Impact of Untrusted Relay on Physical Layer Security in Non Orthogonal Multiple Access Networks Vol (0123456789) Wireless Personal Communications https //doi org/10 1007/s11277 019 06219 y 1 3 Impact[.]
Wireless Personal Communications https://doi.org/10.1007/s11277-019-06219-y Impact of Untrusted Relay on Physical Layer Security in Non‑Orthogonal Multiple Access Networks Dinh‑Thuan Do1,2 · Minh‑Sang Van Nguyen3 © Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract In this study, the wireless sensor network is investigated in scenario of untrusted relay required to user at far distance In particular, an untrusted relay assists long distance transmission in situation of non-existence of the direct link between source and destination This paper employs non-orthogonal multiple access (NOMA) scheme to serve large number of users at different allocated power levels to adapt secure criteria Specifically , to evaluate the security performance we first examine the secure outage probability (SOP) and then strictly positive secrecy capacity (SPSC) is studied To further characterize the trade-off between system security and other controlling coefficients, we then investigate the impacts of power allocation factors and power levels of the eavesdropper In order to find tractable expressions to provide additional insights in term of the performance evaluation, the asymptotic expressions regarding both SOP and SPSC are performed in high signal-tonoise ratio (SNR) region In addition, secure performance of considered NOMA network is compared in two modes related to untrusted relay, including Amplify-and-Forward and Decode-and-Forward mode Finally, simulation results are presented to corroborate the proposed methodology Keywords Strictly positive secrecy capacity · Non-orthogonal multiple access · Jamming signal · Secure outage probability · Physical layer security * Dinh‑Thuan Do dodinhthuan@tdtu.edu.vn Minh‑Sang Van Nguyen sangnguyen.fet@gmail.com Wireless Communications Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam 13 Vol.:(0123456789) D.-T. Do, M.-S. Van Nguyen 1 Introduction To familiarize substantially growth regarding the throughput in the fifth generation (5G) networks, it required the unprecedented evolution of new Internet-enabled smart devices, and related applications and services Considering several techniques to improve the spectral efficiency, key architectures such as novel multiple access (MA) techniques, cognitive radio, heterogeneous networks, millimeter wave communications, multiple-input multipleoutput (MIMO) for large-scale networks can be implemented to upgrade current networks Regarding MA schemes including orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA), these considered main categories are deployed to primarily provide multiple access methodology In MA, it is introduced that signals distinguishing a explicit resource block can be employed by multiple users [1, 2] More specifically, codedomain NOMA and power-domain NOMA are classified for NOMA upon exploring the multiplexing gain from the different domains [3] Lately, cooperative jamming and artificial noise (AN) assisted model to improve physical layer security (PLS), even if the the legitimate receivers have worse channel conditions than the eavesdroppers [4, 5] Goel and Negi in [6] proposed a technique by generating AN at the transmitter to decrease the eavesdroppers reception In principle, improving the security by producing AN at the transmitter is different scheme compared with a detrimental effect of noise and interference, because it destroys the channel conditions of eavesdroppers without disturbing those of the legitimate receivers The perfect and imperfect channel state information (CSI) at both the transmitter and receiver are examined in an AN based multi-antenna assisted secure transmission scheme affected by colluding eavesdroppers [7] As a further development, the authors in [8] using both beamforming and sectoring techniques to achieve the secrecy enhancement in wireless Ad Hoc networks Specially, the authors in [8–12] presented an effective technique to confuse the eavesdropper by deploying AN at the legitimate transmitter As an effective method to enhance the system security, the authors in [9] have also been performed cooperative full-duplex relay In [7], a relay networks can be able to largely improve the physical layer security through using AN-aided strategy In other trends, many secure transmission strategies