Error performance of underwater wireless optical communications with spatial diversity under turbulence channels

In underwater optical wireless communications (UOWC), absorption, scattering, and turbulence severely degrade the reliability and transmission rate of the UOWC link. In this paper, spatial diversity (SD) is exploited to improve the error performance of UOWC links, which involves the deployment of multiple transmit/receive apertures. Channel impulse responses for various configurations in a coastal ocean water link are obtained by Monte Carlo simulation. By using maximum-likelihood sequence detection depending on the Euclidean distance, the error probability of the SD UOWC is derived. We further present an efficient approximated closed-form expression with one-dimensional integral for the error probability of single-input multiple-output and multiple-input single-output systems. Our analytical derivations build upon an approximation to the sum of correlated log-normal random variables. Both the derived bit error probability expressions and simulations are used to quantify the effect of SD, and the performance of SD UOWC is compared with a single-input single-output link. Our numerical results indicate that SD combats the impairing effects of fading and considerably improves the UOWC system performance.