Analysis of Optical Wireless Communication Links in Turbulent Underwater Channels With Wide Range of Water Parameters

In this study, the performance of underwater optical wireless communication links is investigated by taking into account turbulence, absorption and scattering effects. Weak turbulent channel is modeled using log-normal distribution while moderate and strong turbulence channels are modeled using gamma-gamma distribution. Rytov variance of Gaussian beam is derived analytically for oceanic turbulence optical power spectrum. Subsequently, scintillation index is calculated using the computed Rytov variance. Moreover, the closed-form expression of bit-error-rate (BER) for underwater wireless optical communication (UWOC) systems using intensity-modulated/direct detection (IM/DD) implementation and on-off-keying (OOK) modulation scheme is obtained. Results show that the performance of wireless optical communication link between two platforms in underwater medium is degraded significantly due to turbulence, absorption and scattering. In fact, as the turbulence level increases, its effect becomes quantitatively comparable to those of absorption and scattering effects. The variation of both scintillation index and BER performance are presented for various underwater medium and communication system parameters, such as chlorophyll concentration, average temperature, average salinity concentration, temperature and dissipation rates, wavelength, link length and receiver aperture size. Optical network and internet of underwater things (IoUT) applications, which are growing day by day and requiring high data rates, will benefit from the results of this study.

communication and imaging, internet of underwater things (IoUT), underwater to ground communication, or underwater to satellite communication; underwater wireless optical communications (UWOC) have attracted the attention of many researchers in the last decades. However, the link length of UWOC systems is around tens of meters because of the combined effect of absorption, scattering and turbulence phenomena caused by the chaotic and harsh nature of the underwater medium. Absorption and scattering are the dominant factors that attenuate propagating optical wave in underwater medium. The attenuation and scattering coefficients are experimentally measured and formulated depending on the wavelength [2], [3], [4] in widely accepted water types classified by Jerlov, which are mainly based on the chlorophyll concentration [5], [6]. These absorption and scattering coefficients are the input of the Beer-Lambert Law to estimate the power attenuation. The characteristics of waters and particulate matters in underwater medium are analyzed in terms of absorption and scattering effects and also a UWOC channel modeling was investigated including various sources of noise by using radiative transfer theory [7]. The intensity fluctuations, represented by the scintillation index, resulting from turbulence in underwater medium were also investigated and the significant effect of the turbulence has been shown [8], [9].
The BER performance of FSO systems were analyzed for atmospheric turbulent channel conditions in various studies to characterize the turbulent channel effects [10], [11], [12]. Similar to atmospheric turbulence, studies are also carried out on the effect of underwater turbulent channels. The BER performance of UWOC systems was studied in various studies for different aspects and modulation schemes. The power, the signal-to-noise ratio (SNR) and BER of UWOC systems were investigated numerically for OOK, phase-shift keying (PSK) and pulse position modulation (PPM) modulation schemes when absorption and scattering effects are present in [13]. In [14], the signal response of orthogonal OOK modulated system was simulated. The performance of a UWOC system which uses 450 nm blue laser diode and orthogonal frequency division multiplexed (OFDM) quadrature amplitude modulation (QAM) was analyzed for 5.4 m distance and 4.8 Gbit/s data rate in clear water [15]. Similarly, OFDM QAM modulated UWOC system with 405 nm laser source for 4.8 m distance and 1. 45 Gbit/s data rate was studied in [16]. A UWOC system using multi-pulse pulse position modulation (MPPM) scheme and spatial receiver diversity was examined for weak underwater turbulence with lognormal distribution in [17]. An experimental study was performed on real-time video transmission with 520 nm laser diode for 5 m link using PSK and QAM modulation schemes [18]. The performance of PPM modulated UWOC system was studied in weak [19] and strong [20] oceanic turbulence depending on the medium's parameters. In [21], the efficiency of PPM and OOK modulations in UWOC systems was provided for a turbulent channel having exponentiated Weibull distribution. The performance of a UWOC system exercising differential PSK (DPSK) was evaluated for strong turbulence conditions using the gamma-gamma turbulence model [22] and for moderate to strong turbulence channels with aperture averaging effect [23]. The effect of the turbulence on OOK modulated UWOC system was presented for different types of channel models with different probability density functions [24]. Recently, an analysis of M-QAM modulated UWOC system operating in gamma-gamma turbulence channel with attenuation effects was reported [25].