are introduced, for example cooperative beamforming (CB) [8] and cooperative jamming (CJ) [9] by conveying the benefits of AN assistance in cooperation with relaying transmission It can be realized the randomness and time-varying nature of the wireless channels to support for network security without deploying any encryption algorithm, PLS is proposed in both information security and wireless communications [13] Zhang et al proved that the secrecy sum rate performance of NOMA better than the one of the conventional OMA in scenario of the security performance of single-input-single-output (SISO) NOMA system [14] Qin et al [15] derived new secrecy outage probability (SOP) in forms of exact and asymptotic expressions to explore physical channel-assisted security of NOMA networks in large-scale networks wherein spatially randomly location deployment for both NOMA users and eavesdroppers Furthermore, the authors in [16] presented the exact and asymptotic expressions for SOP in term of the secrecy performance in case of NOMA employing multiple antenna and artificial noise as well To improve the secrecy performance of a MIMO system, optimal antenna selection (OAS) and suboptimal antenna selection (SAS) schemes are proposed which based on whether the base station has the global channel state information (CSI) of both the main and wiretap channels [17], and those performance were compared with the outdated space time transmission (STT) scheme The the exact and asymptotic SOP in closed-form expressions is derived for an underlay MIMO 13 Impact of Untrusted Relay on Physical Layer Security in… system system [18] Recently, stochastic geometry model is deployed in networks wherein the physical layer security was considered for applications in 5G NOMA [19] Later, single antenna and multiple-antenna stochastic geometry networks were untaken in [20] in which two different schemes were suggested to evaluate the secrecy performance In [21], their results showed that optimal designs of decoding order, transmission rates, and power allocated to each user are examined to satisfy secrecy considerations in a new design of NOMA To the best of the authors’ knowledge, the analysis of the physical layer security in cooperative NOMA systems is still considered in few related works In particular, the design of system to examine secrecy performance for cooperative NOMA is still not perfect in in many scenarios related to signal or channel at physical layer As a result, these observation motivate us to perform analytical expressions as detailed study in this work The secure performance of NOMA using untrusted relay circumstance in cooperative manner is examined as main aim of this work We focus on a related scenarios reflected in [22–25] to answer this important question However, these papers did not consider system model with assistance of untrusted relay Furthermore, in order to examine practical situation regarding the network security, wherein AN-aided relay and related illegal channel between source and untrusted relay is in degrading performance due to imperfect AN cancellation The primary contributions of the paper are shortened as follows We comprehensively investigate the design of NOMA against the untrusted relay (eavesdropper) under the secrecy outage constraint The main contributions of this paper can be shown as: – The new architecture related to untrusted relay-aware NOMA communication is investigated and the main impacts of related channel gains and secure target rates on system performance are studied Such system model is built as combination of the unstrusted reaying model and NOMA protocol in unique system model to evaluate secure in physical layer – We derive some analytical expressions of SOP and SPSC in term of signal-to-noise ratio (SNR) In this paper, the wiretap network model is constructed according to the technical characteristics of both NOMA and untrusted relaying network In addition, new asymptotic expressions of these important secure metrics including SOP and SPSC are derived in special case of high SNR at source node – The power allocation factor for two separated signals in NOMA is derived to evaluation optimal secure performance of such NOMA system The interesting finding exhibits power fractions which can be chosen reasonably to achieve balancing optimal performance for both SOP and SPSC – Moreover, the accuracy of the derived results are validated via Monte-Carlo simulations The results show that the SOP, SPSC corresponding distinctive characterizations of secure performance for the such proposed NOMA system with selected key parameters are investigated to provide insights in practical design The remainder of this paper is organized as follows: Sect. 2 presents the system model and signal analysis with secure capacity deployed in NOMA system is investigated In Sect. 3, we derive the analytical expressions of SOP and SPSC in AF mode of concerned NOMA while DF mode is considered as a benchmark as present in Sect. Section examines the simulation results Finally, Sect. 6 completes with conclusion remarks for the paper and reviews the important results 13 D.