¼</sup> <sup>1</sup>:<sup>9</sup> · <sup>10</sup>�<sup>4</sup> , and ATS <sup>¼</sup> <sup>9</sup>:<sup>41</sup> · <sup>10</sup>�<sup>3</sup> . The unitless variable w is the relative strength of the fluctuations caused by either temperature or salinity.

Cs ¼ 0:01739ðg=mgÞ Cce

226 Turbulence Modelling Approaches - Current State, Development Prospects, Applications

Cl ¼ 0:76284ðg=mgÞ Cce

tions are mainly caused by variations in temperature and salinity of the oceanic water.

ing phenomenon, the scintillation index is expressed as the sum of two components

Ι,l

k � �

κΦnðκ<sup>Þ</sup> exp � <sup>Λ</sup>Lκ<sup>2</sup>ξ<sup>2</sup>

is the radial component. In the above equations, λ is the wavelength, k is the wave number, L is the direction of propagation, κ is the magnitude of spatial frequency, ξ is the normalized path length, I0ðxÞ is the zero order Bessel function, and Λ, Θ are parameters of the Gaussian beam given by

> 2L kW<sup>2</sup> 0

<sup>þ</sup> <sup>1</sup> � <sup>L</sup> F0

F0

<sup>þ</sup> <sup>1</sup> � <sup>L</sup> F0

! , L, <sup>λ</sup>Þ ¼ <sup>σ</sup><sup>2</sup>

κΦnðκ<sup>Þ</sup> exp � <sup>Λ</sup>Lκ<sup>2</sup>ξ<sup>2</sup>

σ2 <sup>Ι</sup>ðr

Optical wireless communications are greatly affected by optical turbulence, which refers to random fluctuations of the refraction index. In the case of underwater systems, these fluctua-

An important parameter for the description of oceanic turbulence is the scintillation index, which expresses the variance of the wave intensity. As shown in Ref. [32], when a Gaussian beam propagates through weak turbulence and without taking into consideration the scatter-

<sup>ð</sup>0, L, <sup>λ</sup>Þ þ <sup>σ</sup><sup>2</sup>

<sup>Ι</sup>,rðr

· 1 � cos

k � � Lκ<sup>2</sup> k ξ �

� �� � �

! , L, <sup>λ</sup>Þ, <sup>ð</sup>16<sup>Þ</sup>

1 � ð1 � ΘÞξ

½I0ð2ΛrξκÞ � 1�dκ dξ ð18Þ

� �<sup>2</sup> <sup>ð</sup>19<sup>Þ</sup>

� �<sup>2</sup> <sup>ð</sup>20<sup>Þ</sup>

3.4. Oceanic turbulence

<sup>ð</sup>0, L, <sup>λ</sup>Þ ¼ <sup>8</sup>π<sup>2</sup>

σ2 <sup>Ι</sup>,rðr k2 L ð 1

is the longitudinal component and

0

! , L, <sup>λ</sup>Þ ¼ <sup>8</sup>π<sup>2</sup>

k 2 L ð 1

0

ð ∞

0

Λ ¼

2L kW<sup>2</sup> 0 � �<sup>2</sup>

<sup>Θ</sup> <sup>¼</sup> <sup>1</sup> � <sup>L</sup>

2L kW<sup>2</sup> 0 � �<sup>2</sup>

where W<sup>0</sup> is the radius of the Gaussian beam at the 1/e amplitude at the plane of propagation and F<sup>0</sup> is the radius of curvature of the beam wavefront. The function ΦnðκÞ is the power spectrum of turbulence and for homogeneous and isotropic oceanic waters takes the form [32]

ð ∞

0

where

σ2 Ι,l

and

0:11631 Cc C0 c � �

0:03092 Cc C0 c � � ð14Þ

ð15Þ

dκ dξ

ð17Þ

The separation between weak and strong turbulence is usually done via Rytov variance σ<sup>2</sup> R, which is the scintillation index when a plane wave is considered. More specifically, values of σ2 <sup>R</sup> ≪ 1 correspond to weak fluctuations, whereas σ<sup>2</sup> <sup>R</sup>≫1 indicates a strong turbulence regime. In contrast to atmospheric studies, strong oceanic turbulence appears at distances shorter than 100m [32].

