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10018 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 70, NO. 10, OCTOBER 2021
ASER Analysis of Hybrid Receiver Based SWIPT
Two-Way Relay Network
Deepak Kumar , Praveen Kumar Singya , and Vimal Bhatia , Senior Member, IEEE
Abstract—In this paper, we investigate the performance of a hy-
brid receiver-based simultaneous wireless information and power
transfer (SWIPT) two-way relay network over Nakagami-mfaded
channels. A hybrid receiver is adopted at the relay node that utilizes
both the time switching (TS) and power splitting (PS) protocols
for energy harvesting and information transmission. Amplify-and-
forward relaying protocol is utilized at the relay node to process
the information in half-duplex mode. In the considered network,
impact of a practical non-linear power amplifier (NLPA) at the
relay node is considered. Selection combining is performed at the
destination node to utilize the direct-link and relay assisted signals.
For the considered system, the analytical expressions of outage
probability (OP) and asymptotic OP are derived over Nakagami-m
faded channels for both the integer and non-integer value of m.
The analytical expression of the system throughput and energy
efficiency of the considered network are also derived. Further, the
analytical expression of ergodic capacity is derived in terms of the
Meijer-G function. By utilizing a cumulative distribution function
based approach, analytical expressions of average symbol error
rate (ASER) for general order hexagonal quadrature amplitude
modulation (QAM), general order rectangular QAM, and 32-cross
QAM schemes are derived. For different QAM constellations,
a comparative ASER analysis is also illustrated. Furthermore,
the impact of TS factor, PS ratio, energy conversion efficiency,
NLPA, and threshold data-rates on the considered network is also
highlighted. Finally, Monte-Carlo simulations are performed for
validation of the derived analytical expressions.
Index Terms—Two-way relay, non-linear PA, SWIPT, ASER,
QAM, Nakagami-mfading.
I. INTRODUCTION
COOPERATIVE communication has attracted significant
attention both from academic and industrial researchers
due to its capability of extending coverage, enhancing spectral
efficiency, and gain in diversity at low cost [1]. In cooperative
communication, the two-way relaying (TWR) technique pro-
vides bidirectional information exchange between two users [2],
where two-phase (2P) TWR and three-phase (3P) TWR net-
works have been deliberated in the literature [3]–[5]. However,
Manuscript received February 9, 2021; revised May 27, 2021; accepted July
4, 2021. Date of publication July 14, 2021; date of current version October 15,
2021. This work was supported by the Ministry of Electronics and Information
Technology (MietY). The review of this article was coordinated by Prof. Daniel
Benevides da Costa. (Corresponding author: Deepak Kumar.)
Deepak Kumar and Vimal Bhatia are with the Department of Electrical En-
gineering, Indian Institute of Technology Indore, Indore 453552, India (e-mail:
phd1901102017@iiti.ac.in; vbhatia@iiti.ac.in).
Praveen Kumar Singya is with the CEMSE Division, King Abdullah Uni-
versity of Science and Technology, Thuwal 23955, Saudi Arabia (e-mail:
praveen.singya@kaust.edu.sa).
Digital Object Identifier 10.1109/TVT.2021.3096833
3P-TWR provides better diversity gain as compared to 2P-TWR
which provides better spectral efficiency [5]. Hence, 3P-TWR is
considered in this work. In wireless communication networks,
the limited lifespan of a battery is a major issue for increasing
coverage in hard to reach areas where grid power is not available,
energy harvesting (EH) and especially, simultaneous wireless
information and power transfer (SWIPT) has come out as a
favorable technology [6]. The time switching (TS) and power
splitting (PS) based receiver architectures are commonly used at
the relay for EH and information transmission (IT) [7]. For TS,
the received signal is switched between EH and IT periodically,
whereas in case of PS, a fraction of the received power is intended
for EH and IT. In [8], an optimal value of TS factor and PS
ratio are numerically determined for a delay-limited (DL) relay
network. In [9], the secrecy rate and throughput of an unmanned
aerial vehicle aided non-orthogonal multiple access network are
investigated by using PS at the passive receiver. Zhao et al.
[10] investigated a novel artificial noise assisted interference
alignment scheme with wireless power transfer to exploit the
benefit from the artificial noise and interference among users.
In literature [11]–[13], hybrid receiver-based SWIPT relay net-
works which combine both TS and PS are studied. The hybrid
receiver is most suitable, since it can operate as TS, PS, or
hybrid receivers for best performance. In [11], to maximize
the throughput of a DL relay network, optimal values of TS
factor and PS ratio for a hybrid receiver are investigated. Yuan
et al. [12] investigated that a hybrid receiver-based SWIPT relay
network outperforms both TS and PS in terms of outage proba-
bility (OP). An improved hybrid relaying protocol is introduced
in [13], and observed that it performs better as compared to
the TS, and PS receivers in terms of system capacity. In [14],
Men et al. studied the joint optimization problem for relay
selection and power allocation for a SWIPT-enabled amplify-
and-forward (AF) TWR network. In [15], optimization of PS
ratio and relay processing matrix for an AF TWR network is
performed. In [16], resource allocation for a decode-and-forward
(DF) TWR network is investigated to obtain optimal OP, while
both the TS and PS at the relay node are considered. To obtain
the maximum achievable sum-rate for a DF TWR network, an
optimal value of PS ratio is obtained in [17]. In [18], [19],
the performance of a SWIPT-enabled 3P-TWR network for AF
and DF protocols is studied. In [18], the performance of a TS
based AF TWR network is investigated under three different
power transfer policies namely: a) dual source power transfer,
b) single-fixed-source power transfer, and c) single-best-source
power transfer. The analytical expressions of OP, throughput,
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KUMAR et al.: ASER ANALYSIS OF HYBRID RECEIVER BASED SWIPT TWO-WAY RELAY NETWORK 10019
and system energy efficiency are derived over Rayleigh faded
channels. Van et al. [19] derived the analytical expression of OP
for a DF 3P-TWR network. In [20], the performance of a hybrid
decode-amplify-forward 3P-TWR network is investigated in
terms of OP and system throughput. Solanki et al. [21] studied
the impact of transceiver hardware impairments on 3P-TWR
network and demonstrated useful insights for transceiver design.
In [22], OP and throughput of a full-duplex (FD) wireless
powered relay network with TS and PS are obtained. Recently,
system OP of a PS SWIPT receiver for an AF TWR network
over Nakagami-mfaded channels is derived in [23].
In practice, the exponential rise in multimedia applications for
5G and beyond demands high bandwidth which makes it difficult
to design a linear power amplifier (PA). Since high PA introduces
non-linear distortion (NLD) that severely reduces the quality of
the amplified signal [24]. Hence, the impact of non-linear PA
(NLPA) on the system performance is an important parameter
for system design. In the literature [25]–[29], the effect of NLPA
is studied for the relay networks. Balti et al. [25] investigated
the impact of NLD on the performance of a multi-relay network
with opportunistic relay selection strategy over the Rayleigh
faded channels. In [26], the performance of a multi-relay AF
orthogonal frequency division multiplexing (OFDM) system
is analyzed in terms of OP by adopting NLPA at the relays.
Simmon et. al. [27] derived analytical expression of OP for fixed
and variable gain non-linear AF TWR network over Rayleigh
faded channels. In [28], the impact of imperfect channel state
information (CSI) and NLPA on the performance of 3P-analog
network coding two-way multi-relay system over Nakagami-m
faded channels is observed. In [29], the impact of NLPA on the
performance of a TS based SWIPT 3P-TWR is observed over
Nakagami-mfaded channels.