-T. Do, M.-S. Van Nguyen 2 System Model We consider an untrusted relaying NOMA network shown in Fig. 1, where a source (S) communicates with two destination nodes (D1, D2) through an untrusted relay (R) In this paper, it can be assumed that source node S generates the artificial noise (AN) signal, the destination node can cancel it prior to information decoding which is different with the untrusted relay It is further assumed that the untrusted relay node is considered in situation of noncolluding, it is refer as they independently intercept the information More importantly, we assume that design of AN precoding matrix related to the jammer is performed in such a way that the jamming signal is injected to only degrade the untrusted relay’s channel It is assumed that a straight link between S and destination nodes are unavailable due to deep fading Consider a NOMA system including two users (D1, strong user, and D2, weak user) can be deployed in several networks such as mobile network, sensor wireless communication or IoT systems In such system model, S is situated in the center point within coverage range regarding serving cell, and users D1 and D2 are very near with border of such cell where contains received signal at weak level of power We extra undertake that single antenna equipped in all nodes in the network It is familiarity with works in the literature all the channels exhibit independent Rayleigh fading In additional assumption, it is recalled that block Rayleigh fading is applied, i.e., each channel is still constant in one block and changes via different the( coherence blocks Initially, the superimposed mixture is transmit) ted in the first time slot, 𝛼1 s1 + 𝛼2 s2 from S to the relay, where si (i = 1, 2) is the unit power signal received by user Di and 𝛼i denoted as the power allocation factor To achieve destination node’s QoS requests, it is required that 𝛼1 ≥ 𝛼2 and these allocated coefficients must be constrained by equation 𝛼12 + 𝛼22 = 1 In addition, noise term namely additive white Gaussian noise (AWGN) happens at each receiver with zero mean and variance N0 We call Ps , Pr are transmit power at source and relay respectively We denote the fading coefficients corresponding link between source and relay is gs,r while link between relay and destination users Di are gr,i We denote 𝛺1 , 𝛺2 as the Rayleigh channel parameters corresponding to gs,r , gr,i , respectively Similar to many works in literature, it is noted that two links from relay to two destination in NOMA scheme is similar and average channel gain is the same In our proposed scheme, full channel state information (CSI) of the communication links should be available at the node where need it to obtain related calculations Considering secure performance in this work, to make it possible for reliable and secure communication between S and destination nodes, we utilized the widely-adopted Wyners Fig. 1 System model of secure NOMA under impact of untrusted relay 13 Impact of Untrusted Relay on Physical Layer Security in… wiretap code [26] This coding scheme consists of the codeword transmission rate, R0 and confidential information rate, Ri The rate increment of Re = R0 − Ri is the expense of confusing listener The untrusted relay will try attempt to overhear on the ongoing transmissions from S to two destination nodes The untrusted relay nodes are assumed to be non-colluding which means that they intercept the information independently It worth noting that the jamming signal intends to eavesdropper will affect the received signal at the untrusted relay, i.e using artificial noise signal It is practical that relay can be classify between pure signal from source transfers to destination and artificial noise term ([24, 25]) It is worth noting that relay in such NOMA is assumed to detach received mixture signal