Free-space optical communications over imperfect $${\mathcal {F}}$$ F turbulence channels with pointing errors

In this paper, we examine the performance of a free-space optical (FSO) communication system under imperfect Fisher-Snedecor $${\mathcal {F}}$$ F atmospheric turbulence channels. Taking into consideration the atmospheric turbulence, channel estimation errors, and pointing errors, simple and accurate analytical expressions for the probability density function and cumulative density function under intensity modulation direct detection (IM/DD) and heterodyne detection techniques are derived. Consequently, new analytical expressions for useful performance metrics such as outage probability, average bit error rate, and ergodic capacity are derived. To get more insight into the system diversity gain, asymptotic analytical expressions, in the high signal-to-noise ratio regime, for the outage probability and average BER are obtained. Our analysis is validated by means of numerically and Monte-Carlo simulations under various turbulence conditions and system parameters. The numerical results demonstrate that the derived analytical expressions are very accurate and provide precise evaluations for the proposed performance analyses. In addition, the results show that imperfect CSI seriously affects the FSO communication systems. However, the performance of heterodyne detection outperforms its counterpart the intensity modulation/direct-detection under all scenarios.