On the other hand, for 5G and beyond, a power-efficient
high speed wireless communication system can be designed by
reducing the average transmit power at a specified bit error rate
(BER) or symbol error rate (SER). The adaptive modulation
offers spectrally efficient high data-rates by utilizing optimum
power [30]. The spectrally efficient higher-order modulation
schemes such as the family of quadrature amplitude modulations
(QAMs) (i.e. rectangular QAM (RQAM), cross QAM (XQAM),
and hexagonal QAM (HQAM)) have attracted significant atten-
tion due to their high power and bandwidth efficiency. RQAM
scheme is frequently used due to its versatile nature as various
modulation schemes are its special cases [31]. RQAM is com-
monly used in applications such as microwave communication,
high data-rate mobile communication, asymmetric subscriber
loop, etc [32]. However, due to improved power efficiency and
lower peak-to-average-power ratio (PAPR), XQAM is preferred
over RQAM for odd power of 2 constellations [31]. XQAM
is adopted in practical applications such as in very high bit-rate
digital subscriber line (VDSL) and asymmetric digital subscriber
line (ADSL) [33]. Further, the demand of high data-rates led
to emergence of an optimum two-dimensional (2D) hexagonal
shaped constellation called HQAM. HQAM comprises densest
2D packing for a given optimum Euclidean distance between
the constellation points (CPs) which provides better power effi-
ciency with lower PAPR as constellation size (M) increases.
Hence, the BER/SER performance of the HQAM scheme is
better as compared to the other QAM schemes [34].
The average SER (ASER) performance of various QAM
schemes (specially HQAM) is studied in the literature [34]–[38].
In [35], analytical ASER expressions of HQAM and RQAM are
derived for AF multi-relay network over Nakagami-mfaded
channels. The impact of NLPA and channel estimation error on
the ASER performance of a multi-relay network are depicted
in [38] over Nakagami-mfaded channels with both the integer
and non-integer fading parameters, and the analytical ASER ex-
pressions of HQAM, RQAM, and XQAM schemes are derived.
Motivated with the above-mentioned literature and to utilize
the advantages of both the TS and PS for future wireless commu-
nication systems, in this paper, a hybrid receiver-based SWIPT
AF 3P-TWR network is considered wherein the SWIPT-enabled
relay node harvests energy from the received RF signals and
utilizes the harvested power for signal transmission. We have
considered a practical scenario where the system suffers from
the NLD caused due to NLPA employed at the relay node. The
selection combining (SC) scheme is less complex and provides
same diversity as compared to the maximal ratio combining
(MRC) scheme. Hence, we have applied SC scheme at the
receiver node to make use of both the relayed and direct link
signals. To the best of authors’ knowledge, for the considered
network, OP and asymptotic OP for non-integer values of m,
ergodic capacity, and ASER analysis of different QAM schemes
over generalized Nakagami-mfaded channels with a practical
NLPA at the relay are not available in the literature. In summary,
major contributions of the paper are:
rAnalytical expression of OP is derived for a hy-
brid receiver1based SWIPT AF 3P-TWR network over
Nakagami-mfaded channels for both the integer and
non-integer values of m. The presence of a direct link2
is also considered. Further, the impact of TS, PS, fading
parameter, threshold data-rate, and NLPA are observed on
the outage performance.
rAnalytical expression of asymptotic OP is derived over
Nakagami-mfaded channels for both the integer and non-
integer values of mby using high SNR approximation and
with this, the diversity order of the considered network is
evaluated.
rSystem throughput (ST) and energy efficiency (EE) are also
examined for the considered network and useful insights
are drawn.
rErgodic capacity (EC) of the considered network is derived
in terms of the Meijer-G function. Further, the impact of
fading parameter, TS, PS, and NLPA are observed on it.
1Hybrid receiver based SWIPT includes both the TS and PS receiversproperty
and improves the performance of the system.
2Since the range of wireless power transfer is typically very small, the presence
of direct link in SWIPT-enabled network is considerable.
Notations: fW(·)and FW(·)represent the probability density function
(PDF) and cumulative distribution function (CDF) of a random variable W,
respectively. Pr[·],Γ(·),Υ(·,·),andΓ(·,·)represent probability, complete
gamma function, lower incomplete gamma function, and upper incomplete
gamma function, respectively. Kl(·)denotes the lth order modified Bessel
function of second kind [39, (8.432.1)] and Wm,n(·)denotes the Whittaker
function [39, (9.222)]. 1F1(a;b;z)represents the generalized hypergeometric
series [39, (9.14.1)].
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10020 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 70, NO. 10, OCTOBER 2021
Fig. 1. (a) System model, (b) Frame structure of hybrid receiver based SWIPT.
rFinally, the analytical expressions of ASER for the gen-
eral order RQAM, general order HQAM and 32-XQAM
are derived by using CDF based approach. The impact
of system parameters on the ASER analysis are investi-
gated. Thereafter, a comparative analysis of ASER among
RQAM, HQAM, and XQAM is presented.
The paper is organized as follows: in Section II, we present
the considered system model, after that the EH and IT-phases
are described. The performance of the considered network is
assessed by analyzing OP, asymptotic OP, ST, EE, EC, and
ASER in Section III. In Section IV numerical and simulation
results are presented. Conclusions are drawn in Section V.
II. SYSTEM MODEL
In this paper, we consider a 3P-TWR network as shown in
Fig. 1(a), where two source nodes Scand Sdexchange their
information with each other via SWIPT-enabled relay node R.A
direct link between Scand Sdis also considered for information
exchange. Further, it is considered that all the participating nodes
are equipped with a single antenna and operate in half-duplex
mode. A hybrid receiver-based SWIPT (which includes both TS
and PS) is used at Rfor EH and IT.The battery-enabled Rutilizes
the harvested power for information transmission while source
nodes Scand Sdare connected with a dedicated power supply.
The overall EH and bidirectional information exchange between
Scand Sdare executed in four-time slots as shown in Fig. 1(b). In
the first slot, Rharvests energy using TS whereas, PS is utilized
for the same in the second and third slots, respectively. In TS, the
received signal switches between EH and IT in αT :(1−α)T
proportion, respectively, where 0 <α<1 is a time switching
factor and Tdenotes the transmission block duration. However,
the PS splits the received power into β:(1−β)proportion for
EH and IT in the second and third slot, respectively, where 0 <
β<1 is the power splitting ratio. The bidirectional information
exchange between Scand Sdoccurs in three IT phases. During
IT Phase-I (second slot), Sctransmits the signal to R, whereas,
in the IT Phase-II (third slot), Sdtransmits its signal to R.R
amplifies the received signals in IT Phase-I and IT Phase-II after
that it is passed through the NLPA. In IT Phase-III (fourth slot), R
transmits the information to Scand Sdby utilizing the harvested
power stored in the battery.
We consider that all the channels follow reciprocity, quasi-
static, and subjected to independent and non-identically dis-
tributed Nakagami-mfading. The channel coefficients for the
links Si→Sjand Si→Rare denoted as hij and hir, respec-
tively, with i, j ∈{c, d},i=j. Here, hij and hir are Nakagami-
mfaded channels having maand mias severity parameters, and
Ωaand Ωias average powers, respectively.