The fading coefficient can be computed statistically using a proper distribution depending on the turbulence regime. As discussed in Ref. [33], the log-normal distribution is used in situations of weak fluctuations, and its probability density function (PDF) can be written as follows [34]

$$f\_{\tilde{h}}(\tilde{h}) = \frac{1}{2\tilde{h}\sqrt{2\pi\sigma\_X^2}} \exp\left(-\frac{(\ln\tilde{h} - 2\mu\_X)^2}{8\sigma\_X^2}\right) \tag{22}$$

The fading coefficient in the above Eq. (22) takes the form <sup>~</sup><sup>h</sup> <sup>¼</sup> <sup>e</sup><sup>2</sup><sup>X</sup>, where <sup>X</sup> is the fading logamplitude with mean μΧ and variance σ<sup>2</sup> <sup>Χ</sup>. Normalizing the fading coefficient so as to ensure that fading does not affect the average power leads to μΧ ¼ �σ<sup>2</sup> Χ.

For strong turbulence, the distribution that is usually used is the K distribution with PDF [34]

$$f\_{\tilde{h}}(\tilde{h}) = \frac{2\alpha}{\Gamma(\alpha)} (\alpha \tilde{h})^{\frac{(\alpha - 1)}{2}} K\_{\alpha - 1} \left( 2\sqrt{\alpha \tilde{h}} \right) \tag{23}$$

where <sup>Γ</sup>ðα<sup>Þ</sup> is the Gamma function, <sup>α</sup> <sup>¼</sup> <sup>2</sup>=ðσ<sup>2</sup> <sup>Ι</sup> � 1Þ is a positive parameter, and KpðxÞ is the pth order modified Bessel function of the second kind.

Jamali et al. [34] also proposed the combination of exponential and log-normal distributions, creating a two-lobe distribution, to better describe situations of received signals with a large dynamic range. Such a case corresponds to the extensive intensity fluctuations of the received signal, due to the presence of air bubbles. The PDF of this two-lobe distribution is as follows

$$f\_{\tilde{h}}(\tilde{h}) = \frac{k}{\mathcal{Y}} \exp\left(-\frac{\tilde{h}}{\mathcal{Y}}\right) + \frac{(1-k)\exp\left(-\frac{(\ln\tilde{h}-\mu)^2}{2\sigma^2}\right)}{\tilde{h}\sqrt{2\pi\sigma^2}}\tag{24}$$

where k determines the balance between the two distributions, γ is the mean of the exponential distribution, and μ, σ<sup>2</sup> are the mean and variance of the log-normal distribution, respectively.

## 4. Link budget and modulation techniques

#### 4.1. Link budget

Empirical path loss models are effective enough to estimate the received optical power for underwater communications under LOS conditions. Several models appeared in the literature but the most generic is the following which considers the transmitter power, telescope gain, and losses [6, 19]

$$P\_r = P\_t \eta\_t \eta\_r \varepsilon^{\frac{-c(\lambda)\mathbb{R}}{\text{COS}}} \frac{A\_R \cos \theta}{2\pi \, R^2 (1 - \cos \theta\_0)} \tag{25}$$

where P<sup>t</sup> is the transmitted power, η<sup>t</sup> and η<sup>r</sup> are the optical efficiencies of the Tx and Rx correspondingly, c(λ) is the extinction coefficient, R is the perpendicular distance between the Tx plane and the Rx plane, θ<sup>0</sup> is the Tx beam divergence angle, θ is the angle between the perpendicular to the Rx plane and the Tx-Rx trajectory, and Ar is the receiver aperture area [19].

#### 4.2. Optical modulation techniques

The most simple and widespread modulation technique is the indirect modulation with direct detection (IM/DD) with on-off keying (OOK). OOK is divided into two categories, the return to zero (RZ) OOK and the non-return to zero (NRZ). The expressions for the anticipated bit error rate (BER) are usually produced using the Poisson model for photon arrival in photon counters [6, 19].