as destination using SIC Detailed explanations of untrusted relay to detect its own signals is beyond the scope of our paper The transmission in such system model is divided into two phases In the first phase, the received signal at the untrusted relay can be expressed as � �√ yr = gs,r 𝛼1 s1 + 𝛼2 s2 Ps + 𝜔r (1) For AF scheme in untrusted relaying NOMA network, two users employ two concurrence time slots to obtain received signal via help of relay which is called as untrusted device Then, the expected signal can be computed at Di as yAF = Gyr gr,i + 𝜔r,i r,i (2) where 𝜔r,i stands for noise term concerning as additive Gaussian noise and it’s characterization of zero mean and variance N0 It is noted that the amplifying factor is G in AF mode given by G2 = Pr | Ps |gs,r || + N0 (3) Without loss of generality, we assume that Pr = Ps , then the the amplifying factor is reexpressed as G2 = |gs,r |2 + | | (4) 𝜌 where 𝜌 = Ps ∕N0 = Pr ∕N0 denotes the average SNR achieved at legal links Then, the instantaneous signal-to-interference-plus-noise ratio (SINR) at D1 can be computed by AF 𝛾r,1 = |g |2 |gs,r |2 𝛼 | r,1 | | | |gr,1 |2 |gs,r |2 𝛼 + |g |2 + |g |2 + | | | | 𝜌 | r,1 | 𝜌 | s,r | 𝜌2 (5) Following principle of NOMA, to detect signal need be achieved at receiver it requires implementation of successive interference cancellation (SIC) to signal si is obtained for user Di As a result, the received SNR at D2 can be expressed by AF 𝛾r,2 = 2 𝜌||gs,r || ||gr,2 || 𝛼22 |gr,2 |2 + |gs,r |2 + | | | | 𝜌 (6) 13 D.-T. Do, M.-S. Van Nguyen Hence, considering link between the relay and user, the AF-based transmission capacity from can be written as ( ) AF AF Cr,i = log2 + 𝛾r,i (7) In this work, it is assumed that jamming signal is imperfect canceled at the untrusted relay to distinguish the superimposed mixture It worth noting that the received average SNR corresponding with the illegal link in situation in which untrusted relay is activated AF 𝛾E,i = 𝛼i2 𝜌𝜅 ||gs,r || = 𝛼i2 𝜌E ||gs,r || , (8) where 𝜅 is affected factor due to imperfect jamming signal cancellation It worth noting that channel gain in S–R link in case that existence of jamming signal is different with case that main channel of S–R link reserved for pure signal communication Therefore, we call 𝜌E is SNR corresponding with jamming-aware channel and average channel gain denoted by 𝜆0 Similarly, the channel capacity from the relay for received signal related jamming signal can be computed as ( ) AF AF CE,i = log2 + 𝛾E,i (9) Therefore, the secrecy rate of the AF-based NOMA systems for user is formulated by [ ]+ AF AF CiAF = Cr,i − CE,i , (10) where [x]+ = max {x, 0} As benchmark of AF-NOMA, we consider scenario of DF untrusted relay, in which the relay initially decodes its received superimposed message from S in the first phase and then re-encodes and onwards it to the destination in the second phase Then, the received signals at Di can be shown as � �√ Ps + 𝜔r,i yDF r,i = gr,i 𝛼1 s1 + 𝛼2 s2 (11) The equivalent SNR in DF-NOMA case is expressed by { } 2 𝜌||gs,r || 𝛼12 𝜌||gr,i || 𝛼12 DF 𝛾r,i = , (12) 2 𝜌||gs,r || 𝛼22 + 𝜌||gr,i || 𝛼22 + } { The channel capacity of a DF relaying system is related to CS−R , CR−Di , where CS−R and CR−Di denote the capacity from S to relay and relay to Di , respectively Hence, the capacity of the main channels for D1 is ( { }) 2 𝜌||gs,r || 𝛼12 𝜌||gr,1 || 𝛼12 DF CS−D1 = log2 + , (13) 2 𝜌||gs,r || 𝛼22 + 𝜌||gr,1 || 𝛼22 + And, the capacity of the main channels for D2 is 13 Impact of Untrusted Relay on Physical Layer Security in… DF CS−D2 = ( { }) 2 log2 + 𝜌||gs,r || 𝛼22 , 𝜌||gr,2 || 𝛼22 (14) Similarly, the capacity of the eavesdropping channel is ( ) DF CR−Ei = log2 + 𝛼i2 𝜌E ||gs,r || (15) By conveying definition of the secrecy capacity, it can be expressed for considered DFbased NOMA systems at Di as [ DF,i ] DF + CiDF = CS−Di − CR−Ei (16) 3 Secure Performance Analysis in Case of AF‑Based NOMA System 3.1 SOP Performance Analysis In this subsection, we evaluate the secrecy performance in terms of SOP metrics Motivated by novel results from [27], we further analyse secure performance in untrusted scenario To achieve tractable form of derived formula, we also provide the asymptotic SOP analysis The SOP is initiated by the fact that R successfully intercepts the source private signals, which reflects the secure communication In NOMA systems, with regard to the help of untrusted relay for forwarding two signals transmitted from the source to D1 and