Based on the unified statistical studies, turbulent channel models were examined based on both experimental and simulation data by using lognormal, gamma-gamma, generalized gamma, Weibull, exponentiated Weibull and K distributions, and results were obtained in the presence of variations in temperature, salinity and air bubbles [26], [27], [28], [29], [30]. In [26], the validity of statistical distributions was evaluated by using experimental results for weak to strong turbulence regimes. In [27], the irradiance fluctuations resulting from air bubbles and temperature gradients were obtained experimentally and it was shown that results perfectly match the simulation results obtained from the exponential generalized gamma distribution. The expectation and second order moment of the received power at the aperture were calculated depending on the statistics of air bubbles that obstruct the received power [28]. Furthermore, the distribution of the received power modeled by Weibull distribution and two of the Dirac delta functions and analytical results were verified with the simulation results. The performance of a dual-hop UWOC system operating in underwater medium (both outage probability and average BER) was analyzed for exponential-generalized Gamma distributed channel model in the presence of air bubbles and temperature gradients and it was shown that dual-hop UWOC system has potential to mitigate the turbulence effect [29]. The impact of spatial diversity techniques for orbital angular momentum (OAM) beams was investigated in [30] and significant improvement in the average channel capacity, BER and outage probability was reported. The unified statistical method related studies for optical wireless communication were also performed for adaptive optics that remains an important tool in terms of mitigating the turbulence effect [31], [32]. In [31], a defocud measurement aided adaptive optics compensation methdod was proposed for an OAM-based UWOC system to mitigate the turbulence induced crosstalk effect and to improve the security performance. The average BER, outage porobability and ergodic capacity of an OAMbased coherent UWOC link operating in Internet of Underwater Things (IoUT) system was studied in [32] and a noticeable performance improvement was obtained with the application of random-amplitude-masks-based adaptive optics technique.
The aforementioned turbulent channel analyses are based on the widely-used Nikishov's power spectrum [33]. Although Nikishov's power spectrum affords one the possibility of assessing the performance of the turbulent medium, it accepts the estimated ratios of temperature and salinity gradients. This allows for an inaccurate description of the underwater turbulent conditions. A new oceanic power spectrum model, called Oceanic Turbulence Optical Power Spectrum (OTOPS), has been introduced recently that accepts the practical average temperature and average salinity concentration of the underwater turbulent medium as inputs [34]. The OTOPS model has been developed for the average temperature <T> in the range of [0°C to 30°C] and the average salinity concentration in the range of [0 ppt to 40 ppt]. These ranges cover most of the natural water conditions in Earth basins.
Gamma-gamma and lognormal distributed channel models have found a wide usage since they have a simple mathematical form that is easy to compute. Moreover, lognormal and gammagamma channel models still yield more accurate results in weak and moderate-strong turbulence regimes, respectively, compared to their counterparts. With the development of UWOC, the longitudinal UWOC channel model with depth-dependent attenuation characteristics has received more attention. However, the depth-dependent characterization of underwater medium in terms of turbulence effect has not been expressed with an exact model yet. Although some works have been done assuming the layered structure and vertical link structure [35], [36], [37], the depth-dependent attenuation caharacteristics of underwater medium remain a hot topic to be further investigated among reseachers.
