MIMO Underwater Visible Light Communications: Comprehensive Channel Study, Performance Analysis, and Multiple-Symbol Detection

This paper presents a comprehensive study of underwater visible light communications (UVLC), from channel characterization, performance analysis, and effective transmission and reception methods. To this end, we first simulate the fading-free impulse response (FFIR) of UVLC channels using Monte Carlo numerical procedure to take into account the absorption and scattering effects; and then to characterize turbulence effects, we multiply the aforementioned FFIR by a fading coefficient modeled as a lognormal random variable (RV) for weak oceanic turbulence. Based on this general channel model, we analytically study the bit error rate (BER) performance of UVLC systems with binary pulse position modulation (BPPM). In the next step, to mitigate turbulence effects, we employ multiple transmitters and/or receivers, i.e., we apply spatial diversity technique over UVLC links. Closed-form expressions for the system BER are provided, when an equal gain combiner is employed at the receiver side, thanks to the Gauss-Hermite quadrature formula as well as approximation to the sum of lognormal RVs. We further apply saddle-point approximation, an accurate photon-counting method, to evaluate the system BER in the presence of shot noise. Both laser-based collimated and light emitting diode based diffusive links are investigated. Additionally, in order to reduce the intersymbol interference (ISI), introduced by the multiple-scattering effect of UVLC channels on the propagating photons, we also obtain the optimal multiple-symbol detection (MSD) algorithm, as well as the suboptimal generalized MSD (GMSD) algorithm. Our numerical analysis indicate good matches between the analytical and photon-counting results implying the negligibility of signal-dependent shot noise, and also between the analytical results and numerical simulations confirming the accuracy of our derived closed-form expressions for the system BER. Besides, our results show that spatial diversity significantly mitigates fading impairments while (G)MSD considerably alleviates ISI deterioration.