Expressing oceanic turbulence parameters by atmospheric turbulence structure constant

Optical wireless communication system performance in natural water turbulence of any strength

The recently introduced power spectrum model for natural water turbulence, i.e., that at any average temperature, average salinity, and stratification [J. Opt. Soc. Am. A37, 1614 (2020)JOAOD61084-752910.1364/JOSAA.399150], is extended from weak to moderate-to-strong regimes with the help of the spatial filtering approach. Based on the extended spectrum, the expressions for the scintillation index (SI) are obtained, and based on its signal-to-noise ratio and bit error rate of the underwater wireless optical communication (UWOC) system with the on-off-keying modulation and gamma-gamma irradiance distribution model, the analysis is performed. The obtained results are compared with those derived from the widely used Nikishov and Nikishov spectrum. It is shown that the natural water turbulence results in the SI for plane (spherical) waves attaining higher maxima values at shorter propagation distances, about 20 m (40 m) with respect to 30 m (50 m) of Nikishovs turbulence. Therefore, it predicts a stronger degradation of the UWOC system performance in weak and moderate turbulence regimes.

Scintillation and BER analysis of cosine and cosine-hyperbolic-Gaussian beams in turbulent ocean

Effects of source beam, link, and oceanic turbulence parameters on the scintillation index and bit error rate (BER) performance of cosine (cos) and cosine-hyperbolic (cosh) Gaussian light beams have been investigated in order to improve wireless optical communication link performance in oceanic turbulence. The Nikishov and Nikishov power spectrum of oceanic water and extended Huygens Fresnel principle were used in our evaluations; the results were obtained via MATLAB. The scintillation index and BER were examined versus oceanic turbulence parameters, which are the rate of dissipation of mean-square temperature, the ratio of temperature and salinity contributions to the refractive index spectrum, and the dissipation rate of kinetic energy per unit fluid mass of fluid. Further, the scintillation index and BER are investigated against the source size, propagation distance, and complex displacement parameters of cos- and cosh-Gaussian beams. This study aimed to select the suitable sinusoidal beam to be employed in order to increase the performance of underwater wireless optical communication systems operating in oceanic turbulence.

Scintillation index of an optical wave propagating through moderate-to-strong oceanic turbulence

In this paper, based on the extended Rytov theory that combines modified large-scale and small-scale amplitude spatial-frequency filters, we theoretically derive the scintillation index (SI) of the plane and spherical waves by means of the approximate oceanic refractive-index spectrum with the variable eddy diffusivity ratio propagating through moderate-to-strong oceanic turbulence. The mean bit-error rate (BER) of the underwater optical wireless communication systems is analyzed by use of the predicted SI and the gamma-gamma distribution model. Numerical results show that the obtained SI models are in good agreement with the results in weak-fluctuation regions. Also, we find that in weak turbulence, the mean BER drops sharply with the increase in mean signal-to-noise ratio, while in moderate-to-strong turbulence, the situation is opposite. We also note that the mean BER differs between the cases of unity and the variable eddy diffusivity ratio.

Average capacity of a UWOC system with partially coherent Gaussian beams propagating in weak oceanic turbulence

The average capacity of a single-input single-output (SISO) underwater wireless optical communication (UWOC) system with partially coherent Gaussian beams in a weak oceanic turbulence regime is investigated. An approximate analytical expression of scintillation index is derived mathematically to characterize the impact of oceanic turbulence on the propagation behavior of the partially coherent Gaussian beams. Then, the path loss caused by absorption and scattering in the ocean is numerically simulated with the Monte Carlo method. With consideration for absorption, scattering, and oceanic turbulence, the combined channel fading model is established, and the average capacity of the UWOC system (defined as the maximum mutual information between the input and output) is examined. Results show that the scintillations are reduced by decreases in propagation distance, the dissipation rate of mean-square temperature, and the ratio of the temperature and salinity contributions to the refractive index spectrum. Scintillations are also decreased by increases in source beam width, degree of partial coherence, and the dissipation rate of turbulent kinetic energy per unit mass of fluid. As a result, the average capacity of the UWOC system is enhanced. Moreover, the average capacity of the UWOC system can be promoted with the availability of channel state information at the receiver. This work will benefit the research and development of UWOC systems.

Oceanic spectrum of unstable stratification turbulence with outer scale and scintillation index of Gaussian-beam wave

We develop a new spectrum of the refractive-index fluctuations for the unstable stratification ocean based on the linear combination of the temperature spectrum, salinity spectrum and coupling spectrum that all include the outer scale. Our oceanic spectrum agrees better with the experimental data than others do from low wave-number regions to high wave-number regions. Based on our proposed oceanic spectrum, we derive the analytical expression of the scintillation index of Gaussian-beam wave and investigate the influence of the light source and the channel parameters on the scintillation index of Gaussian-beam wave.

