Content uploaded by Lu Lv
Author content
All content in this area was uploaded by Lu Lv on Sep 13, 2021
Content may be subject to copyright.
SCIENCE CHINA
Information Sciences
.RESEARCH PAPER .
Secure NOMA and OMA coordinated transmission
schemes in untrusted relay networks
Lu LV1, Zan LI1, Haiyang DING2& Jian CHEN1*
1State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an 710071, China;
2School of Information and Communications, National University of Defense Technology, Xi’an 710106, China
Abstract This paper investigates secure cooperative communications in untrusted relay networks, where
a source coordinately communicates with multiple near users and a far user, and the transmission between
the source and the far user is aided by an untrusted relay. We propose two novel secure non-orthogonal
multiple access (NOMA) and orthogonal multiple access (OMA) transmission schemes with user scheduling
and cooperative jamming to intentionally degrade the decoding capability of the untrusted relay, thereby
improving the physical-layer security. For each of the two proposed schemes, we analytically derive the
closed-form/semi-closed-from expressions for the ergodic secrecy rate (ESR) lower bounds and the asymptotic
ergodic secrecy rate scaling laws to characterize the achievable network security performance. Simulation
results confirm the derived analytical results, and indicate that the secure NOMA coordinated transmission
scheme achieves a high ergodic secrecy sum rate, while the secure OMA coordinated transmission scheme
guarantees a balanced tradeoff for the ESR between the near user and the far user.
Keywords physical-layer security, multiple access, cooperative jamming, user scheduling, untrusted relay
Citation Lv L, Li Z, Ding H Y, Chen J. Secure NOMA and OMA coordinated transmission schemes in untrusted
relay networks. Sci China Inf Sci, for review
1 Introduction
Faced with the explosion of Internet of Things (IoT) applications, the radio spectrum resource becomes
unprecedentedly scarce, which makes resource allocation based on the conventional orthogonal multiple
access (OMA) methods difficult to support the massive access. Against this background, non-orthogonal
multiple access (NOMA) has emerged as a promising technique to realize ubiquitous connectivity by
removing the orthogonality in resource allocation [1,2]. At the transmitter, with the use of the power-
domain superposition coding, signals of multiple users can be simultaneously transmitted in the same
time-frequency resource. While at the receiver, successive interference cancellation (SIC) is employed
to recover the signals sequentially. Thus, an enhanced spectrum usage and massive connectivity can
be achieved. Due to its outstanding benefits, NOMA has recently been integrated with more advanced
wireless concepts, such as full-duplex communication [3], cooperative relaying [4], and cognitive radio [5],
for further improving the network performance.
However, over the wireless channels, the transmitted signals are vulnerable to eavesdropping attacks.
This necessitates the efforts to guarantee privacy and secrecy for physical-layer NOMA communication.
To overcome this problem, physical-layer security, which exploits the inherent characteristics of wireless
channels (i.e., fading, interference, and noise) [6–11], is considered as an effective means of promising
* Corresponding author (email: jianchen@mail.xidian.edu.cn)
Lv L, et al. Sci China Inf Sci 2
secrecy for NOMA networks. In [12], a comprehensive secrecy outage analysis for NOMA in large-
scale networks was examined by using stochastic geometry tools. Secure beamforming optimizations for
NOMA against internal and external eavesdropping were investigated in [13, 14]. A security-enhanced
transmission scheme for hybrid automatic repeat request assisted NOMA networks was proposed in [15].
Physical-layer security for cooperative NOMA networks are investigated in the following works. To achieve
both secure and reliable NOMA transmission, joint beamforming and power allocation scheme and joint
artificial noise aided beamforming and power allocation scheme were presented in [16]. Performance
analysis of security-reliability tradeoff for user-aided cooperative cognitive radio NOMA networks was
studied in [17]. Design of multi-antenna full-duplex relay assisted secure NOMA communications was
presented in [18]. Several relay selection schemes for secure one-way relay based NOMA were developed
in [19, 20]. Secrecy two-way relay based NOMA with cooperative jamming schemes were designed and
analyzed in [21, 22].
A common assumption in [17–22] is that the cooperative relay is trusted and carried out the expected
information forwarding without any data interception. However, in some practical communication sce-
narios, such as military and heterogeneous networks, the relay may be data-level untrusted and want to
decode the confidential data from its received information, giving rise to a high risk of the confidential
information leakage [23]. Therefore, information security needs to be guaranteed in the presence of such
type of untrusted relays. Very limited research efforts, such as those in [24–27], investigated secure co-
operative NOMA against an untrusted relay. In [24], a NOMA-inspired relaying and jamming strategy
was proposed, where the downlink NOMA principle is used to transmit a jamming signal to confuse the
relay and the uplink NOMA principle is applied to exploit the multiplexing gain at the destination for
secrecy rate improvement. Collaborative destination based jamming and opportunistic destination based
jamming schemes for degrading the decoding capability of the untrusted relay were developed in [25, 26].
