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Outage Trade-offs between Full/Half-duplex Relaying for NOMA
Aided Multicarrier Cooperative D2D Communications System
Rahul Bajpai, Naveen Gupta
Department of Electrical and Electronics Engineering, BITS-Pilani K.K. Birla Goa Campus, Goa, India
(e-mail: p20190003@goa.bits-pilani.ac.in, naveeng@goa.bits-pilani.ac.in)
Non-orthogonal multiple access (NOMA) and full-duplex (FD) have recently emerged as a potential candidate for the fifth-generation
and beyond (B5G) cellular networks with the target of increasing spectral efficiency and guaranteeing the quality-of-services (QoS). This
paper proposes an orthogonal frequency division multiple access (OFDMA) based FD cooperative device-to-device (C-D2D) communications
system, wherein a D2D transmitter (DT) acts as an FD relay to support simultaneous bidirectional communication between a base station
(BS) and a cellular user (CU). In addition, a power splitting protocol using NOMA is incorporated for the FD C-D2D system to share the
resources between the cellular and D2D user. Further, the successive interference cancellation (SIC) is used to decode the signals, while
self-interference suppression (SIS) is employed at DT to mitigate self-interference (SI). The analytical expressions for achievable rates of
the cellular and D2D links and their outage probabilities for the FD and half-duplex (HD) systems are derived. Outage trade-offs between
FD/HD relaying have been analyzed. Results show that the proposed model enhances the overall outage performance of the cellular and
D2D users. Moreover, for high cellular outage constraints, DT as an FD relay outperforms the conventional HD C-D2D communications
system wherein DT acts as an HD relay.
Index Terms—Device-to-device communications, Full-duplex, Outage probability, Quality-of-service, Signal-to-interference-plus-noise
ratio.
I. INTRODUCTION
The unprecedented growth of cellular data traffic due to the
evolution of new services such as cloud-based gaming and
high-definition video on demand has increased the number
of interconnected mobile devices, and the amount of mobile
traffic exponentially [1]. Quantitative studies foresee that this
exponential growth would continue in the future as well.
Beyond fifth-generation (B5G) cellular networks are antici-
pated to effectuate stringent requirements instigated by this
rapid proliferation of mobile traffic. Moreover, B5G cellular
networks are expected to meet ultra-reliable, and low latency
connectivity with massive data rates for the connecting users
[2]. Embracing several rising communication technologies de-
fined in B5G cellular networks such as full-duplex (FD) radios,
device-to-device (D2D) communications, cooperative relaying,
and non-orthogonal multiple access (NOMA) facilitate the
B5G cellular networks to fulfill the rapidly growing capacity
requirements of the existing cellular networks [3].
D2D communications allow direct interaction between two
devices in proximity with minimal involvement of the base
station (BS) [4]. The BS is only involved in carrying signaling
and controlling information [5], [6]. D2D communications
have been incorporated in the long-term evolution-advanced
(LTE-A) Release 12-15 to improve the spectral efficiency by
utilizing the proximity information of the communication de-
vices [7]. In B5G cellular networks, D2D users exist together
with cellular users adopting one of the two possible modes
out-band or in-band [8]. Here, out-band D2D mode refers
to an environment where D2D users transmit and receive
over an unlicensed band like Bluetooth or Wi-Fi. In contrast,
in-band D2D mode refers to an environment where D2D
users utilize licensed cellular spectrum provided the quality-
of-services (QoS) of a cellular user (CU) is satisfied. Further,
an in-band mode is sub-divided into three popular frameworks:
underlay, overlay, and cooperative-D2D (C-D2D). A dedicated
spectrum is assigned for D2D communication in the overlay
framework, which is orthogonal to the spectrum assigned for
cellular communication, thus no interference. In contrast, de-
vices utilize the same radio resources for the cellular and D2D
transmissions in the underlay framework, causing interference
to each other. In the C-D2D framework, single or multiple
D2D users operate as an FD or half-duplex (HD) relay for
either cellular downlink or uplink transmission to fulfill a CU’s
QoS requirement. Specifically, a D2D transmitter (DT) work-
ing as a relay forwards the cellular data and simultaneously
uses a fraction of a licensed cellular band for direct interaction
with a D2D receiver (DR) [9]. Authors in [9] have shown that
the C-D2D framework outperforms the overlay and underlay
frameworks in terms of cellular and D2D user’s QoS.
D2D user working as a relay in the C-D2D framework for
cellular uplink/downlink transmission operates either in HD
or FD mode depending upon the possibility of concurrent
transmission and reception (CTAR) in the same frequency
spectrum. Recently, FD is evolved as an indispensable tech-
nology for theoretically doubling the spectral efficiency of
wireless networks [10]. However, due to the deteriorating
effects of self-interference (SI), FD has not seen widespread
use until now. SI refers to the interference derived due to the
CTAR at the node operating in FD mode [11]. In [12], it
has shown that adopting a self-interference suppression (SIS)
technique can reduce the impact of SI up to the level of the
noise floor, which makes the FD operation feasible in wireless
systems. However, owing to some practical obligations, SIS
techniques are unable to cancel SI completely, and hence the
residual self-interference (RSI) becomes a restraining factor
for the simultaneous transmission, and reception [12]. In [13],
authors proposed that RSI can be sufficiently attenuated using
a two-stage SI cancellation mechanism. The first stage is
radio-frequency SI-cancellation which suppresses the SI to an
2
adequately low level and, the second stage is baseband SI
cancellation which subsequently reduces the SI. Due to the
development in SIC schemes, the integration of FD mode in
the C-D2D communications system is feasible, which leads to
improving the data rate and QoS, as shown in [14].