The main disadvantage of OOK modulation is that it requires dynamic thresholding for the direct detection; something not necessary for pulse position modulation (PPM). Here, the transmitter transmits a light pulse and creates a specific time slot, while the receiver detects the pulse, calculates its position, and reforms the signal to the original pulse [35]. PPM consumes lower energy but it has lower bandwidth efficiency. For the L-PPM scheme, the symbol corresponds to M ¼ log2 L bits. Other modified PPM modulations have been proposed such as differential pulse position modulation (DPPM), dual pulse interval modulation (DPIM), and dual header pulse interval modulation (DH-PIM).

By exploiting the different polarization states of light, we can improve the performance of UOWC systems in case of intense backscattering, turbulence, and ambient light. Such a way was proposed in Ref. [36], where a binary polarization shift keying (BPolSK) system was employed. Another modulation technique with better numerical results is the polarized PPM (P-PPM) [37]. P-PPM is a combination of PPM and PolSK and manages to maintain the benefits of both schemes improving data rate, BER, and link distance.

## 5. Research on UOWC systems

Research on UOWC is a quite intriguing topic, and several experiments were carried out worldwide. The following are some indicative of the many studies presented in the open technical literature. For more information, the readers are referred to the complete surveys of Refs. [38, 39], which examine the UOWC area in more details.

4. Link budget and modulation techniques

228 Turbulence Modelling Approaches - Current State, Development Prospects, Applications

Pr ¼ Ptη<sup>t</sup>

(DPIM), and dual header pulse interval modulation (DH-PIM).

of both schemes improving data rate, BER, and link distance.

5. Research on UOWC systems

ηre �cðλÞR COS θ

Empirical path loss models are effective enough to estimate the received optical power for underwater communications under LOS conditions. Several models appeared in the literature but the most generic is the following which considers the transmitter power, telescope gain,

2π R<sup>2</sup>

where P<sup>t</sup> is the transmitted power, η<sup>t</sup> and η<sup>r</sup> are the optical efficiencies of the Tx and Rx correspondingly, c(λ) is the extinction coefficient, R is the perpendicular distance between the Tx plane and the Rx plane, θ<sup>0</sup> is the Tx beam divergence angle, θ is the angle between the perpendicular to the Rx plane and the Tx-Rx trajectory, and Ar is the receiver aperture area [19].

The most simple and widespread modulation technique is the indirect modulation with direct detection (IM/DD) with on-off keying (OOK). OOK is divided into two categories, the return to zero (RZ) OOK and the non-return to zero (NRZ). The expressions for the anticipated bit error rate (BER) are usually produced using the Poisson model for photon arrival in photon counters

The main disadvantage of OOK modulation is that it requires dynamic thresholding for the direct detection; something not necessary for pulse position modulation (PPM). Here, the transmitter transmits a light pulse and creates a specific time slot, while the receiver detects the pulse, calculates its position, and reforms the signal to the original pulse [35]. PPM consumes lower energy but it has lower bandwidth efficiency. For the L-PPM scheme, the symbol corresponds to M ¼ log2 L bits. Other modified PPM modulations have been proposed such as differential pulse position modulation (DPPM), dual pulse interval modulation

By exploiting the different polarization states of light, we can improve the performance of UOWC systems in case of intense backscattering, turbulence, and ambient light. Such a way was proposed in Ref. [36], where a binary polarization shift keying (BPolSK) system was employed. Another modulation technique with better numerical results is the polarized PPM (P-PPM) [37]. P-PPM is a combination of PPM and PolSK and manages to maintain the benefits

Research on UOWC is a quite intriguing topic, and several experiments were carried out worldwide. The following are some indicative of the many studies presented in the open

AR cos θ

<sup>ð</sup><sup>1</sup> � cosθ0<sup>Þ</sup> <sup>ð</sup>25<sup>Þ</sup>

4.1. Link budget

and losses [6, 19]

[6, 19].

4.2. Optical modulation techniques

An optical modem capable of optical data mulling was designed and implemented in 2005 at Massachusetts Institute of Technology by Vasilescu et al. [40]. They used a LED with 532nm, 700mW radiant power and a PIN photodiode receiver with surface area of 8 mm2 . They employed DPIM at an average data rate of 320kb/s with 2bits per pulse. A 4% packet loss communication over 7m distance and a close to error-free over 6.4m through clear waters was noticed.

