  In general, a buoy relay is used to connect the underwater communication to
the terrestrial network over a radio or optical wireless communication (OWC)
link. The use of relay deployment may pose security and deployment issues. This
paper investigates the feasibility of direct air-to-underwater (A2UW)
communication from an over-the-sea OWC system to an underwater submarine
without deploying a relaying node. We analyze the statistical performance of
the direct transmission over the combined channel fading effect of atmospheric
turbulence, random fog, air-to-water interface, oceanic turbulence, and
pointing errors. We develop novel analytical expressions for the probability
density function (PDF) and cumulative distribution function (CDF) of the
resultant signal-to-noise ratio (SNR) in terms of bivariate Meijer-G and Fox-H
functions. We use the derived statistical results to analyze the system
performance by providing exact and asymptotic results of the outage probability
in terms of system parameters. We use computer simulations to demonstrate the
performance of direct A2UW transmissions compared to the relay-assisted system.