The goal of this study is to investigate the turbulent channel characteristics from weak to strong regimes by using the OTOPS model. First, the Rytov variance of a Gaussian beam propagating in underwater turbulent medium is obtained analytically by using OTOPS model. Then, the scintillation index variation is presented for a wide range of turbulent channels based on obtained Rytov variance. The weak underwater turbulence channel is modeled with lognormal distribution while moderate and strong underwater turbulence channels are modeled with gamma-gamma distribution. The closed-form analytical BER expressions are obtained for both lognormal and gamma-gamma turbulent channels. Moreover, the attenuations due to absorption and scattering are included and analyzed together with the turbulence effect. The analytical expression of BER is also obtained for lognormal and gamma-gamma turbulence channels including absorption and scattering effects. The absorption and scattering attenuations are calculated for practically used different water types, such as pure sea, clean ocean, coastal ocean and turbid harbor waters which are classified based on chlorophyll concentration. Then, using the closed-form expressions, the average BER performance of a UWOC system using Gaussian beam and exercising intensity modulation direct detection OOK modulation scheme is analyzed for various underwater turbulence parameters, such as temperature dissipation rate, energy dissipation rate, average temperature and average salinity concentration. The effects of receiver aperture size, wavelength and link length also are investigated. Finally, the BER variations in different water types are compared with each other and with only turbulence case.
Our motivation in this study is to: r utilize practical scenarios with real parameters to estimate the performance of UWOC systems operating between underwater platforms. We believe that our results will be useful for the exploration of turbulence, absorption and scattering effects on point-to-point or network-centric communication of underwater platforms using UWOC systems.

II. RYTOV VARIANCE AND SCINTILLATION INDEX FOR GAUSSIAN BEAM
To classify the strength of the turbulence, the Rytov perturbation theory, which models the perturbations as multiplicative terms and is obtained for unbounded plane wave, is conventionally used. Rytov perturbation theory, which is first validated for weak turbulence, was later extended for moderate to strong turbulence and is called extended Rytov theory. In this way, it was possible to calculate the scintillation index for wide range of turbulence regimes including Gaussian beam wave [38]. Here, we obtain a closed-form expression of Rytov variance for Gaussian beam and then use it to calculate the scintillation index in weak, moderate and strong turbulent regimes depending on the small-scale and large-scale log irradiance variances.

A. Rytov Variance
The Rytov variance of the Gaussian beam is [38] where k = 2π/λ is the wavenumber, λ is the wavelength, ξ is the normalized distance parameter, L is the propagation distance, κ is the magnitude of spatial frequency, Λ = Λ 0 /(Θ 2 0 + Λ 2 0 ) is the Fresnel ratio of Gaussian beam at receiver, Λ 0 = 2L/kW 2 0 , W 0 is the beam radius, Θ 0 = 1 − L/F 0 is the beam curvature parameter at the transmitter, F 0 is the phase front radius of curvature,Θ = 1 − Θ is the complementary parameter, is the beam curvature parameter at the receiver. In (1), the power spectrum of underwater turbulent medium is given by OTOPS model as [34] where T is the average temperature, S is the average salinity concentration, A and B are the linear coefficients, the three spectra Φ i (i ∈ {T, S, T S}) are given as [34] Φ i (κ) = 1 4π where η is the Kolmogorov microscale length, β 0 = 0.72, χ T is the rate of dissipation of mean-squared temperature, dissipation rate for co-spectrum, ε is the rate of dissipation of kinetic energy per unit mass of fluid and c i are the non-dimensional parameters and c T = 0.
c /2 respectively, P r and S c are Prandtl and Schmidt numbers.
