Impact of NLPA on SWIPT Enabled Two-Way AF Cooperative Network

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Impact of NLPA on SWIPT Enabled Two-Way AF
Cooperative Network
Deepak Kumar
Electrical Engineering
IIT Indore
Indore, India
phd1901102017@iiti.ac.in
Praveen Kumar Singya
CEMSE Division
KAUST
Thuwal, Saudi Arabia
praveen.singya@kaust.edu.sa
Vimal Bhatia
Electrical Engineering
IIT Indore
Indore, India
vbhatia@iiti.ac.in
Abstract—In this paper, we investigate the impact of non-
linear distortion on the overall system outage probability of
simultaneous wireless information and power transfer enabled
two-way amplify-and-forward relaying network by employing
three different nonlinear power amplifier (NLPA) models such as
traveling wave tube amplifier, soft envelope limiter, and solid-state
power amplifier at the relay node. We consider a time-switching
based protocol at the energy-constrained relay node to harvest
energy and information transmission. We derive the closed-
form expression of the system outage probability by utilizing
the selection combining technique at the source nodes over
Nakagami-mfading channels. System throughput and energy
efficiency of the network are also investigated. The impact of
NLPA, threshold data-rate, fading severity, and time-switching
factor are highlighted on the network’s performance. Finally,
the derived analytical results are validated by the Monte Carlo
simulations.
Index Terms—NLPA, time switching, two-way relay, SWIPT,
AF. I . IN TRO DU CTION
With energy harvesting (EH) becoming an integral part
of the beyond 5G wireless communications, we look to-
wards solutions for increasing the limited battery life [1].
To overcome the energy-constrained problem in the wireless
network, simultaneous wireless information and power transfer
(SWIPT) has emerged as a propitious solution due to its
simultaneous transfer of energy and information capability. To
facilitate EH and information transmission (IT) simultaneously
at the wireless node, time-switching (TS) or power-splitting
(PS) protocols are used [2], [3]. Cooperative relaying has
attracted significant attention due to increased coverage area,
link reliability, and improved throughput [4]. Two-way relay
(TWR) network provides higher spectral efficiency compared
with conventional one-way relay network due to the analog
network coding in two orthogonal time phases, specifically,
multiple access (MA) and broadcast (BC) phases [5]. In [6],
a closed-form expression of the system outage probability
is derived for amplify-and-forward (AF) TS-SWIPT TWR
network. TS ratio and PS factor are jointly optimized in a
decode-and-forward (DF) relaying based TWR network to
achieve optimum system OP [7]. In [8], OP and throughput of
an AF-TWR network are investigated by utilizing PS protocol
at the relay node. The impact of hardware impairments (HIs)
on the performance of a TS protocol based AF-TWR network
is investigated in [9] and closed-form expression of OP is
derived over Nakagami-mfading channels. A novel expression
of the system OP is obtained in [10] for a PS SWIPT-enabled
TWR network with HIs and the ceiling effects due to HIs on
the system performance are also investigated.
AF operation at the relay node is practically non-linear
which introduces non-linear distortion (NLD) [11]. NLD
severely reduces the quality of the amplified signal at the
relay node. The non-linear power amplifier (NLPA) employed
at the relay node like traveling wave tube amplifier (TWTA),
soft envelope limiter (SEL), and solid state power amplifier
(SSPA) can be modeled as memoryless (i.e., frequency- in-
dependent) system [12]. In [13]–[16], the impact of NLPA
on the performance of a relay network is investigated. The
impact of NLPA in a multiple relay network over imperfect
channel state information (CSI) is investigated in [14] in terms
of OP, asymptotic OP, and average symbol error rate for both
integer and non-integer Nakagami-mfading parameters. In
[15], [16], OP for an AF TWR network is obtained under
NLPA at the relay nodes however none of the above work
has considered system OP for NLPA model over Nakagami-
mfading channels.