D2, respectively Therefore, outage event occurs when C1AF , C2AF drop under their own target rates Ri respectively To evaluate the secrecy performance comprehensively of the untrusted relay NOMA network, the secure performance can be further illustrated by SOP In particular, we can expressed SOP in such NOMA network for evaluate secrecy performance as ( ) SOPAF = Pr C1AF < R1 or C2AF < R2 ) ( AF AF + 𝛾r,1 + 𝛾r,2 > Cth , > Cth =1 − Pr (17) AF AF + 𝛾E,1 + 𝛾E,2 =1 − Pr 1, i where Cth =2 2Ri Proposition 1 The approximation of secure performance in DF-NOMA can be found by ( ( 𝜉 ) ) ( ) 1 𝛺2 + B − − SOPAF = + e 𝜌E 𝛺1 − e (1−A)𝛺1 𝛺2 (18) 𝛺1 A + 𝛺 where 𝜉1 = 1−𝛼22 Cth 𝛼12 𝛼22 Cth , A = Cth 𝜌E 𝜌 , B = Cth −1 𝜌𝛼22 Proof See in the “Appendix” □ 3.2 SPSC Analysis In other metric, existence of secrecy capacity should be determined In particular, we consider SPSC as fundamental benchmark which is evaluated to further confirmation on 13 D.-T. Do, M.-S. Van Nguyen secrecy performance In term of the SPSC, secrecy capacity performance corresponding with an AF relaying NOMA system is computed as ( ) SPSCAF = Pr C1AF > 0, C2AF > 0, ( ) (19) AF AF AF AF = Pr 𝛾r,1 > 𝛾E,1 , 𝛾r,2 > 𝛾E,2 Due to influence of jamming signal, it can be noted that 𝜌 > 𝜌E , hence we can obtain new expression as SPSC AF ( = Pr ||gs,r || < } { |gs,r |2 , 𝜌|gr,2 |2 > 𝜌E |gs,r |2 , 𝜌 | | | | | | 𝜌E 𝛼22 ) ( | |2 𝜌E ||gs,r || | | , |gr,2 | > = Pr |gs,r | < 𝜌 𝜌E 𝛼22 ) (20) Then, we further obtain the following formula as ) ) ( ( 𝜌 x x dx exp − exp − E ∫0 𝜌𝛺2 𝜆0 𝜆0 ( ( ) ) 𝜌E 𝜌E 𝛼 1 + exp − x dx = 𝜆0 ∫0 𝜌𝛺2 𝜆0 )] [ ( ( ) 𝛺2 𝜌 𝜌E 1 = − exp − + 𝜆0 𝜌E + 𝛺2 𝜌 𝜌𝛺2 𝜆0 𝜌E 𝛼22 SPSCAF = 𝜌E 𝛼 2 (21) Remark 1 According to [(19) and (21)], we state that for the scenario of untrusted relay happens in main transmission, changing the channel gain factors of all transmission hops can effectively enhance the secrecy performance including SOP and SPSC metrics of such NOMA communications Moreover, the secrecy performance of the NOMA scheme will be influenced by the varying of the predefined threshold secure rates Thus, a good tradeoff between key parameters and secrecy performance is introduced by the numerical simulation in following section In addition, the jamming scheme make worse performance of untrusted relay and then evaluation of impact of jamming on secure performance is also careful considered in these circumstances 4 Secure Performance Analysis in Case of DF‑Based NOMA System 4.1 SOP Analysis in DF‑NOMA Regarding on DF-based NOMA systems, the SOP can be computed by ( ) SOPDF = Pr C1DF < R1 or C2DF < R2 ( ) =1 − Pr C1DF > R1 or C2DF > R2 =1 − Pr 13 (22) Impact of Untrusted Relay on Physical Layer Security in… Similar to the analysis done in previous subsection related AF mode, we can obtain an 2 𝜌|gr,1 | 𝛼12 𝛼2 𝜌|gs,r | 𝛼12 ≈ ≈ 𝛼12 Then, it is noted that upper bound of instantaneous SINR as 2 2 𝜌|gs,r | 𝛼2 +1 𝜌|gr,1 | 𝛼2 +1 Pr2 can be expressed as � � 𝛼2 2 ⎞ ⎛ + 𝛼12 + 𝜌��gs,r �� 𝛼22 , 𝜌��gr,2 �� 𝛼22 ⎜ 2⎟ > Cth , > Cth ⎟ Pr < Pr ⎜ 2 + 𝛼22 𝜌E ��gs,r �� ⎟ ⎜ + 𝛼12 𝜌E ��gs,r �� ⎠ ⎝ � �� � � � 𝜉 2 2 = Pr < Pr ��gs,r �� < + 𝛼22 𝜌E ��gs,r �� , + 𝜌��gs,r �� 𝛼22 , 𝜌��gr,2 �� 𝛼22 > Cth 𝜌E (23) Proposition 2 Secure outage event in DF-NOMA can be computed in closed-form expres- sion as below DF SOP ) ( ( ) − B { 𝛺2 e 𝛺2 A B =1− exp − + 𝜆0 A + 𝛺2 𝛺2 𝜆0 (1 − A) ) )} ( ( 𝜉1 A + − exp − 𝛺2 𝜆0 𝜌E (24) Proof See in “Appendix” □ 4.2 SPSC Analysis in DF‑NOMA In similar manner, we also have 𝜌|gs,r | 𝛼12 𝜌| | case can be expressed as � � SPSCDF = Pr C1DF > 0, C2DF > 0, 𝜌|gr,1 | 𝛼12 2 gs,r 𝛼22 +1 ≈ 𝜌| | gr,1 𝛼22 +1 ≈ 𝛼12 𝛼22 Then, the SPSC for a DF � � 𝛼2 ⎞ ⎛ �gs,r �2 𝛼 , 𝜌�gr,2 �2 𝛼 + 𝛼12 + 𝜌 � � � � ⎟ ⎜ > 1, > 1⎟ ≈ Pr ⎜ 2 + 𝛼22 𝜌E ��gs,r �� ⎟ ⎜ + 𝛼12 𝜌E ��gs,r �� ⎠ ⎝ (25) We consider the situation in untrusted relay where the condition 𝜌 > 𝜌E is satisfied Therefore, SPSC in such DF case can be obtained easily after several computation steps SPSC DF ) | |2 | |2 𝜌E |gs,r | , |gr,2 | > , 𝜌 𝛼22 𝜌E ( ( ) ) 𝜌 x 𝛼 𝜌E x exp − E = exp − dx ∫0 𝜌𝛺2 𝜆0 𝜆0 ) ) ( ( 𝜌E 𝛼 𝜌E 1 + x dx exp − = 𝜆0 ∫0 𝜌𝛺2 𝜆0 ( = Pr ||gs,r || < (26) 13 D.-T. Do, M.