Two early versions of AquaOptical, that is, a lightweight device for high rate long range underwater point-to-point communication are shown in Ref. [41]. The researchers used a Luxeon V LED at 470nm (480 mW) or 532nm (700mW) and a PDB-C156 photodiode in the first version. This is actually a miniaturized version capable of error-free communication in ocean water at data rates of 4Mbps over a distance of 2.2m (470nm) and 2.4m (532nm). In the second one, they employed an array of six such LEDs and an avalanche photodiode, and they managed to achieve a BER of 0.05 at 8m. The improved AquaOptical II with 18 LEDs and APD at the receiver was demonstrated in 2010. It operated at 470nm with total transmit power of 10W. Data rates of 4Mb/s at 50m in a swimming pool were achieved using NRZ amplitude modulation with 2bits per symbol [42, 43]. In Ref. [44], a robot estimating its position according to a sensor node in a data mulling application—another usage of Aquaoptical II was described.

A link budget analysis of NLOS geometries and variations of point-to-point links performed in 2005 and 2006 at Woods Hole Oceanographic Institution (Woods Hole MA USA), by Farr et al. [45]. Their work is only valid in clear waters because they do not take spatial dispersion and multiple scattering into account even if they consider the attenuation coefficient. Their analysis showed that a LOS link could achieve 10Mbps at 100m with 6mW of transmitted power. However, for the NLOS link, a 50-fold increase in transmit power is necessary to achieve the same data rates at similar range due to broader transmit beams. In 2008, they achieved transmission, at a distance of 200m for a data rate of 5Mbps, and in 2010, at a distance of 108m for a data rate of 10Mbps [46, 47].

In 2006, Cochenour et al. used BPSK with a 70-MHz radiofrequency (RF) carrier at Naval Air Warfare Center to accomplice error-free communication at a data rate of 1 Mb/s in deep turbid water. Emission wavelength was 532nm and output power 500mW [48]. The work was extended in 2007, to 5Mbps with QPSK, 8-PSK, 16-QAM and 32-QAM modulations and output power 750mW [49]. Results showed that even in turbid waters (c¼3.0/m and cz¼11), no loss of modulation depth, that is, no temporal dispersion of the 70MHz carrier was observed, even with a large receiver FOV of approximately 100degrees. As such, the only channel impairment was due to attenuation. Therefore, with enough optical power (∼3W), a 32-QAM link achieved almost 5Mbps.

Hanson and Radic [30] presented a Monte Carlo model to predict the spreading of an optical pulse for different water types for various FOVs. They managed to improve the signal to noise ratio (SNR) by increasing the FOV for low frequencies. They also observed temporal dispersion at high frequencies. After some manipulations, they eventually achieved 1GHz transmission over a 2m water pipe that simulated coastal ocean waters with 36dB of attenuation. Moreover, Jaruwatanadilok [50] tried to predict temporal dispersion by following the vector radiative transfer theory to model the UOWC channel which includes the multiple scattering effects and polarization. He examined the effect of the transmission distance on channel dispersion and showed a diminishing value of ISI for high data rates over a long distance.

In 2008, Cochenour et al. [31], conducted an analysis of multiple scattering special effects. They measured the beam-spread function experimentally in a large test tank, by scanning a photodetector laterally to the beam axis after the beam has propagated some distance. Results showed that in clear waters, the intensity falls off rapidly with lateral distance from the beam. However, their estimation ignored any impact of temporal dispersion. In another study on spatial dispersion, they investigated the impact of absorption on forward scattered light [51]. Later the authors also launched a set up which measured the transmission of light modulated at frequencies up to 1GHz in simulated ocean water up to 55 attenuation lengths [52–54]. Finally, the authors examined a retro-reflecting link and managed to reduce the contribution of backscattered light using polarization discrimination techniques [55].

An experiment conducted in North Carolina State University where a 405nm laser with OOK was tested in a water tank of 3.66m long. At first, a reliable transmission at 500kbps was achieved [56]. Some years later, a duplex communication at 1Mbps was attained [57]. Moreover, Simpson et al. created two separated optical beams of 405nm with two transmitters and two receivers combined with a beam splitter [58]. In a later work, they presented two set ups, one in 3m through turbid water and the other over a length of 7.7m through less turbid water and achieved 5Mbps throughput [59].