Adaptive jamming strategies and secrecy performance analysis for downlink and uplink NOMA coordi-
nated direct and untrusted relay transmissions were investigated in [27].
All the existing studies [24–27] concentrate on a typical two-user scenario, i.e., one near user and one
far user, whereas the multi-user cooperative NOMA with an untrusted relay has yet been investigated.
Theoretically, in a multi-user scenario, an appropriate joint design of user scheduling and cooperative
jamming through the unscheduled users can significantly improve the signal reception quality of the
legitimate users as well as degrading the decoding capability of the untrusted relay, which is beneficial
to the physical-layer security. Furthermore, although the use of NOMA increases the ergodic secrecy
sum rate, the ergodic secrecy rate (ESR) of the far user does not increase with the signal-to-noise ratio
(SNR) but converges to a constant in the high SNR regime [27]. This fails to balance the secrecy rate
performance between the near user and far user and cannot promise user fairness. Recall that the ESR of
the far user always increases with the SNR by the OMA non-coordinated transmission scheme in [23], this
scheme may not perform well in a coordinated transmission scenario. How to design OMA coordinated
transmission scheme for securing the confidential information of both near user and far user against the
untrusted relay is still not known.
Motivated by the above observations, in this paper, we investigate secrecy transmission design and
performance analysis for cooperative untrusted relay networks with multiple near users and a far user.
Overall, the main contributions of the paper can be summarized in threefold:
•We propose novel secure NOMA and OMA coordinated transmission schemes to avoid confidential
information leakage against the untrusted relay. For the secure NOMA coordinated transmission scheme,
in the first time slot, a best near user is scheduled to receive its desired signal from the source and the
remaining near users serve as jammers to confuse the untrusted relay. In the second time slot, coordinated
with the relay’s signal forwarding to the far user, the source securely communicates with a best near user
scheduled from the jammers to compensate the jamming service, since the relay cannot listen to the source
transmission with the half-duplex constraint. For the secure OMA coordinated transmission scheme, in
the first time slot, the source transmits the signal of the far user and all the near users collaboratively
send a jamming signal both to the untrusted relay. In the second time slot, the relay forwards its received
signal to the far user, and the source coordinately transmits to a scheduled best near user.
Lv L, et al. Sci China Inf Sci 3
N1
S
R
Nk
NK-1NK-1
F
N2
N1
S
R
Nk
NK-1NK-1
F
Maximal-ra tio
transmission
(a) (b)
Figure 1 Scheme description: (a) Secure NOMA coordinated transmission scheme. (b) Secure OMA coordinated trans-
mission scheme. The solid and dashed lines denote the transmissions in the first and second time slots, respectively.
•For performance evaluation, we derive closed-form/semi-closed-form expressions for the ESR lower
bounds achieved by the proposed secure NOMA and OMA coordinated transmission schemes. To gain
more insights for the network design, we also investigate the asymptotic ESR scaling laws over the average
SNR and the number of near users. Furthermore, a simple yet important power allocation strategy for
secure NOMA coordinated transmission scheme is proposed to achieve the maximum ESR scaling law
over the average SNR.
•Through analytical and numerical results, we reveal several important findings: 1) The secure NOMA
coordinated transmission achieves a higher ergodic secrecy sum rate than the secure OMA coordinated
transmission scheme; 2) The secure OMA coordinated transmission scheme balances the ESR between
the near user and far user (i.e., yielding the same ESR scaling law over the average SNR), while the ESR
scaling law of the far user in the secure NOMA coordinated transmission scheme finally converges to a
constant; 3) Simply increasing the average SNR and/or the number of near users can always benefit the
secrecy rate performance of both schemes.
The rest of the paper is organized as follows. In Section 2, we introduce the system model and propose
the secure NOMA and OMA coordinated transmission schemes. In Section 3, we characterize the network
secrecy performance by deriving the ESR lower bounds and its asymptotic scaling laws over average SNR
and the number of near users. Simulation results and discussions are included in Section 4. Finally, we
briefly summarize the paper in Section 5.
2 System model and scheme description
Consider a cooperative network consisting of a source S, an AF relay R, a far user F, and a cluster of K
near users {N1, . . . , NK}. Each node has a single antenna and works in a half-duplex mode. The direct
S−Fchannel does not exist due to severe path-loss attenuation of the channel. Thus, Scommunicates
with Fvia R, while directly communicating with {N1, . . . , NK}. We assume that Ris untrusted, i.e., it
obeys the amplify-and-forward protocol to retransmit the signal(s) of S, while at the same time serving as
an eavesdropper to decode and intercept the confidential information. All wireless channels are assumed
to be reciprocal and quasi-static with independent Rayleigh fading. The channel between node iand
node jis denoted by hij ∼ CN (0, λij) for i, j ∈ {s, r, f, 1, . . . , K}and i̸=j. Since all the near users form
a cluster and are located close to S, it is reasonable to assume λsk =λsn ,λrk =λrn ,k∈ {1, . . . , K},
and λsn > λsr. Furthermore, the additive white Gaussian noise (AWGN) received at node iis denoted
by ηi∼ CN(0, λ0) for i∈ {s, r, f, 1, . . . , K}.