-S. Van Nguyen As a result, it can be expressed SPSC in DF-NOMA as below [ ( ( )] ) 𝜌E 𝜌𝛺2 1 DF − exp − + SPSC = 𝜆0 𝜌E + 𝜌𝛺2 𝜌𝛺2 𝜆0 𝛼22 𝜌E (27) 5 Simulation Results Unless otherwise stated, regarding on untrusted relay-aware NOMA, source transmission power, Ps = 1 (J/s) and path loss exponent m = (which corresponds to an urban cellular network environment ) In practice, different rates are assigned for different users, but in this study we set the secure target rate, Ri = 3 (bits/s/Hz) in the both transmission links for simple analysis The distances in each hop of relaying NOMA system are normalized to unit value For simplicity, similar noise variances at the relay and the destination nodes are assumed, i.e., different kinds of noise variance is set as N0 = 0.01 Power allocation factors for NOMA 𝛼12 = 0.2, 𝛼22 = 0.8 except to specific simulation results The mean values, 𝛺1 , 𝛺2 of the exponential random variables in two hop of relaying NOMA, respectively, are set to Figure 2 shows the SOP versus transmit SNR at source achieved by the proposed AFNOMA scheme, where a close agreement between the simulated and analytical results can be observed, and they match verwy well in high SNRregime For a comparison, the SOP achieved by the proposed scheme we change power allocation factors From this figure, we have the following informative observations such as high SNR such NOMA system is more secure In particular, simulation and analytical lines are matched very well only at high SNR This is consistent with Proposition 1, in the sense that the proposed NOMA scheme not only intentionally decreases the capability for eavesdropper, but also effectively creates channel difference for same link S–R, thus guaranteeing a forceful secure AF-NOMA transmission Furthermore, the power allocation factor has different impacts on the secure Secure Outage Probability 100 10-1 SOP SOP SOP SOP SOP 10-2 10 15 AF Ana AF: α1 = AF: α1 = AF: α1 = AF: α1 = 20 0.55 0.65 0.75 0.85 25 Sim Sim Sim Sim 30 35 40 45 50 55 SNR (dB) Fig. 2 SOP of untrusted relay AF-NOMA versus transmit SNR at source as varying 𝛼1 13 60 Impact of Untrusted Relay on Physical Layer Security in… Secure Outage Probability 100 10-1 10-2 10 15 20 25 30 35 40 45 50 55 60 SNR (dB) Fig. 3 SOP of untrusted relay DF-NOMA versus transmit SNR at source as varying 𝛼1 0.9 Secure Outage Probability 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Fig. 4 SOP of untrusted relay AF-NOMA versus 𝛼1 as varying jamming-aware channel gains performance As can be seen that a better SOP is always obtained with a larger value of power allocation Therefore, it is of salient implication to choice the suitable power allocation factor for the SOP improvement Interestingly, similar trend can be seen in DF-NOMA scenario as in Fig. 3 Figure 4 plots SOP performance as varying the power of eavesdropper In fact, to guarantee a trustworthy communication, small values power of eavesdropper link should be 13 D.-T. Do, M.-S. Van Nguyen 0.9 Secure Outage Probability 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Fig. 5 SOP of untrusted relay DF-NOMA versus 𝛼1 as varying jamming-aware channel gains 0.9 Secure Outage Probability 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.5 1.5 2.5 3.5 R2 Fig. 6 SOP of untrusted relay AF-NOMA versus the target secure rates as varying jamming-aware channel gains selected since the superimposed message is transmitted to untrusted relay We can see that the curves corresponding to higher power allocation factor provider better secure performance In similar way, we confirmed that similar result can be obtained for DF case as in Fig. 5 It can be observed that SOP performance only change slightly as varying target secure rates as illustrations in Figs. 6 and 7 This main result confirm that required target 13 Impact of Untrusted Relay on Physical Layer Security in… 0.9 Secure Outage Probability 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.5 1.5 2.5 3.5 R2 Fig. 7 SOP of untrusted relay DF-NOMA versus the target secure rates as varying jamming-aware channel gains rates not harm secure performance in NOMA system This observation motivate us to examine other key parameters which can be able to make secure performance fluctuate as controlling related coefficients It can be shown that the optimal power allocation factor 𝛼1 approximate to 0.85 to achieve optimal secure performance in term of SOP In Figs. and 9, we plot the SPSC curves for both AF and DF relaying NOMA systems respectively versus power level of eavesdropper for different values of power Strictly Postitive Secrecy Capacity 100 10-1 10-2 -5 10 15 20 25 30 E Fig. 8 SPSC performance of untrusted relay AF-NOMA versus 𝜌E 13 D.-T. Do, M.