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arXiv:2508.05807 · IEEE Journal of Selected Topics in Quantum Electronics

Modeling Optical Key Distribution Over a Satellite-to-Ground Link Under Weak Atmospheric Turbulence

Artur Czerwiński, Mikołaj Lasota, Marcin Jarzyna, Mateusz Kucharczyk, Michał Jachura, Konrad Banaszek

Published Aug 7, 2025• 5 citations
arXivHTMLPDF

Abstract

In this study, we analyze the secret key capacity of intensity modulation/direct detection optical key distribution (IM/DD OKD) for a free-space optical (FSO) link between a low-Earth orbit satellite and an optical ground station. Focusing on downlink communication, we account for atmospheric turbulence, which causes random variations in the transmittance of the FSO channel. We implement an atmospheric channel model that accounts for absorption and scattering, geometric losses, pointing errors, and intensity fluctuations. The secret key capacity is quantified under different noise scenarios and reconciliation code efficiencies, assuming a hard decoding scheme. The performance of the IM/DD OKD protocol is compared under direct and reverse reconciliation regimes. Additionally, we examine the impact of weak and strong wind on the strength of atmospheric turbulence, leading to different results of the secret key capacity. Furthermore, we analyze the characteristics of error distributions that arise from protocol optimization. Our results provide insights into optimizing IM/DD OKD protocols for varying atmospheric conditions.

