  In underwater wireless optical communications (UWOC), the random obstruction
of light propagation by air bubbles can cause fluctuations in the incoming
light intensity of a receiver. In this paper, we propose a statistical model
for determining the received power by a receiver in the presence of air
bubbles. First, based on real experiments of the behavior of air bubbles
underwater, we propose statistical models for the generation, size, and
horizontal distribution of each air bubble. Second, we mathematically derive
the obstruction caused by the shadow of each bubble as it passes over the beam
area. We then compute the combined obstruction of all generated air bubbles to
determine the total obstructed power, which is a random variable due to the
randomness of bubble behavior. Next, we find the first and second moments of
the total obstructed power to model the statistical distribution of the
obstructed received power by using the method of moments, which shows that the
Weibull distribution suitably matches the simulation data. We also estimate the
shape and scale parameters by using two derived moments. Furthermore, we also
construct a statistical model of the received power with complete blockage in
the presence of air bubbles and we derive the distribution of the composite
channel model combining the proposed bubble-obstruction model with a
Gamma-Gamma turbulence model. Finally, we obtain and verify the analytic forms
of the average bit error rate and the capacity of UWOC systems under this newly
proposed composite channel model.
