Performance investigation of underwater wireless optical system for image transmission through the oceanic turbulent optical medium

Abstract

The importance of resources contained in the sea and on the sea floor is increasing with each passing day. Hence, exploration of the sea and sea floor has become a very important requirement. Underwater imaging is a science that has gained importance over the past two decades. Underwater images indicate the state of sea floor and transmitting such images through the harsh and turbulent oceanic medium can cause deterioration of the information contained in the image due to diminished color reproduction, low contrast and blur. In this paper, we have performed the simulation studies to understand perturbations induced during the transmission of sea floor images using high-speed optical signaling through the underwater channels. The transmitted irradiance often suffers from underwater turbulence and beam attenuation. The bit error rate (BER) of the system proposed to transmit information through channels has been determined through analytic means and validated through Monte-Carlo simulation. Comparison between the transmitted and received images in the presence of turbulence and attenuation have been presented. The BER performance of the proposed system is evaluated in the presence of beam attenuation and underwater turbulence. The turbulence induced errors are minimized using the transmit/receive diversity and multiple input multiple output (MIMO) techniques. In addition to the diversity techniques, median and adaptive median filters used to minimize the distortion in the received image. The BER results show that the $4\times 5$ MIMO system gains 19.50 dB of transmit power at BER of $10^{-5}$, when compared with the single input single output system. Similarly, an improvement of at-least 18 dB peak signal to noise ratio obtain using the adaptive median filter based system over the un-filter based system.

Appendices

Appendices

Appendix A Hyperbolic tangential log-normal (HTLN) distribution

HTLN is a LN distribution function derived using hyperbolic tangent distribution. Normal distribution of a random variable x with mean $\mu _X$ and variance $\sigma _X^2$ is given as,

$$\begin{aligned} \varPhi \left( x\right) =\frac{1}{2}-\frac{1}{2}erf \left( \frac{\mu _X-x}{\sqrt{2\sigma _X^2}}\right) , \end{aligned}$$

(19)

where erf is error function, which can be obtained using HTD as Robin (1997),

$$\begin{aligned} \varPhi \left( x\right) =\frac{1}{2}+\frac{1}{2}\tanh (bx+a), \end{aligned}$$

(20)

where a and b obtained by using Eqs. (19) and (20) for two different values of x. LN distribution function can be obtained by substituting x with $\ln (t)/2$ in Eqs. (19) and (20) i.e., $F(t)=\varPhi \left( \frac{\ln (t)}{2} \right)$ is LN distribution and expanding $\tanh (x)=\frac{e^{2x}-1}{e^{2x}+1}$, yields $F(t)=\frac{\exp \left( 2a\right) t^b}{1+\exp \left( 2a\right) t^b}$ and PDF is $f(t)=\frac{b\exp (2a)t^{b-1}}{\left( 1+\exp (2a)t^b \right) ^2}$. The PDF and CDF comparison of LN and HTLN is shown in Fig. 8.

Fig. 8

a LN and HTLN PDF comparison, b LN and HTLN CDF comparison