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Journal of the Optical Society of America B

Secrecy outage probability analysis in a free-space optical system based on partially coherent beams through anisotropic non-Kolmogorov turbulent atmosphere

Hongyu Wu, Jing Ma, Pengzhen Guo, Qiang Wang, Dongpeng Kang, Jingkai Yang, Jiajie Wu

Published Apr 6, 2022• 5 citations
Publisher

Abstract

In this paper, the secrecy outage probability of a partially coherent beam free-space optical communication system considering the combined effect of anisotropic non-Kolmogorov strong turbulent atmosphere and the eavesdropper’s position is investigated. The Fisher–Snedecor distribution is chosen to model the atmospheric turbulence because it is not only suitable for weak to strong turbulence conditions but is also mathematically simple. Based on the fading channel model and the generalized pointing error model, we derive analytical expressions for the lower bounded secrecy outage probability. Also, we obtain asymptotic closed-form expression at a high signal-to-noise regime. The obtained expressions are corroborated by Monte Carlo simulations. The calculation results based on the analytical expressions show that increasing the source coherence parameter makes the secrecy interruption probability performance first better and then worse for a given condition, and an optimal value is observed. The anisotropic coefficient and power law have a positive effect on the secrecy outage probability of the free-space optical communication system. Under the given conditions, the performance of the secrecy outage probability is significantly improved by the divergent beam, although the increased spot size at the receiver makes it easier for eavesdroppers to tap the link. The secrecy outage probability performance deteriorates as the vertical component of Bob, the jitter variance, and the refractive index structure constant increase.

DOI
10.1364/josab.452857

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In this paper, the secrecy outage probability of a partially coherent beam free-space optical communication system considering the combined effect of anisotropic non-Kolmogorov strong turbulent atmosphere and the eavesdropper’s position is investigated. The Fisher–Snedecor distribution is chosen to model the atmospheric turbulence because it is not only suitable for weak to strong turbulence conditions but is also mathematically simple. Based on the fading channel model and the generalized pointing error model, we derive analytical expressions for the lower bounded secrecy outage probability. Also, we obtain asymptotic closed-form expression at a high signal-to-noise regime. The obtained expressions are corroborated by Monte Carlo simulations. The calculation results based on the analytical expressions show that increasing the source coherence parameter makes the secrecy interruption probability performance first better and then worse for a given condition, and an optimal value is observed. The anisotropic coefficient and power law have a positive effect on the secrecy outage probability of the free-space optical communication system. Under the given conditions, the performance of the secrecy outage probability is significantly improved by the divergent beam, although the increased spot size at the receiver makes it easier for eavesdroppers to tap the link. The secrecy outage probability performance deteriorates as the vertical component of Bob, the jitter variance, and the refractive index structure constant increase.
Physical layer security of a free-space optical (FSO) communication link is investigated for certain eavesdropping scenarios in which the eavesdropper exploits the divergence of the transmitted laser beam, which is subject to atmospheric turbulence, to compromise the security of the transmission link. A solution for physical layer security in which the legitimate receiver is positioned to receive only the coherent component of the transmitted laser beam is proposed. The irradiance fluctuations are modeled with separate distributions for the coherent and non-coherent components of the transmitted beam, corresponding to the main channel and the eavesdropper’s channel, respectively. Complete secrecy analysis of this setup is presented, and closed form expressions of the probability of strictly positive secrecy capacity, average secrecy capacity, and secrecy outage probability are derived. The analytical results are verified by Monte-Carlo simulations. Secrecy performance for worst-case scenarios corresponding to an adversary with powerful resources to capture all of the leaked information is explored. Results are analyzed for different turbulence regimes, and it was found that secure communication is possible even in the region of strong turbulence.
This paper investigates the physical layer security (PLS) of multi-aperture coherent free-space optical (FSO) systems with heterodyne detection over atmospheric turbulence-induced fading channels, while accounting for residual phase distortions after Zernike polynomial-based modal compensation. Unlike prior work focused primarily on intensity modulation/direct detection (IM/DD)-based FSO systems, this study considers coherent multi-aperture reception. Based on a Rician approximation of the turbulence-induced fading envelope, we derive an analytical approximation for the secrecy outage probability (SOP), a tractable semi-closed-form expression for the SOP lower bound, and a closed-form approximation for the strictly positive achievable secrecy rate probability. Moreover, high-SNR and low-SNR asymptotic analyses are presented to characterize the asymptotic secrecy behavior. The results show that the secrecy diversity order equals the number of receive apertures at the legitimate receiver, whereas, in the high-SNR regime at the legitimate receiver, the eavesdropper’s channel parameters affect the leading-order coefficient but not the decay exponent. Numerical results validate the proposed analytical approximations and asymptotic expressions and demonstrate that increasing the number of receive apertures at the legitimate receiver improves secrecy performance under various turbulence conditions.
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.
In this paper, we numerically study the secrecy performance of the free-space optical (FSO) system by considering different eavesdropping scenarios. More precisely, we considered three possible eavesdropping scenarios for Eve : 1) Eve is between Alice and Bob ; 2) Eve and Bob are in the same receiving plane; 3) Eve is behind Bob . We adopt the Málaga ( M )-distribution channel to model atmospheric turbulence due to the presence of link blockage while considering the non-zero boresight pointing error and path loss. To do so, we obtain a novel probability density function (PDF) and cumulative distribution function (CDF) under different eavesdropping scenarios, based on which we derived the secrecy outage probability (SOP) analytical expressions as well as their asymptotic expressions at a high SNR regime. We verified the results using Monte Carlo simulations, which showed that the parameters related to atmospheric turbulence and pointing errors, as well as the location of the eavesdropper, have different effects on different eavesdropping scenarios.
In this paper, we analyze the spatial location of the eavesdropper on the secrecy performance of free-space optical communication systems over Fischer--Snedecor F-distribution fading channel. As a key feature, we investigate the impact of the eavesdropper's location within the range of the beam divergence angle, which is more in line with practical engineering applications. The possible position of the eavesdropper is comprehensively assumed with horizontal and vertical components within the beam divergence angle. To this end, the lower-band secrecy outage probability, asymptotic solutions of SOP at high signal-to-noise-ratio, and the strictly positive secrecy capacity are obtained in closed-form, which are corroborated by exact Monte Carlo simulations respectively.
When the beam waist at the receiver is significantly larger than the receiver size, free-space optical (FSO) links may be vulnerable to some optical tapping risks at the physical layer. In this paper, we conduct a new framework for the analysis of the secrecy performance in terms of the secrecy outage probability (SOP) of FSO systems affected by gamma-gamma (GG) turbulence-induced fading channels with pointing errors. As a key feature, we evaluate the SOP in the presence of an external eavesdropper with generic location and orientation. For that reason, a new misalignment error model is proposed to consider a non-orthogonal optical beam with respect to the photodetector plane at the eavesdropper's receiver, where the effective area is determined by a rotated ellipse. New approximate and asymptotic solutions at high signal-to-noise-ratio (SNR) for the secrecy performance are obtained in closed-form, which are verified by exact Monte Carlo simulations. By using the developed expressions, we analyze in greater detail some effects such as the SNR of the eavesdropper's channel, the normalized beamwidth at the receiver-side, and the location and orientation of the eavesdropper on the secrecy performance for different turbulence conditions.