-S. Van Nguyen Strictly Postitive Secrecy Capacity 100 10-1 10-2 -5 10 15 20 25 30 E Fig. 9 SPSC performance of untrusted relay DF-NOMA versus 𝜌E allocation factors In contrast with trend observed in SOP’s simulation results, lower value of 𝛼1 leads to better SPSC performance Simulation results verify the accuracy of our derivations Also, the SPSC of the AF relaying strategy is very similar with that of the DF case It can be observed that higher power of eavesdropper the SPSC will be improved As results in Figs. 10 and 11, simulations of SPSC versus power allocation factors when the eavesdropper link experiencing different power level This figure demonstrates that the Strictly Postitive Secrecy Capacity 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.1 0.2 0.3 0.4 0.5 0.6 Fig. 10 SPSC performance of untrusted relay AF-NOMA versus 𝛼1 13 0.7 0.8 0.9 Impact of Untrusted Relay on Physical Layer Security in… Strictly Postitive Secrecy Capacity 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Fig. 11 SPSC performance of untrusted relay DF-NOMA versus 𝛼1 curves increase as higher power allocation factors are selected As many previous results, similar trend can be illustrated for both AF and DF scheme In general, SOP and SPSC performance meet similar trend in AF and DF mode Such result confirms that selection of AF or DF scheme does not affect on secure performance of the proposed NOMA 6 Conclusions In this paper, we have studied impact of the untrusted relay in evaluation of NOMA schemes in term of secure performance We have first designed the NOMA scheme that consider the transmit power of eavesdropper link subject to the secrecy outage and QoS constraints We have then designed the NOMA scheme that satisfy confidential information rate subject to the secrecy outage and power allocation constraints The important results confirmed that the SOP of NOMA systems for both AF and DF protocol tends to a constant at high SNR regimes However, reasonable values for the target rate, power allocation factors and the power level of the eavesdropper link under impact of jamming signal should be chosen to ensure a reliable communication, in such NOMA system The optimal power allocation factors for NOMA exhibit optimal SOP performance while the secure target rates not change SOP in the studied problems In addition, SPSC can be improved as increasing the level of power allocated to the untrusted relay and the power allocation constraint for two users in NOMA is careful selected Numerical results have demonstrated that the secure performance of NOMA scheme can be achieved optimal performance if reasonable selected parameters are obtained for untrusted relay and power allocation factors for NOMA’s users 13 D.-T. Do, M.-S. Van Nguyen Acknowledgement This research is funded by Foundation for Science and Technology Development of Ton Duc Thang University (FOSTECT), website: http://fostect.tdt.edu.vn, under Grant FOSTECT.2017.BR.21 Compliance with ethical standards Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest Appendix Proof of Proposition 1 It worth noting results become intractable exact analysis because the variables and are correlated In particular, the key performance metrics such as the SOP is considered Then, to obtain more insights on the system the asymptotic behavior need be investigated Hence, high SNR regime is examined in our analysis and adopt an upper 2 𝛼2 𝜌𝜌|gs,r | |gr,2 | 𝛼22 AF AF < 𝛼12 , 𝛾r,2 < bounds can be shown as 𝛾r,1 2 𝜌|gr,2 | +𝜌|gs,r | Then, an upper bound of Pr1 can be obtained as 𝛼2 ⎛ 2 + 𝛼12 𝜌𝜌��gs,r �� ��gr,2 �� 𝛼22 ⎜ > C , Pr < Pr ⎜ th 2 𝜌��gr,2 �� + 𝜌��gs,r �� ⎜ + 𝛼12 𝜌E ��gs,r �� ⎝ � 2 2 −1 > Cth 𝛼2 𝜌E ��gs,r �� + Cth (A.1) After manipulation steps, it can be expressed above formula as ) 2 |gs,r |2 |g |2 Cth 𝜌E ||gs,r || r,2 | | | | +B , Pr < Pr 𝜌E ||gs,r | < 𝜉1 , > 𝜌 |gr,2 |2 + |gs,r |2 | | | | ( |2 where 𝜉1 = 1−𝛼22 Cth 𝛼12 𝛼22 Cth , A = Cth 𝜌E 𝜌 It can be addressed that , B = 𝛼12 > (A.2) Cth −1 𝛼22 𝜌𝛼 ( 21 ) Cth − due to 𝜉1 = 𝛼12 −𝛼22 (Cth −1) 𝛼12 𝛼22 Cth > 0 Otherwise, SOP in such AF-NOMA equals to worst case as Note that the approximation follows the fact that xy∕(x + y) ≤ {x, y} , Pr1 can be additional approached as ) } { ( 2 2 Pr < Pr 𝜌E ||gs,r || < 𝜉1 , ||gs,r || , ||gr,2 || > A||gs,r || + B (A.3) Unfortunately, it is hard to gain a closed-form for (A.3) In order to derive the tractable expression, we use the fact that ( ) ( ) ) ( P 𝜀1 , 𝜀2 = P 𝜀1 − P 𝜀1 , 𝜀2 , where 𝜀2 represents the complementary event of 𝜀2 Then, we have 13 Impact of Untrusted Relay on Physical Layer Security in… } { 2 𝜀1 = ||gs,r || , ||gr,2 || > A||gs,r || + B (A.4) 𝜀2 = 