For the sake of simplicity, setting Δ 1i = 21.61η 0.61 c 0.02 We will use the following formula based on Eq. (3.478-1) of [39] for the integration of κ terms in (4): (5) Applying (5) to (4), we see that the second and third terms have very close coefficients and powers (0.52835 and 0.55835) and the signs of coefficients are opposite. Then, leaving the first term with 5/6 power and neglecting the small terms, we arrive at To solve the integration of the second part in (6), we will use Eq. (3.194-1) of [39] u 0 Using the relationship in (7) and then combining the results for three spectra, the total Rytov variance for the Gaussian beam will be as

B. Scintillation Index
The aperture averaged scintillation index of Gaussian beam depending on the Rytov variance is found to be [38] here D G is the aperture size, σ 2 ln X (D G ) is the large-scale log variance and σ 2 ln Y (D G ) is the small-scale log variance, respectively, and are given by where σ 2 R is the Rytov variance of plane wave and found as [40], and Ω G = 2L/kW 2 G is the parameter characterizing the spot radius of the collecting lens, W G is the radius of the Gaussian lens and D 2 G = 8W 2 G . Here, the aperture-averaged scintillation index variation with different parameters is computed for various parameters. From this point on, the parameters in this study are fixed to L = 20 m, Parameter values are chosen to consider a wide range of turbulence conditions. The weak, moderate and strong (including saturation regime) turbulence boundaries described as σ 2 and σ 2 R > 1, respectively [41]. Any parameters that deviate from these values are defined on the figures or in the figure captions. Simulation results are obtained from MATLAB software package and parameters are chosen in the following way. Since absorption is the most dominant factor in underwater medium, the blue region of the visible light spectrum (∼ λ = 450 − 485 nm) yields minimal attenuation compared to other color ranges. However, to keep optical beam in weak, moderate and strong turbulence conditions, the wavelength is chosen in violet color region (λ = 417 nm) because of the dependency of the turbulent power spectrum on the wavelength and the tendency of the optical beam to fall in stronger turbulence conditions with the smaller wavelengths. Collimated Gaussian beam (F 0 = ∞) having the radius of W 0 = 2 cm is used. The average temperature and average salinity concentration are selected as T = 15 • C and S = 20 ppt to be at moderate levels. The distance is defined as L = 20 m that is a challenging distance but is in a realistic range for the optical wireless communication in underwater medium impacted by absorption, scattering and turbulence effects.
In Fig. 1, the scintillation indexes of plane, spherical and Gaussian beam waves are plotted versus link length. In [38], it was shown that the plane and spherical wave cases can be reproduced from Gaussian beam case by setting the Fresnel ratio and the beam curvature parameter of the Gaussian beam at the receiver as Λ = 0, Θ = 1(plane wave), and Λ = 0, Θ = 0 (spherical wave), respectively. The variations for the plane and spherical waves in Fig. 1 are obtained by setting Θ = 1, Λ = 0, and Θ = 0, Λ = 0. It can be seen that spherical wave yields smaller scintillation but the advantage of using spherical wave is lost when turbulence becomes strong. The scintillation indexes of all waves increase with the distance in weak, moderate and up to a certain level of strong turbulence regime then start to decrease slightly. This trend is related to the saturation phenomenon in turbulence regimes and it is explained by the persistence of the small scales of irradiance fluctuations. The occurrence of the saturation in the scintillation index is defined by Tatarskii's theory, which was experimentally analyzed in [42] in which it was evaluated that the eddies smaller than the Fresnel zone cause this effect. The saturation phenomenon is also observed in Fig. 4.
The variation of the scintillation index of a Gaussian beam with the receiver aperture size is given in Fig. 2 for several  wavelengths. It can be seen from Fig. 2 that the scintillation increases with a decrease of the wavelength. The scintillation index varies from σ 2 I (D G ) = 0.12 to σ 2 I (D G ) = 0.25 when wavelength decreases from λ = 750 nm to λ = 417 nm for a receiver with D G = 1 mm at the distance of L = 20 m. But we note that the superiority of higher wavelength is valid for turbulence effect. An optimization between absorption, scattering and turbulence is required to select the optimum operation wavelength of UWOC systems in underwater medium. The undeniable benefit of the aperture averaging effect can also be seen from The effects of temperature dissipation rate and average temperature on the scintillation index are shown in Fig. 3. Scintillation index tends to increase with the increase of temperature dissipation rate. Fixing average temperature to T = 20 • C, scintillation index changes from σ 2 I (D G ) = 0.00055 to σ 2 I (D G ) = 0.1161 with the variation of temperature dissipation rate from   Fig. 4, it is also seen that the combined effect of low energy dissipation rate and high average salinity concentration puts the Gaussian beam into saturation regime earlier. Therefore, the scintillation index for higher values of average salinity concentration remains lower than that of lower average salinity concentration in saturation regime. The scintillation index increase with the salinity and salinity gradient variation was shown in a water tank having 43 cm x 27 cm x 26 cm dimensions. The results presented showed that increasing the salinity from S = 0 ppt to S = 40 ppt results in an increase in the scintillation index from 3.1 to 3.4 [43].
