In this work, a novel approximate closed-form probability density function for the sum of Gamma–Gamma random variates with Rayleigh pointing errors is derived by means of the well-known Jensen’s inequality. We employ the Kolmogorov–Smirnov goodness-of-fit statistical tests to verify the accuracy of the proposed approximation. The test results demonstrate that an exact distribution can be efficiently approximated by this derived approximate expression over a wide range of channel conditions. Also, the analysis of the approximation error is presented to indicate that a higher approximation accuracy can be achieved for small pointing errors. The series representation of this approximate expression is also developed, which enables us to avoid dealing with the integration. To reveal the importance of proposed approximation, new approximate closed-form expressions of the average bit error rate (BER) and ergodic capacity are derived. The performance for multiple-input multiple-output (MIMO) free-space optical (FSO) systems with equal gain combining (EGC) diversity technique are analyzed with different parameters, including the number of transmit and receive apertures, strength of atmospheric turbulence, and presence of pointing errors. It is observed that the pointing errors significantly degrade the performance of MIMO FSO systems. The numerical results and simulation are further utilized to illustrate the accuracy of the proposed approach.

在这项工作中，借助于众所周知的詹森不等式，推导了具有瑞利指向误差的伽玛-伽玛随机变量之和的新颖的近似封闭形式概率密度函数。我们使用Kolmogorov–Smirnov拟合优度统计检验来验证所提出近似值的准确性。测试结果表明，通过这种推导的近似表达式可以在广泛的信道条件范围内有效地近似精确的分布。此外，对近似误差的分析表明，对于较小的指向误差，可以实现更高的近似精度。还开发了这种近似表达式的级数表示，这使我们能够避免处理积分。为了揭示拟议近似的重要性，推导了平均误码率（BER）和遍历容量的新的近似封闭形式表达式。利用不同的参数，包括发射和接收孔径的数量，大气湍流强度以及存在指向错误。可以看出，指向错误会严重降低MIMO FSO系统的性能。数值结果和仿真被进一步用来说明所提出方法的准确性。利用不同的参数，包括发射和接收孔径的数量，大气湍流强度以及存在指向错误。可以看出，指向错误会严重降低MIMO FSO系统的性能。数值结果和仿真被进一步用来说明所提出方法的准确性。使用不同的参数分析了具有等增益组合（EGC）分集技术的多输入多输出（MIMO）自由空间光学（FSO）系统的性能，这些参数包括发送和接收孔的数量，大气湍流强度以及存在指向错误。可以看出，指向错误会严重降低MIMO FSO系统的性能。数值结果和仿真被进一步用来说明所提出方法的准确性。