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On secrecy analysis of UAV-enabled relaying NOMA systems

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Abstract

In this paper, we analyze the secrecy outage performance for an unmanned aerial vehicle (UAV) -enabled relaying non-orthogonal multiple access (NOMA) system, in which a source transmits a superimposed signal under the NOMA protocol to two users via a UAV-enabled decode-and-forward relay in the presence of an eavesdropper. Assuming the channels experience Nakagami-m fading and both hops are wiretapped, the probability density function (PDF) and cumulative distribution function (CDF) of the instantaneous signal-to-noise ratio are first characterized, and then based on those PDF and CDF expressions, the analytical expressions for secrecy outage probability of two users are derived. Finally, Monte Carlo simulations are used to verify the accuracy of the derived expressions.

Introduction

Non-orthogonal multiple access (NOMA), which can utilize the power domain multiplexing to support multiple users simultaneously by sharing the same time slots, frequency bands, and code resources, has been recognized as a potential multiple access technique in the fifth generation wireless networks [1], [2], [3], and this issue is also attracted a lot of attention and has been investigated in literature [4], [5], [6], [7], [8], [9]. Considering the joint constraints of transmission power budgets for the base station (BS) and minimum rate requirements per user, the relationship between power allocation (PA) and sum capacity was investigated when a central BS communicates with multiple randomly distributed users in [4]. The system performance in terms of outage probability (OP) was studied for an overlay amplify-and-forward cognitive hybrid satellite-terrestrial system when the satellite-to-terrestrial links are subject to Ricean fading and Nakagami-m fading, respectively, in [5]. Saito et al. [6] derived the system throughput in the scenarios that the radio interface of the key link is with and without adaptive function for a NOMA system. The closed-form and asymptotic expressions for OP, ergodic capacity (EC), and energy efficiency were derived for both cooperative and non-cooperative NOMA systems with residual transceiver hardware impairments in [7]. The authors in [8] analyzed the effect of imperfect channel state information on system outage performance for an underlay cognitive radio NOMA system with multiple secondary users. In [9], the achievable rates were derived under different pilot signaling schemes for a NOMA multiuser multiple-input multiple-output system.

On the other hand, unmanned aerial vehicle (UAV) has been regarded as a promising solution to provide a more convenient wireless communication connection, as it can extend wireless networks and improve transmission rate as well as the quality of service, which in turn can further improve the system performance for the next-generation wireless communications [10]. In addition, due to the high mobility of UAV and the ability to provide better quality of line-of-sight links, UAV is also valuable in some special scenarios, such as natural disaster and poor ground communication environments [11]. Taking the scenario that multiple UAVs can act as relays to form either a single multi-hop link or multiple dual-hop links into account, the closed-form expressions for OP and bit error rate (BER) was derived in [12]. To minimize the decoding error probability, a joint optimization algorithm of the blocklength allocation and the UAV location was proposed for an ultra-reliable and low latency communication enabled UAV relaying system in [13]. Later, the same performance indicator was studied by jointly optimizing the UAV location and the transmission power under both free space channel and three-dimensional channel models in [14]. Assuming that the destination is corrupted by multiple co-channel interferers, the authors in [15] derived an analytical expression for the OP in a dual-hop UAV-relaying system with multiple sources. The effects of terrestrial user mobility, propagation environment, and channel fading on UAV system performance in terms of OP and BER were analyzed in [16]. Zhou et al. [17] proposed a low-complexity iterative algorithm to maximize the minimum secrecy capacity (SC) for UAV-enabled mobile edge computing systems. A performance metric was proposed in [18] to maximize the minimum average rate for a secondary UAV-aided Internet of Things (IoTs) network.