𝜌E ||gs,r || < 𝜉1 (A.5) and Therefore, it can be obtained the secure outage event as ( ) } { 2 Pr ||gs,r || , ||gr,2 || > A||gs,r || + B ( { } ) 2 2 − Pr 𝜌E ||gs,r || > 𝜉1 , ||gs,r || , ||gr,2 || > A||gs,r || + B (A.6) = P1 − P2 In next step, we further compute each component as below ) ( 2 2 P1 = Pr ||gs,r || > A||gs,r || + B, ||gr,2 || > A||gs,r || + B ( ∞ ) ) ( B = Pr ||gs,r | > Pr ||gr,2 || > Ax + B f|g |2 (x)dx s,r 1−A ∫ |2 (A.7) In such case, P1 can be rewritten as below ∞ − P1 =e B (1−A)𝛺1 ∫ e − ( 𝛺2 − e = 𝛺1 A + 𝛺 (Ax+B) 𝛺2 (1−A)𝛺1 − 𝛺x1 e dx 𝛺1 + 𝛺1 ) B (A.8) In similar way, P2 can be computed as ) } ( { 2 2 P2 = Pr 𝜌E ||gs,r || > 𝜉1 , ||gs,r || , ||gr,2 || > A||gs,r || + B ( ) ) ( 𝜉1 𝜉 − = Pr ||gs,r || > P1 = e 𝜌E 𝛺1 P1 𝜌E (A.9) Finally, with important results in (A.8), (A.9) together with (A.6), the performance in AF relaying NOMA systems in term of the SOP can be expressed by SOPAF = − P1 + P2 (A.10) 13 D.-T. Do, M.-S. Van Nguyen Plugging expressions of P1 and P2 as previous findings, we achieve final expression This is □ end of the proof Proof of Proposition 2 Also, it can be rewritten secure outage for DF case as ) } ( { 2 Pr < Pr ||gs,r || , ||gr,2 || > A||gs,r || + B ( ) 𝜉 2 − Pr ||gs,r || > , ||gr,2 || > A||gs,r || + B 𝜌E (B.1) After some simple manipulations, the first term in above expression can be shown as ( ) } { 2 Pr ||gs,r || , ||gr,2 || > A||gs,r || + B ( ( ) ) ∞ A −B = e 𝛺2 exp − + x dx ∫ B 𝜆0 𝛺2 𝜆0 (1−A) (B.2) ( ( ) ) 𝛺2 e A B exp − + 𝜆0 A + 𝛺2 𝛺2 𝜆0 (1 − A) − 𝛺B = Next, the second term in above expression can be shown as ( ) 𝜉 2 Pr ||gs,r || > , ||gr,2 || > A||gs,r || + B 𝜌E ) ) ( ( ∞ B A − = e 𝛺2 + x dx exp − ∫ 𝜉1 𝜆0 𝛺2 𝜆0 𝜌E (B.3) [ ( ( ) )] 𝛺2 e A 𝜉1 exp − + 𝜆0 A + 𝛺2 𝛺2 𝜆0 𝜌E − 𝛺B = Finally, the SOP for the DF-based NOMA systems is DF SOP ) ( ( ) − B 𝛺2 e 𝛺2 A B = exp − + 𝜆0 A + 𝛺2 𝛺2 𝜆0 (1 − A) ( ( ) )] − 𝛺B [ 𝛺2 e A 𝜉1 exp − + − 𝜆0 A + 𝛺2 𝛺2 𝜆0 𝜌E (B.4) Finally, a high SNR 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Van Nguyen 23 Zheng, B., et al (2018) Secure NOMA based two-way relay networks using artificial noise and full duplex IEEE Journal on Selected Areas in Communications, 36(7), 1426–1440 24 Le, N Q., Do, D.-T., & An, B (2017) Secure wireless powered relaying networks: Energy harvesting policies and performance analysis International Journal of Communication Systems (Wiley), 30(18), e3369 25 Chen, D., et al (2018) Energy-efficient secure transmission design for the Internet of Things with an untrusted relay IEEE Access, 6, 11862–11870 26 Wyner, A D (1975) The wiretap channel Bell System Technical Journal, 54(8), 1355–1387 27 Chen, J., Yang, L., & Alounini, M.-S (2018) Physical layer security for cooperative NOMA systems IEEE Transactions on Vehicular Technology, 67(5), 4645–4649 Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations Dinh‑Thuan Do received the B.S degree, M Eng degree, and Ph.D degree from Vietnam National University (VNU-HCMC) in 2003, 2007, and 2013 respectively, all in Communications Engineering He was a visiting Ph.D student with Communications Engineering Institute, National Tsing Hua University, Taiwan from 2009 to 2010 Prior to joining Ton Duc Thang University, he was senior engineer at the VinaPhone Mobile Network from 2003 to 2009 Dr Thuan was recipient of Golden Globe Award from Vietnam Ministry of Science and Technology in 2015 His research interests include signal processing in wireless communications network, NOMA, full-duplex transmission and energy harvesting Minh‑Sang Van Nguyen was born in Ben Tre province, Vietnam He is currently pursuing his Ph.D He is currently a member of Wireless Communications research group at Industrial University of Ho Chi Minh City (IUH) His research interests include wireless communication, 5G wireless communication networks, network security, energy harvesting, relay selection, cognitive radio networks 13 ... Y., Ding, Z., Gao, Y., & Elkashlan, M (2016) Physical layer security for 5G non- orthogonal multiple access in large-scale networks In Proceedings of international conference on communications... impact of untrusted relay 13 Impact of? ?Untrusted Relay on? ?Physical Layer Security in? ?? wiretap code [26] This coding scheme consists of the codeword transmission rate, R0 and confidential information... 15 Qin, Z., Liu, Y., Ding, Z., Gao, Y., & Elkashlan, M (2016) Physical layer security for 5G non- orthogonal multiple access in large-scale networks In Proceedings of IEEE international conference