In this work, we derive the closed-form expression of system
OP for TS-SWIPT enabled AF-TWR network with NLPA at
the relay node over Nakagami-mfading channels. System
throughput and energy efficiency are also investigated. To
the best of the authors’ knowledge, the derived system OP
expression for the considered network is not available in the
literature.
The rest of the paper is arranged as follows. The details
about the considered system model are described in Section
II. In Section III, analytical expressions of system OP, system
throughput, and EE are derived. Simulation and numerical re-
sults are demonstrated in Section IV. In Section V, conclusions
are drawn from the obtained results.
Notations: Notations used throughout the paper are: Γ(·),
Γ(·,·), and γ(·,·)represent the complete, upper incomplete,
and lower incomplete gamma functions, respectively. Pr(·)
denotes probability and Kv(·)denotes vth order modified
Bessel function of second kind [17, eq. (8.432.1)].
II. SYSTE M MOD EL
As shown in Fig. 1(a), we consider a TS-SWIPT enabled
AF-TWR network where bidirectional information exchange
takes place between two source nodes Scand Sdwith the
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2021 IEEE 93rd Vehicular Technology Conference (VTC2021-Spring) | 978-1-7281-8964-2/20/$31.00 ©2021 IEEE | DOI: 10.1109/VTC2021-Spring51267.2021.9448815
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R
ScSd
EH Phase
ScR
SdR
IT Phase-I
ScR & Sd
IT Phase-II
SdR & Sc
IT Phase-III
R Sc& Sd
αT(1-α)T/3 (1-α)T/3 (1-α)T/3
(1-α)T
EH Phase
IT Phase-I
IT Phase-II
IT Phase-III
(a)
(b)
mc
ma
md
Fig. 1: (a) System model, (b) Frame structure of TS-SWIPT.
aid of a relay node R. A direct link between Scand Sd
is also present. Sc,Sd, and Rare considered to transmit
in half-duplex mode and equipped with a single antenna.
The energy-constrained node Rharvests energy and process
information, from the received signals Scand Sdby utilizing
TS protocol. The frame structure of a TS-SWIPT receiver
is depicted in Fig. 1(b), where one transmission block is
divided between the EH phase and information transmission
(IT) phase. During αT period of the EH phase, Rharvests
energy from the RF sources Scand Sd, where α(0 < α < 1)
and Tdenotes time switching factor and transmission block
duration, respectively. Rutilizes the harvested energy for
broadcasting the information in the IT phase. The information
exchange between Scand Sdtakes place in three IT phases.
In IT Phase-I, Scbroadcasts its information to Sdand R.
Similarly in IT Phase-II, Sdbroadcasts its information to Sc
and R. Thereafter Rapplies AF operation on the combined
signal received in IT Phase-I and IT Phase-II, respectively. The
amplified signal is applied to an NLPA and Rbroadcasts the
NLPA output signal in IT Phase-III by utilizing the harvested
energy. Without loss of generality, all links are quasi-static
and follow reciprocity. Channel coefficients between Sc→R,
R→Sd, and Sc→Sdare denoted as hcr,hr d, and hcd,
respectively. Channel coefficients hcr ,hrd, and hcd follow the
Nakagami-mdistribution with severity parameters mc,md,
and maand average powers Ωc,Ωd, and Ωa, respectively.
A. Energy Harvesting
TS-SWIPT protocol is adopted at Rfor EH and IT. During
one transmission block, EH at Roccurs for αT period. Since
αdecides the amount of harvested energy at R, it plays an
important role to maintain the trade-off between throughput
and link reliability of the system. The amount of harvested
energy during the EH phase for one transmission block can
be given as Eh=αT η(Pc|hcr|2+Pd|hdr |2)[16], where
Pc,Pd, and 0< η ≤1are transmit power at Sc, transmit
power at Sd, and energy conversion efficiency of EH circuit,
respectively. Power transmitted at Rduring the IT Phase-III
can be expressed as Pr=3αη
1−α(Pc|hcr|2+Pd|hdr |2).