2.1 Secure NOMA coordinated transmission scheme
The secure NOMA coordinated transmission scheme with cooperative jamming and user scheduling con-
sists of two time slots, shown in Figure 1(a) and operated as follows. In the first time slot, assuming
Lv L, et al. Sci China Inf Sci 4
that Nkis scheduled as the receiving near user, Suses the NOMA principle to transmit a superimposed
signal of xkand xfto Nkand R, where xk∈ CN (0,1) and xf∈ CN(0,1) are the signals intended for Nk
and F. Concurrently, the remaining K−1 near users (called jammers) cooperatively transmit a jamming
signal z∈ CN (0,1) to confuse R. The received signals at Nkand Rare written as
yk=αkP hskxk+αfP hsk xf+√Phkf1z+ηk,(1)
yr=αkP hsrxk+αfP hsr xf+√Phrf1z+ηr,(2)
where Pis the transmit power, αkand αfare the power allocation coefficients satisfying αk+αf= 1
and αf> αk,hkdenotes the channels between the jammers and Nk,hrdenotes the channels between
the jammers and R, and f1denotes the beamforming vector. To ensure that zwill not affect the signal
reception of Nk, the beamforming vector should be designed based on zero-forcing, which satisfies hkf1= 0
and fH
1f1= 1. In this time slot, Fcan receive and cache zfor the subsequent jamming cancellation.
Based on (1), Nkfirst decodes xfby treating xkas noise and then removes xfusing SIC to decode
xk, yielding signal-to-interference-plus-noise ratio (SINR) and signal-to-noise ratio (SNR) as γk:xf=
αf|hsk|2
αk|hsk|2+1/ρ and γk:xk=αkρ|hsk |2, where ρ=P /λ0is the average SNR. Similarly, Ralso uses SIC to
decode the signals with SINRs as γr:xf=αf|hsr |2
αk|hsr|2+|hrf1|2+1/ρ and γr:xk=αk|hsr |2
|hrf1|2+1/ρ .
In the second time slot, Ramplifies and forwards its received signals to F. To compensate the jamming
service offered by the jammers, one jammer, say ¯
Nk, is scheduled to receive its own signal ¯xk∈ CN (0,1)
in this time slot. Thus, coordinated with R’s transmission, Stransmits a superimposed signal of ¯xkand
xkto ¯
Nk, where xkis used to facilitate ¯
Nk’s interference cancellation. The received signals at Fand ¯
Nk
are expressed as
yf=φ1hrf yr+ηf,(3)
y¯
k=φ1hr¯
kyr+hs¯
kP−Pk¯xk+wkxk+η¯
k,(4)
where φ1=1/(λsr +λrn + 1/ρ) is the relay amplifying gain, Pkis the transmit power of xk, and wk
is the weight coefficient of xksatisfying E[|wk|2] = Pk. Due to R’s half-duplex feature, it cannot listen
to S’s signal transmission in this time slot, and thus, the transmission of ¯xkis definitely secured.
Based on (3), Ffirst subtracts zfrom its observations because zis a copy which is already cached by
Fin the previous time slot. Then, Fdecodes xfwith SINR as γf:xf=αfρ|hsr |2|hrf |2
αkρ|hsr|2|hr f |2+|hrf |2+1/φ2
1. On
the other hand, using (4), ¯
Nkfirst cancels zsince zis a copy which is previously transmitted by ¯
Nk, and
then tries to cancel xk. To achieve this, we have the following equality √αkP φ1hsr hr¯
kxk+wkhs¯
kxk= 0,
from which the solution is derived as wk=−√αkP φ1hsrhr¯
k/hs¯
k. Using E[|wk|2] = Pk, we obtain that
Pk=αkλsrλr n
λsn(λsr +λrn +1/ρ)P. Since λsrλr n
λsn(λsr +λrn +1/ρ)<λsr λrn
λsn(λsr +λrn )≈min(λsr ,λrn )
λsn <λsr
λsn <1, Pk< P
always satisfies. This indicates that xkcan be perfectly cancelled by ¯
Nk. After that, ¯
Nkdecodes ¯xkusing
SINR as γ¯
k:¯xk=ϖ1ρ|hs¯
k|2
φ2
1αfρ|hsr|2|hr¯
k|2+φ2
1|hr¯
k|2+1 , where ϖ1= 1 −αkλsr λrn
λsn(λsr +λrn +1/ρ).
