In this paper, we analytically study the bit error rate (BER) performance of
underwater visible light communication (UVLC) systems with binary pulse
position modulation (BPPM). We simulate the channel fading-free impulse
response (FFIR) based on Monte Carlo numerical method to take into account the
absorption and scattering effects. Additionally, to characterize turbulence
effects, we multiply the aforementioned FFIR by a fading coefficient which for
weak oceanic turbulence can be modeled as a lognormal random variable (RV).
Moreover, to mitigate turbulence effects, we employ multiple transmitters
and/or receivers, i.e., spatial diversity technique over UVLC links.
Closed-form expressions for the system BER are provided, when equal gain
combiner (EGC) is employed at the receiver side, thanks to Gauss-Hermite
quadrature formula and approximation to the sum of lognormal RVs. We further
apply saddle-point approximation, an accurate photon-counting-based method, to
evaluate the system BER in the presence of shot noise. Both laser-based
collimated and light emitting diode (LED)-based diffusive links are
investigated. Since multiple-scattering effect of UVLC channels on the
propagating photons causes considerable inter-symbol interference (ISI),
especially for diffusive channels, we also obtain the optimum multiple-symbol
detection (MSD) algorithm to significantly alleviate ISI effects and improve
the system performance. Our numerical analysis indicates good matches between
the analytical and photon-counting results implying the negligibility of
signal-dependent shot noise, and also between 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 MSD considerably alleviates ISI
deteriorations