A. Energy Harvesting
We adopt a hybrid-receiver based SWIPT at Rwhich harvests
energy from the received radio frequency (RF) signals Scand Sd
by utilizing both TS and PS. As depicted in Fig. 1(b), Rharvests
energy for αT duration through RF signals Scand Sdin the first
slot by using TS. In general, the harvested energy is non-linear
with respect to the received RF power [40]. However, there is no
generic EH model in the literature that includes all the practical
constraints [41]. Therefore, a linear EH model is considered for
simplicity. The amount of harvested energy at Rduring the first
slot can be given as [21], [29]
ETS
h=ηαT(Pc|hcr |2+Pd|hdr |2),(1)
where ηdenotes the energy conversion efficiency of EH circuit
(0<η≤1), and Pcand Pddenote the transmit power at Sc
and Sd, respectively. Note that we have ignored the noise power
in (1) due to its low strength [20], [21], [29]. In the second
slot, Rharvests energy from the RF signal received from Scfor
(1−α)T/3 duration by using PS. Similarly, in the third slot
of (1−α)T/3 duration, Rharvests energy from the RF signal
received from Sdby using PS. The amount of harvested energy
at Rduring the second and the third slots can be obtained as [23]
EPS
h=(1−α)T
3ηβ(Pc|hcr |2+Pd|hdr|2).(2)
Therefore, the overall harvested energy for one transmission
block duration Tcan be given as
Eh=ETS
h+EPS
h
=(3α+(1−α)β)T
3η(Pc|hcr|2+Pd|hdr |2).(3)
By utilizing (3), the transmit power3at Rcan be given as
Pr=δ(Pc|hcr|2+Pd|hdr |2),(4)
where δ=(η(3α+(1−α)β))/(1−α).
B. Information Transmission
In the IT Phase-I, let Sctransmits a unit energy symbol
xc, then the signal received at Sdand Rcan be given ycd =
√Pchcdxc+ndand ycr =(1−β)Pchcr xc+(1−β)nr,
respectively, where nd∼CN(0,σ
2
d)and nr∼CN(0,σ
2
r)are
the additive white Gaussian noises (AWGNs) at Sdand R,
3Note that we have considered that power required by transmit/receive cir-
cuitry at Rto process the information is negligible as compared to the power
required for signal transmission [8], [21].
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KUMAR et al.: ASER ANALYSIS OF HYBRID RECEIVER BASED SWIPT TWO-WAY RELAY NETWORK 10021
respectively. The corresponding SNRs at Sdand Rare γcd =
Pc|hcd|2
σ2
d
and γcr =Pc|hcr|2
σ2
r, respectively. Similarly, in the IT
Phase-II, Sdtransmits unit energy symbol xd, then the signal re-
ceived at Scand Rare expressed as ydc =√Pdhdcxd+ncand
ydr =(1−β)Pdhdrxd+(1−β)nr, respectively, where
nc∼CN(0,σ
2
c)is the AWGN at Sc. The corresponding SNRs
at Scand Rare γdc =Pd|hdc|2
σ2
cand γdr =Pd|hdr|2
σ2
r, respectively.
Rcombines signals received in IT Phase-I and IT Phase-II,
and then amplifies the combined signal by using AF relay-
ing which can be given as yAF
r=G(ycr +ydr), where G=
Pr
(1−β)(Pc|hcr|2+Pd|hdr |2+2σ2
r)is the amplification gain. Fur-
ther, we consider an NLPA at Rwhich can be designed as
a memoryless or frequency-independent function [25]. As per
the Bussgang linearization theory, output of an NLPA can be
expressed in terms of a linear scale parameter A0and an NLD
NDwhich is uncorrelated with the applied signal [25]–[29].
Hence, output of the NLPA can be expressed as
yNLPA
r=A0yAF
r+ND,(5)
where A0is a constant and ND∼CN(0,σ
2
ND). For soft enve-
lope limitter, the expressions for A0and σ2
NDare given as [28],
[29]
A0=1−exp −A2
sat
Pr+√πAsat
2√Pr
erfc Asat
√Pr,
σ2
ND=Pr1−exp −A2
sat
Pr−|A0|2,(6)
where erfc(·) and Asat represent the complementary error func-
tion and saturation amplitude of NLPA, respectively. Thereafter,
Rbroadcasts the signal in IT Phase-III by utilizing the harvested
power. Thus, the signal received at node Sican be given as
yri =hriyNLPA
r+ni,
=hri(A0G((1−β)Pchcr xc+(1−β)Pdhdrxd
+(1−β)ˆnr)+ND)+ni,(7)
where ˆnr∼CN(0,2σ2
r)and ni∼CN(0,σ
2
i)are the AWGNs
at Rand Si, respectively, with i∈{c, d}. Since Siknows its own
transmitted signal, Sican perfectly remove the self-interference
term. After canceling the self-interference term from (7) and
considering the approximation (1−β)(Pc|hcr|2+Pd|hdr |2+
2σ2
r)≈(1−β)(Pc|hcr|2+Pd|hdr |2),4the SNR at Sican be
4The considered approximation provides accurate results for entire SNR
range, which is demonstrated in Section IV.
given as
γri =r|hri|2|hjr|2
2|hri|2+C1|hri|2+C2
,(8)
where r=Pj
σ2
r,C1=σ2
ND
δA2
0σ2
r, and C2=σ2
i
δA2
0σ2
r, with i, j ∈
{c, d},i=j.
III. PERFORMANCE ANALYSIS
In this Section, we derive the analytical expression of OP
for the considered hybrid receiver-based SWIPT 3P-TWR net-
work over Nakagami-mfaded channels for both the integer and
non-integer values of m. Then, the analytical expression of the
asymptotic OP is derived for both the integer and non-integer
values of mand the diversity order of the considered network is
obtained. Further, the ST and EE of the considered system are
formulated with the help of derived OP expression. After that,
an analytical expression of ergodic capacity is derived in terms
of the Meijer-G function. Finally, the analytical expressions
of ASER are derived for general order RQAM, general order
HQAM, and 32-XQAM.
A. Outage Probability
For a delay-limited transmission, OP is a crucial performance
metric which is defined as the link failure probability. For the
considered hybrid receiver-based SWIPT 3P-TWR network, Si
will be in outage if the instantaneous data-rate falls below a
pre-defined threshold data-rate rth. Since the destination node
receives the signal from the relay and direct links, SC is em-
ployed to select a signal corresponding to maximum SNR.
Therefore, the instantaneous data-rate at the destination node
Sican be given as
RSC,i =((1−α)/3)log2(1+max(γri,γ
ji)).(9)
We have considered more general case of Nakagami-mfading,
where mcan be an integer and non-integer.
1) Integer Value of Fading Parameter: For integer valued
fading parameter m, OP at node Sican be given as
Pout,i(γth )=Pr[RSC,i <r
th],
=Pr[max(γr,i ,γ
j,i)<γ
th],
=Pr[γr,i <γ
th]Pr[γj,i <γ
th],
=Fγri (γth)Fγji (γth ),(10)
where γth =23rth
1−α−1. The CDF expression Fγri(γth )is given
in (11), as shown at the bottom of this page.
P roof :See Appendix A.
Further, Fγji(γth)is given in the lemma 1.
Fγri (γth)=1−
mi−1
p1=0
mj−1
p2=0mj−1
p2mi
Ωip1mj
Ωjmj(C2)p1(2+C1)mj−p2−1
p1!Γ(mj)mj
r
e−mj(2+C1)γth
Ωjr
×γ
2mj+p1−p2−1
2
th 2miΩjrC2
mjΩi
p2−p1+1
2
Kp2−p1+12mimjC2γth
ΩiΩjr(11)
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10022 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 70, NO. 10, OCTOBER 2021
Lemma 1: The CDF expression Fγji (γth)is obtained as
Fγji(γth )=Pr|hji|2<γth
i,
=1−
ma−1
p3=0
1
p3!ma
Ωaip3
γp3
the−maγth
Ωai,(12)
where i=Pj
σ2
i
. By substituting (11) and (12) in (10), we obtain
the analytical expression of OP at Sifor integer value of m.
2) Non-Integer Value of Fading Parameter: For non-integer
valued fading parameter m, OP at node Sican be given as
Pout,i(γth )=F
γri (γth)F
γji(γth ).(13)
The CDF expression F
γri (γth)is given in (14), as shown at the
bottom of this page.