An orthogonal frequency division multiplexing (OFDM)
based C-D2D communications system supported by multiple
FD relay nodes is proposed in [15] wherein the exact out-
age probabilities expressions considering per-subcarrier and
bulk relay selection have been derived. In [16], FD relay-
assisted D2D communications system is proposed, wherein
interference due to cellular uplink transmission is considered
at the relay and the D2D receiver. Additionally, a sub-optimal
power allocation method between the relay and the source has
also been implemented. Outage probability (OP) expression
with a single integral function has been derived for the
proposed model, which is further approximated as a closed-
form expression when RSI is small. However, in [15], [16],
the proposed model incurs overhead by deploying extra relay
nodes. An OFDMA aided C-D2D communications system has
been proposed in [17], and the cellular, as well as D2D OP
expressions, are derived. However, the proposed system is
confined to HD mode only, and the prospective benefits of the
proposed scheme with the FD relaying have not been explored.
NOMA [18], [19] has evolved recently to address the
high spectral efficiency and capacity demands of the next-
generation cellular networks. In NOMA, exploiting non-
orthogonal resources with tolerable interference, cellular users
can obtain high spectral efficiencies. Specifically, NOMA uti-
lizes power domain multiplexing to superimpose various user
data with different power levels over the same time-frequency
resource block1. The users present in NOMA systems are
sorted according to their respective channel gains. NOMA
guarantees that users are allocated power according to their
respective channel gains, i.e., the user with the lowest effective
channel gain obtains a larger portion of the total available
power. Decoding of the transmitted signals at the receiver
is done by utilizing a multi-user detection technique named
successive interference cancellation (SIC).
In [20]- [21], authors proposed a D2D NOMA-based co-
operative network utilizing decode-and-forward (DF) relaying
protocol and also derived the analytical expressions of OP.
The authors have considered an additional diversity power line
link along with a wireless link between D2D strong and weak
users. An optimal value of power splitting factor minimizing
OP has also been derived. However, the proposed model is
restricted to a single D2D pair, and the advantages of FD
radios have not been explored. Subsequently, in [22], authors
considered a hybrid communication network comprising of
D2D cellular communication on the receiver side and power
line communication at the transmitter side to provide last-
mile connectivity. The authors also provided a closed-form
expression of symbol error probability. The obtained numerical
results highlighted the optimality of D2D links operating at the
lower signal-to-noise ratio (SNR) values. However, the analy-
1In this paper, NOMA has been applied over each subcarrier of the OFDM
symbol.
sis is limited to smart grid communications, and performance
gain due to FD and NOMA has not been explored.
FD mode and NOMA are an integral part of the B5G
cellular networks, and hence, the integration of both promising
technologies will exhibit high throughput, and spectral effi-
ciency [10], [23]–[25]. In [26], authors proposed a hybrid
FD/HD cooperative NOMA system wherein the near user
works as a DF relay for a far user. Analytical results of
ergodic sum rate and OP showed that FD NOMA outperforms
the HD NOMA for the low SNR values. Additionally, the
authors also discussed energy efficiencies for FD and HD
relaying. However, the proposed model is limited to only
two users within the cell. The proposed model has not been
tested for the multiuser environment. Similarly, in [27], an
FD D2D aided cooperative NOMA system comprising of one
BS and two users are proposed. Here, the NOMA strong user
(a user having better channel condition) operates as an FD
relay to assist the NOMA weak user to improve the outage
performance. The OP expressions are derived to evaluate the
performance of proposed system model.
In [28], authors have proposed millimeter-wave based FD
C-D2D communications systems in which an FD node DT
utilizes NOMA to transmit D2D and cellular uplink signal
simultaneously. OP expressions of D2D and cellular users are
derived. However, the analysis is restricted to FD mode only
with a single CU and D2D pair, and no trade-offs between HD
and FD mode are shown. Similarly, in [29], a D2D assisted
FD relaying cooperative protocol using NOMA is proposed,
wherein BS interacts with NOMA strong and weak users via
a direct link and DT, respectively. Additionally, the theoretical
expressions of OP and ergodic capacity are derived under
both the assumptions of imperfect and perfect interference
cancellation. However, the analysis in [26]–[29], are limited
to single carrier transmission, and hence, there is a necessity
to explore the FD aided C-D2D system with multi-carrier
modulation such as OFDM. In [30], authors have proposed
OFDMA based NOMA-aided C-D2D communications system,
wherein the uplink cellular transmission is supported by DT
working as an FD relay. OP expressions for cellular and
D2D links have been derived. However, the proposed model
consists of a single CU and D2D user, and given analysis
lacks the comparison of results with the conventional C-D2D
system wherein DT works as an HD relay. To the best of
our knowledge, the outage performance of OFDMA based
multiuser NOMA-aided C-D2D communications system has
not been investigated yet.