In addition, recent studies show that introducing NOMA into UAV can serve as a promising solution to achieve massive connectivity [19], [20], [21], [22], [23], [24], [25]. Based on a UAV assisted heterogeneous IoTs communication system, a distributed successive interference cancellation free NOMA-based multi-objective resource allocation scheme was proposed to yield better performance in terms of the sum rate of the users and the access ratio of the devices in [19]. In [20], a general expression for OP was derived when a relay selection scheme was adopted in a multiple UAV-relaying system. The authors in [21] analyzed the spectrum efficiency (SE) of a UAV assisted terrestrial BS system, in which a resource allocation scheme was employed to improve the SE. The effects of transmitting duration and signal power of a high-speed UAV on system performance in terms of throughput were analyzed in [22]. Taking into account serious co-channel interference in the cellular-connected UAV networks, a new cooperative scheme was proposed to enhance the achievable rate of two communication networks in [23]. Such scenario was also considered in [24], in which the authors proposed a trajectory optimization and precoding scheme to maximize the throughput for a UAV communication network. Considering both backhaul-constrained and self-interference in a mobile UAV-relaying NOMA system, two optimization issues, i.e., UAV position and resource allocation, were investigated in [25].

Physical-layer security has received remarkable attention as it can exploit the randomness of wireless fading channels rather than using cryptography techniques to secure the communication [26]. This issue is also studied for UAV systems with NOMA [27], [28], [29], [30], [31], [32], [33]. In [27], the closed-form expressions for secrecy outage probability (SOP) and effective security throughput were derived in a simultaneous wireless information and power transfer (SWIPT) UAV network with a directional modulation scheme. The authors in [28] first proposed both a placement optimization strategy and a PA optimization scheme to meet the rate threshold of the secure user, and then utilized beamforming to guarantee the secure transmission. Zhang et al. [29] investigated the secrecy outage performance for a low-altitude UAV swarm secure network in the presence of multiple UAV eavesdroppers. Considering the legitimate UAV receiver and the eavesdropping UAVs are randomly distributed, the analytical expressions for SOP and average secrecy rate of a UAV communication system were derived in [30]. The authors in [31] studied the secrecy performance for a NOMA-UAV network in three different wiretapping scenarios, e.g., one eavesdropper, non-colluding, and colluding eavesdroppers. Based on a SWIPT UAV-assisted NOMA system with multiple ground passive receivers, a new cooperative interference scheme was proposed to enhance the secrecy performance in [32]. Assuming the presence of the residual hardware impairments at the transceivers, Li et al. [33] presented the analytical and asymptotic analysis of the achievable sum-rate for a UAV-aided NOMA multi-way relaying system.

Observed from the above-mentioned literature, it is interesting and promising to investigate the UAV-enabled relaying NOMA system in the context of physical-layer security, especially when the information in the dual hops are incorporated with NOMA technique and both hops are wiretapped. To the best of the authors’ knowledge, no existing literature has studied such issue. Therefore, in this paper, we investigate the secrecy performance in terms of SOP for a UAV-enabled relaying NOMA system over Nakagami-m fading channels in the scenario that both hops of information transmission are wiretapped. The main contributions are as follows:

(1) We investigate the secrecy performance for a UAV-enabled relaying system deploying NOMA over Nakagami-m fading channels. In addition, the probability density function (PDF) and cumulative distribution function (CDF) of the instantaneous signal-to-noise ratio (SNR) of all links are characterized.

(2) Based on those obtained expressions, the analytical expressions for the SOP of the two users are derived and verified with Monto Carlo simulation.

(3) Furthermore, the impacts of several system parameters, i.e., distances among the nodes, power allocation factors as well as path loss factor, on the secrecy performance are also investigated.

Section snippets

System and channel model

As shown in Fig. 1, we consider a UAV-enabled relaying system, which consists of a source (S), a UAV-relay (R), a pair of users Di, (i=1,2), and an eavesdropper (E). We assume that there is no direct links between S and Di due to severe blockage on the ground, and a UAV is used as a relay to build the connections between S and Di. Compared with traditional ground relaying systems, the major advantage of employing the UAV as a relay is its mobility, which in turn makes the UAV-enabled relaying

Secrecy outage performance

In this section, we present the detailed derivation of the SOP for the two users.

