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The Impact of Rain–Fog Coexistence on Quantum Positioning

Xuchang Qu, Min Nie, Guang Yang

Published Mar 20, 2026• 0 citations
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Abstract

To investigate the impact of rain-fog coexistence on quantum positioning performance, we analyzed-using raindropsize distribution functions and extinction coefficients-how visibility and propagation distance in such compound conditions affect photon energy, positioning error, quantum-channel fidelity, and bit-error rate. For a $\mathbf{1 0 ~ k m}$ link, the energy of a single photon drops to $1.87 \times 10^{-6} \mathrm{~J}$ when visibility is 0.7 km and to $1.59 \times 10^{-6} \mathrm{~J}$ when visibility falls to 0.6 km. While visibility decreases from 0.7 km to 0.5 km, and the photon energy is kept at $10 \times 10^{-5} \mathrm{~J}$, the positioning error grows from 0.826 cm to 1.017 cm. Although the exact decline differs slightly among channels, the fidelity of the quantum communication channel invariably decreases as visibility worsens. At a 1 km range, the channel bit-error rate rises to 0.24 when visibility is 0.50 km and to 0.14 when it is 0.55 km. These results demonstrate that rain-fog coexistence markedly degrades quantum positioning performance. Consequently, system parameters must be adjusted in real time according to the prevailing visibility and propagation distance to maintain the stability and reliability of quantum positioning systems operating in rain-fog environments.

DOI
10.1109/icnlp69856.2026.11528122

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To investigate the impact of rain-fog coexistence on quantum positioning performance, we analyzed-using raindropsize distribution functions and extinction coefficients-how visibility and propagation distance in such compound conditions affect photon energy, positioning error, quantum-channel fidelity, and bit-error rate. For a 10 km\mathbf{1 0 ~ k m}10 km link, the energy of a single photon drops to 1.87×10−6 J1.87 \times 10^{-6} \mathrm{~J}1.87×10−6 J when visibility is 0.7 km and to 1.59×10−6 J1.59 \times 10^{-6} \mathrm{~J}1.59×10−6 J when visibility falls to 0.6 km. While visibility decreases from 0.7 km to 0.5 km, and the photon energy is kept at 10×10−5 J10 \times 10^{-5} \mathrm{~J}10×10−5 J, the positioning error grows from 0.826 cm to 1.017 cm. Although the exact decline differs slightly among channels, the fidelity of the quantum communication channel invariably decreases as visibility worsens. At a 1 km range, the channel bit-error rate rises to 0.24 when visibility is 0.50 km and to 0.14 when it is 0.55 km. These results demonstrate that rain-fog coexistence markedly degrades quantum positioning performance. Consequently, system parameters must be adjusted in real time according to the prevailing visibility and propagation distance to maintain the stability and reliability of quantum positioning systems operating in rain-fog environments.
In order to study the effect of the coexistence of rain and fog on the communication performance of satellite terrestrial quantum link, the relationship between link attenuation and transmission distance and visibility was analyzed based on the attenuation model of optical quantum under the coexistence of rain and fog, and the influence of the coexistence of rain and fog on channel capacity, channel fidelity, channel survival function and channel bit error rate was studied. The findings reveal that at a visibility of 0.5 km and a transmission distance of 0.3 km, the link experiences an attenuation of1 0. 2 2 d B⋅k m−1\text{1 0. 2 2 d B} \cdot \text{k m}-\text{1}1 0. 2 2 d B⋅k m−1. Furthermore, at the same visibility of 0.5 km and transmission distance of 0.25 km, the channel capacities for the amplitude damped and depolarized channels are recorded as 0.41 bit/s/ \mathrm{s}/sand 0.29 bit/s respectively. When visibility is 0.5 km and transmission distance is 0.3 km, the survival function values of amplitude damped channel and depolarized channel are 0.901 and 0.979 respectively. At a visibility of 0.5 km and with a transmission distance of 1 km, the channel's bit error rate reaches 0.24. Consequently, the coexistence of rain and fog significantly affects the efficiency of satellite terrestrial quantum communication systems. System parameters should be adjusted adaptively according to different environmental parameters to ensure the stability and reliability of the system.
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