P roof :See Appendix B.
Further, F
γji(γth )is given in the lemma 2.
Lemma 2: The CDF expression F
γji(γth )is given as
F
γji(γth )=e−maγth
Ωai
∞
g4=0
1
Γ(ma+g4+1)maγth
Ωaima+g4
.
(15)
By substituting (14) and (15) in (13), we obtain the analytical
expression of OP at Sifor non-integer value of m.
B. Asymptotic Outage Probability
To obtain the diversity order of the considered network,
asymptotic analysis is performed at high SNR. For this, OP is ap-
proximated using high SNR approximation of Υ(a, y)≈
y→0(ya
a)
[28].
1) Integer Value of Fading Parameter: The asymptotic OP
for integer value of fading parameter mis obtained by utilizing
(10). The asymptotic OP at node Sican be given as
Pasym
out,i (γth)≈Fasym
γri (γth)Fasym
γji (γth).(16)
By utilizing high SNR approximation in (41), the CDF
Fasym
γri (γth)is expressed in (17), as shown at the bottom of
this page. Further, Fasym
γji (γth)can be approximated as
Fasym
γji (γth)≈1
maΓ(ma)maγth
Ωaima
.(18)
Invoking (17) and (18) in (16), we obtain the analytical expres-
sion of asymptotic OP (19), as shown at the bottom of this page.
The diversity order of the considered network is obtained from
(19), which can be given as [min(ma+mj,m
a+2mi+mj)].
2) Non-Integer Value of Fading Parameter: The asymptotic
OP for non-integer value of fading parameter mis obtained by
utilizing (13). The asymptotic OP at node Sican be given as
Pasym
out,i (γth)≈Fasym
γri (γth)Fasym
γji (γth).(20)
By utilizing high SNR approximation in (43), the CDF
Fasym
γri (γth)is expressed in (21), as shown at the bottom of
the next page. Further, Fasym
γji (γth)can be approximated as
Fasym
γji (γth)≈1
maΓ(ma)maγth
Ωaima
.(22)
F
γri (γth)= ∞
g1=0
1
Γ(mj+g1+1)mjγth(2+C1)
Ωjrmj+g1
+∞
g2=0
∞
g3=0mj−1
g3mj
ΩjmjmiC2
Ωimi+g2
×(2+C1)mj−g3−1
Γ(mj)Γ(mi+g2+1)mj
r
e−mjγth(2+C1)
Ωjrγ
mi+2mj+g2−g3−1
2
th 2miC2Ωjr
mjΩi
g3−g2−mi+1
2
×K
g3−g2−mi+12mimjC2γth
ΩiΩjr(14)
Fasym
γri (γth)≈1
mjΓ(mj)mjγth(2+C1)
Ωjrmj
+
mj−1
p4=0mj−1
p4mj
Ωjmi+mj−p4−1miC2
Ωimi
×(2+C1)mj−p4−1Γ(−mi+p4+1)
miΓ(mi)Γ(mj)mi+mj−p4−1
r
e−mjγth(2+C1)
Ωjrγmi+mj−p4−1
th (17)
Pasym
out,i (γth)≈γma+mj
th
mamjΓ(ma)Γ(mj)ma
Ωaimamj(2+C1)
Ωjrmj
+
mj−1
p4=0mj−1
p4miC2
Ωimima
Ωaima
×mj
Ωjmi+mj−p4−1(2+C1)mj−p4−1Γ(−mi+p4+1)
mamiΓ(ma)Γ(mi)Γ(mj)mi+mj−p4−1
r
e−mjγth(2+C1)
Ωjrγmi+mj+ma−p4−1
th (19)
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KUMAR et al.: ASER ANALYSIS OF HYBRID RECEIVER BASED SWIPT TWO-WAY RELAY NETWORK 10023
Invoking (21) and (22) in (20), we obtain the analytical expres-
sion of asymptotic OP (23), as shown at the bottom of this page.
The diversity order of the considered network is obtained from
(23), which can be given as [min(ma+mj,m
a+2mi+mj)].
C. System Throughput
ST of the considered network is defined as the summation of
the individual threshold data-rates achieved successfully at both
the Scand Sd. For performance analysis, ST is a key parameter
that describes the spectrum utilization. By utilizing the derived
analytical OP expression (10), ST can be given as
τ=(1−α)
3[(1−P
out,c)rth +(1−P
out,d)rth ].(24)
D. Energy Efficiency
EE is an important performance parameter in a wireless
network to appreciate a green communication system. EE of the
considered network is defined as the overall data transferred to
the overall consumed energy [18]. For the considered network,
overall data transferred can be measured by ST as defined in (24).
While the overall consumed energy is the sum of the consumed
energy by Scand Sdduring EH, IT Phase-I, and IT Phase-II,
respectively [21]. Thus, for the considered network, EE can be
given as
ηEE =(1−α)[(1−P
out,c)rth +(1−P
out,d)rth ]
(1+2α)(Pc+Pd).(25)
E. Ergodic Capacity
EC quantifies the ultimate reliable communication limit over
the faded channels and is measured in bps/Hz. EC is obtained
by averaging the instantaneous capacity over the faded channels.
For the considered network, EC can be calculated by using CDF
based approach as [42], [43]
Ce=1
2 ln(2) ∞
0
1
1+γ(1−P
out,c(γ))dγ
+1
2 ln(2) ∞
0
1
1+γ(1−P
out,d(γ))dγ. (26)
For simplicity it is considered that Scand Sdhave similar
parameters then we have Pout,c(γ)=Pout,d(γ). Hence, (26)
can be expressed as
Ce=2
2 ln(2) ∞
0
1
1+γ(1−P
out,i(γ))dγ. (27)
Representing 1
1+γin terms of Meijer-G function by using the
identity 1
1+γ=G1,1
1,1[γ|0
0], substituting Pout,i(γ)from (10) in
(27), and using [39, (7.813.1)] and [44, (07.34.21.0093.01)],
we obtain the analytical EC expression as shown in (28),
as shown at the bottom of the next page, where Ψ1=
mi−1
p1=0mj−1
p2=0mj−1
p2(mi
Ωi)p1(mj
Ωj)mj2(C2)p1(2+C1)mj−p2−1
p1!Γ(mj)mj
r
(miΩjrC2
mjΩi)p2−p1+1
2,Ψ2=ma−1
p3=0
1
p3!(ma
Ωai)p3,μ1=mj(2+C1)
Ωjr,
μ2=mimjC2
ΩiΩjr,μ3=μ1+ma
Ωai,l1=2mj+p1−p2−1
2, and
l2=p2−p1+1.
F. ASER Analysis
For digital modulation technique, the generalized ASER ex-
pression by using the CDF based approach can be given as [34]
Pe=−∞
0P
s(e|γ)Pout,i(γ)dγ, (29)
where P
s(e|γ)represents the first order derivative of the condi-
tional SEP (Ps(e|γ)) for the received SNR.
