In this paper, we investigate the transmission probabilities in three cases (depending only on the legitimate receiver, depending only the eavesdropper, and depending on both legitimate receiver and eavesdropper) in quantum key distribution (QKD) systems over free-space optical links. To be more realistic, we consider a generalized pointing error scenario, where the azimuth and elevation pointing error angles caused by stochastic jitters and vibrations in the legitimate receiver platform are independently distributed according to a non-identical normal distribution. Taking these assumptions into account, we derive approximate expressions of transmission probabilities by using the Gaussian quadrature method. To simplify the expressions and get some physical insights, some asymptotic analysis on the transmission probabilities is presented based on asymptotic expression for the generalized Marcum Q-function when the telescope gain at the legitimate receiver approaches to infinity. Moreover, from the asymptotic expression for the generalized Marcum Q-function, the asymptotic outage probability over Beckmann fading channels (a general channel model including Rayleigh, Rice, and Hoyt fading channels) can be also easily derived when the average signal-to-noise ratio is sufficiently large, which shows the diversity order and array gain.
In this paper, we investigate the transmission probabilities in three cases (depending only on the legitimate receiver, depending only the eavesdropper, and depending on both legitimate receiver and eavesdropper) in quantum key distribution (QKD) systems over free-space optical links. To be more realistic, we consider a generalized pointing error scenario, where the azimuth and elevation pointing error angles caused by stochastic jitters and vibrations in the legitimate receiver platform are independently distributed according to a non-identical normal distribution. Taking these assumptions into account, we derive approximate expressions of transmission probabilities by using the Gaussian quadrature method. To simplify the expressions and get some physical insights, some asymptotic analysis on the transmission probabilities is presented based on asymptotic expression for the generalized Marcum Q-function when the telescope gain at the legitimate receiver approaches to infinity. Moreover, from the asymptotic expression for the generalized Marcum Q-function, the asymptotic outage probability over Beckmann fading channels (a general channel model including Rayleigh, Rice, and Hoyt fading channels) can be also easily derived when the average signal-to-noise ratio is sufficiently large, which shows the diversity order and array gain.
In this letter, the performance of a quantum key distribution (QKD) free-space optical (FSO) system is analyzed while taking a generalized pointing error model into account. More specifically, closed-form expressions for the average received powers at both the legitimate receiver and eavesdropper are derived. In addition, their corresponding asymptotic results valid in the high telescope gain regime are also presented. To capture the secure performance, we also investigate the ratio of received powers at the eavesdropper and at the legitimate receiver. Further, in some special cases, we find the optimal telescope gains for the received powers at both the legitimate receiver and eavesdropper, as well as the power ratio, which is important and useful for a secure QKD FSO system design. Finally, some selected numerical results are presented to illustrate the mathematical formalism and validate the accuracy of the derived analytical expressions.
We devoted to analyzing information transfer in quantum channels in terms of the performance of quantum key distribution (QKD) free-space optical (FSO) communication systems through Bennett and Brassard 84 (BB84) protocol by taking into account the combined effect of attenuation, turbulence, pointing error, and angle of arrival (AOA) fluctuations. Path loss is modeled by Beer-Lambert law, and the turbulent channel is assumed to be Fisher-Snedecor F distributed. The pointing error and AOA fluctuations are modeled by Hoyt and Rayleigh distributions, respectively. The error and sift probabilities, quantum bit error rate, and secret key rate of a QKD FSO system are obtained in analytical form, and results are presented depending on various parameters. It is shown that increased beam waist, beam deviation, AOA fluctuations, and propagation distance cause performance degradation and less secure information transmission. However, an increase in the ratio of horizontal and vertical beam misalignments, field of view, average photon number per pulse, visibility of the atmospheric environment, and optical beam wavelength impact the performance of QKD FSO systems positively. The effect of the turbulence structure constant is observed to be modest on the performance of the QKD FSO system.
Unmanned aerial vehicles (UAV) based on free-space optical (FSO) systems combine the benefits of both the high data rate of the FSO and the mobility of UAV. However, cumulative effects of laser beam divergence and turbulence-induced fading on the received irradiance in the FSO link might allow an external eavesdropper located near the authorized receiver to break the transmission under certain conditions. Quantum key distribution (QKD) is a technique of secure communication that employs quantum mechanics-based cryptography principles. A combination of a continuous-variable quantum key distribution (CV-QKD) and Gaussian modulation of quantum coherent states (GMCS) enables a relatively secure communication system against collective attacks over FSO transmission links. However, the performance is restricted and degraded due to the influence of atmospheric turbulence and excess noise. This paper aims to evaluate the performance of a secured UAV-based FSO system utilizing prepare and measure CV-QKD protocol based on GMCS under collective attack in terms of quantum bit error rate (QBER), outage probability, and secret key rate (SKR) considering the impairments of the FSO channel, link budget, deviations in the position and attitude angles of the UAV, channel fluctuating transmittance, and excess noise. The system parameters, including transmit power, receiver’s field-of-view, and beam divergence angle, are optimized to satisfy the system’s design criteria of threshold-QBER=10−3and threshold outage probability=10−2. The proposed system tolerates boresight displacement up to 7 cm with the optimized values. The Closed-form expressions and analytical results are confirmed by Monte-Carlo simulations.
