Physical-Layer Security in Orbital Angular Momentum Multiplexing Free-Space Optical Communications Volume 8, Number 1, February 2016 Xiaole Sun Ivan B. Djordjevic
DOI: 10.1109/JPHOT.2016.2519279 1943-0655 Ó 2016 IEEE
IEEE Photonics Journal
Physical-Layer Security in FSO Communication
Physical-Layer Security in Orbital Angular Momentum Multiplexing Free-Space Optical Communications Xiaole Sun1 and Ivan B. Djordjevic1,2 1
Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ 85721 USA 2 College of Optical Sciences, University of Arizona, Tucson, AZ 85721 USA
DOI: 10.1109/JPHOT.2016.2519279 1943-0655 Ó 2016 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
Manuscript received December 7, 2015; revised January 12, 2016; accepted January 14, 2016. Date of publication January 19, 2016; date of current version January 29, 2016. This paper was supported by the Office of Naval Research Multidisciplinary Research Initiative (ONR MURI) Program. Corresponding author: X. Sun (e-mail:
[email protected]).
Abstract: The physical-layer security of a line-of-sight (LOS) free-space optical (FSO) link using orbital angular momentum (OAM) multiplexing is studied. We discuss the effect of atmospheric turbulence to OAM-multiplexed FSO channels. We numerically simulate the propagation of OAM-multiplexed beam and study the secrecy capacity. We show that, under certain conditions, the OAM multiplexing technique provides higher security over a single-mode transmission channel in terms of the total secrecy capacity and the probability of achieving a secure communication. We also study the power cost effect at the transmitter side for both fixed system power and equal channel power scenarios. Index Terms: Atmospheric turbulence, free-space optical (FSO) communication, physicallayer security, secrecy capacity, orbital angular momentum (OAM) multiplexing.
1. Introduction Free-space optical (FSO) communication, also known as optical wireless communication, is a promising communication technology for high-data-rate information transmission that is available at optical frequencies. Secrecy issues of FSO links have been studied recently for realizing a secure communication between two legitimate peers. Because of the high directionality of laser beam, the FSO communication is more secure than traditional RF wireless communications. However, it could also be susceptible to optical tapping eavesdropping. In [1], physical layer security in FSO links was studied based on an On-Off Keying (OOK) modulation with direct detection scenario. Effects of atmospheric turbulence on the receiving intensity were characterized with well-developed statistical models, e.g., lognormal and Gamma-Gamma distributions. A probabilistic metric for characterizing communication secrecy was presented as probability of strictly positive secrecy capacity. In [2], physical layer security of visible light communications (VLC) is discussed in a broadcasting scenario. Null-steering and artificial noise strategies were utilized to achieve positive secrecy rates when the eavesdropper’s channel state information (CSI) is perfectly known or entirely unknown to the transmitter. The secrecy analyzed with such optical tapping channel, also called optical wiretap channel, is typically referred to as information theoretic security (ITS). The ITS scenario has been compared against an extremely secure physical layer security scenario provided by quantum key distribution (QKD) in [3].
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Physical-Layer Security in FSO Communication
From the transmission perspective, orbital angular momentum (OAM) multiplexing technology has been studied and demonstrated to increase the capacity of FSO communications by using OAM beams as carriers [4], [5]. OAM of light is related to the spatial phase profile [6]–[10]. An OAM beam comprising an azimuthal phase term l has an OAM of lh per photon [11]. Since OAM beams with different l values are mutually orthogonal, in principle, there is no interference between multiplexing channels. However, in the presence of atmospheric turbulence, orthogonality between OAM modes is no longer preserved after certain propagation distance. The random refractive index distribution will distort the helical phase fronts of the OAM beam and induce crosstalk between channels. As a result, part of the energy is redistributed into other adjacent OAM modes. This turbulence effect will greatly degrade the performance of the OAM multiplexed FSO communications. In this paper, we study the FSO channel with OAM multiplexing under different atmospheric turbulence conditions. We numerically simulate the propagation of Laguerre-Gaussian (LG) beam over a turbulent line-of-sight (LOS) link and provide an information theoretic security analysis based on optical tapping scenarios. We show that by using OAM multiplexing, a higher secrecy capacity can be achieved over conventional OOK FSO channels under certain channel conditions, when adaptive optics is not used. The paper is organized as follows. In Section 2, OAM multiplexing and the propagation of OAM modes over atmospheric turbulence channels are studied. In Section 3, the informationtheoretic secrecy capacity of OAM multiplexing is studied assuming the worst-case scenario in which Eve is located on transmitter side, except for Section 3.3. In Section 3.1, the aggregate secrecy capacity of OAM multiplexing is studied for different power allocation strategies. On the other hand, in Section 3.2, the probability of positive secrecy capacity is studied. Further in Section 3.3, the aggregate secrecy capacity is studied assuming that Eve is located on receiver side. Some important concluding remarks are provided in Section 4.
2. OAM Beams Multiplexing and FSO Channel Modeling 2.1. Generating Information-Carrying Laguerre-Gaussian Beams and Multiplexing Among the beams that can carry OAM, the Laguerre-Gaussian (LG) beam has a well-defined OAM equal to l h per photon, where l is the azimuthal index. The field distribution of LG mode is given as h i sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " pffiffiffi #jlj h r 2 i ikr 2 z 2 1 z i ð 2pþjljþ1 Þtan 2 þz 2 2p! 1 r 2 2r 2 z 2 z R uðr ; ; zÞ ¼ eil Llp 2 (1) e w ðzÞ e ð R Þ e ðp þ jljÞ! w ðzÞ w ðzÞ w ðzÞ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where w ðzÞ ¼ w0 1 þ ðz=zR Þ2 is the beam radius at propagation distance z, w0 is the beam waist at z ¼ 0, zR ¼ w02 = is the Rayleigh range, is the wavelength, and k ¼ 2= is the propagation constant. Llp ðÞ denotes the generalized Laguerre polynomial with azimuthal index l and radial index p. For p ¼ 0 and l 6¼ 0, the intensity of a LG mode is a ring. In this paper, we only consider the LG modes with the radial index p ¼ 0 and denote as LGl;0 mode. The LG beams are of special interest because they can easily be generated. To generate OAM-multiplexed beam, first, a number of Gaussian beams carrying data information are generated independently from different transmitters, and these beams are then shone onto a series of computer generated holograms (CGHs) or spatial light modulators (SLMs) which are well programmed with interference pattern between reference beam and specific LG beam. The output (or reflected) information-carrying LG beams are then made collinear or optically multiplexed through non-polarizing beamsplitters. The resulting OAM-multiplexed beam is expanded by a telescope and such obtained OAM multiplexed beam is propagated through the FSO channel. pffiffiffiffiffiffiffiffiffiffiffi At the receiver side, a receiver telescope with aperture diameter DRX ¼ 2wz jlmax j is used to collect 99.9% of the transmitted power in the absence of turbulence [12], where wz is the zeroorder beam radius at distance z, which is followed by a set of mode filters for demultiplexing. In
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IEEE Photonics Journal
Physical-Layer Security in FSO Communication
the absence of atmospheric turbulence, the received field un ðr ; ; zÞ of LGl¼n;0 mode and the analyzing field um ðr ; ; zÞ for LGl¼m;0 mode satisfy the orthogonality principle: Z ðr ; ; zÞ um ðr ; ; zÞ; un ðr ; ; zÞ ¼ rdrd un ðr ; ; zÞum 8 0 8n 6¼ m