1) Rectangular QAM: The generalized expression of con-
ditional SEP for MI×MQ-ary rectangular QAM in AWGN
channel can be given as [32]
PRQAM
s(e|γ)=2[r0Q(g0√γ)(1−2s0Q(h0√γ))
+s0Q(h0√γ)] ,(30)
where r0=1−1
MI,s0=1−1
MQ,g0=
6/((M2
I−1)+(M2
Q−1)),h0=g0, and =dQ/dI
is the ratio of distance between quadrature and in-phase
decision. MIand MQdepict in-phase and quadrature
phase CPs, respectively. Afterwards, substituting Gaussian
Q-function Q(x)=1
2[1−erf(x
√2)], where erf(·) represents the
error function and using [45, (7.1.21)] in (30), the first order
Fasym
γri (γth)≈1
mjΓ(mj)mjγth(2+C1)
Ωjrmj
+∞
g5=0mj−1
g5mj
Ωjmi+mj−g5−1miC2
Ωimi
×(2+C1)mj−g5−1Γ(−mi+g5+1)
miΓ(mi)Γ(mj)mi+mj−g5−1
r
e−mjγth(2+C1)
Ωjrγmi+mj−g5−1
th (21)
Pasym
out,i (γth)≈γma+mj
th
mamjΓ(ma)Γ(mj)ma
Ωaimamj(2+C1)
Ωjrmj
+∞
g5=0mj−1
g5miC2
Ωimima
Ωdima
×mj
Ωjmi+mj−g5−1(2+C1)mj−g5−1Γ(−mi+g5+1)
mimaΓ(ma)Γ(mi)Γ(mj)mi+mj−g5−1
r
e−mjγth(2+C1)
Ωjrγmi+mj+ma−g5−1
th (23)
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10024 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 70, NO. 10, OCTOBER 2021
derivative of conditional SEP is given as
PRQAM
s(e|γ)= 1
√γg0r0(s0−1)
√2πe−g2
0γ
2+h0(r0−1)s0
√2π
×e−h2
0γ
2−g0h0r0s0
πe−(g2
0+h2
0)γ
2
×1F11;3
2;g2
0γ
2+1F11;3
2;h2
0γ
2.
(31)
Substituting (31) and (10) in (29), and the integrals are solved
by using the series representation of the generalized hyper-
geometric function 1F1(a;b;x)=∞
s1=0
(a)s1
(b)s1s1!(x)s1and [39,
(3.381.1), (6.643.3)]. The analytical expression of ASER
for general order RQAM is obtained which is given in
(32), shown at the bottom of this page, where F(ϕ, χ)=
Γ(ϕ+l2
2+1
2)Γ(ϕ−l2
2+1
2)
2μ2χ−ϕe
μ2
2
2χW−ϕ, l2
2
(μ2
2
χ).
2) Hexagonal QAM: Generalized expression of conditional
SEP for M-ary HQAM scheme in AWGN channel can be given
as [37]
PHQAM
s(e|γ)=μQ(γθ)+2/3μcQ2(2γθ/3)
−2μcQ(γθ)Q(γθ/3),(33)
where θ,μ, and μcfor irregular HQAM (optimum) are given
in [34, TABLE I]. By using [45, (7.1.19), (7.1.21)], the first
order derivative of (33) can be given as
PHQAM
s(e|γ)= 1
√γ1
2θ
2π(μc−μ)e−γθ
2
−μc
3θ
3πe−γθ
3+μc
2θ
6πe−γθ
6
+2μcθ
9πe−2γθ
31F11;3
2;γθ
3
−μcθe−2γθ
3
2√3π1F11;3
2;γθ
2
+1F11;3
2;γθ
6.(34)
By substituting (34) and (10) in (29), and solving the integrals
by using the series representation of the generalized hyperge-
ometric function and [39, (3.381.1), (6.643.3)], we obtain the
analytical expression of ASER for general order HQAM as given
in (35), as shown at the bottom of the next page.
3) Cross QAM: The conditional SEP for 32-XQAM in
AWGN channel can be expressed as [38]
PXQAM
s(e|γ)
=1
826Q(2qγ)+Q(2√qγ)−23Q2(2qγ),(36)
where q=48/(31M−32). By using [45, (7.1.19), (7.1.21)],
the first order derivative of (36) can be given as
PXQAM
s(e|γ)= −3
16 q
2π
e−qγ
√γ−1
8q
2π
e−2qγ
√γ
−23q
8πe−2qγ1F11;3
2;qγ.(37)
Invoking (37) and (10) in (29) and utilizing series repre-
sentation of the generalized hypergeometric function and [39,
(3.381.1), (6.643.3)], we obtain the analytical expression of
ASER for 32-XQAM as given in (38), as shown at the bottom
of the next page.
Ce=2
2ln(2)Ψ2ma
Ωai−(p3+1)
G1,2
2,1Ωai
ma|−p3,0
0+Ψ
1
∞
n=0
(−μ1)n
n!2μ2l1+2n+2
2
G1,3
3,11
μ2
2|1−2l1+l2+2n+2
2,1−2l1−l2+2n+2
2,0
0
−Ψ1Ψ2
∞
h=0
(−μ3)h
h!2μ2l1+2p3+2h+2
2
G1,3
3,11
μ2
2|1−2l1+l2+2p3+2h+2
2,1−2l1−l2+2p3+2h+2
2,0
0 (28)
PRQAM
e=g0r0(s0−1)
√2π−g2
0
2−1
2
Γ1
2+Ψ
1Fl1,μ
1+g2
0
2+Ψ
2g2
0
2+ma
Ωai−(p3+1
2)
Γp3+1
2−Ψ1Ψ2
×Fl1+p3,μ
3+g2
0
2+h0(r0−1)s0
√2π−h2
0
2−1
2
Γ1
2+Ψ
1Fl1,μ
1+h2
0
2+Ψ
2h2
0
2+ma
Ωai−(p3+1
2)
×Γp3+1
2−Ψ1Ψ2Fl1+p3,μ
3+h2
0
2+∞
s1=0
(1)s1
(1.5)s1s1!
g0h0r0s0
πg2
0
22
+h2
0
22g2
0+h2
0
2−(s1+1)
×Γ(s1+1)−Ψ1Fl1+s1+1
2,μ
1+g2
0+h2
0
2−Ψ2ma
Ωai
+g2
0+h2
0
2−(p3+s1+1)
Γp3+s1+1
+Ψ
1Ψ2Fl1+p3+s1+1
2,μ
3+g2
0+h2
0
2 (32)
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KUMAR et al.: ASER ANALYSIS OF HYBRID RECEIVER BASED SWIPT TWO-WAY RELAY NETWORK 10025
IV. SIMULATION AND NUMERICAL RESULTS
In this Section, simulation and numerical results of the OP,
asymptotic OP, ST, EC, and ASER of various QAM schemes
for the considered network are compared. We consider a linear
relaying model where Scand Sdare located unity distance
apart. We follow a path-loss model with Ωc=r−band Ωd=
(1−r)−b, where ris the distance between Scand R, and set
the path-loss exponent b=3 [29]. We also set Pc=Pd=P,
σ2
i=σ2
r=σ2, and P
σ2is defined as the SNR. The fading severity
of Sc→R,Sd→R, and Sc→Sdlinks are denoted as mc,
md, and ma, respectively, and indicated as {mc,m
d,m
a}in the
figures. The infinite series presents in the analytical expression
of OP, asymptotic OP, EC, and ASER are truncated to fixed finite
values to obtain the numerical results. Truncation is performed
to reduce the computational complexity with considerable ac-
curacy. Thus, infinite summations g1,g2,g3,g4,g5,n,h, and
s1are truncated to fixed finite values G1,G2,G3,G4,G5,N,
H, and S1, respectively, and G1=G2=G3=G4=G5=50
and N=H=S1=40 are considered for acceptable compu-
tational complexity with considerable accuracy.