Motivated by existing literature, this paper proposes a
NOMA-aided C-D2D communications system where DT op-
erates either as an HD or FD relay for cellular downlink signal
utilizing DF relaying protocol. The system model consists of
PD2D pairs along with MCUs and a BS. Using OFDMA,
available cellular bandwidth is split into Nindependent and
orthogonal subcarriers, wherein every subcarrier acquires the
same subchannel bandwidth. In the proposed model, we have
assumed that the D2D communication is operator-controlled
[31], i.e., the BS assigns resources between CU and D2D
users. According to the proposed scheme, BS broadcasts N
subcarriers to CU and D2D pair. Out of Nreceived subcar-
3
riers, D(where D < N ) subcarriers are assigned to DT for
relaying the downlink cellular transmission signal, and the re-
maining (N−D)subcarriers are assigned to the D2D user for
its own transmission. BS utilizes NOMA for simultaneously
transmitting cellular downlink and D2D signals. Precisely,
the D2D and cellular downlink signals are superimposed by
the BS employing power domain multiplexing. Further, this
superimposed signal is broadcasted by the BS to CU as well as
the D2D user. SIC is utilized at DT, wherein cellular downlink
signal is decoded first assuming D2D signal as interference,
and subsequently, it is subtracted from the superimposed signal
for decoding the D2D signal.
Compared to the existing work, contributions of this paper
are summarized as follows:
•An OFDMA based NOMA-aided C-D2D communica-
tions system is proposed, where DT acts as an FD/HD
relay to support cellular downlink transmission.
•Analytical expressions of achievable rates and OPs for
cellular and D2D users are derived.
•The impact of different values of power allocation fac-
tors and distances between nodes for both FD and HD
mode has been investigated. An optimal range of power
allocation factors has also been derived.
•A comparative performance trade-offs between HD and
FD mode has been investigated. The results show that
with high cellular outage constraint FD mode outperforms
the HD mode whereas, with low cellular outage constraint
HD mode performs better in terms of D2D OP.
•A comparison of the proposed OFDMA-based NOMA-
aided C-D2D communications system is done with the
benchmark OMA-based system.
The remainder of the paper is structured as follows. The
system model is shown in Section II. Section III gives the
derivations and the analytical expressions for CU and D2D
user’s OP. Section IV contains the simulation results, while
Section V concludes the paper.
II. SY ST EM MO DE L
As shown in Fig. 1, our proposed system model consists
of a circular cell of radius Rhaving one BS positioned
at the center of this cell. There are MCUs and PD2D
pairs present inside the cellular cell. Specifically, a CU is
represented as CUm, where m= 1,2, .., M , and a D2D pair
is represented as DTp−DRp, where p= 1,2, .., P . OFDMA
is utilized as an access technology by means of which the
available bandwidth is distributed among MCUs by assigning
Nindependent and orthogonal subcarriers to each CU. Here,
peer exploration and link establishment between D2D users
is accomplished by the BS [32]. The channels between any
two nodes for lth subcarrier is considered as Rayleigh flat
fading with Ψxy,l ∼ CN (0, ρ−n
xy ), where, nis path-loss
exponent and ρxy is the distance between any transmitter x
(x∈ {B, tp}) and corresponding receiver y(y∈ {cm, tp, rp}),
defined separately for each pair of transmitter-receiver. Here,
Bdenotes the BS, tpdenotes DTp,rpdenotes DRp, and
cmdenotes CUm. The channel corresponding to BS−CUm,
DTp−CUm, BS−DTp, DTp−DRpand BS−DRpare denoted
Figure 1. System model
TABLE I
LIS T OF SY MB OLS
Symbol Description
RRadius of cellular cell
NTotal number of subcarriers
DSubcarriers transmitted from DT to DR
PtTransmission power from BS
Pdt Transmission power of DT
β, λ Non-negative constants of RSI
ρxy Distance between node xand y
nPath loss exponent
αPower splitting factor
Ψxy Channel Coefficient between node xand y
γxy Instantaneous channel gain between node xand y
σ2
jNoise Variance
Rth Cellular and D2D target rate
by ΨBcm,l ,Ψtpcm,l,ΨBtp,l,Ψtprp,l and ΨBrp,l , respectively,
over subcarrier l(1 ≤l≤N).γxy,l =|Ψxy,l|2denotes the
instantaneous channel gain corresponding to lth subcarrier.
Noise at the receivers DTp, CUm, and DRpare expressed
as additive white Gaussian noise (AWGN) which are denoted
as ntp,l,ncm,l ,nrp,l ∼ CN(0, σ2
b), where b={1,2,3},
defined for DTp, CUmand DRp, respectively2.stp,l and scm,l
denote the D2D and CU’s signals transmitted on lth subcarrier,
respectively. It is worth mentioning that scm,l and stp,l are
considered to have a mean of zero and E{s∗
cm,lscm,l }=
E{s∗
tp,lstp,l }= 1. Channel gain between any transmitter x
and receiver yover lth subcarrier is denoted by γxy,l which
is exponentially distributed with probability density function
(PDF).
f(γxy,l) = ρxy,le−ρxy ,lγxy,l .(1)
A. Residual Self-Interference Model
The recent literature in FD systems has proposed that SI
cancellation schemes do not suppress the SI completely. After
2Without loss of generality, it is assumed that σ1=σ2=σ3=σj.
4
the active and passive SI cancellation, the RSI is modelled as a
Gaussian random variable as per the central limit theorem [14],
[33], [34]. Hence, we have modelled RSI similar to the existing
literature and represented as, At FD node DTp, the received
signal is affected by AWGN as well as SI due to imperfect
self-interference suppression (SIS). As per [35], the RSI at
DTpis modeled as an additive gaussian random variable:
vs∼CN 0, β pλ
dt,l,(2)
where, pdt,l ∈(0, Pdt,l) denotes the power of the signal
transmitted from node DTpover lth subcarrier, and Pdt,l
denotes maximum available power that DTpcan use to trans-
mit over lth subcarrier. βand λare the RSI parameters
reflecting the performance of SIS. These RSI parameters are
non-negative and derived from the characteristics of the best-
fit line in the simulation of SI cancellation plots in [36].