Given the above SINRs, the secrecy rates for xk,xf, and ¯xkare defined, respectively, as
Cnoma
xk=1
2log 1 + γk:xk−log 1 + γr:xk+,(5)
Cnoma
xf=1
2log 1 + min(γk:xf, γf:xf)−log 1 + γr:xf+,(6)
Cnoma
¯xk=1
2log 1 + γ¯
k:¯xk−0+,(7)
where [x]+= max(x, 0) and the first term in (6) follows the fact that xfneeds to be decoded by Nkin
SIC. Based on (5)–(7), we propose a simple user selection criterion as follows:
k∗= arg max
k∈{1,...,K}γk:xk,¯
k∗= arg max
¯
k∈{1,...,K}\k∗
γ¯
k:¯xk.(8)
Lemma 1. The user scheduling criterion of (8) is optimal in the secrecy rates for xk,xf, and ¯xk.
Lv L, et al. Sci China Inf Sci 5
Proof. From (5) and (7), it can be known that R’s eavesdropping rates for xkand ¯xkdo not depend on
k∗and ¯
k∗. Thus, the maximization of the secrecy rates for xkand ¯xkis equivalent to the transmission
rates for xkand ¯xk, which is exactly the user scheduling scheme of (8).
On the other hand, according to (6), it is necessary to maximize the transmission rate for xftowards
the secrecy rate maximization, which is discussed in two cases: 1) When γk:xf6γf:xf, the transmission
rate for xfis dominated by γk:xf. In this case, since γk:xfmonotonically increases with |hsk |2, it can
be concluded that the maximization of γk:xfis equivalent to the maximization of γk:xk. This indicates
that k∗is also optimal in the secrecy rate for xf. 2) When γk:xf> γf:xf, the transmission rate for xfis
dominated by γf:xf, which is not related to k∗. Combining the results, Lemma 1 is proved.
2.2 Secure OMA coordinated transmission scheme
The secure OMA coordinated transmission scheme with cooperative jamming and user scheduling is
carried out in two time slots, shown in Figure 1(b) as follows. In the first time slot, Stransmits xfto
R, and simultaneously, all {N1, . . . , NK}transmit zin a collaborative manner to intentionally confuse
R. The received signals at Rare given by
yr=√P hsrxf+√Phr nf2z+ηr,(9)
where hrn denotes the channels between {N1, . . . , NK}and R, and f2denotes the beamforming vector
in OMA. To maximally degrade R’s eavesdropping capability, the beamforming vector can be selected
based on distributed beamforming with maximal-ratio transmission as f2=h†
r1/|hr1|, . . . , h†
rK /|hrK |T.
In this time slot, Falso receives zand caches it for the subsequent jamming cancellation.
Using (9), Rtries to decode xfwith SINR as ˆγr:xf=|hsr |2
µr+1/ρ , where µr=
K
k=1 |hrk |
2.
In the second time slot, Rforwards its received signals to Fand Scoordinately transmits a superim-
posed signal of xkand xfto the scheduled Nk, where xfis aimed at Nk’s interference cancellation. The
received signals at Fand Nkare expressed as
yf=φ2hrf yr+ηf,(10)
yk=φ2hrk yr+hskP−Pfxk+wfxf+ηk,(11)
where φ2=1/(λsr + ¯µr+ 1/ρ) denotes the relay amplifying gain in OMA with ¯µr=E[µr], Pfis the
transmit power of xf, and wfis the weight coefficient of xfwith E[|wf|2] = Pf. While Rcannot overhear
the transmitted signals from Sin this time slot due to the half-duplex constraint.
Using (10), Ffirst removes zsince Falready caches a copy of zand then decodes xfwith SNR as
ˆγf:xf=ρ|hsr |2|hrf |2
|hrf |2+1/φ2
2. Using (11), Nkfirst cancels zsince zis a copy which is previously transmitted by Nk
and then removes xf. For this, equality √P φ2hsr hrk xf+wfhskxf= 0 should hold, such that we have
wf=−√P φ2hsrhr k/hsk and Pf=λsr λr n
λsn(λsr + ¯µr+1/ρ)P. Based on the fact that λrn <¯µrand λsr < λsn ,
inequality Pf< P holds, which implies that Nk’s interference cancellation is always successful. Then,
Nkdecodes xkwith SNR as ˆγk:xk=ϖ2ρ|hsk|2
φ2
2|hrk|2+1 , where ϖ2= 1 −λsr λrn
λsn(λsr + ¯µr+1/ρ).
Accordingly, the secrecy rates for xkand xfare given, respectively, by
Coma
xk=1
2log 1 + ˆγk:xk−0+,(12)
Coma
xf=1
2log 1 + ˆγf:xf−log 1 + ˆγr:xf+.(13)
Utilizing (12), the near user who has the largest SNR is scheduled as follows:
k∗= arg max
k∈{1,...,K}ˆγk:xk.(14)
Clearly, this simple user scheduling criterion maximizes the secrecy rate for xk.
Lv L, et al. Sci China Inf Sci 6
3 Secrecy performance analysis
In this section, we analyze the ESR lower bound and its scaling law achieved by the proposed secure
NOMA and OMA coordinated transmission schemes.