Structure parameter of anisotropic atmospheric turbulence expressed in terms of anisotropic factors and oceanic turbulence parameters

The structure parameter of the anisotropic atmospheric turbulence is expressed in terms of atmospheric, oceanic anisotropic factors in x and y directions, and the oceanic turbulence parameters, which are the wavelength, the link length, the ratio of temperature to salinity contributions to the refractive index spectrum, the rate of dissipation of mean-squared temperature, and the rate of dissipation of kinetic energy per unit mass of fluid. For the purpose of expressing the structure parameter of the anisotropic atmospheric turbulence in terms of atmospheric, oceanic anisotropic factors and the oceanic turbulence parameters, the spherical wave scintillation indices that are found in weak anisotropic atmospheric turbulence and in weak oceanic turbulence are equated to each other. We aim to utilize the structure parameter expressed in this paper in the evaluations of various physical entities such as the average intensity, scintillation index, and beam spread in anisotropic oceanic turbulence by exploiting the existing solutions for the same physical entities in anisotropic atmospheric turbulence. Use of this structure parameter will help us to obtain the anisotropic oceanic turbulence results easily because such results will be found by just inserting the structure parameter expressed in this paper to the already reported corresponding results of anisotropic atmospheric turbulence.

Underwater optical communication performance under the influence of the eddy diffusivity ratio

Generally, the eddy diffusivity ratio of salinity to temperature is not equal to one, especially in the upper and mid-to-high latitude ocean. In this paper, the performance of practical underwater optical communication (UOC) systems is investigated by considering the influence of the eddy diffusivity ratio other than one. Specifically, using the Rytov theory in weak turbulence, the aperture-averaged scintillation indices for the plane and spherical waves are derived. The typical performance criteria including the mean signal-to-noise ratio and bit error rate are further studied. It is found that the scintillation index and the associated UOC performance differ between the cases of the unity and variable eddy diffusivity ratio. Such a difference becomes smaller as the receiving aperture increases.

Power spectrum of refractive-index fluctuations in turbulent ocean and its effect on optical scintillation

Recent simulations and experiments have shown that the viscous-range temperature spectrum in water can be well described by the Kraichnan spectral model. Motivated by this, a tractable expression is developed for the underwater temperature spectrum that is consistent with both the Obukhov-Corrsin law in the inertial range and the Kraichnan model in the viscous range. In analogy with the temperature spectrum, the formula for the salinity spectrum and the temperature-salinity co-spectrum are also derived. The linear combination of these three scalar spectra constitutes a new form of the refractivity spectrum. This spectral model predicts a much stronger optical scintillation than the previous model.

Improving the performance of underwater wireless optical communication links by channel coding

We investigate the efficacy of error correcting codes in improving the performance of underwater wireless optical communication systems. For this purpose, the effectiveness of several coding schemes, i.e., the classical Reed-Solomon and a recent family of low-density parity check codes, is studied in the physical (PHY) and the upper layers assuming negligible water turbulence. The presented numerical results testify to the interest of using efficient codes both at the PHY and upper protocol layers, although we are concerned by a non-fading channel. Furthermore, we discuss the choice of coding schemes and the appropriate degree of data protection in the PHY and upper layers.

Practical approximation of the oceanic refractive index spectrum

Oceanic turbulence is described by the oceanic refractive-index spectrum (ORIS), which considers several important hydrodynamic parameters. Based on ORIS, many optical oceanic quantities can be calculated using numerical integration. However, it is difficult to calculate the analytical solutions. In this paper, an approximate oceanic temperature spectrum is obtained by multiplying the non-Kolmogorov spectrum with a correction factor. By analogy with the obtained temperature spectrum, an approximate salinity spectrum and an approximate coupling spectrum are obtained. A linear summation of these three approximate spectra forms the approximate form of ORIS. The approximate form of ORIS we obtained helps calculate the analytical solutions of the relevant oceanic optical quantities.

