## 1 Introduction  
Owing to its many attractive advantages [1; 2; 3], considerable research has already been carried out to apply free-space optical (FSO) communication to terrestrial environments. Recently, research has been conducted with the objective of applying FSO communication to maritime environments [4; 5]. However, in the system design of FSO communication for application in maritime environments, various impairments must be considered. First, the performance of FSO links is affected by various weather conditions; among these, fog is considered one of the most serious limiting factors because, in the worst case, a high attenuation of up to 480 dB/km can reduce visibility to several meters [3]. Most of the work carried out in modeling foggy channels over the past decade has assumed that the channel is deterministic [6]. However, a recent study has demonstrated that the fog attenuation effect follows a random behavior following the Gamma distribution [7]. Another possible impairment is the motion of mobile platforms. Unlike the conventional FSO case in terrestrial environments, platforms in maritime environments float over water. Therefore, in maritime environments, mobile platforms should be considered, and communication on mobile platforms leads to degradation factors such as pathloss and pointing error. Pathloss occurs according to a change in the distance between the transmitter (Tx) and receiver (Rx) and can be expressed as visibility that can be measured directly in the atmosphere [8]. With regard to pointing error issues, the rolling, pitching, and yawing motions of the mobile platform in maritime environments lead to pointing error that does not typically arise in FSO communication between fixed platforms [2] and this can lead to considerable performance degradation. Studies have been conducted on the factors that degrade the performance of FSO communication systems [1; 3; 9; 10; 11; 12]. In [3], various metrics such as signal-to-noise ratio (SNR), channel capacity, and bit error rate (BER) were used to study the performance under different types of fog conditions. Moreover, in [9; 10], the performance analysis considering the combined effects of both atmospheric turbulence and pointing error was conducted using composite statistics (i.e., probability density functions (PDF)). In [9], based on the Beckmann distribution, the generalized pointing error model was studied, and the general asymptotic channel capacity expression was derived under complex impairments caused by both turbulence and generalized pointing error. In [10], the statistical analysis of the channel model considering both weak atmospheric turbulence and pointing error was performed. In [1; 11; 12], considering the pathloss to be deterministic with propagation length, a performance analysis was undertaken that considered the combined effects of pathloss, atmospheric turbulence, and pointing error based on the composite PDF. In [1], the ergodic capacity performance of widely used detection techniques (i.e., heterodyne detection (HD) and intensity modulation/direct detection (IM/DD)) with nonzero boresight pointing errors under the Lognormal, Rician-lognormal, and Malaga turbulence models was studied. In [11], the authors assumed the pointing error model following the Rician distribution and analyzed the error rate with IM/DD over the Lognormal/Gamma-Gamma fading channels. In [12], BER performance over a strong turbulence channel with the pointing error model of the Rayleigh distribution was investigated. There are existing research results of some performance analyses that consider three factors: fog, pathloss, and pointing error in terrestrial or maritime environments. However, there were no results analyzing ergodic capacity, which is one of the important performance indicators, while considering the combined effects of all three factors based on the most commonly applied HD or IM/DD-based detection techniques.