3.1 ESR for secure NOMA coordinated transmission scheme
Using Jensen’s inequality, the ESRs of Nk,F, and ¯
Nkcan be lower bounded, respectively, by
¯
Cnoma
xk,lb =1
2A1−A2+,(15)
¯
Cnoma
xf,lb =1
2A3−A4+,(16)
¯
Cnoma
¯xk,lb =1
2A5,(17)
where A1=E[log(1 + γk∗:xk)], A2=E[log(1 + γr:xk)], A3=E[log(1 + min(γk∗:xf, γf:xf))], A4=E[log(1 +
γr:xf)], and A5=E[log(1 + γ¯
k∗:¯xk)].
Based on the user scheduling criterion of (8), we can derive A1as
A1=∞
0K
i=1 K
i(−1)i+1e−ix
αkρλsn
1 + xdx
=
K
i=1 K
i(−1)iei
αkρλsn Ei−i
αkρλsn ,(18)
where we use [28, eq. (3.352.4)]. Also, since |hrf1|2is exponentially distributed with λrn , the cumulative
distribution function (CDF) of γr:xkis Fγr:xk(x) = 1 −δ
x+δe−x
αkλsr , where δ=αkλsr/λr n. By using this
result, A2can be computed by
A2=∞
0δ/(1 −δ)
x+δ−δ/(1 −δ)
x+ 1 e−x
αkλsr dx
=δ[e1
λrn Ei(−1/λrn )−e1
αkλsr Ei(−1/(αkλsr))]
δ−1.(19)
Substituting (18) and (19) into (15), a closed-form ¯
Cnoma
xk,lb is derived.
Denote X= min(γk∗:xf, γf:xf), its CDF is obtained by FX(x)=1−e−(Kλsr +λsn )x
ρλsrλsn (αf−αkx)ξ(x)K1(ξ(x)),
where ξ(x) = 2
φ1x
ρλsrλr f (αf−αkx). Thus, A3can be calculated as
A3=
αf
αk
0
e−(Kλsr +λsn )x
ρλsrλsn (αf−αkx)
1 + xξ(x)K1(ξ(x))dx
≈π
M
M
m=1
αf(1 −x2
m)1
2
2αk+αf(xm+ 1)e−(Kλsr +λsn )(xm+1)
ρλsrλsn αk(1−xm)ξαf(xm+ 1)
2αkK1ξαf(xm+ 1)
2αk,(20)
where we use the Gauss-Chebyshev quadrature approximation and K1(·) is the modified first-order Bessel
function of the second kind. Similar to the derivation of A2, we can approximate A4as
A4≈π
M
M
m=1
αk(1 −xm)3
2e−xm+1
ραk(1−xm)
(2αk/αf+ 1 + xm)(λrn +αk+ (λrn −αk)xm).(21)
Substituting (20) and (21) into (16), a closed-form ¯
Cnoma
xf,lb is obtained.
Since the user scheduling processes in the first and second time slots are disjoint, the CDF of γ¯
k:¯xkis
attained as Fγ¯
k:¯xk(x) = 1 + ε(x)e−x
ρλsnϖ1+ε(x)+ 1
λsrαfEi(−ε(x)−1
λsrαf)K−1, where ε(x) = ρλsnϖ1
λsrλr nφ2
1αfx.
Lv L, et al. Sci China Inf Sci 7
Thus, a semi-closed-form of A5is derived as follows: A5=∞
0(1 −Fγ¯
k:¯xk(x))/(1 + x)dx, which can be
easily evaluated using standard software such as Matlab or Mathematica.
To investigate how the network parameters ρand Kaffect the secrecy performance of the proposed
secure NOMA scheme and provide more intuitive insights, we analyze the scaling laws of the ESR in the
following theorem.
Theorem 1. With a finite Kvalue and ρ→ ∞, we obtain that: 1) The ESR of Nkscales as 1
2log ρ;
2) The ESR of ¯
Nkscales as 1
2log ρ, which is achieved by the power allocation of αf=c
ρgiven a positive
constant c, otherwise, the ESR of ¯
Nkconverges to a constant independent of ρ; 3) The ESR of Fconverges
to a constant independent of ρ.
Proof. Using the fact that max(x1, x2, . . . , xK)>xk,γk∗:xkcan be lower bounded as: γk∗:xk>αkρ|hsk |2.
While γr:xkconverges to a constant if ρis sufficiently large. Thus, we can asymptotically express ¯
Cnoma
xk,lb
as ¯
Cnoma
xk,lb ∼log(αkρ)∼log ρ. Similarly, we can prove the ESR scaling laws of ¯
Nkand F.
Theorem 2. When ρis limited and K→ ∞, we achieve that: 1) The ESR of Nkscales as 1
2log log K;
2) The ESR of ¯
Nkscales as 1
2log log(K−1); 3) The ESR of Ffinally converges to a constant.