Statistical properties of a radially polarized twisted Gaussian Schell-model beam in an underwater turbulent medium

Average intensity and the normalized powers of the completely polarized and the completely unpolarized portions of a radially polarized twisted Gaussian Schell-model (TGSM) beam propagating in underwater turbulence are examined. In our formulation, our previously obtained atmospheric turbulence solution for the same radially polarized TGSM beam using the extended Huygens-Fresnel principle is utilized, with the inclusion of our recently derived expression for the atmospheric turbulence structure constant in terms of underwater turbulence parameters. Effects of the rate of dissipation of mean-squared temperature, rate of dissipation of kinetic energy per unit mass of fluid, kinematic viscosity, and the contribution of the temperature-to-salinity ratio to the refractive index spectrum on the average intensity, and the normalized powers of the completely polarized and completely unpolarized portions of a radially polarized TGSM beam propagating in underwater turbulence are presented.

Scintillations of LED sources in oceanic turbulence

The scintillation index of light emitting diode (LED) sources is evaluated when such sources are employed in oceanic wireless optical communication (UWOC) links. In the formulation, LED source radiation is taken to be perfectly incoherent with a Gaussian field distribution. We have utilized the scintillation index solution of an incoherent source in atmospheric turbulence, together with our recently obtained expression that expresses the structure constant of atmospheric turbulence in terms of the oceanic turbulence and UWOC link parameters. Oceanic turbulence parameters of interest are the ratio of temperature to salinity contributions to the refractive index spectrum, rate of dissipation of kinetic energy per unit mass of fluid, rate of dissipation of mean-squared temperature, and viscosity. UWOC link parameters are the LED source size, link length, and the wavelength. Scintillation index results are presented for various variations of the oceanic turbulence and UWOC link parameters.

Average intensity and directionality of partially coherent model beams propagating in turbulent ocean

We studied Gaussian beams with three different partially coherent models, including the Gaussian-Schell model (GSM), Laguerre-Gaussian Schell model (LGSM), and Bessel-Gaussian Schell model (BGSM), propagating through oceanic turbulence. The expressions of average intensity, beam spreading, and beam wander for GSM, LGSM, and BGSM beams in the paraxial channel are derived. We make a contrast for the three models in numerical simulations and find that the GSM beam has smaller spreading than the others, and the LGSM beam needs longer propagation distance to transform into a well-like profile of average intensity than the BGSM beam in the same conditions. The salinity fluctuation has a greater contribution to the wander of LGSM and BGSM beams than that of the temperature fluctuation. Our results can be helpful in the design of an optical wireless communication link operating in oceanic environment.

Scintillation analysis of multiple-input single-output underwater optical links

Multiple-input single-output (MISO) techniques are employed in underwater wireless optical communication (UWOC) links to mitigate the degrading effects of oceanic turbulence. In this paper, we consider a MISO UWOC system which consists of a laser beam array as transmitter and a point detector as receiver. Our aim is to find the scintillation index at the detector in order to quantify the system performance. For this purpose, the average intensity and the average of the square of the intensity are derived in underwater turbulence by using the extended Huygens-Fresnel principle. The scintillation index and the average bit-error-rate (⟨BER⟩) formulas presented in this paper depend on the oceanic turbulence parameters, such as the rate of dissipation of the mean-squared temperature, rate of dissipation of kinetic energy per unit mass of fluid, Kolmogorov microscale, and the ratio of temperature to salinity contributions to the refractive index spectrum, the link length, and the wavelength. Recently, we have derived an equivalent structure constant of atmospheric turbulence and expressed it in terms of the oceanic turbulence parameters [Appl. Opt.55, 1228 (2016)APOPAI0003-693510.1364/AO.55.001228]. In the formulation in this paper, this equivalent structure constant is utilized, which enables us to employ the existing similar formulation valid in atmospheric turbulence.

Fourth-order mutual coherence function in oceanic turbulence

We have recently expressed the structure constant of atmospheric turbulence in terms of the oceanic turbulence parameters, which are the ratio of temperature to salinity contributions to the refractive index spectrum, rate of dissipation of kinetic energy per unit mass of fluid, rate of dissipation of the mean-squared temperature, wavelength, Kolmogorov microscale, and link length. In this paper, utilizing this recently found structure constant and the fourth-order mutual coherence function of atmospheric turbulence, we present the fourth-order mutual coherence function to be used in oceanic turbulence evaluations. Thus, the found fourth-order mutual coherence function of oceanic turbulence is evaluated for the special case of a point source located at the transmitter origin and at a single receiver point. The variations of this special case of the fourth-order mutual coherence function of oceanic turbulence against the changes in the ratio of temperature to salinity contributions to the refractive index spectrum, the rate of dissipation of kinetic energy per unit mass of fluid, the rate of dissipation of the mean-squared temperature, the wavelength, and the Kolmogorov microscale at various link lengths are presented.