B. Signal model and transmission protocol
In our proposed model, BS decides the communication
mode of each user as per their channel quality, as described
in [37]. For a specific time-frequency resource block, one CU
maps with a single D2D pair. We have considered that owing
to heavy obstacles or shadowing, the effective channel gain
of BS−CUmlink is lower than BS−DTplink, and hence,
CUmand DTpare observed as NOMA weak and NOMA
strong user, respectively. Since DTpacts as an FD relay, it will
experience SI as modelled in (2). BS transmits a superimposed
signal s=pP1,lstp,l +pP2,lscm,l over lth subcarrier to CUm
and DTp, where P1,l =αPt,l,P2,l = (1 −α)Pt,l , and Pt,l is
the total transmit power of BS over lth subcarrier. According
to NOMA systems, NOMA weak user (CUm) is assigned more
power than NOMA strong user (DTp). Thus, power allocation
factor α∈(0,0.5), as specified in [27].
At the receiver end, the superimposed signal from BS is
decoded at DTpand CUmby performing SIC. Specifically,
CUmbeing the NOMA weak user decodes CU’s signal
directly whereas, the DTpbeing the NOMA strong user first
decodes and cancels CU’s signal from the received superim-
posed signal to decode D2D signal. Further, DTpforwards the
decoded cellular data to CUmwith Dsubcarriers whereas, the
remaining subcarriers (N−D) will be utilized by DTpfor D2D
transmission. CUmcombines the signals which it has received
from the BS and DTpusing maximal ratio combining (MRC).
Additionally, we have also described our protocol using a
flowchart as shown in Fig. 2.
III. CEL LU LA R RATE AN D OUTAG E PROBABILITY
BS superimposes the cellular downlink and DTpsignal
on the same time-frequency resource block and hence, the
superimposed signal received by CUmand DTpover lth
subcarrier is given as
s=pP1,lstp,l +pP2,l scm,l.(3)
Figure 2. Protocol description
A. DT Working in FD Mode
The NOMA strong user, DTpreceives a cellular downlink
signal, and is also affected by SI, thus its received signal
over lth subcarrier, and at kth time slot (k= 1,2,3, ...)is
represented as
y1[k]=ΨBtp,l [k](pP1,l stp,l[k]+pP2,l scm,l [k])
+vs,l[k] + ntp,l [k],(4)
where, vs,l denotes the RSI over lth subcarrier. Downlink
signal received by the NOMA weak user CUmat kth time
slot (k= 1,2,3, ...)over lth subcarrier is given as
y2[k]=ΨBcm,l [k](pP1,l stp,l[k]+pP2,l scm,l[k])+ncm,l[k].
(5)
The instantaneous rate at DTpto detect signal of CUmover
Nsubcarriers is
RDT =
N
X
l=1
log2 1 + γBtp,l (1 −α)Pt,l
αγBtp,l Pt,l +βpλ
dt,l +σ2
j!,(6)
where, βpλ
dt,l is due to RSI at DTpover lth subcarrier. Pt,l
and pdt,l are the transmitted power of BS and DTpover lth
subcarrier, respectively. From [9],
Pt,l =Pt,∀l;pdt,l =pdt,∀l;γxy,l =γxy ,∀l. (7)
OP for BS-DT transmission is given as
PDT
out =Pr(RDT < Rth) = P r γBtp<Θ
=ZΘ
0
ρBtpe−ρBtpγB tpdγBtp,(8)
5
where, Θ = µ(βpλ
dt+σ2
j)
Pt[1−α(1+µ)] , and µ= 2Rth/N −1.Rth represents
the minimum acceptable rate below which the communication
between two nodes is not reliable.
On solving (8),
PDT
out =(1−e−ρBtpΘ; 0 <µ< 1−α
α,
1; µ≥1−α
α.(9)
Similarly, the instantaneous rate for signal received at CUm
from BS is
RCU =
N
X
l=1
log2 1 + γBcm,l (1 −α)Pt,l
αγBcm,l Pt,l +σ2
j!.(10)
From (7) and (10), OP is
PCU
out =Pr(RCU < Rth ) = Pr(γBcm< δ)
=Zδ
0
ρBcme−ρBcmγB cmdγBcm,(11)
where, δ=µσ2
j
Pt[1−α(1+µ)] . Solving further,
PCU
out =(1−e−ρBcmδ; 0 < µ < 1−α
α,
1; µ≥1−α
α.(12)
DTpbeing the NOMA strong user, first decodes the cellular
downlink signal and forwards to BS over Dsubcarriers,
succesively it removes the downlink signal from the received
superimposed signal to decode D2D signal which is simul-
taneously forwarded to DRpusing the remaining N−D
subcarriers. The received signal at CUmforwarded from DTp
is given by
y
0
2[k] = √pdt,lΨtpcm,l [k]s
0
tp[k−k0] + ncm,l[k],(13)
where k0is processing delay [14]. Signal received at the
CUmfrom BS and DTpare combined by using MRC. The
instantaneous rate at CUmis given as
RCU
MRC =
D
X
l=1
log2 1 + γBcm,l (1 −α)Pt,l
αγBcm,l Pt,l +σ2
j
+γtpcm,l pdt,l
σ2
j!