We would like to emphasize that the temperature and salinity dependent variations given in Figs. 3 and 4 are the practical values that can be encountered in the most of the Earth's basins. This shows the superiority of the OTOPS model over Nikishov's model in terms of real values of average temperature and average salinity concentration. In Nikishov's power spectrum model, the effect of salinity and temperature is estimated by salinity and temperature contribution ratio that is denoted by ω and changes in the interval [−5,0]. The underwater turbulence is characterized as salinity dominant or temperature dominant when ω approaches 0 or -5, respectively. However, the value of ω does not give information about actual the values of temperature and salinity. This is the drawback of the Nikishov's power spectrum model compared to OTOPS model. The uncertainty of the temperature and salinity values in Nikishov's model does not allow one to make comparison between Nikishov and OTOPS power spectrum models.

III. UNDERWATER TURBULENT CHANNEL ANALYSIS
In this section, the BER performance of a UWOC system in underwater medium is investigated and results are derived only in terms of wide range turbulence effect.
The received signal (current in the output of the load resistance) for an optical wireless communication (OWC) system using intensity-modulated/direct detection (IM/DD) implementation and on-off-keying (OOK) modulation scheme can be modeled as [10] where , and T b denoting the responsivity of the p-i-n photodetector in A/W, the received optical power in watts, the j th data symbol taking on {01} with equal probability, the data pulse shape, and the bit duration in seconds, respectively. Without the loss of generality, we assume that p(t) is a unit amplitude, non-returnto-zero (NRZ) pulse shape. We also assume that h is the channel state (almost stationary as compared to the bit duration) and n 0 (t) is the additive white Gaussian noise (AWGN) having a zero mean. Considering only the turbulence effect; the channel state will be h = h a , where h a shows the attenuation due to underwater turbulence.
To perform data detection, the output current is integrated over a bit duration. We then have the decision variable for the j th bit duration as follows: where now n j is a zero-mean Gaussian random variable with the variance σ 2 n = σ 2 b + σ 2 dc + σ 2 th . In this equation, σ 2 b = P b R res T b denotes the contribution of the background radiation with the power of P b watts, σ 2 dc is the contribution of dark current and σ 2 dc = 2qI dc B w is the dark current variance with q and I dc denoting the charge of an electron (q = 1.6 × 10 −19 Coulombs) and the dark current in A, B w is the electronic bandwidth and σ 2 is the impact of thermal noise with k bolt = 1.3807 × 10 −23 , T 0 and R L denoting the Boltzmann's constant in J/K, the receiver temperature in Kelvin, and the load resistance in ohms, respectively. E b denotes the signal energy per bit for the OOK system. In this formulation, we assume a background noise/thermal noise limited detection.
When conditioned on h a , the conditional probability of bit error for the OOK system described above is P r (E|h a ) = is the signal-to-noise ratio (SNR) at the receiver in the absence of turbulence and erfc is the complementary error function.
The unconditional probability of error, or Bit-Error Rate (BER), for the UWOC system that uses the OOK modulation scheme is given by the expression (14) where f h (h) is the Probability Density Function (PDF) of the fluctuating light's intensity.