B. Information Transmission Phase
We consider that Sctransmits unit energy symbol Xcduring
IT Phase-I, then the signals received at Sdand Rcan be given,
respectively, as
Ycd =pPchcdXc+Nd,(1)
Ycr =pPchcrXc+Nr,(2)
where Nd∼ CN (0, σ2
d)and Nr∼ CN (0, σ2
r)are the additive
white Gaussian noises (AWGNs) at Sdand R, respectively.
From (1) and (2), the SNR at Sdand Rare given as
γcd =Pc|hcd|2
σ2
d
and γcr =Pc|hcr|2
σ2
r, respectively. Likewise, in
IT Phase-II, Sdtransmits unit energy symbol Xdthen signals
received at Scand Rare given as
Ydc =pPdhdcXd+Nc,(3)
Ydr =pPdhdrXd+Nr,(4)
respectively, where Nc∼ CN(0, σ2
c)is AWGN at Sc. From
(3) and (4) the SNRs at Scand Rare expressed as γdc =
Pd|hdc|2
σ2
cand γdr =Pd|hdr|2
σ2
r, respectively. Rcombines both
the received signal in IT Phase-I and IT Phase-II and applies
AF operation on them, which can be given as
XAF
r=G(Ycr +Ydr),(5)
where G=pPr/(Pc|hcd|2+Pd|hdc |2+ 2σ2
r). Further,
NLPA is adopted at Rwhich can be modeled as a frequency-
independent function [11]. Bussgang’s linearization theorem
states that the output of an NLPA can be given as a linear
scale factor A0of the applied signal with an NLD N0which
is uncorrelated with the applied signal [14]. This can be
expressed as
Yr=A0XAF
r+N0,(6)
where A0represents a constant value and N0∼ CN(0, σ 2
0)
is NLD. To show the impact of NLPA, we have considered
various memoryless high power amplifiers (HPAs) such as
TWTA, SEL, and SSPA models at R.
1) TWTA : TWTA HPA used to investigate the impact of
NLD in OFDM systems. The non-linear parameters A0and
σ2
0are given as [11]
A0=A2
sat
Pr1 + A2
sat
Pr
expA2
sat
PrEi−A2
sat
Pr,(7)
σ2
0=A2
sat
Pr1 + A2
sat
PrexpA2
sat
PrEi−A2
sat
Pr+ 1
−PrA2
sat,(8)
where Asat denotes saturation amplitude of the HPA and Ei(·)
denotes an exponential integral function.
2) SEL: SEL is used to model HPA with perfect predistor-
tion system and the parameters A0and σ2
0are given as [15]
A0= 1 −exp−A2
sat
Pr+Asat√π
2√Pr
erfcAsat
√Pr,(9)
σ2
0=Pr1−exp−A2
sat
Pr− |A0|2.(10)
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3) SSPA: SSPA is used to model amplitude characteristic
of an amplitude to amplitude conversion. NLPA parameters
A0and σ2
0are given as [11]
A0=Asat
2√Pr2Asat
√Pr−√πerfcAsat
√PrexpA2
sat
Pr
×2A2
sat
Pr−1,(11)
σ2
0=PrA2
sat
Pr1 + A2
sat
Pr
expA2
sat
PrEi−A2
sat
Pr−Pr.
(12)
Finally, Rbroadcasts the output signal of NLPA in IT
Phase-III with utilizing the harvested power. The signal re-
ceived at Sican be given as
Yr,i =hriYr+Ni,(13)
where Ni∼ CN(0, σ2
i)is the AWGN at Si, with i∈ {c, d}.