Proof. According to the extreme-value theory [29], we have maxk∈{1,...,K}γk:xk∼log K+O(log log K)
and max¯
k∈{1,...,K}\k∗γ¯
k:¯xk∼log(K−1) + O(log log(K−1)), while γr:xkis independent of K. Thus,
we obtain that ¯
Cnoma
xk,lb ∼1
2log log Kand ¯
Cnoma
¯xk,lb ∼1
2log log(K−1). Furthermore, using the fact that
min(γk∗:xf, γf:xf)6γf:xfwhich is independent of K, and γr:xfis also independent of K, we know that
¯
Cnoma
xf,lb converges to a constant. Hence, we complete the proof.
Theorems 1 and 2 indicate that for the proposed secure NOMA coordinated transmission scheme,
increasing the transmit power and/or the number of near users are beneficial in enhancing the ESRs of
Nkand ¯
Nk, but not helpful in enhancing the ESR of F.
3.2 ESR for secure OMA coordinated transmission scheme
The ESRs of Nkand Fcan be lower bounded, respectively, by
¯
Coma
xk,lb =1
2B1,(22)
¯
Coma
xf,lb =1
2B2−B3+,(23)
where B1=E[log(1 + ˆγk∗:xk)], B2=E[log(1 + ˆγf:xf)], and B3=E[log(1 + ˆγr:xf)].
According to the user scheduling criterion of (14), we can calculate the CDF of ˆγk∗:xkas Fˆγk∗:xk(x) =
K
i=1 K
i(−1)i+1(ϵ
x+ϵ)ie−ix
ϖ2ρλsn , where ϵ=ϖ2ρλsn
φ2
2λrn . Based on this result, a semi-closed-form expression
of B1can be obtained as
B1=
K
i=1 K
i(−1)i+1 ∞
0
log(1 + x)ϵ
x+ϵie−ix
ϖ2ρλsn dx. (24)
The CDF of ˆγf:xfis given by Fˆγf:xf(x)=1−ν(x)K1(ν(x))e−x
ρλsr , where ν(x) = 2
φ2x
ρλsrλr f . Then,
we can derive B2in semi-closed-form as
B2=∞
0
ν(x)K1(ν(x))
1 + xe−x
ρλsr dx. (25)
On the other hand, B3can be upper bounded by
B3=∞
0
1−Fˆγr:xf(x)
1 + xdx
=∞
0
e−x
ρλsr ∞
0e−xy
λsr dFµr(y)
1 + xdx
6∞
0
e−x
ρλsr ∞
0e−xy
λsr dFµr,ub(y)
1 + xdx, (26)
Lv L, et al. Sci China Inf Sci 8
0 5 10 15 20 25 30
0
0.5
1
1.5
2
2.5
3
3.5
Figure 2 ESR vs. average SNR of the secure NOMA coordinated transmission scheme.
where the inequality in (26) is obtained by using the well-known arithmetic-geometric mean inequality and
Fµr,ub(y) is given by [30, eq. (20)]. Overall, combining the expressions of B2and B3, a semi-closed-form
lower bound for ¯
Coma
xf,lb is obtained.
Although the derived semi-closed-form ESR expressions can be evaluated using standard mathematical
software without doing extensive computer simulations, they fail to provide more intuitive insights. This
motivates us to investigate the scaling laws of the ESR in the following.
Theorem 3. With a finite Kvalue and ρ→ ∞, the ESRs of Nkand Fboth scale as 1
2log ρ.
Proof. Similar to the proof of Theorem 1.
This theorem indicates that compared to the secure NOMA coordinated transmission scheme, the
proposed secure OMA coordinated transmission scheme can balance the secrecy performance between
the scheduled near user and the far user, since both ESRs of Nkand Fincrease by increasing the
transmit power.
Theorem 4. When ρis limited and K→ ∞, we obtain that: 1) The ESR of Nkscales as 1
2log log K;
2) The ESR of Fconverges to a constant independent of K.
Proof. Similar to the proof of Theorem 2.
4 Numerical results
This section includes numerical results to characterize the secrecy performance achieved by the proposed
secure NOMA and OMA coordinated transmission schemes. Without loss of generality, we assume that
the average channel gains are set as λsr = 0.8, λsn = 1, λrf = 0.7, and λrn = 1, respectively.
Figure 2 shows the ESR achieved by the proposed secure NOMA coordinated transmission scheme
with K= 2 and αf= min(0.1,1/ρ). It is clear from Figure 2 that the derived ESR lower bounds exactly
match the simulation results for Nk,F, and ¯
Nk, which confirms our theoretical analysis in Section 3.3.1.
As can be observed from Figure 2, the ESR lower bounds of Nkand ¯
Nkimprove with the increased ρand
increase to 1
2log ρin the high ρregime. However, when αfis fixed to 0.8, the ESR lower bound of ¯
Nk
saturates in the high ρregime. The above observations are consistent to the conclusions in Theorem 1.
Furthermore, it is also observed from Figure 2 that the ESR of Fconverges to a constant in the high ρ
regime. This is because Fdecode its xfby treating xkas interference, and the received power of xfand
xkboth increase with ρ, such that the ESR of Fgoes to a constant when ρis sufficiently large.
