Free space optical (FSO) communication systems are subject to turbulence-induced fading as a result of fluctuations in the refractive index. Gamma-Gamma (GG) distribution is commonly used in the literature to characterize moderate-to-strong turbulence conditions. The performance of FSO systems is further degraded by pointing error-induced fading as a result of building sways. While the asymptotic analysis presented in earlier works is important to understand the maximum diversity gains of FSO systems attainable over fading channels, such gains might not be available in practical range of signal-to-noise ratio (SNR). Furthermore, different systems with the same asymptotic slope may have different slopes in the range of finite SNR values. In this paper, we consider a multiple-input multiple-output (MIMO) FSO system with intensity modulation and direct detection (IM/DD). We derive approximate expression for the finite-SNR diversity order over GG turbulence channels in the presence of pointing errors. We also investigate convergence speed to full diversity. We provide numerical results to demonstrate the accuracy of our derivations and corroborate on our analytical findings.

中文翻译：

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具有指向误差的 Gamma-Gamma 衰落信道上 FSO 系统的有限 SNR 分集增益分析

由于折射率的波动，自由空间光 (FSO) 通信系统会受到湍流引起的衰落的影响。Gamma-Gamma (GG) 分布在文献中常用来表征中强湍流条件。FSO 系统的性能会因建筑物摇摆导致的指向错误引起的衰落而进一步降低。虽然早期工作中提出的渐近分析对于了解 FSO 系统在衰落信道上可获得的最大分集增益很重要，但在实际的信噪比 (SNR) 范围内可能无法获得此类增益。此外，具有相同渐近斜率的不同系统在有限 SNR 值范围内可能具有不同的斜率。在本文中，我们考虑具有强度调制和直接检测 (IM/DD) 的多输入多输出 (MIMO) FSO 系统。我们在存在指向错误的情况下推导出 GG 湍流通道上有限 SNR 分集阶数的近似表达式。我们还研究了完全多样性的收敛速度。我们提供数值结果来证明我们推导的准确性并证实我们的分析结果。