+
N−D
X
l=1
log2 1 + γBcm,l (1 −α)Pt,l
αγBcm,l Pt,l +σ2
j!.(14)
Thus, when DTpworks as an FD relay, the cellular OP is
given as
PCU =1−PDT
out PrRCU
MRC < Rth+PDT
out PCU
out .
(15)
Proposition 1: The cellular OP for the proposed NOMA
aided C-D2D communications system where DTpworks in
FD mode is obtained as
PCU =(1−e−ρBcmδ−ρB cme−ρBtpΘΓ; 0 < µ < 1−α
α
1; µ≥1−α
α
.
(16)
Proof :The detailed derivation of the Proposition 1 is in-
cluded in Appendix A.
B. DT working in HD mode
When DTpis working in an HD mode, transmission takes
place in two Phases. In Phase 1, CUmand DTpreceive
the superimposed signal from BS, whereas, in Phase 2, DTp
forwards the decoded CU’s signal with Dsubcarriers and the
remaining subcarriers (N−D) are utilized by DTpfor D2D
transmission. The received signal in Phase 1 from BS over lth
subcarrier, and at kth time slot (k= 1,2,3, ...), is represented
as
y3[k]=ΨBtp,l [k](pP1,l stp,l[k] + pP2,l scm,l [k]) + ntp,l[k].
(17)
Similarly, the downlink signal received by CUmat kth time
slot (k= 1,2,3, ...)over lth subcarrier will be same as defined
in (5).
The instantaneous rate of the signal at DTpover Nsubcar-
riers is
RHD
DT =1
2
N
X
l=1
log2 1 + γBtp,l (1 −α)Pt,l
αγBtp,l Pt,l +σ2
j!,(18)
where, the factor 1
2is included in the rate equation due to
the two-phase transmission. From (7) and (18), OP for BS-DT
transmission is given as
PHD
out,DT =Pr(RHD
DT < Rth) = P r γBtp< δ1
=Zδ1
0
ρBtpe−ρBtpγB tpdγBtp,(19)
where, δ1=µ1σ2
j
Pt[1−α(1+µ1)] , and µ1= 22Rth/N −1. On further
solving (19),
PHD
out,DT =(1−e−ρBtpδ10< µ1<1−α
α
1µ1≥1−α
α
.(20)
Similarily, when DTpworks as an HD relay, from (7) and
(10), OP is given as
PHD
out,CU =Pr1
2RCU < Rth =Pr(γBcm< δ1)
=Zδ1
0
ρBcme−ρBcmγB cmdγBcm.(21)
On further solving (21),
PHD
out,CU =(1−e−ρBcmδ10< µ1<1−α
α
1µ1≥1−α
α
.(22)
Similar to the case of FD relay, DTpincorporates the SIC to
decode cellular downlink and D2D signal and then forwards
these signals with Dand N−Dsubcarriers to CUmand
DRp, respectively. Signal received at the CUmare similarly
combined with MRC, and the cellular OP when DTpworks
in HD mode is given as
PHD
CU =1−PH D
out,DT Pr1
2RCU
MRC < Rth
+PHD
out,DT PHD
out,CU .(23)
Proposition 2: The cellular OP for the proposed NOMA
aided C-D2D communications system where DTpworks in
HD mode is obtained as
6
PHD
CU =(1−e−ρBcmδ1−ρB cme−ρBtpδ1Γ1; 0 < µ < 1−α
α,
1; µ≥1−α
α.
(24)
Proof :The detailed derivation of the Proposition 2 is in-
cluded in Appendix B.
IV. ACHIEVABLE D2D RATE A ND OU TAGE PRO BABILITY
A. DT Working in FD Mode
The FD node DTptransmits the signal sdt to DRpover
N−Dsubcarriers. Signal received by DRpover lth subcarrier,
and at kth time slot (k= 1,2,3, ...)is represented as
y5[k] = √pdt,l Ψtprp,l[k]stp[k] + pPt,l ΨB rp,l[k]scm[k]
+nrp,l[k],(25)
where, pdt,l is the power transmitted by DTpover lth subcar-
rier, and scu is the interference signal received at DRpdue to
CU’s transmission. Now, there are two cases arises:
(a) Signal from BS could not be decoded by the DRp, thus
no interference for D2D transmission.
(b) Signal from BS is overheard by the DRpand it acts as
an interference for the D2D transmission.
The OP for D2D transmission is
PD2D
out =Pa
D2DPDR +Pb
D2D(1 −PDR),(26)
where, PDR is the OP for the BS-DRplink, Pa
D2Dis the OP
when the superimposed signal from BS could not be overheard
by DRpand Pb
D2Dis the OP when BS-DRpsignal acts as an
interference for D2D transmission. The Achievable rate for the
link from BS to DRpis given as.
