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.

中文翻译：

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水下气泡对光学无线信道影响的统计建模

在水下无线光通信（UWOC）中，气泡对光传播的随机阻碍会导致接收器的入射光强度发生波动。在本文中，我们提出了一种统计模型，用于确定存在气泡时接收器的接收功率。首先，基于对水下气泡行为的真实实验，我们为每种气泡的产生，大小和水平分布提出了统计模型。第二，我们从数学上推导每个气泡在光束区域上通过时阴影所引起的障碍。然后，我们计算所有产生的气泡的总阻塞，以确定总阻塞功率，由于气泡行为的随机性，该总阻塞功率是一个随机变量。下一个，我们使用矩量法找到了总阻塞功率的第一和第二矩，以对阻塞接收功率的统计分布进行建模，这表明威布尔分布与仿真数据相匹配。我们还通过使用两个派生矩来估计形状和比例参数。此外，我们还构建了在存在气泡的情况下具有完全阻塞的接收功率的统计模型，并推导了将拟议的气泡阻塞模型与Gamma-Gamma湍流模型相结合的复合通道模型的分布。最后，我们获得并验证了该新提出的复合信道模型下平均误码率和UWOC系统容量的解析形式。