Dalgleish et al. [60] developed a Monte Carlo simulation method to estimate impulse responses for a particular system hardware design over a large range of environmental conditions in turbid ocean environments. Furthermore, a powerful tool to evaluate the performance of an underwater system for autonomous underwater vehicle communications was presented in Ref. [61]. Experimental tests were also carried out. Hardware modules and circuits design for underwater optical point to point links are also discussed in Ref. [62].

NLOS arrangements where optical beams are reflected in the atmosphere-water interface were discussed in Ref. [6]. These geometries have the benefit to avoid occasional obstructions but they do not have the same performance as LOS links. Gabriel et al. [27] assumed a Monte Carlo model of an underwater channel and simulated the trajectories of the emitted photons. They considered several parameters, for example, the transmitter beam width and beam divergence, beam wavelength, link distance, FOV, water types and turbidity, and aperture size. They reached the conclusion that the channel delay spread is nearly zero when the scattering albedo is moderate in small distances.

In the last years, the research is focused on spatial diversity, as a way to improve overall the performance contaminated by turbulence. This is usually accomplished by adding more sources or detectors. Moreover, aperture averaging methods were proposed. In Ref. [63], Yi et al. implemented an aperture averaging technique on the scintillation index for either plane or spherical waves, in order to annihilate the negative effects of fading resulting from oceanic turbulence. A multiple-input single-output (MISO) link was described in Ref. [64], where the source is replaced by a uniform circular array of sources, and the photons are collected by a single detector. The numerical results indicated a degradation in BER, under turbulence conditions. A single-input multiple-output (SIMO), consisting of a LED as a source and a concentric circular array of lenses as a detector, was discussed in Ref. [65]. The system manages to extend the effective communication range by about 20m, even in the case of strong turbulence. A more general set up of the multiple-input multiple-output (MIMO) systems was presented in Ref. [66]. Finally, in Ref. [67], a spatial diversity technique in combination with optical amplification to further improve performance was proposed.

## 6. Conclusions

at high frequencies. After some manipulations, they eventually achieved 1GHz transmission over a 2m water pipe that simulated coastal ocean waters with 36dB of attenuation. Moreover, Jaruwatanadilok [50] tried to predict temporal dispersion by following the vector radiative transfer theory to model the UOWC channel which includes the multiple scattering effects and polarization. He examined the effect of the transmission distance on channel dispersion and

In 2008, Cochenour et al. [31], conducted an analysis of multiple scattering special effects. They measured the beam-spread function experimentally in a large test tank, by scanning a photodetector laterally to the beam axis after the beam has propagated some distance. Results showed that in clear waters, the intensity falls off rapidly with lateral distance from the beam. However, their estimation ignored any impact of temporal dispersion. In another study on spatial dispersion, they investigated the impact of absorption on forward scattered light [51]. Later the authors also launched a set up which measured the transmission of light modulated at frequencies up to 1GHz in simulated ocean water up to 55 attenuation lengths [52–54]. Finally, the authors examined a retro-reflecting link and managed to reduce the contribution

An experiment conducted in North Carolina State University where a 405nm laser with OOK was tested in a water tank of 3.66m long. At first, a reliable transmission at 500kbps was achieved [56]. Some years later, a duplex communication at 1Mbps was attained [57]. Moreover, Simpson et al. created two separated optical beams of 405nm with two transmitters and two receivers combined with a beam splitter [58]. In a later work, they presented two set ups, one in 3m through turbid water and the other over a length of 7.7m through less turbid water

Dalgleish et al. [60] developed a Monte Carlo simulation method to estimate impulse responses for a particular system hardware design over a large range of environmental conditions in turbid ocean environments. Furthermore, a powerful tool to evaluate the performance of an underwater system for autonomous underwater vehicle communications was presented in Ref. [61]. Experimental tests were also carried out. Hardware modules and circuits design

NLOS arrangements where optical beams are reflected in the atmosphere-water interface were discussed in Ref. [6]. These geometries have the benefit to avoid occasional obstructions but they do not have the same performance as LOS links. Gabriel et al. [27] assumed a Monte Carlo model of an underwater channel and simulated the trajectories of the emitted photons. They considered several parameters, for example, the transmitter beam width and beam divergence, beam wavelength, link distance, FOV, water types and turbidity, and aperture size. They reached the conclusion that the channel delay spread is nearly zero when the scattering albedo

In the last years, the research is focused on spatial diversity, as a way to improve overall the performance contaminated by turbulence. This is usually accomplished by adding more sources or detectors. Moreover, aperture averaging methods were proposed. In Ref. [63], Yi et al. implemented an aperture averaging technique on the scintillation index for either plane

showed a diminishing value of ISI for high data rates over a long distance.