Figure 3 plots the ESR achieved by the proposed secure OMA coordinated transmission scheme with
K= 2. It can be seen that the derived ESR lower bounds in Section 3.3.2 agree well with the simulated
ones throughout the whole ρregime. Compared with the secure NOMA coordinated transmission scheme
Lv L, et al. Sci China Inf Sci 9
0 5 10 15 20 25 30
0
0.5
1
1.5
2
2.5
3
3.5
Figure 3 ESR vs. average SNR of the secure OMA coordinated transmission scheme.
0 5 10 15 20 25 30
0
1
2
3
4
5
6
Figure 4 Comparison of the secure NOMA and OMA coordinated transmission schemes as a function of ρ.
given in Figure 2, it can be seen from Figure 3 that both the ESR lower bounds of Nkand Fachieved by
the secure OMA transmission scheme increase by increasing ρand scale as 1
2log ρin the high ρregime,
which validates the result in Theorem 3. Therefore, the secure OMA coordinated transmission scheme
achieves a balanced tradeoff for the secrecy rate performance between the near user and the far user.
Figure 4 and Figure 5 compare the ergodic secrecy sum rate achieved by the secure NOMA and
OMA coordinated transmission schemes, where the ergodic secrecy sum rates are defined as ¯
Cnoma
sum ,
¯
Cnoma
xk,lb +¯
Cnoma
xf,lb +¯
Cnoma
¯xk,lb for NOMA and ¯
Coma
sum ,¯
Coma
xk,lb +¯
Coma
xf,lb for OMA, respectively. We assume K= 2
in Figure 4 and ρ= 15 dB in Figure 5. As can be observed from Figure 4, the secure NOMA and OMA
coordinated transmission schemes exhibit a very similar increasing trend in the high ρregime, and the
secure NOMA coordinated transmission scheme achieves a higher ergodic secrecy sum rate than that of
the secure OMA coordinated transmission scheme. It can be also observed from Figure 4 that the ergodic
secrecy sum rate of the secure NOMA coordinated transmission scheme with fixed power becomes inferior
to that of the secure OMA coordinated transmission scheme in the medium to high ρregime, due to its
reduced ESR scaling law of ¯
Nk, as indicated by Theorem 1. Similarly, as can be observed from Figure 5,
the secure NOMA coordinated transmission scheme achieves the highest ergodic secrecy sum rate versus
K. Furthermore, the ergodic secrecy sum rates of all the schemes increase with the same slope in the
large Kregion, which confirms Theorems 2 and 4.
Lv L, et al. Sci China Inf Sci 10
2345678910
1.8
2
2.2
2.4
2.6
2.8
3
Figure 5 Comparison of the secure NOMA and OMA coordinated transmission schemes as a function of K.
5 Conclusion
In this paper, secure cooperative communications in an untrusted relay network was investigated, where
two new secure NOMA and OMA coordinated transmission schemes with user scheduling and cooperative
jamming for preventing information leakage against the untrusted relay were proposed. To characterize
the network security performance of the proposed schemes, we analytically derived the closed-form/semi-
closed-form expressions for the ESR lower bounds. The asymptotic behaviors in terms of the ESR scaling
laws over the average SNR and the number of near users were further studied to gain more insights. Both
analytical and numerical results show that the secure NOMA coordinated transmission schemes achieve
a high ergodic secrecy sum rate, while the secure OMA coordinated transmission scheme balances the
ESRs between the near user and far user.
Acknowledgements This work was supported by National Natural Science Foundation of China (Grant Nos. 61901313,
61941105, and 61771366), National Natural Science Foundation of China for Outstanding Young Scholars (Grant No.
61825104), Natural Science Fundamental Research Plan of Shaanxi Province (Grant No. 2020JQ-306), and China Postdoc-
toral Science Foundation (Grant Nos. BX20190264 and 2019M650258).