In Fig. 2, simulation and numerical results of OP for TS,
PS, and hybrid receiver are compared for the set of parameters
{1,1,1},η=0.7, and rth =0.5 bps/Hz. For comparison, we
Fig. 2. Outage performance for TS, PS, and hybrid receiver based SWIPT.
have considered the cases studied in [19]–[21], [29] as the bench-
marks. Since [19] has considered Rayleigh faded channels, so we
set {mc,m
d,m
a}={1,1,1}for our system. The considered
hybrid receiver at the relay performs better than both the TS and
PS receivers. For OP of 10−2, the considered hybrid receiver
achieves ≈1.023 dB and ≈2.198 dB SNR gains over TS [20],
[21] and PS [19] receivers, respectively, for LPA. Further, the
PHQAM
e=(μc−μ)
2θ
2π−θ
2−1
2
Γ1
2+Ψ
1Fl1,μ
1+θ
2+Ψ
2ma
Ωai
+θ
2−(p3+1
2)
Γp3+1
2−Ψ1Ψ2
×Fl1+p3,μ
3+θ
2+μc
3θ
3πθ
3−1
2
Γ1
2−Ψ1Fl1,μ
1+θ
3−Ψ2ma
Ωai
+θ
3−(p3+1
2)
×Γp3+1
2+Ψ
1Ψ2Fl1+p3,μ
3+θ
3+μc
2θ
6π−θ
6−1
2
Γ1
2+Ψ
1Fl1,μ
1+θ
6+Ψ
2
×ma
Ωai
+θ
6−(p3+1
2)
Γp3+1
2−Ψ1Ψ2Fl1+p3,μ
3+θ
6+∞
s1=0
(1)s1
(1.5)s1s1!
×2μcθ
9πθ
3s1
−μcθ
2√3πθ
2s1
+θ
6s1−2θ
3(s1+1)
Γ(s1+1)+Ψ
1Fl1+s1+1
2,μ
1+2θ
3
+Ψ
2ma
Ωai
+2θ
3−(p3+s1+1)
Γp3+s1+1−Ψ1Ψ2Fl1+p3+s1+1
2,μ
3+2θ
3 (35)
PXQAM
e=3
16 q
2π(q)−1
2Γ1
2−Ψ1F(l1,μ
1+q)−Ψ2ma
Ωai
+q−(p3+1
2)
Γp3+1
2+Ψ
1Ψ2
×F(l1+p3,μ
3+q)+1
8q
2π(2q)−1
2Γ1
2−Ψ1Fl1,μ
1+2q−Ψ2ma
Ωai
+2q−(p3+1
2)
×Γp3+1
2+Ψ
1Ψ2F(l1+p3,μ
3+2q)+∞
s1=0
(1)s1
(1.5)s1s1!
23qs1+1
8π(2q)−(s1+1)Γ(s1+1)−Ψ1
×Fl1+s1+1
2,μ
1+2q−Ψ2ma
Ωai
+2q−(p3+1
2)
Γp3+1
2+Ψ
1Ψ2Fl1+p3+s1+1
2,μ
3+2q
(38)
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10026 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 70, NO. 10, OCTOBER 2021
Fig. 3. Impact of NLPA on the outage performance.
considered hybrid receiver achieves ≈0.785 dB SNR gain over
TS [29], for NLPA. Furthermore, the outage performance of the
relay-assisted network is significantly better than the direct link
transmission due to improvement in the spatial diversity.
For the considered network, simulation and numerical results
of OP are compared in Fig. 3. It is observed that the simulation
and theoretical results match perfectly and validates the derived
analytical OP expression (10) and (13). The asymptotic OP
curves also match with the OP at high SNR which validates (19)
and (23). We observed that the outage performance degrades
significantly when NLPA is used at Ras compared to LPA.
This is due to the NLD which severely diminishes the quality of
the amplified signal at R.Forrth =0.5 bps/Hz and {1,1,1},
≈1.311 dB SNR degradation is received to achieve an OP
of 10−2when NLPA is considered over LPA at R. Further,
the OP of the considered network improves with the increase
in fading parameter. From Fig. 3, we observed that as fading
parameter increases from {1,1,1}to {1,2,1}or {2,1,2}or
{5/2,3/2,5/2}or {5/2,5/2,5/2}, OP improves significantly.
Since the increase in fading parameter represents better channel
condition which results in improved outage performance. For
OP of 10−2at fixed rth=0.5 bps/Hz, when fading parameter
increases from {1,1,1}to {2,1,2}the considered network
receives ≈3.044 dB and ≈2.479 dB SNR gains when NLPA
and LPA are used, respectively. We also observed that at a fixed
SNR, OP corresponding to lower rth performs better than a
higher value of rth.
In Fig. 4, the impact of time switching factor αand energy
conversion efficiency ηon the considered network at a fixed
SNR are investigated. We observed that OP improves initially
with α, but further increase in αdeteriorates performance of the
considered network. Consequently, an optimal value of αexists
for which the considered network exhibits minimal OP. From
Fig. 4, we observed that for η=0.1, the optimum value of α
lies approximately around 0.3 and 0.2 for NLPA and LPA at R,
respectively. Such OP behavior occurs due to the fact that the
amount of harvested energy at Rincreases with αbecause of
the longer time allocated for EH, whereas further increase in α
results in lower time allocation for information processing (IP)
at R. Hence, the outage performance of the considered network
Fig. 4. Impact of αand ηon the outage performance.
Fig. 5. Impact of βon the outage performance.
improves initially due to the availability of more harvested power
at R, whereas the further increase in αdeteriorates the outage
performance due to the less time available for IP. In contrast, OP
always improves with η. This is because the amount of harvested
power increases with ηduring the EH phase.
The impact of power splitting ratio βontheOPofthe
considered network for α=0.1, {1,1,1},SNR =20 dB, and
rth =0.2 bps/Hz is shown in Fig. 5. We observed that the OP
improves with an increase in β. This is due to the fact that
as βincreases the amount of harvested power increases at R.
Consequently, Rtransmits signal with a higher power which
results in improved OP. On the other hand, the increase in
βresults in lower power allocation for IP, since we consider
that negligible power is required for information processing as
compared to that required for signal transmission [8]. The OP of
the considered network improves with β. We also observed that
OP improves with ηdue to increase in the amount of harvested
power.
In Fig. 6 and Fig. 7, ST of the considered network is illustrated
which provides insights about spectral efficiency. From Fig. 6,
we observed that ST increases with the SNR and attains satu-
ration after a fixed SNR value. For a certain rth, the saturation
value of ST corresponds to maximum achievable ST. ST corre-
sponding to higher rth attains saturation at relatively high SNR.
This is due to the fact that outage performance corresponding
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KUMAR et al.: ASER ANALYSIS OF HYBRID RECEIVER BASED SWIPT TWO-WAY RELAY NETWORK 10027
Fig. 6. System throughput versus SNR.
Fig. 7. Impact of rth on the system throughput.
to higher rth shows degraded performance than for lower rth.
For a ST of 0.5 bps/Hz, rth =1 bps/Hz, α=0.2, β=0.2,
η=0.7, and {1,1,1},≈2.096 dB SNR degradation is achieved
when NLPA is considered over LPA at R. The impact of rth on
the ST for a fixed value of SNR is shown in Fig. 7. From the
relevant curves, it can be observed that ST increases with rth and
attains a maximum achievable ST (≈1.2 bps/Hz at rth =2.5
for NLPA and ≈0.9 bps/Hz at rth =2 for LPA, at SNR=30
dB) afterwards it decreases. Further, presence of NLPA at R
shows degraded performance than LPA due to NLD.
For the considered network, EE versus SNR plot is shown
in Fig. 8(a). From the pertinent curves, it can be observed that
for a fixed rth, EE of the system increases with the SNR and
exhibits a maximum EE at a fixed SNR (≈0.167 bit/Joule and
≈0.176 bit/Joule at ≈1.033 dB and ≈1.339 dB for NLPA and
LPA, respectively under rth =0.5 bps/Hz). We also observed
that the considered network exhibits low EE in the high SNR
regime. This is because at high SNR power consumed by the
considered network is more than ST. The SNR value for which
the considered network exhibits maximum EE changes with the
rth. EE decreases with the increase in the value of rth because
outage corresponding to higher value of rth shows degraded
performance. We also observed that for α=0.2, β=0.2, η=
0.7, and {2,2,2}, to receive EE of 0.1 b/Joule, ≈0.329 dB,
≈0.447 dB, and ≈0.871 dB additional SNRs are required for
NLPA as compared to the LPA for rth =0.5, rth =1, and rth =
1.5, respectively.