230 Turbulence Modelling Approaches - Current State, Development Prospects, Applications

of backscattered light using polarization discrimination techniques [55].

for underwater optical point to point links are also discussed in Ref. [62].

and achieved 5Mbps throughput [59].

is moderate in small distances.

The need to provide broadband wireless communications for underwater applications will be increasing in the forthcoming years. UOWC constitutes an alternate and effective transmission technique which can attain this scope, instead of the traditional acoustic one. Due to this fact, several studies on UOWC systems were devised worldwide in the recent years. The present study provided a concise review of the key advances in channel modeling and experimental works reported so far in the technical literature.

## Author details

Lydia K. Gkoura<sup>1</sup> , George D. Roumelas<sup>1</sup> , Hector E. Nistazakis<sup>1</sup> \*, Harilaos G. Sandalidis2 , Alexander Vavoulas<sup>2</sup> , Andreas D. Tsigopoulos<sup>3</sup> and George S. Tombras1

\*Address all correspondence to: enistaz@phys.uoa.gr

1 Department of Electronics, Computers, Telecommunications and Control, Faculty of Physics, National and Kapodistrian University of Athens, Athens, Greece

2 Department of Computer Science and Biomedical Informatics, University of Thessaly, Lamia, Greece

3 Department of Battle Systems, Naval Operations, Sea Studies, Navigation, Electronics and Telecommunications, Hellenic Naval Academy, Piraeus, Greece

## References

[1] Stojanovic M. Preisig J., (2009), ''Underwater Acoustic Communication Channels: Propagation Models and Statistical Characterization'', IEEE Communications Magazine Volume: 47 Issue: 1


[17] Lanbo L., Shengli Zhou, and Jun-Hong Cui, (2008) "Prospects and problems of wireless communication for underwater sensor networks", Wireless Communications and Mobile Computing, Vol. 8, No. 8, pp. 977–994

[2] Vall L.D., (2011), Towards Underwater Video Transmission, MSc Thesis, Massachusetts

[3] Ainslie M. A., McColm J. G., (1998), "A simplified formula for viscous and chemical absorption in sea water", Journal of the Acoustical Society of America, Vol. 103, No. 3,

[4] Stojanovic M., (2008), "Underwater acoustic communications: Design considerations on the physical layer", IEEE/IFIP Fifth Annual Conference on Wireless On demand Network Systems and Services (WONS 2008), Garmisch-Partenkirchen Germany, January 2008,

[5] Urick Robert J., (1983), "Principles of underwater sound", Book, Peninsula Publishing,

[6] Arnon S. and Kedar D., (2009), "Non-line-of-sight underwater optical wireless communication network", Journal of the Optical Society of America A, Vol. 26, No. 3, pp. 530–539

[7] Li B., Stojanovic M., Freitag L., and Willett P., (2008), "Multicarrier communication over underwater acoustic channels with nonuniform Doppler shifts". IEEE Journal of Oceanic

[8] Akyildiz I.F., Pompili D., and Melodia T., (2005), "Underwater acoustic sensor networks:

[9] Kilfoyle D. B., and Baggeroer A. B., (2000), "The state of the art in underwater acoustic

[10] Glegg S.A.L., Pirie R., LaVigne A.,(2000) "A study of ambient noise in shallow water",

[11] Stojanovic M.,(2003) "Acoustic (underwater) communications", in J.G. Proakis (Ed.),

[12] Stojanovic M., (1996), "Recent advances in high-speed underwater acoustic communica-