References
1 Dai L L, Wang B C, Yuan Y F, et al. Non-orthogonal multiple access for 5G: solutions, challenges, opportunities, and
future research trends. IEEE Commun Mag, 2015, 53: 74–81
2 Ma Z, Zhang Z Q, Ding Z G, et al. Key technologies for 5G wireless communications: network architecture, physical
layer, and MAC layer perspective. Sci China Inf Sci, 2015, 58: 041301
3 Zhong C, Zhang Z Y. Non-orthogonal multiple access with cooperative full-duplex relaying. IEEE Commun Lett, 2016,
20: 2478–2481
4 Yue X W, Liu Y W, Kang S L, et al. Modeling and analysis of two-way relay non-orthogonal multiple access. IEEE
Trans Commun, 2018, 66: 3784–3796
5 Lv L, Chen J, Ni Q, et al. Design of cooperative non-orthogonal multicast cognitive multiple access for 5G systems:
user scheduling and performance analysis. IEEE Trans Commun, 2017, 65: 2641–2656
6 Qi Q, Chen X M, Zhong C J, et al. Physical layer security for massive access in cellular Internet of Things. Sci China
Inf Sci, 2020, 63: 121301
7 Qi X H, Huang K Z, Li B, et al. Physical layer security in multi-antenna cognitive heterogeneous cellular networks: a
unified secrecy performance analysis. Sci China Inf Sci, 2018, 61: 022310
8 Wu Y P, Khisti A, Xiao C S, et al. A survey of physical layer security techniques for 5G wireless networks and
challenges ahead. IEEE J Sel Areas Commun, 2018, 36: 679–695
9 Zheng T X, Wang H M, Yuan J H. Physical-layer security in cache-enabled cooperative small cell networks against
randomly distributed eavesdroppers. IEEE Trans Wirel Commun, 2018, 17: 5945–5958
10 Pan G F, Lei H J, Deng Y S, et al. On secrecy performance of MISO SWIPT systems with TAS and imperfect CSI.
IEEE Trans Commun, 2016, 64: 3831–3843
11 Deng H, Wang H M, Guo W, et al. Secrecy transmission with a helper: to relay or to jam. IEEE Trans Inform Forensic
Lv L, et al. Sci China Inf Sci 11
Secur, 2015, 10: 293–307
12 Liu Y W, Qin Z J, Elkashlan M, et al. Enhancing the physical layer security of non-orthogonal multiple access in
large-scale networks. IEEE Trans Wirel Commun, 2017, 16: 1656–1672
13 Li Y Q, Jiang M, Zhang Q, et al. Secure beamforming in downlink MISO nonorthogonal multiple access systems.
IEEE Trans Veh Technol, 2017, 66: 7563–7567
14 Feng Y H, Yan S H, Yang Z, et al. Beamforming design and power allocation for secure transmission with NOMA.
IEEE Trans Wirel Commun, 2019, 18: 2639–2651
15 Xiang Z W, Yang W W, Pan G F, et al. Secure transmission in HARQ-assisted non-orthogonal multiple access
networks. IEEE Trans Inform Forensic Secur, 2020, 15: 2171–2182
16 Cao K R, Wang B H, Ding H Y, et al. Secure transmission designs for NOMA systems against internal and external
eavesdropping. IEEE Trans Inform Forensic Secur, 2020, 15: 2930–2943
17 Li B, Qi X H, Fei Z S, et al. Security-reliability tradeoff analysis for cooperative NOMA in cognitive radio networks.
IEEE Trans Commun, 2019, 67: 83–96
18 Cao Y, Zhao N, Pan G F, et al. Secrecy analysis for cooperative NOMA networks with multi-antenna full-duplex relay.
IEEE Trans Commun, 2019, 67: 5574–5587
19 Lei H J, Yang Z X, Park K H, et al. Secrecy outage analysis for cooperative NOMA systems with relay selection
schemes. IEEE Trans Commun, 2019, 67: 6282–6298
20 Feng Y H, Yan S H, Liu C X, et al. Two-stage relay selection for enhancing physical layer security in non-orthogonal
multiple access. IEEE Trans Inform Forensic Secur, 2019, 14: 1670–1683
21 Zheng B X, Wen M W, Wang C X, et al. Secure NOMA based two-way relay networks using artificial noise and full
duplex. IEEE J Sel Areas Commun, 2018, 36: 1426–1440
22 Zhang H J, Yang N, Long K P, et al. Secure communications in NOMA systems: subcarrier assignment and power
allocation. IEEE J Sel Areas Commun, 2018, 36: 1441–1452
23 Sun L, Ren P Y, Du Q H, et al. Security-aware relaying scheme for cooperative networks with untrusted relay nodes.
IEEE Commun Lett, 2015, 19: 463–466
24 Lv L, Zhou F H, Chen J, et al. Secure cooperative communications with an untrusted relay: a NOMA-inspired jamming
and relaying approach. IEEE Trans Inform Forensic Secur, 2019, 14: 3191–3205
25 Arafa A, Shin W, Vaezi M, et al. Secure relaying in non-orthogonal multiple access: trusted and untrusted scenarios.
IEEE Trans Inform Forensic Secur, 2020, 15: 210–222
26 Xiang Z W, Yang W W, Pan G F, et al. Secure transmission in non-orthogonal multiple access networks with an
untrusted relay. IEEE Wirel Commun Lett, 2019, 8: 905–908
27 Lv L, Jiang H, Ding Z G, et al. Secrecy-enhancing design for cooperative downlink and uplink NOMA with an untrusted
relay. IEEE Trans Commun, 2020, 68: 1698–1715
28 Gradshteyn I S, Ryzhik I M. Table of Integrals, Series, Products. San Diego, CA, USA: Academic, 2007
29 Leadbetter M R, Lindgren G, Rootzen H. Extremes and Related Properties of Random Sequences and Processes. New
York: Springer-Verlag, 1983
30 Karagiannidis G K, Tsiftsis T A, Sagias N C. A closed-form upper-bound for the distribution of the weighted sum of
Rayleigh variates. IEEE Commun Lett, 2005, 9: 589–591