A. Log-Normal Channel Model
For weak turbulence conditions, the lognormal distribution of normalized irradiance fluctuations is given by [38] where σ 2 l = ln(σ 2 I + 1) is the log-irradiance variance. Expanding the square term in (15), we obtain (16) The erfc function given in (14) can be expanded by using the following expansion given in Eq. (8.4.14.2) of [44] as is the Meijer's G-functions. Then, substituting (16) and erfc expansion into (14), we obtain Changing variable as δ = ln(h a ) / 2σ 2 l , (17) becomes Using the approximation of Gauss-Hermite integration where w i s are the weight factor and x i s are the zeros of m th order Hermite polynomial, respectively, the average BER of a UWOC system operating in weak turbulent channel with log-normal distribution becomes

B. Gamma-Gamma Channel Model
In moderate to strong turbulence, we will use the gammagamma distributed channel model given [38] Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. According to (14) of [45], the modified Bessel function can be . Applying this approximation to the term in (21) and inserting (21) into (14), we have Using Eq. (2.24.1.1) of [44], the integral part with two Meijer's G functions can be solved. Then, the average BER for the moderate-to-strong turbulent channel with gamma-gamma distribution will be obtained as The Rytov variance and scintillation index obtained in Section II are used for BER performance analysis in both lognormal and gamma-gamma distributions. Looking at lognormal distribution in (15), the term σ 2 l = ln(σ 2 I + 1) uses the scintillation index σ 2 I as input using the small-scale, large-scale log variances and the Rytov variance sequentially. For gamma-gamma channel model in (21), the main parameters α and β are directly dependent on the small-scale log variance σ 2 lnX and large-scale log variance σ 2 lnY . Here, the average BER variation of a UWOC system with only the turbulence effects will be given. The average SNR is set toγ = 20 dB.
In Fig. 5, the average BER increases with the distance. The average BER increase is faster in weak turbulence than the moderate and strong turbulence. A UWOC system using D G = 5 mm aperture-sized receiver operates with the average BER values of 1 × 10 −4 , 3 × 10 −3 and 1 × 10 −2 at the distances of L = 15 m, L = 30 m and L = 50 m, respectively, showing the weak, moderate, and strong turbulence regimes. The considerable improvement in the average BER is obvious in Fig. 5. The average BER for a point receiver in weak, moderate, and strong turbulence takes the values of 2.87 × 10 −4 , 1.17 × 10 −2 , Fig. 6. BER as a function of receiver aperture size length for different wavelengths. Fig. 7.
BER as a function of temperature dissipation rate for different receiver aperture sizes. Fig. 8. BER as a function of energy dissipation rate for different receiver aperture sizes. and 2.55 × 10 −2 at the distances of L = 10 m, L = 30 m, and L = 50 m, respectively. However, the average BER value at the same distances falls to 4.57 × 10 −7 , 1.37 × 10 −5 , and 1.13 × 10 −4 when a receiver with D G = 2 cm aperture size is used. The decreasing trend of the average BER with the aperture averaging can also be seen from Figs. 6-10. For example, in Fig. 6, a UWOC system operating with λ = 532 nm yields the average BER values of 1.96 × 10 −3 , 3.04 × 10 −5 , and 4.15 × 10 −7 for the receiver aperture sizes D G = 1 mm, D G = 1 cm, and D G = 10 cm, respectively. This shows the significant improvement in the average BER with the increase of the receiver aperture size. The decrease in the average BER with an increase in the wavelength is also shown in Fig. 6.