[13] Pelekanakis C., Stojanovic M., Freitag L., (2003), "High rate acoustic link for underwater video transmission", OCEANS 2003, 22–26 September 2003, Vol. 2, pp. 1091–1097 [14] Balanis C. A., (1989), Advanced Engineering Electromagnetics, John Wiley & Sons, New

[15] Pei L.V., Junhua H., Renkui Z., Haiying L., (2008), "The application of underwater optics and its development", Information Optics and Photonics Technologies II, Vol. 6837, pp. 7–8

[16] Gkoura L.K., Nistazakis H.E, Vavoulas A., Tsigopoulos A.D., and Tombras G.S., (2014) "Underwater optical wireless communications possibilities disadvantages and possible solutions" 6th International Conference from Scientific Computing to Computational

Research challenges", Ad Hoc Networks, Vol. 3, No. 3, pp. 257–279

telemetry", IEEE Journal of Oceanic Engineering, Vol. 25, No. 1, pp. 4–27

tions", IEEE Journal of Oceanic Engineering, Vol. 21, No. 2, pp. 125–136

Institute of Technology. https://seagrant.mit.edu/publications/

232 Turbulence Modelling Approaches - Current State, Development Prospects, Applications

pp. 1671–1672

Science , Los Altos CA

Engineering, Vol. 2, No. 33, pp. 198–209

Florida Atlantic University Technical Report

Engineering IC-SCCE, 9–12 July Athens

Encyclopedia of Telecommunications, Wiley, New York.

pp. 2–3

York, NY.


[43] Doniec M. and Rus D., (2010), "Bidirectional optical communication with AquaOptical II," in Communication Systems (ICCS), 2010 IEEE International Conference on, Nov. 2010, pp. 390–394

[30] Hanson R., and Radic S,(2008) "High bandwidth underwater optical communication",

[31] Cochenour B., Mullen L., Laux A., (2008), "Characterization of the beam-spread function for underwater wireless optical communications Links", IEEE Journal of Oceanic Engi-

[32] Korotkova O., Farwell N., and Shchepakina E., (2012) "Light scintillation in oceanic turbulence", Waves in Random and Complex Media, Vol. 22, No. 2, pp. 260–266

[33] Andrews L.C. and Phillips R.L., (2005) Laser Beam Propagation through Random Media, Date Published: 16 September 2005, Pages: 808, ISBN: 9780819459480, Volume: PM152, Published by SPIE The International Society of Optical Engineering, Bellingham Wash-

[34] Jamali M.V., Khorramshahi P., Tashakori A., Chizari A., Shahsavari S., Abdollah-Ramezani S., Fazelian M., Bahrani S., and Salehi J.A., (2016) "Statistical distribution of intensity fluctuations for underwater wireless optical channels in the presence of air bubbles", Iran Workshop on Communication and Information Theory IWCIT 2016, 3–4

[35] Meihong S., Xinsheng Y. and Fengli Z., (2009), "The evaluation of modulation techniques for underwater wireless optical communications", International Conference on Communication Software and Networks, Chengdu Sichuan China, 27–28 February 2009, pp. 138–142

[36] Cox W.C., Hughes B.L, and Muth J.F., (2009) "A polarization shift-keying system for underwater optical communications", OCEAN 2009, Biloxi MS USA, 26–29 October 2009

[37] Dong Y., Zhang T., and Zhang X., (2013) "Polarized pulse position modulation for wireless optical communications", 2013 47th Annual Conference on information Sciences and

[38] Kaushal H. and Kaddoum G., (2016), "Underwater optical wireless communication",

[39] Zeng Z., Zhang H., Dong Y, and Cheng J., (2017) "A Survey of underwater wireless

[40] Vasilescu I., Kotay K., Rus D., Dunbabin M., Corke P., (2005), "Data collection, storage, and retrieval with an underwater sensor network", ACM Proc. 3rd International Conference on Embedded Networked Sensor Systems (SenSys), San Diego California USA, 2–4