The impact of TS factor αand PS ratio βon the EE are
depicted in Fig. 8(b) and Fig. 8(c), respectively. Herein, we
set rth =0.2, {1,1,1}, and SNR =−5 dB. From Fig. 8(b),
we observed that EE increases with αand attains a maximum
value for a fixed value of α. Further increase in αresults in
decreasing EE. This is because OP of the considered network
decreases with αand attains an optimal value of OP, and further
increase in αshows poor outage performance as shown in
Fig. 4. Consequently, an optimal value of αexist (≈0.2 and
≈0.15 for NLPA and LPA, respectively under η=0.1) for
which considered network shows maximum EE. From Fig. 8(c),
it can be seen that EE of the considered network increases with β.
This is because outage performance improves with βas depicted
in Fig. 5. From Fig. 8(b) and Fig. 8(c), we observed that EE
increases with ηdue to the increase in harvested energy at R.
For the considered network, EC versus SNR is depicted in
Fig. 9. The simulation and numerical results overlap perfectly
which verifies the accuracy of the derived analytical expression
(28). For EC of 4 bps/Hz, we observed that as the severity
parameter {1,1,1}increases to {2,1,2},≈0.761 dB and ≈
0.553 dB SNR gains are achieved for NLPA and LPA cases,
respectively. We also observed that the EC of the considered
network increases with the increase in η. For EC of 4 bps/Hz,
when αincreases from 0.1 to 0.3, ≈1.3134 dB and ≈0.513 dB
SNR gains are achieved for NLPA and LPA cases, respectively.
Also, the effect of NLPA on the considered network diminishes
the EC performance as compared with LPA case.
For ASER performance of the considered network, the sim-
ulation and numerical results are compared for general order
RQAM, general order HQAM, and 32-XQAM in Fig. 10,
Fig. 11, and Fig. 12, respectively. It can be observed that the
simulation results perfectly match the numerical results which
validates the derived analytical expressions (32), (35), and (38)
respectively. From Fig. 10, it is observed that for {2,1,2},
η=0.1, β=0.1, and α=0.1, ≈3.508 dB SNR degradation
is received to obtain 10−2ASER for 8 ×4-RQAM when NLPA
is considered over LPA. For 8 ×4-RQAM with parameters
{2,1,2},β=0.1, and α=0.1forvariationinηfrom 0.1 to
0.7, ≈0.706 dB and ≈1.472 dB SNR degradation are achieved
for 10−2ASER in case of NLPA and LPA cases, respectively.
For {2,1,2},η=0.7, β=0.3, and α=0.3, ≈8.791 dB and
≈6.915 dB SNR degradation are achieved for 10−2ASER for
8×4-RQAM over 4 ×2-RQAM, in case of NLPA and LPA
cases, respectively. In Fig. 11, for η=0.1, β=0.1, α=0.1,
and M=32 for 32-HQAM of ASER 10−1, when severity
parameter changes from {1,1,1}to {2,1,2},≈2.661 dB and
≈1.088 dB SNR gains are achieved for NLPA and LPA cases,
respectively. We also observed that for an ASER of 10−2for
HQAM, keeping η=0.7, β=0.3, {2,1,2}, and M=32,
when αincreases from 0.1 to 0.3, ≈1.411 dB and ≈0.221 dB
SNR gains are received for NLPA and LPA cases, respectively. In
case of 32-HQAM, for α=0.3, β=0.3, η=0.7, and {2,1,2},
for ASER of 10−2,≈2.52 dB SNR is degraded for NLPA
over LPA cases. From Fig. 12, to attain an ASER of 10−2
for 32-XQAM with η=0.7, α=0.1, and {2,1,2}, when β
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10028 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 70, NO. 10, OCTOBER 2021
Fig. 8. Energy efficiency. (a) Energy efficiency versus SNR. (b) Impact of TS factor on energy efficiency. (c) Impact of PS ratio on energy efficiency.
Fig. 9. Ergodic capacity versus SNR.
Fig. 10. ASER of RQAM versus SNR.
increases from 0.1 to 0.3, ≈0.484 dB and ≈0.141 dB SNR
gains are received for NLPA and LPA cases, respectively. For
32-XQAM, keeping η=0.7, α=0.1, β=0.3, and {2,1,2},
≈3.729 dB SNR is degraded to achieve an ASER of 10−2when
NLPA is considered over LPA. From the above discussion, it can
be concluded that increase in severity parameter and ηprovides
significant SNR gain in medium and high SNR regime. Further,
NLPA consideration over LPA significantly degrades the ASER
performance in medium and high SNR regime.
Fig. 11. ASER of HQAM versus SNR.
Fig. 12. ASER of 32-XQAM versus SNR.
Fig. 13 compares different CPs of the HQAM for the consid-
ered network. For an ASER of 10−2, with α=0.2, β=0.2,
η=0.7, and {1,1,1}, approximately 5.463 dB, 5.184 dB,
4.945 dB SNR improvement is obtained when Mchanges from
32 to 16, 16 to 8, and 8 to 4 for NLPA used at R, respectively.
Further, it is observed that for an ASER of 10−2, approximately
5.827 dB, 3.608 dB, 1.835 dB, and 0.968 dB SNR degradation
is received for M=32, M=16, M=8, and M=4 when
NLPA is considered over LPA, respectively.
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KUMAR et al.: ASER ANALYSIS OF HYBRID RECEIVER BASED SWIPT TWO-WAY RELAY NETWORK 10029
Fig. 13. ASER of HQAM versus SNR.
Fig. 14. Comparative analysis of 8x4-RQAM, 32-HQAM, and 32-XQAM.
In Fig. 14, numerical results of 8 ×4-RQAM, 32-HQAM and
32-XQAM are compared for thc considered network. Herein, we
set the parameters α=0.2, β=0.2, η=0.7, and {1,1,1}.We
observed that 32-XQAM provides better ASER performance
than 8 ×4-RQAM because of its low PAPR. For an ASER of
10−2, it is observed that 32-HQAM achieves ≈1.895 dB and ≈
0.101 dB SNR improvement over 8 ×4-RQAM and 32-XQAM,
respectively, in case of NLPA. However, for an ASER of 10−2,
32-HQAM provides ≈1.129 dB and ≈0.081 dB SNR gains
over 8 ×4-RQAM and 32-XQAM, respectively, in case of LPA.
Hence, 32-HQAM shows superiority over 32-XQAM and 8 ×4-
RQAM for the considered network.
V. C ONCLUSION
In this paper, analytical expressions of outage probability and
asymptotic outage probability have been derived for a hybrid
receiver-based SWIPT 3P-TWR network over Nakagami-m
faded channels for both the integer and non-integer values of m.
The diversity order of the considered network has been obtained
by using asymptotic outage probability. System throughput and
energy efficiency have also been derived for the considered
network. Further, an analytical expression of ergodic capacity
has been derived in terms of Meijer-G function. Various higher
order modulation schemes have been presented and CDF based
analytical expressions of ASER for general order RQAM, gen-
eral order HQAM, and 32-XQAM have been derived. We have
obtained an optimal value of TS factor for which optimum outage
performance and energy efficiency are achieved. Further, the
impact of TS factor, PS ratio, fading severity, and other system
parameters have been highlighted on the system performance.
A comparative analysis among various QAM schemes has been
performed which illustrates the superiority of HQAM over other
QAM schemes.