Similar to our findings showing the performance improvement with aperture averaging in Figs. 5-10, the benefit of using a receiver with larger aperture size was experimentally shown Fig. 9. BER as a function of average temperature for different receiver aperture sizes. in [46] for aperture sizes D G = 0.5 cm, D G = 1.5 cm, and D G = 2.5 cm. Fig. 7 depicts the average BER variation versus temperature dissipation ratio when the receiver aperture size takes different values for a link of length L = 20 m. The average BER takes the higher values with the increase in temperature dissipation rate. For example, fixing the receiver aperture size at D G = 1 cm, the average BER is 3.26 × 10 −7 , 8.75 × 10 −7 , 3.66 × 10 −5 , and 6 × 10 −4 while the temperature dissipation rate increases as χ T = 1 × 10 −7 K 2 s −1 , χ T = 1 × 10 −6 K 2 s −1 , χ T = 1 × 10 −5 K 2 s −1 and χ T = 1 × 10 −4 K 2 s −1 , respectively. In Fig. 8, we have plotted the average BER variation versus the energy dissipation rate. It is observed that the average BER increases with the decrease in the energy dissipation rate. There is a slight decrease in the average BER in strong turbulence regime for some cases due to the saturation phenomenon. Setting the receiver aperture size to D G = 1 cm, the average BER increases as follows 2.19 × 10 −6 , 3.66 × 10 −5 , 2 .59 × 10 −4 , 7.33 × 10 −4 and then slightly decrease to 4.14 × 10 −4 when energy dissipation rate takes the values of ε = 1 × 10 −2 m 2 s −3 , ε = 1 × 10 −4 m 2 s −3 , ε = 1 × 10 −6 m 2 s −3 , ε = 1 × 10 −8 m 2 s −3 and ε = 1 × 10 −10 m 2 s −3 , respectively.
Figs. 9 and 10 reveal that the average BER increases monotonically with the rise of both average temperature and the average salinity concentration. However, the rate of increase in BER with the average salinity concentration remains a little lower than that of average temperature variation. The variation of the probability of error for a UWOC system was presented in [27] depending on the temperature and salinity gradients experimentally and another performance parameter, the outage probability, was shown to be increasing with an increase in both temperature and salinity gradients. Results and variation trends are consistent with our findings.

IV. UNDERWATER CHANNEL ANALYSIS WITH ABSORPTION, SCATTERING AND TURBULENCE EFFECTS
Here, we will analyze the combined effect of absorption, scattering and turbulence. Considering the absorption and scattering effect, the channel state becomes as h = h l h a , where h l is the attenuation due to the absorption and scattering. We note that the attenuation coefficient h l is a deterministic variable while the turbulence dependent channel state h a remains as a random variable with the lognormal and gamma-gamma distributions in this study. The absorption and scattering phenomenon are mainly dependent on the wavelength and distance. These phenomena cause attenuation of propagating optical beam resulting in energy loss. Besides absorption and scattering effects, refractive index fluctuations with random nature also affect optical beam in various aspects. It is known that statistically lognormal distributed channel model yields better results in weak turbulent regime and gamma-gamma distributed channel model becomes more effective in moderate-to-strong turbulence regimes. According to Beer-Lambert's law, the path loss resulting from absorption and scattering is given by where c(λ) is the attenuation coefficient depending on the wavelength λ and it is expressed as c (λ) = a(λ) + b(λ) where a(λ) and b(λ) are absorption and scattering coefficients, respectively. The most dominant factor in underwater medium is the absorption and it is mainly dependent on the Chlorophyll concentration (C c in mg/m 3 ) and waters are classified based on chlorophyll concentration [47] as given in Table I.

A. Absorption and Scattering Model
The absorption coefficient a(λ) is modeled as [48] a(λ) = a w (λ) + a cl (λ) + a f (λ) + a h (λ), where a w (λ) is the absorption coefficient of pure water (1/m) and is given for optically and chemically pure water depending on the wavelength [4], a cl (λ) = a 0 c (λ)(C c /C 0 c ) 0.0602 is the absorption coefficient produced by chlorophyll with a 0 c (λ) denoting the specific absorption coefficient of chlorophyll C 0 c = 1 mg/m 3 denoting the chlorophyll concentration, and C c denoting the total concentration of the chlorophyll in mg/m 3 , is the absorption coefficient due to where b w (λ) = 0.005826(400/λ) 4.322 is the scattering coefficient of pure water [4], b 0 s (λ) = 1.151302(400/λ) 1.7 is the scattering from small particles, b 0 l (λ) = 0.3411(400/λ) 0.3 is the scattering from large particles, The cubic spline interpolated variation of the experimental results for absorption and scattering coefficients of optically and chemically pure water is given in Fig. 11.  In what follows, the average BER variation in underwater medium depending on the absorption, scattering and turbulence is investigated. Fig. 12 presents the average BER of a UWOC system as a function of link length for different water types. Keeping the link length L = 10 m, the total average BER including the absorption, scattering and turbulence stands at the levels of 2.28 × 10 −3 , 1.79 × 10 −1 , 4.42 × 10 −1 , and 5 × 10 −1 in the pure sea, clean ocean, coastal, and harbor waters, respectively. At this link length, the average BER only due to turbulence is 4.57 × 10 −7 . These results show a drastic increase with the contribution of the absorption and scattering.
