Free space optical (FSO) communication systems experience atmospheric turbulence-induced fading, which is typically modelled by lognormal distribution. Since the decreasing rate of error probability over lognormal fading channels does not converge to a finite value, the conventional definition of diversity order yields infinity and does not provide any insight into system design. In this letter, we propose the so-called incremental diversity order (IDO), which is defined as the incremental change in the decreasing rate of bit error rate (BER) on a log-log scale. As an example, we consider multiple-input multiple-output (MIMO) FSO system over lognormal turbulence channels. We derive a novel closed-form BER expression in terms of Lambert-W function and obtain IDO as a function of the number of laser sources, the number of photodetectors and the variance of the log-amplitude coefficient. We further present numerical results to validate the derived BER expression and associated IDO.

中文翻译：

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在对数正态衰落信道上表征 FSO 通信系统的增量分集顺序

自由空间光 (FSO) 通信系统会经历大气湍流引起的衰落，这通常由对数正态分布建模。由于对数正态衰落信道上错误概率的下降率不会收敛到一个有限值，因此分集阶数的传统定义产生无穷大并且不提供对系统设计的任何洞察。在这封信中，我们提出了所谓的增量分集阶数 (IDO)，它被定义为对数尺度上误码率 (BER) 下降率的增量变化。例如，我们考虑对数正态湍流信道上的多输入多输出 (MIMO) FSO 系统。我们根据 Lambert-W 函数推导出一种新的封闭形式 BER 表达式，并获得 IDO 作为激光源数量的函数，光电探测器的数量和对数幅度系数的方差。我们进一步提供数值结果来验证派生的 BER 表达式和相关的 IDO。