Performance Analysis of Photon-Limited Free-Space Optical Communications with Practical Photon-Counting Receivers

TL;DR

This paper develops an analytical framework for modeling photon counts in practical photon-counting receivers for free-space optical communications, accounting for non-ideal effects like dead time and afterpulsing, and evaluates system performance.

Contribution

It introduces a closed-form approximation for photon count distribution in practical TG-SPAD receivers considering non-Markovian effects, enhancing the accuracy of SER analysis in photon-limited FSO systems.

Findings

Photon counts approximate a binomial distribution, not Poisson.

Background radiation must be suppressed below a threshold.

Maintaining sufficient gating improves system performance.

Abstract

The non-perfect factors of 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 presence of dead time, non-photon-number-resolving and afterpulsing effect. Drawing upon the non-Markovian characteristic of afterpulsing effect, we formulate a closed-form approximation for the probability mass function (PMF) of photon counts, when high-order pulse amplitude modulation (PAM) is used. Unlike the photon counts from a perfect photon-counting receiver, which adhere to a Poisson arrival process, the photon counts from a practical TG-SPAD based receiver are instead approximated by a binomial distribution. Additionally, by employing the maximum likelihood (ML) criterion, we derive a refined closed-form formula for determining the threshold in high-order PAM, thereby facilitating the development of an analytical model for the symbol error rate (SER). Utilizing this analytical SER model, the system performance 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.