We consider Pc=Pd=Pand σ2
r=σ2
c=σ2
d=σ2for
simplicity [9]. After canceling the self-interference term from
(13), and taking approximation (Pc|hcr|2+Pd|hdr |2+ 2σ2
r)≈
(Pc|hcr|2+Pb|hdr |2), SNR at Sican be expressed as
γri =|hri |2|hjr |2
2|hri|2+k1|hr i|2+k2
,(14)
where =P
σ2,k1=(1−α)σ2
0
3ηαA2
0σ2, and k2=1−α
3ηαA2
0. After applying
selection combining technique at Si, the end-to-end instanta-
neous received SNR at the ith source is γi=max{γji, γri }
with i, j ∈ {c, d},i6=j.
III. PERFORMANCE ANALYSIS
In this section, system OP, system throughput, and energy
efficiency of the considered TWR network are derived.
A. Outage Probability
In the considered system, outage will occur when either the
transmission rate rcfrom Sc→Sdor the transmission rate rd
from Sd→Scis less than a predefined threshold rth.
Pout =Pr(min(rc, rd)< rth)
=Pr(min(γc, γd)< γth)
=Pr(γcd < γth)(Pr(γrc < γth ) + Pr(γrd < γth)
−Pr(γrc < γth, γr d < γth)),(15)
where γth = 23rth
1−α−1. Let, X∆
=|hrc|2,Y∆
=|hrd|2, and
Z∆
=|hcd|2, then Pout can be re-expressed as
Pout =Pr(Z < γth
)
| {z }
P1
Pr(Y < γth
(2 + k1+k2
X))
| {z }
P2
+Pr(X < γth
(2 + k1+k2
Y))
| {z }
P3
−Pr(Y < γth
(2 + k1+k2
X), X < γth
(2 + k1+k2
Y)
| {z }
P4

=P1(P2+P3−P4).(16)
Closed-form expressions of P1,P2,P3, and P4are given in
the following lemmas.
Lemma 1: The closed-form expression of P1is given as
P1=1
Γ(ma)γma,maγth
Ωa.(17)
Lemma 2: The closed-form expression of P2is given as
P2= 1 −Ψ1mdΩck2γth
mcΩdmc−p2
2
e−md(2+k1)γth
Ωd
×Kmc−p2(C1√γth),(18)
where C1= 2qmcmdk2
ΩcΩdand Ψ1=
Pmd−1
p1=0 Pp1
p2=0 p1
p2(mc
Ωc)mc(mdγth
Ωd)p12kp2
2(2+k1)p1−p2
p1!Γ(mc).
P roof :See Appendix A.
Lemma 3: The closed-form expression of P3is given as
P3= 1 −Ψ2mcΩdk2γth
mdΩcmd−p4
2
e−mc(2+k1)γth
Ωc
×Kmd−p4(C1√γth),(19)
where Ψ2=Pmc−1
p3=0 Pp3
p4=0 p3
p4(md
Ωd)md(mcγth
Ωc)p32kp4
2(2+k1)p3−p4
p3!Γ(md).
Lemma 4: The closed-form expression of P4can be ex-
pressed either as P1
4or as P2
4, where P1
4represents the
case when l1and l3have no intersection point and P2
4
represents when l1and l3have one intersection point as given
in Appendix B. The term P1
4is expressed as
P1
4=P2+P3−1,(20)
and
P2
4= 1 −Ψ1C2(Cn)mc−p2−1e−(mcCn
Ωc+mdk2γth
ΩdCn)−
md−1
X
p5=0
×mc
Ωcmcmd
Ωdp5C−(mc+p5)
3
p5!Γmc
Γ(mc+p5, C3xin)
−Ψ2C2(Cn)md−p4−1e−(mdCn
Ωd+mck2γth
ΩcCn)−
mc−1
X
p6=0
×mc
Ωcp5md
ΩdmdC−(md+p5)
3
p5!Γ(md)Γ(md+p5, C3xin),
(21)
where C2=πxin
2NPN
n=1 p1−v2
n,vn=Cos((2n−1)π
2N),
Cn=xinvn
2+xin
2,xin =(2+k1)γth+√((2+k1)γth )2+4k2γth
2,
and C3=mc
Ωc+md
Ωd.
