Performance analysis of photon-limited free-space optical communications with practical photon-counting receivers

The non-perfect factors of the practical photon-counting receiver are recognized as a significant challenge for long-distance photon-limited free-space optical (FSO) communication systems. This paper presents a comprehensive analytical framework for modeling the statistical properties of time-gated single-photon avalanche diode (TG-SPAD) based photon-counting receivers in the presence of dead time, non-photon-number-resolving and afterpulsing effects. Drawing upon the non-Markovian afterpulsing effect, we formulate a closed-form approximation for the probability mass function (PMF) of photon counts. Additionally, by employing the maximum likelihood (ML) criterion, we derive a refined closed-form formula to determine the threshold, thereby facilitating the development of an analytical model for the symbol error rate (SER). Using the analytical model, the performance of the system is investigated. The numerical results underscore the crucial need to suppress background radiation below the tolerated threshold and to maintain a sufficient number of gates in order to achieve a target SER.