RDR =
N
X
l=1
log2 1 + PtγBrp,l
σ2
j!.(27)
Using (7) and (27) OP is given as
PDR =Pr(RDR < Rth )=1−e
−ρBrpσ2
jµ
Pt.(28)
The achievable rate for DT-DR link, when there is no inter-
ference from BS:
Ra
D2D=
N−D
X
l=1
log2 1 + pdt,lγtprp,l
σ2
j!.(29)
Using (7), and (29) OP is
Pa
D2D=Pr(Ra
D2D< Rth) = 1 −e
−ρtprpAσ2
j
pdt ,(30)
where, A= 2Rth/(N−D)−1. If the signal from BS to DRpis
received successfully, the transmitted signal from DTpto DRp
will experience it as an interference, and hence, the achievable
rate is
Rb
D2D=
N−D
X
l=1
log2 1 + pdt,l γtprp,l
σ2
j+PtγBrp,l !.(31)
The OP expression is given by
Pb
D2D=P r Rb
D2D< Rth.(32)
Further, using (7), (31), and (32) OP is given as
Pb
D2D=P r γtprp<(σ2
j+PtγBrp)(2Rth /N−D−1)
pdt !.
(33)
Since, γtprpand γBrpare exponentially distributed, their joint
PDF is given by ρtprpe−ρtprpγtprpρBrpe−ρBrpγBrpand hence,
the OP expression is given as
Pb
D2D=Z∞
0Zf(γBrp)
0
ρtprpe(−ρtprpγtprp)
×ρBrpe−ρBrpγB rpdγtprpdγBrp
=1 −e
−Aρtprpσ2
j
pdt
1 + AρtprpPt
pdtρBrp
,(34)
where,
f(γBrp) = "σ2
j+PtγBrp(2Rth /N−D−1)
pdt #
and, A= 2Rth/(N−D)−1.
Now, from equations (26), (28), (30) (34),
PD2D
out =
1−e
−Aρtprpσ2
j
pdt
1 + AρtprpPt
pdtρBrp
e
−ρBrpσ2
jµ
Pt!
+ 1−e
−ρBrpσ2
jµ
Pt! 1−e
−ρtprpAσ2
j
pdt !.(35)
B. DT Working in HD Mode
When DTpis working as an HD relay, signal received by
DRpover lth subcarrier in Phase 2 of kth time slot, (k=
1,2,3, ...)is represented as
y6[k] = √pdt,l Ψtprp,l[k]stp[k] + nrp,l [k].(36)
Now, the achievable rate for the link DT-DR is given as
RHD
D2D=1
2
N−D
X
l=1
log2 1 + pdt,lγtprp,l
σ2
j!.(37)
Using (7) and (37) OP is
PHD
D2D=PrRHD
D2D< Rth= 1 −e
−ρtprpA1σ2
j
pdt ,(38)
where, A1= 22Rth/(N−D)−1.
Corollary 1: We can derive the optimal value of α, which
can restrict the OP to be one for both cases DTpworking as
an HD and FD relay. Since, µ= 2Rth −1and µ1= 22Rth −1,
it is clear that µ1> µ. From (16) and (24),
0< µ < µ1<1−α
α.(39)
It is already defined that α∈(0,0.5), and solving (39) in
terms of α, we get:
0< α < 1
1 + µ1
<1
1 + µ<0.5.(40)
7
TABLE II
SIMULATION PARAMETERS
Variables Value
σ2
j−150 dBm
N32
Pt30 dBm
β10−10
λ0.8
pdt 20 dBm
n4
R800m
ρBcm400m
ρtpcm300m
ρBrp500m
Figure 3. Simulation model
V. RES ULTS A ND DISCUSSIONS
This section represents the simulation, and analytical results
for D2D and cellular OPs of the proposed NOMA aided
C-D2D communications system. Moreover, outage trade-offs
between FD/HD relaying is analyzed in this section. Here,
we consider a circular cell having a radius of R= 800m.
Considering urban areas, path loss exponent is taken as n= 4,
and the target rate (Rth) for both cellular and D2D link is
considered as 1 bit/sec/Hz. All other simulation parameters
are similar to [30] and listed in Table II. Additionally, we
have included Fig. 3 describing the simulation model of our
proposed system.
Fig. 4 represents the cellular OP versus Dfor different
values of α. The distances between BS and DTp(ρBtp)
has been taken 100m. We can observe from Fig. 4 that the
cellular OP increase with α. This is due to the fact that the
power allocated for cellular transmission increases with α. For
instance, when DTpis working as an FD relay, for D= 15
and α= 0.1,0.2, cellular OPs are approximately 3.2×10−3,
4.0×10−3, respectively. In contrary, when DTpis working as
5 10 15 20 25 30
10-3
10-2
10-1
Figure 4. Cellular outage probability vs subcarriers alloted to CU (varying
α)
5 10 15 20 25 30
10-3
10-2
10-1
Figure 5. Cellular outage probability vs subcarriers alloted to CU (varying
ρBtp)
an HD relay, the cellular OPs for α= 0.1,0.2are 3.4×10−2,
6.0×10−2, respectively. It is evident from the results that the
proposed system with DTpworking as an FD relay always
performs better than the DTpworking as an HD relay in
terms of cellular OP. Please note that from (40), for Rth = 1
bit/sec/Hz, the upper limit for αcan be calculated as 0.25.
Fig. 5 shows the cellular OP versus Dfor different distances
between BS and DTp, i.e., ρBtp= 100,300.αhas been
set to 0.2. From Fig. 5, it is evident that as the number
of forwarded subcarriers from DTpto CUm(D) increases,
the cellular OP decreases. For instance, when D= 25 and
ρBtp= 100, the OPs for DTpworking as an HD and FD re-
lay are approximately 3.1×10−2and 3.1×10−3, respectively.
