Ergodic Capacity Analysis of Decode-and-Forward Relay-Assisted FSO Systems Over Alpha–Mu Fading Channels Considering Pointing Errors

The ergodic capacity of decode-and-forward (DF) relay-assisted free-space optical (FSO) communication systems when line of sight is available is analyzed over gamma-gamma fading channels with pointing errors. A novel closed-form approximate ergodic capacity expression is obtained in terms of the H-Fox function for a three-way FSO communications system when the α-μ distribution to efficiently approximate the probability density function (PDF) of the sum of gamma-gamma with pointing-error variates is considered. Moreover, we present novel asymptotic expressions at high signal-to-noise ratio (SNR), as well as low SNR for the ergodic capacity of DF relay-assisted FSO systems. The main contribution in this paper lies in an in-depth analysis about the impact of pointing errors on the ergodic capacity for cooperative FSO systems. In order to maintain the same performance in terms of capacity, it is corroborated that the presence of pointing errors requires an increase in SNR, which is related to the fraction of the collected power at the receive aperture, i.e., A₀. Simulation results are further demonstrated to confirm the accuracy and usefulness of the derived results.