Incremental Diversity Order for Characterization of FSO Communication Systems Over Lognormal Fading Channels

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.