Numerical results

In this section, we present the analytical and simulation results. Each simulation result is obtained by performing with 3×106 independent trials. Unless otherwise stated, the parameters are set as follows: ρSE=ρRE=10  dB, ρR=20  dB, α1=0.8, α2=0.2, θ=2, LRD1=120  m, LRD2=100  m, LSR=120  m, LRE=300  m, dSE=350  m, H=80  m, mSR=mRD1=mRD2=mSE=mRE=2, ΩSR=ΩRD1=ΩRD2=ΩSE=ΩRE=1, Cth1=Cth2=0.0001  bits/s/Hz, and N1=N2=50.

As depicted in Fig. 2, Fig. 3, the SOP versus ρD1 and ρD2 for D1 and D2 under

Conclusion

In this paper, we have studied the secrecy performance for a UAV-enabled relaying system deploying NOMA over Nakagami-m fading channels in the scenario that both hops are wiretapped. Considering the effects of the distance among the nodes, power allocation coefficients, and path loss, the analytical expressions of the SOP for two NOMA users have been derived. Numerical results show that the secrecy performance can be significantly improved as ρD1 and ρD2 increase in the low-to-medium regimes.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Jiliang Zhang received the Ph.D. degree from Nanyang Technological University in 2011. In 2011, he joined the School of Electronic and Information Engineering, Southwest University, Chongqing, China, where he is currently an Associate Professor. His research interest spans special topics in communications theory and signal processing, including secure communications and CR/cooperative communications.

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    Jiliang Zhang received the Ph.D. degree from Nanyang Technological University in 2011. In 2011, he joined the School of Electronic and Information Engineering, Southwest University, Chongqing, China, where he is currently an Associate Professor. His research interest spans special topics in communications theory and signal processing, including secure communications and CR/cooperative communications.

    Xinyu Zheng is currently a postgraduate student at Southwest University, China. His research interest covers the areas of UAV communication, NOMA, cooperative communication, physical layer security, and so on.

    Gaofeng Pan (M’12) received the B.Sc. degree in communication engineering from Zhengzhou University, Zhengzhou, China, in 2005, and the Ph.D. degree in communication and information systems from Southwest Jiaotong University, Chengdu, China, in 2011. He was with Ohio State University, Columbus, OH, USA, from 2009 to 2011 as a joint-trained Ph.D. student under the supervision of Prof. E. Ekici. From 2012 to 2019, he was with the School of Electronic and Information Engineering, Southwest University, Chongqing, China, as an Associate Professor. In 2019, he joined the School of Information and Electronics, Beijing Institute of Technology, Beijing, China, as a Professor. Since 2016, he has been with School of Computing and Communications, Lancaster University, Lancaster, U.K., where he is a Post-Doctoral Fellow under the supervision of Prof. Z. Ding. His research interest spans special topics in communications theory, signal processing and protocol design, including visible light communications, secure communications, CR/cooperative communications, and MAC protocols. He is a TPC Member of Globecom’16 WEHCH, Globecom’17 MWN/WEHCH, and VTC’17 Spring HMWC. He has also served as a reviewer for major international journals, e.g., the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, the IEEE TRANSACTIONS ON COMMUNICATIONS, the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, the IEEE TRANSACTIONS ON SIGNAL PROCESSING, and the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY.

    Yiyuan Xie received the Ph.D. degree in optical engineering from the Chinese Academy of Science in 2009. He was a Visiting Scholar with the Hong Kong University of Science and Technology, Hong Kong. He joined the School of Electronic and Information Engineering, Southwest University, Chongqing, China, as a Full Professor, in 2010. He has authored or co-authored over 60 papers in peerreviewed journals and international conferences. His current research interests include network-on-chip, optical communications, nano photonics, and wireless communications.

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