Nowadays, a high level of security is required for the transmission of critical information. Quantum Key Distribution (QKD) systems are considered the best option to protect such information. Many studies have shown the efficiency of the QKD optical fiber inspired by M-ary pulse position modulation (MPPM). Free-Space Optical (FSO) links provide an efficient and effective data transmission system. However, cumulative effects of laser beam divergence, misalignment, and turbulence-induced fading on the received irradiance in the FSO link might allow an external eavesdropper located near the authorized receiver to break the transmission under certain conditions. This paper introduces the development of an FSO system based on the MPPM and the BB84 protocol (MPPM-BB84) over the Gamma-Gamma (GG) turbulence channel with pointing errors. Time Binning is implemented using MPPM to increase system security and reduce the quantum bit error rate (QBER). The system security is investigated under photon number splitting attack and excess noise. Closed-form expressions for asymptotic expressions of the average symbol error probability (SER), raw key rate (RKR), and secret key rate (SKR) are introduced. Moreover, the Monte-Carlo simulations are then used to prove the validity of the analytical results. The optimal values for the average photon number per pulse (to achieve the maximum RKR and SKR) for each symbol length can guarantee the stability of the FSO system under different weather conditions. Smaller symbol lengths are more tolerant of detector loss. The proposed system supports linking distances from 1 km to 3 km while keeping the SKR almost constant.
This paper considers transmit antenna selection (TAS) and receive generalized selection combining (GSC) for secure communication in the multiple-input-multiple-output wiretap channel, where confidential messages transmitted from an NA-antenna transmitter to an NB-antenna legitimate receiver are overheard by an NE-antenna eavesdropper. We assume that the main channel and the eavesdropper's channel undergo Nakagami-m fading with fading parameters mB and mE, respectively. In order to assess the secrecy performance, we present a new unifying framework for the average secrecy rate and the secrecy outage probability. We first derive expressions for the probability density function and the cumulative distribution function of the signal-to-noise ratio with TAS/GSC, from which we derive exact expressions for the average secrecy rate and the secrecy outage probability. We then derive compact expressions for the asymptotic average secrecy rate and the asymptotic secrecy outage probability for two distinct scenarios: 1) the legitimate receiver is located close to the transmitter, and 2) the legitimate receiver and the eavesdropper are located close to the transmitter. For these scenarios, we present new closed-form expressions for several key performance indicators: 1) the capacity slope and the power offset of the asymptotic average secrecy rate, and 2) the secrecy diversity order and the secrecy array gain of the asymptotic secrecy outage probability. For the first scenario, we confirm that the capacity slope is one and the secrecy diversity order is mBNBNA. For the second scenario, we confirm that the capacity slope and the secrecy diversity order collapse to zero.
In this paper, the secrecy performance of the physical layer security (PLS) of the hybrid free-space optical/radio frequency (FSO/RF) communication system is analyzed. The transmission protocol of the considered system is performed under the eavesdropper's attempt to overhear the RF link between the transmitter and legitimate receiver of the hybrid system. The FSO link is characterized by Málaga-M distribution while the RF links are modeled by Nakagami-m distribution. The two practical eavesdropping modes considered in this paper include: colluding and non-colluding. Exact closed-form expressions for the system's secrecy outage probability (SOP), the asymptotic of the SOP (SOP∞), the probability of strictly positive secrecy capacity (SPSC), the average secrecy capacity (ASC), and the asymptotic of the ASC (ASC∞), are specifically derived under the influence of both eavesdropper modes. Our derived analytical expressions present an efficient tool to investigate the impact of some channel parameters on the secrecy performance, namely the fading severity of the RF links, atmospheric turbulence severity, pointing error of the FSO link, number of eavesdroppers, and the power of the eavesdropper links. The results show that the increase of the eavesdroppers' number under both modes profoundly degrades the considered system secrecy performance. The accuracy of the numerical results obtained is validated by Monte-Carlo simulations.