Similarly, for ρBtp= 300, the OPs for DTpworking as an
HD and FD relay are approximately 6.3×10−2and 1.0×10−2,
respectively. Hence, we can observe that as ρBtpincreases,
cellular OP also increases, which is due to decrease in the
decoding probability of the superimposed signal at DTp. Trend
8
5 10 15 20 25 30
10-4
10-3
10-2
10-1
100
Figure 6. D2D outage probability vs subcarriers alloted to CU
similar to Fig. 4 can be observed here that the proposed system
with DTpworking in FD mode performs better than the system
with DTpworking in HD mode.
Fig. 6 shows the D2D OP versus the number of subcarriers
Dfor distance between the D2D pair (ρtprp) = {50,100}.
The distance between BS and DTp(ρBtp) has been set to
300m. As observed from Fig. 6, D2D OP increases with an
increase in Dfor both cases DTpworking in FD or HD
mode. It is owing to the fact that with an increase in D,
the remaining subcarriers (N−D) decrease, and hence the
subcarriers available for D2D transmission also decrease. For
instance, when D= 15 and ρtprp= 50m, the OPs for DTp
working as an HD and FD relay are approximately 7.8×10−4
and 2.6×10−3, respectively. Similarly, for ρtprp= 100m and
D= 15, the OPs for DTpworking as an HD and FD relay are
approximately 1.2×10−2and 4.1×10−2, respectively. Hence,
it is evident from Fig. 6 that with an increase in ρtprp, D2D
OP increases. It is also apparent from Fig. 6 that DTpworking
as an HD relay performs better than the DTpworking as an
FD relay till D= 23 for ρtprp= 50m and 100m both. This
is due to external interference received at DRpfrom cellular
downlink transmission, which degrades the performance of
D2D user. However, as the number of subcarriers allocated
for relaying CU’s data (D) increases, the remaining subcarriers
N−Dfor D2D transmission decreases, and hence the effect
of external interference decreases.
Fig. 7 shows the cellular OP comparison of our proposed
system with OMA based C-D2D system or ρBtp= 100 m. As
observed from Fig. 7, cellular OP decreases with an increase
in D. Further, it is evident from Fig. 7 that NOMA with FD
relaying outperforms the NOMA with HD relaying and OMA-
based C-D2D system. For instance, when D= 20 cellular OP
for OMA, NOMA HD, and NOMA FD schemes are 7.2×
10−2,4.1×10−2, and 2.8×10−3, respectively. Impact of RSI
parameters β,λon cellular OP has been shown in Fig. 8 and 9
of this response letter. It is evident from Fig. 8, that increasing
the value of βwill also increase the cellular OP. For instance,
when D= 20, cellular OP is 3.3×10−3, and 3.7×10−2for
TABLE III
SUBCARRIERS REQUIRED BY THE D2D USER SATISFYING THE CELLULAR
OUTAGE PROBABILITY CONSTRAINT WITH VARIATION IN α
Cellular Outage Constraint 10−110−2
N−D(FD) α= 0.132 25
α= 0.232 24
D2D Outage
Probability FD
1.0×10−31.4×10−3
1.0×10−31.5×10−3
N−D(HD) α= 0.129 Not Satisfied
α= 0.222 Not Satisfied
D2D Outage
Probability HD
2.2×10−4-
4.0×10−4-
5 10 15 20 25 30
10-3
10-2
10-1
Figure 7. Cellular outage probability comparison of OMA with NOMA
β= 10−12, and β= 10−9, respectively. Similarly, from Fig.
9, we can observe that the cellular OP decreases with increase
in λ. For instance, when D= 20, cellular OP is 1.9×10−2,
and 8.0×10−3for λ= 0.4, and λ= 1, respectively.
Table III shows a comparison of D2D OP satisfying cellular
outage constraint for DTpworking as an HD and FD relay with
different values of α. We can observe from Table III that,
•When DTpworks as an HD relay, cellular OP constraint
10−2is not satisfied for α=0.1 and 0.2 whereas, the
same cellular OP constraint is satisfied for same values
of αwhen DTpworks as an FD relay. Cellular outage
constraint higher than 10−2is satisfied only by FD mode
when ρBtp= 100m.
•It is also evident from Table III as αincreases the number
of available subcarriers for D2D transmission satisfying
cellular outage constraint decreases.
•Table III also depicts that FD mode outperforms the
HD mode in terms of D2D OP while maintaining the
high cellular outage constraint. In contrast to this, the
performance of FD mode degrades with comparatively
low cellular outage constraint due to SI and external
interference from cellular downlink signal.
9
5 10 15 20 25 30
10-2
Figure 8. Cellular outage probability vs Dvarying β
5 10 15 20 25 30
0.01
0.015
0.02
0.025
0.03
0.035
Outage probability
Figure 9. Cellular outage probability vs Dvarying λ
VI. CONCLUSION
This paper proposes OFDMA based NOMA-aided coopera-
tive D2D communications system, where a D2D user performs
as an FD or HD relay utilizing DF relaying technique for
cellular downlink transmissions. In our proposed model, BS
employs NOMA to transmit a superimposed signal to DT
and CU. Utilizing SIC, DT decodes and forwards the cellular
downlink signal over Dsubcarriers. As a compensation, the
remaining subcarriers (N−D) are utilized by DT to transmit
D2D signal to DR. The analytical expressions for cellular and
D2D achievable rates and OPs are derived, and the outage
trade-offs between FD/HD relaying has been investigated.