P roof :See Appendix B.
B. System Throughput
Throughput is an important parameter to find the spectrum
utilization. By utilizing OP expression derived in (16), system
throughput can be defined as
τ=(1 −α)
3[(1 −Pout)rth ].(22)
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C. System Energy Efficiency
System energy efficiency (EE) is defined as the total data
transferred to the total consumed power. EE of the considered
network can be defined as [9]
ηEE =(1 −α)τ
(1 + 2α)(Pc+Pd).(23)
IV. SIMULATION AND NUMERICAL RESULTS
In this section, simulation results are presented to validate
the derived analytical results and to investigate the impact of
system parameters on the considered network. We consider a
linear relay model, where Scand Sdare located unity distance
apart and Ris located at a distance xfrom Sc. By utilizing the
path-loss model, we set Ωc=x−nand Ωd= (1−x)−n, where
n= 3 is the path-loss exponent. Fading severity parameter mc,
md, and maare represented as {mc, md, ma}in the figures.
We consider that η= 0.9,α= 0.2,T= 1 sec, and N= 8
[10].
In Fig. 2, the impact of various NLPAs on the system OP
is shown. For SEL NLPA incorporated R, system performs
relatively better among all NLPAs. Henceforth, for results
shown in Fig. 3, Fig. 4, and Fig. 5NLPA refers to SEL
NLPA. The performance of the system is better when R
is incorporated with LPA whereas performance is degraded
with NLPA because NLPA introduces NLD in the system.
We also observed that the system performance improves
when the network is incorporated with Ras compared with
direct transmission. The simulation results overlap with the
numerical results which validate the derivations.
Fig. 3, depicts the impact of various system parameters
on the performance of the considered network. System OP
improves with an increase in severity parameter because the
channel condition improves with an increase in fading severity.
System OP degrades with an increase in α, because less time
is allocated for IT. The amount of harvested energy increases
with ηwhich results in improved system OP.
0 5 10 15 20 25 30
SNR ( dB )
10-4
10-3
10-2
10-1
100
System Outage Probability
Direct Transmission
TWTA NLPA
SSPA NLPA
SEL NLPA
LPA
Simulation
Fig. 2: System outage probability versus SNR.
System throughput versus SNR is shown in Fig. 4. The
system throughput improves with SNR up to a specific SNR
(≈20 dB for rth = 0.5bps/Hz and ≈26dB for rth = 1
0 5 10 15 20 25 30
SNR ( dB )
10-6
10-5
10-4
10-3
10-2
10-1
100
System Outage Probability
= 0.2, = 0.5, NLPA
= 0.2, = 0.5, NLPA
= 0.2, = 0.5, NLPA
= 0.2, = 0.2, NLPA
= 0.9, = 0.2, NLPA
= 0.9, = 0.2, NLPA
= 0.2, = 0.5, LPA
= 0.2, = 0.5, LPA
= 0.2, = 0.5, LPA
= 0.2, = 0.2, LPA
= 0.9, = 0.2, LPA
= 0.9, = 0.2, LPA
Simulation
rth= 0.5 bps/Hz
{1,1,2}
{1,1,1}
rth= 2 bps/Hz
rth= 1 bps/Hz
Fig. 3: Impact of various parameters on system OP.
0 5 10 15 20 25 30
SNR ( dB )
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
System Throughput
rth= 1, = 0.2, NLPA
rth= 0.5, = 0.2, NLPA
rth= 0.5, = 0.5, NLPA
rth= 1, = 0.2, LPA
rth= 0.5, = 0.2, LPA
rth= 0.5, = 0.5, LPA
Simulation
Fig. 4: System throughput versus SNR.