DOI
10.1109/jstqe.2025.3597073

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In this study, we analyze the secret key capacity of intensity modulation/direct detection optical key distribution (IM/DD OKD) for a free-space optical (FSO) link between a low-Earth orbit satellite and an optical ground station. Focusing on downlink communication, we account for atmospheric turbulence, which causes random variations in the transmittance of the FSO channel. We implement an atmospheric channel model that accounts for absorption and scattering, geometric losses, pointing errors, and intensity fluctuations. The secret key capacity is quantified under different noise scenarios and reconciliation code efficiencies, assuming a hard decoding scheme. The performance of the IM/DD OKD protocol is compared under direct and reverse reconciliation regimes. Additionally, we examine the impact of weak and strong wind on the strength of atmospheric turbulence, leading to different results of the secret key capacity. Furthermore, we analyze the characteristics of error distributions that arise from protocol optimization. Our results provide insights into optimizing IM/DD OKD protocols for varying atmospheric conditions.
We propose and analyze numerically concurrent intensity modulation/direct detection (IM/DD) optical key distribution (OKD) combined with conventional data transmission over a LEO-to-ground optical link. The idea is validated by numerical simulations which indicate that in a realistic scenario it is possible to generate simultaneously up to 200 Mbits of a secret key and downlink transmit up to 140 Gbits of data during a single nearly-zenithal pass of a LEO satellite. Such lengths of the secret key are three orders of magnitude higher in comparison to typical quantum key distribution systems, although they are generated under different security assumptions. The simplicity and robustness of IM/DD OKD protocols could make them an attractive and cost-effective option to provide security in the physical layer of space communication systems.
This paper explores the secrecy performance of the recently proposed intensity modulation/direct detection (IM/DD) terrestrial free-space quantum key distribution (QKD) system, by using a Gaussian-beam propagation model and considering the combined effects of atmospheric turbulence and legitimate transceivers’ misalignment. Secrecy performance metrics including quantum bit error rate (QBER) and ergodic secret-key rate are newly derived in closedform expressions, taking into account all combined effects of turbulence- and misalignment-induced fading channels, the eavesdropper’s location relative to the legitimate receiver, and receiver noises. To satisfy security constraints, the system designs based on the intensity modulation depth and beam waist of the Gaussian beam at the transmitter, and dualthreshold (D-T) selection at the receiver, are comprehensively discussed under turbulence and misalignment conditions as well as different eavesdropper’s locations. Monte-Carlo (M-C) simulations are also implemented to verify the analytical results. Remarkably, this paper also offers the first framework in the literature to evaluate the secrecy performance of free-space optical (FSO) systems considering the eavesdropper’s location under the effect of misalignment between legitimate transceivers.
Abstract Quantum Key Distribution (QKD) provides information-theoretic security for future communication networks by exploiting the fundamental principles of quantum mechanics. However, satellite-to-ground QKD links suffer significant performance degradation due to atmospheric turbulence, absorption, scattering, and satellite-induced pointing errors. This paper investigates the BB84 QKD protocol over a Free-Space Optical (FSO) channel modeled using the Gamma–Gamma distribution, which accurately captures both small-scale and large-scale atmospheric irradiance fluctuations. Closed-form and numerical results for outage probability and Quantum Bit Error Rate (QBER) are presented under weak, moderate, and strong turbulence regimes. The Secure Key Rate (SKR) is analyzed as a function of link distance under clear and foggy weather conditions. Additionally, the impact of satellite vibration is evaluated using a jitter-dependent pointing error model, demonstrating that misalignment significantly reduces link reliability. Simulation results show that strong turbulence conditions introduce more than 15 dB SNR penalty compared to clear-sky operation, while haze conditions limit QKD range to under 8–10 km. These findings provide practical performance benchmarks for Low-Earth Orbit (LEO) quantum downlinks in realistic atmospheric environments. The results provide practical insights for electronic receiver design and system implementation of satellite quantum communication links.
Security issues of free-space optical (FSO) communications are discussed. Based on a subcarrier intensity-modulated air-to-ground FSO system model, we first analyze the coherence time of the air-to-ground FSO link and show that under practical assumptions, scintillation reciprocity holds in the FSO communication system. A private secret-key-based cryptosystem with key management is introduced to enhance FSO security, and a key agreement approach is proposed based on statistics of the random atmospheric-turbulence-induced fading channel measurements. The secret key rate of the key agreement scheme is investigated for the gamma–gamma turbulence model. Practical key agreement protocols based on bidirectional channel identification are designed for different FSO communication scenarios. Our numerical results reveal that the key rate is not sensitive to the strength of the atmospheric turbulence; the per-symbol signal-to-noise ratio and the training sequence length are the dominating factors.
This paper presents a comprehensive analysis of the link budget for free-space optical systems involving Low Earth Orbit (LEO) and Medium Earth Orbit (MEO) satellites. We develop a detailed model of the satellite-to-ground channel that accounts for the primary physical processes affecting transmittance: atmospheric absorption and scattering, free-space diffraction, and turbulence-induced fluctuations. The study introduces a general method for computing transmittance along a slant path between a satellite and an optical ground station, incorporating zenith angle, slant range, and altitude-dependent attenuation. The proposed framework is intended to support the design and evaluation of space-based optical links and serves as a critical tool for defining technical specifications in satellite communication demonstrators and simulations. Numerical estimates are provided to illustrate the magnitude of losses under typical operational conditions, including the role of aperture averaging. In addition to the link budget analysis, we introduce a satellite-based quantum use case. We propose a scheme for quantum state tomography performed on states generated by an onboard photon source on an LEO or MEO satellite and transmitted to the optical ground station. This approach enables continuous verification of the quality of quantum resources that can be used to perform quantum protocols within quantum information networks.
This work is concerned with the secrecy performance of a free-space optical (FSO) communication system over Fisher-SnedecorF\mathcal {F}F-distribution turbulence fading channel. Considering the influence of pointing error, atmospheric turbulence and different detection technique (i.e., the intensity modulation with direct detection and heterodyne detection), we derive the exact closed-form expressions for the average secrecy capacity (ASC), the secrecy outage probability (SOP) and the strictly positive secrecy capacity (SPSC) in terms of Meijer’s G-function. Furthermore, the asymptotic expression for SOP is analyzed as the electrical signal-to-noise ratio approaches infinity. Monte Carlo simulations are provided to validate analytical results.