[41] Doniec M., Vasilescu I., Mandar C., Detweiler C., Hoffmann-Kuhnt M., Rus D., "AquaOptical: A Lightweight Device for High-rate Long-range Underwater Point-to-Point Communication" Marine Technology Society Journal, Vol. 44, No. 4, pp. 55–65 [42] Doniec M., Detweiler C., Vasilescu I, and Rus D., (2010), "Using optical communication for remote underwater robot operation", 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Taipei Taiwan, 18–22 October 2010, pp. 4017–4022

optical communication," IEEE Communication. Survey Tutorials, to appear

Systems (CISS), Baltimore Maryland, 20–22 March 2013

IEEE Access, Vol. 4, pp. 1518–1547

November 2005, pp. 154–165

Applied Optics, Vol. 47, No. 2, pp. 277–283

234 Turbulence Modelling Approaches - Current State, Development Prospects, Applications

neering, Vol. 33, No.4, pp. 513–521

ington 98227-0010 USA

May 2016


[56] Cox W., (2008), "A 1Mbps underwater communication system using a 405nm laser diode and photomultiplier tube," MSc Thesis, North Carolina State University USA

[57] Cox W., Simpson J., and Muth J., (2011), "Underwater optical communication using software defined radio over led and laser based links," Military Communications Con-

[58] Simpson J., Hughes B., and Muth J., (2009), "A spatial diversity system to measure optical fading in an underwater communications channel," OCEANS 2009, Biloxi MS USA, 26–

[59] Simpson J, Cox W., Krier J, Cochenour B., Hughes B., and Muth J., (2010), "5 Mbps optical wireless communication with error correction coding for underwater sensor nodes"

[60] Dalgleish F.R., Caimi F.M., Vuorenkoski A. K., Britton W.B., Ramos B, (2010),"Efficient laser pulse dispersion codes for turbid undersea imaging and communications applica-

[61] Anguita D., Brizzolara D., Parodi G., and Hu Q., (2011), "Optical wireless underwater communication for AUV: Preliminary simulation and experimental results", OCEANS

[62] Anguita D., Brizzolara D., and Parodi G., (2010), "Optical wireless communication for underwater wireless sensor networks: Hardware modules and circuits design and imple-

[63] Yi X., Li Z., and Liu Z., (2015) "Underwater optical communication performance for laser beam propagation through weak oceanic turbulence", Applied Optics, Vol. 54, No. 6, pp.

[64] Dong Y. and Liu J., (2016) "On BER performance of underwater wireless optical MISO links under weak turbulence", OCEANS 2016, Monterey CA USA, 19–23 September 2016

[65] Liu W., Xu Z., and Yang L., (2015) "SIMO detection schemes for underwater optical wireless communication under turbulence", Photonics Research, Vol. 3, No. 3, pp. 48–53

[66] Jamali M.V. and Salehi J.A., (2015) "On the BER of multiple-input multiple-output underwater wireless optical communication systems," 4th International Workshop on Optical Wireless Communications IWOW 2015, Istanbul Turkey, 07–08 September 2015, pp. 26–30

[67] Boucouvalas A., Peppas K., Yiannopoulos K., and Ghassemlooy Z., (2016) "Underwater optical wireless communications with optical amplification and spatial diversity," IEEE

ference, 2011 MILCOM 2011, Baltimore MD USA, pp. 2057–2062

236 Turbulence Modelling Approaches - Current State, Development Prospects, Applications

29 October 2009

1273, 2015

Sydney Australia, 24–27 May 2010

2011, Waikoloa HI USA, 19–22 September 2011

mentation", OCEANS 2010, Sydney Australia, 24–27 May 2010

Photonics Technology Letters, Vol. 28, No. 22, pp. 2613–2616

tions", Proc. SPIE, Vol. 7678

## *Edited by Konstantin Volkov*

Accurate prediction of turbulent flows remains a challenging task despite considerable work in this area and the acceptance of CFD as a design tool. The quality of the CFD calculations of the flows in engineering applications strongly depends on the proper prediction of turbulence phenomena. Investigations of flow instability, heat transfer, skin friction, secondary flows, flow separation, and reattachment effects demand a reliable modelling and simulation of the turbulence, reliable methods, accurate programming, and robust working practices. The current scientific status of simulation of turbulent flows as well as some advances in computational techniques and practical applications of turbulence research is reviewed and considered in the book.

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Turbulence Modelling Approaches - Current State, Development Prospects, Applications

Turbulence Modelling

Approaches

Current State, Development Prospects,

Applications

*Edited by Konstantin Volkov*