0 5 10 15 20 25 30
SNR ( dB )
0
0.05
0.1
0.15
0.2
0.25
Energy Efficiency
rth= 1, NLPA
rth= 1.5, NLPA
rth= 2, NLPA
rth= 1, LPA
rth= 1.5, LPA
rth= 2, LPA
Fig. 5: Energy efficiency versus SNR.
bps/Hz) and then attains saturation. The saturation value rep-
resents the maximum attainable throughput of the considered
network for a fixed rth. We observe that a higher value of
the target rate attains saturation at a higher value of SNR
because, at a fixed SNR, a higher target rate exhibits poor
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OP performance.
Fig. 5, shows EE of the system versus SNR, by setting the
fading severity parameters as {2,2,2},α= 0.1, and η= 0.9.
The system shows maximum EE at a particular value of SNR
for a fixed rth. When rth changes the corresponding value of
SNR also changes for which the system exhibits maximum
EE. We also observed that at high SNR, the EE of the system
degrades because the power consumed by the system is more
than the system throughput.
V. CONCLUSION
Performance of a TS-SWIPT enabled AF-TWR network
with NLPA is analyzed over Nakagami-mfading channels. For
this, we derived the closed-form expressions of system OP and
also system throughput and energy efficiency are investigated.
We found that the performance of the system is better when
relay node is incorporated with SEL NLPA model. Finally, the
impact of various NLPAs, fading severity, and various system
parameters on the system performance are illustrated.
APPENDIX A
Since, we have considered Nakagami-mfading channel,
random variables X,Y, and Zfollow Gamma distribution
with PDF fW(w)=(mi
Ωi)miwmi−1
Γ(mi)e−miw
Ωi, w ≥0, with
W∈ {X, Y, Z},w∈ {x, y, z }, and i∈ {c, d, a}.
P2=Pr(Y < γth
(2 + k1+k2
X))
=Z∞
0Zγth
(2+k1+k2
x)
0
fX(x)fY(y)dydx. (24)
By substituting the PDFs of fX(x)and fY(y)in (24) and
evaluating the integration with the help of [17, 3.471.9], we
get the expression of P2as given in (18).
APPENDIX B
Since P4=Pr(Y < δa, X < δb), where δa=γth
(2 + k1+
k2
X)and δb=γth
(2 + k1+k2
Y). There is a high correlation
between δaand δb, so it is difficult to obtain P4directly. We
obtain the closed-form expression of P4on the basis of integral
region. We consider X=xand Y=ythen integral region
of P4is bounded by lines l1:y=P(x)and l2:x=P(y),
where P(x) = γth
(2+k1+k2
x)and P(y) = γth
(2+k1+k2
y).
In addition, we consider line l3as y=x. On the basis of
intersection points between l1and l3, there are two possibilities
for P4as P1
4and P2
4.
i): When curves l1and l3have no intersection point, then
l1and l2also don’t have intersection point. Hence, P1
4can be
derived as
P1
4= 1 −Z∞
0Z∞
P(x)
fX(x)fY(y)dydx
−Z∞
0Z∞
P(y)
fY(y)fX(x)dxdy. (25)
Its derivation is similar to P2and P3hence, we get the
expression of P1
4as given in (20).
ii): When l1and l3have only one intersection point, then
by solving l1=l2, we get a quadratic function and consider
that one positive real root exist. Intersection point between l1
and l3are obtained by equating l1=l3which gives xin. The
expression of P2
4is evaluated as
P2
4= 1 −Zxin
0Z∞
P(x)
fX(x)fY(y)dydx −Z∞
xin Z∞
x
fX(x)
×fY(y)dydx −Zxin
0Z∞
P(y)
fY(y)fX(x)dxdy
−Z∞
xin Z∞
y
fY(y)fX(x)dxdy. (26)
By using Gaussian-Chebyshev quadrature approximation [10]
and with the help of [17, 3.381.1], we obtain the expression
of P2
4as given in (21).
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