Performance Studies of Underwater Wireless Optical Communication Systems with Spatial Diversity: MIMO Scheme

In this paper, we analytically study the performance of multiple-input multiple-output underwater wireless optical communication (MIMO UWOC) systems with on-off keying (OOK) modulation. To mitigate turbulence-induced fading, which is amongst the major degrading effects of underwater channels on the propagating optical signal, we use spatial diversity over UWOC links. Furthermore, the effects of absorption and scattering are considered in our analysis. We analytically obtain the exact and an upper bound bit error rate (BER) expressions for both optimal and equal gain combining. In order to more effectively calculate the system BER, we apply Gauss-Hermite quadrature formula as well as approximation to the sum of lognormal random variables. We also apply photon-counting method to evaluate the system BER in the presence of shot noise. Our numerical results indicate an excellent match between the exact and upper bound BER curves. Also {a good match} between {the} analytical results and numerical simulations confirms the accuracy of our derived expressions. Moreover, our results show that spatial diversity can considerably improve the system performance, especially for channels with higher turbulence, e.g., a $3\times1$ MISO transmission in a $25$ {m} coastal water link with log-amplitude variance of $0.16$ can introduce $8$ {dB} performance improvement at the BER of $10^{-9}$.