From Fig. 13, it can be concluded that the wavelength of the optical beam has a significant effect on the performance of the UWOC systems in underwater medium. Looking at the average BER for pure sea, clean ocean, coastal, and harbor waters, the blue-green region of the visible light spectrum has superiority over other color regions. For the wavelength of λ = 532 nm that falls in the green region of the visible light spectrum, the average BER takes relatively smaller values as 3.62 × 10 −3 , 1.21 × 10 −1 , 3.91 × 10 −1 , and 5 × 10 −1 for pure sea, clean ocean, coastal, and harbor waters, respectively, when compared to the other wavelength regions of the visible spectrum. However, the average BER remains very high due to the combined effects of absorption, scattering and turbulence. Finally, the average BER variation with the SNR is shown for different types of water for link length L = 15 m in Fig. 14. The benefit of the higher SNR values can be seen for all water types. While only the turbulence effect is taken into account, the average BER becomes smaller than ∼ 10 −6 , that is accepted the practical communications, at approximately the SNR level of γ =∼ 20 dB. When combined effect of absorption, scattering and turbulence is taken into account, the required SNR levels are approximatelyγ =∼ 28 dB,γ =∼ 42 dB, andγ =∼ 67 dB to keep the average BER under ∼ 10 −6 for pure sea, clean ocean, and coastal waters, respectively. The average BER value does not fall under ∼ 10 −6 for harbor water in the selected interval that is due to the severe absorption and scattering effects resulting from high chlorophyll concentration.
Since waters are classified depending on the chlorophyll concentration, the significant effect of chlorophyll concentration and performance degradation with the increase of chlorophyll concentration are obviously seen from Figs. 12-14. A UWOC system operating in underwater medium presents the best and worst performances in pure sea water and harbor water where the chlorophyll concentration is at the lowest and highest levels, respectively. For example, keeping the wavelength of the communication system as λ = 450 nm in Fig. 13, the average BER takes the values of 3.1 × 10 −3 , 1.7 × 10 −1 , 4 .7 × 10 −1 , and 5 × 10 −1 for the chlorophyll concentrations of C c = 0.005 mg/m 3 , C c = 0.31 mg/m 3 , C c = 0.83mg/m 3 , and C c = 5.9 mg/m 3 , respectively. Particularly in the harbor water, the BER stands at such a low level that there is no improvement in the average BER in either short range (Fig. 12) or high SNR values (Fig. 14).

V. CONCLUSION
The closed-form expressions were obtained for weak, moderate and strong turbulence conditions using both log-normal and gamma-gamma distributed channel models. The Rytov variance of a Gaussian beam was analytically derived by using the recently introduced OTOPS model. The scintillation index variation was calculated from weak to strong underwater turbulence regimes. Also, the closed-form expressions for the combined absorption, scattering and turbulence effects in both weak and moderate-to-strong turbulence were obtained. The BER performance of a UWOC system was compared for pure sea, clean ocean, coastal and harbor waters. Results were presented for various parameters such as link length, average temperature, average salinity concentration, temperature and energy dissipation rates, receiver aperture size, wavelength and chlorophyll concentration. The underwater medium still remains challenging for the optical spectrum due to the various severe effects. To keep the average BER in acceptable practical ranges in several tens of meters, the mitigation techniques such as adaptive optics correction, spatial diversity or aperture averaging should be considered.