The accuracy of derived expressions is verified through the
simulation results. Results represent that cellular OP decreases
with Dwhile D2D OP increases with D. It is also apparent
from the results that the proposed system with FD relaying
outperforms the system with HD relaying in terms of D2D
OP with low cellular OP constraint.
APPENDIX
Proof of Proposition 1: From (15),
PCU = (1 −PDT
out )Pr(RCU
MRC < Rth) + PDT
out (PCU
out ).(41)
Since, γBcmand γtpcmare independent and exponentially
distributed random variables,and their joint PDF is given as
ρBcme−ρBcmγB cm×ρtpcme−ρtpcmγtpcm. Using (7) and (14),
OP,
PMRC
out =Pr(RCU
MRC < Rth) = Prγtpcm< f (γBcm).
(42)
where,
f(γBcm) = σ2
j
Pdt
2Rth/D −1 + γBcm(1−α)Pt
σ2
j+αγBcmPtN/D
1 + γB cm(1−α)Pt
σ2
j+αγBcmPtN−D
D
.
For exponential random variable γBcm, f(γBcm)>0or,
σ2
j
Pdt
2Rth/D −1 + γBcm(1−α)Pt
σ2
j+αγBcmPtN/D
1 + γB cm(1−α)Pt
σ2
j+αγBcmPtN−D
D
>0,(43)
which on solving yields to
γBcm<µσ2
j
[1 −α(1 + µ)] Pt
or, γBcm< δ
.
On further solving, the OP is
PMRC
out =Zδ
γBcm=0
ρBcme−ρBcmγB cm
× Zf(γBcm)
γtpcm=0
ρtpcme−ρtpcmγtpcmdγtpcm!dγBcm
=Zδ
γBcm=0
ρBcme−ρBcmγB cm1−e−ρtpcmf(γBcm)dγBcm
=1 −e−ρBcmδ−ρBcmΓ,(44)
where,
3Γ = Zδ
γBcm=0
e−[ρBcmγBcm+ρtpcmf(γBcm)] dγBcm.(45)
Thus, the cellular OP when DTpis working in FD mode is
PCU = (1 −PDT
out )(PMRC
out ) + PDT
out (PCU
out ).(46)
From (9), (12), (44), and (46) the cellular OP is derived as
given in (16).
Proof of Proposition 2: From (23),
PHD
CU =1−PH D
out,DT Pr1
2RCU
MRC < Rth
+PHD
out,DT PHD
out,CU .(47)
3Γin (45) is intractable, thus it has been solved by numerical integration.
10
Using (7) and (14), OP with MRC at CUmis given as
Pr1
2RCU
MRC < Rth=Prγtpcm< h(γBcm),(48)
where,
h(γBcm) = σ2
j
pdt
22Rth/D −1 + γBcm(1−α)Pt
σ2
j+αγBcmPtN/D
1 + γB cm(1−α)Pt
σ2
j+αγBcmPtN−D
D
.
For exponential random variable γBcm,h(γBcm)>0or,
σ2
j
pdt
22Rth/D −1 + γBcm(1−α)Pt
σ2
j+αγBcmPtN/D
1 + γB cm(1−α)Pt
σ2
j+αγBcmPtN−D
D
>0,(49)
on further solving, γBcm<µ1σ2
j
[1−α(1+µ1)]Pt.
Let µ1σ2
j
[1−α(1+µ1)]Pt=δ1, the OP is
PHD
out,MRC =Zδ1
γBcm=0
ρBcme−ρBcmγB cm
× Zh(γBcm)
γtpcm=0
ρtpcme−ρtpcmγtpcmdγtpcm!dγBcm
=Zδ1
γBcm=0
ρBcme−ρBcmγB cm1−e−ρtpcmf(γBcm)dγBcm
=1 −e−ρBcmδ1−ρBcmΓ1,(50)
where,
4Γ1=Zδ1
γBcm=0
e−[ρBcmγBcm+ρtpcmh(γBcm)] dγBcm.(51)
Thus, the cellular OP when DTpis working in HD mode is
given as
PHD
CU = (1−PH D
out,DT )(PHD
out,MR C )+PHD
out,DT (PHD
out,CU ).(52)
From (20), (22), (50) and (52) the cellular OP is derived as
given in (24).
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Rahul Bajpai received the M.Tech. degree in
digital communication from the ABV-IIITM,
Gwalior, India, in 2014. He is currently pursuing
the Ph.D. degree with the Department of
Electrical and Electronics Engineering, BITS
Pilani K.K. Birla Goa Campus, India. His research
interests are non-orthogonal multiple access,
full-duplex, millimeter-wave and device-to-device
communication. He has served as a reviewer of the
Springer Wireless Networks and Springer Wireless
Personal Communications.
Email Id: p20190003@goa.bits-pilani.ac.in (Corresponding Author)
Naveen Gupta is working as an Asst. Professor
with the Department of EEE, BITS Pilani K.K.
Birla Goa Campus, India. He has obtained his PhD
in wireless communications from IIIT-Delhi India
in 2017, and M.Tech in Advanced Communication
Systems from NIT-Warangal in 2011. His research
interests are resource allocations for next generation
wireless communication techniques, non-orthogonal
multiple access, full-duplex, millimeter-wave and
device-to-device communication. He has served as
a reviewer of the IEEE Transactions on Cognitive
Communications and Networking, IEEE Transactions on Communications,
IEEE Access and the IETE Technical Review journals.
Email Id: naveeng@goa.bits-pilani.ac.in