APPENDIX A
Let UΔ
=|hri|2and VΔ
=|hjr|2for i, j ∈{c, d},i=j. Since,
we consider Nakagami-mfading channel, random variables
Uand Vfollow Gamma distribution with PDF fW(w)=
(m
Ω)mwm−1
Γ(m)e−mw
Ω,w ≥0, with W∈{U, V },w∈{u, v }. Here,
mand Ωdenote fading severity and average power of W,
respectively. For the integer value of fading parameter, the CDF
FW(w)[38, (27)] is given as
FW(w)=1−e−mw
Ω
m−1
p=0
1
p!mw
Ωm
,w ≥0.(39)
The CDF Fγri (γth)can be expressed using (8) as
Fγri (γth)=Prr|hri|2|hjr|2
2|hri|2+C1|hri|2+C2
<γ
th,
=PrU< C2γth
rV−γth(2+C1),(40)
which can be obtained as
Fγri (γth)= γth (2+C1)
r
0
fV(v)dv +∞
γth(2+C1)
r
fV(v)
×C2γth
rv−γth(2+C1)
0
fU(u)dudv. (41)
By substituting PDFs and applying [39, (3.471.9)], we obtain
(11).
APPENDIX B
For the non-integer value of fading parameter, the CDF
FW(w)[46, (36)] is given as
FW(w)=e−mw
Ω
∞
g=0
1
Γ(m+g+1)mw
Ωm
,w ≥0.(42)
The CDF F
γri (γth)can be obtained using (8) as
F
γri (γth)= γth (2+C1)
r
0
fV(v)dv +∞
γth(2+C1)
r
fV(v)
×C2γth
rv−γth(2+C1)
0
fU(u)dudv. (43)
By substituting PDFs, using binomial series expansion, and
applying [39, (3.471.9)], we obtain (14).
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10030 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 70, NO. 10, OCTOBER 2021
REFERENCES
[1] A. Chaoub et al., “6G for bridging the digital divide: wireless connec-
tivity to remote areas,” IEEE Wireless Commun., to be published, doi:
10.1109/MWC.001.2100137.
[2] Y. Yang, H. Hu, J. Xu, and G. Mao, “Relay technologies for WiMax and
LTE-advanced mobile systems,” IEEE Commun. Mag., vol. 47, no. 10,
pp. 100–105, Oct. 2009.
[3] B. Rankov and A. Wittneben, “Spectral efficient protocols for half-duplex
fading relay channels,” IEEE J. Sel. Areas Commun., vol. 25, no. 2,
pp. 379–389, Feb. 2007.
[4] M. Ju and I.-M. Kim, “Relay selection with ANC and TDBC protocols
in bidirectional relay networks,” IEEE Trans. Commun., vol. 58, no. 12,
pp. 3500–3511, Dec. 2010.
[5] S.Yadav and P. K. Upadhyay, “Performance of three-phase analog network
coding with relay selection in Nakagami-mfading,” IEEE Commun. Lett.,
vol. 17, no. 8, pp. 1620–1623, Aug. 2013.
[6] J. Huang, C.-C. Xing, and C. Wang, “Simultaneous wireless information
and power transfer: Technologies, applications, and research challenges,”
IEEE Commun. Mag., vol. 55, no. 11, pp. 26–32, Nov. 2017.
[7] T. D. P. Perera, D. N. K. Jayakody, S. K. Sharma, S. Chatzinotas, and J. Li,
“Simultaneous wireless information and power transfer (SWIPT): Recent
advances and future challenges,” IEEE Commun. Surv. Tut., vol. 20, no. 1,
pp. 264–302, Dec. 2017.
[8] A. A. Nasir, X. Zhou, S. Durrani, and R. A. Kennedy, “Relaying protocols
for wireless energy harvesting and information processing,” IEEE Trans.
Wireless Commun., vol. 12, no. 7, pp. 3622–3636, Jul. 2013.
[9] W. Wang et al., “Joint precoding optimization for secure SWIPT in
UAV-aided NOMA networks,” IEEE Trans. Commun., vol. 68, no. 8,
pp. 5028–5040, Aug. 2020.
[10] N. Zhao, Y. Cao, F. R. Yu, Y. Chen, M. Jin, and V. C. Leung, “Artificial
noise assisted secure interference networks with wireless power transfer,”
IEEE Trans. Veh. Technol., vol. 67, no. 2, pp. 1087–1098, Feb. 2018.
[11] S. Atapattu and J. Evans, “Optimal energy harvesting protocols for wire-
less relay networks,” IEEE Trans. Wireless Commun., vol. 15, no. 8,
pp. 5789–5803, May 2016.
[12] T. Yuan, M. Liu, and Y. Feng, “Performance analysis for SWIPT coopera-
tive DF communication systems with hybrid receiverand non-linear energy
harvesting model,” Sensors, vol. 20, no. 9, Mar. 2020, Art no. 2472.
[13] Y. Ye, Y. Li, L. Shi, R. Q. Hu, and H. Zhang, “Improved hybrid relaying
protocol for DF relaying in the presence of a direct link,” IEEE Wireless
Commun. Lett., vol. 8, no. 1, pp. 173–176, Aug. 2018.
[14] J. Men, J. Ge, C. Zhang, and J. Li, “Joint optimal power allocation and
relay selection scheme in energy harvesting asymmetric two-way relaying
system,” IET Commun., vol. 9, no. 11, pp. 1421–1426, Jul. 2015.
[15] R. Hu and T.-M. Lok, “Power splitting and relay optimization for two-way
relay SWIPT systems,” in Proc. IEEE Int. Conf. Commun., May 2016,
pp. 1–6.
[16] T. P. Do, I. Song, and Y. H. Kim, “Simultaneous wireless transfer of power
and information in a decode-and-forward two-way relaying network,”
IEEE Trans. Wireless Commun., vol. 16, no. 3, pp. 1579–1592, Mar. 2017.
[17] C. Peng, F. Li, and H. Liu, “Optimal power splitting in two-way decode-
and-forward relay networks,” IEEE Commun. Lett., vol. 21, no. 9, pp.
2009–2012, Sep. 2017.
[18] Y. Liu, L. Wang, M. Elkashlan, T. Q. Duong, and A. Nallanathan, “Two-
way relay networks with wireless power transfer: Design and performance
analysis,” IET Commun., vol. 10, no. 14, pp. 1810–1819, Jun. 2016.
[19] N. T. P. Van, S. F. Hasan, X. Gui, S. Mukhopadhyay, and H. Tran, “Three-
step two-way decode and forward relay with energy harvesting,” IEEE
Commun. Lett., vol. 21, no. 4, pp. 857–860, Apr. 2016.
[20] D. S. Gurjar, U. Singh, and P. K. Upadhyay, “Energy harvesting in hybrid
two-way relaying with direct link under Nakagami-M fading,” in Proc.
IEEE Wireless Commun. Netw. Conf., Apr. 2018, pp. 1–6.
[21] S. Solanki, V. Singh, and P. K. Upadhyay, “RF energy harvesting in hybrid
two-way relaying systems with hardware impairments,” IEEE Trans. Veh.
Technol., vol. 68, no. 12, pp. 11 792–11 805, Sep. 2019.
[22] G. Chen, P. Xiao, J. R. Kelly, B. Li, and R. Tafazolli, “Full-duplex wireless-
powered relay in two way cooperative networks,” IEEE Access,vol.5,
pp. 1548–1558, Jan. 2017.
[23] Z. Liu, G. Lu, Y. Ye, and X. Chu, “System outage probability of PS-SWIPT
enabled two-way AF relaying with hardware impairments,” IEEE Trans.
Veh. Technol., vol. 69, no. 11, pp. 13 532–13 545, Nov. 2020.
[24] P. K. Singya, N. Kumar, and V. Bhatia, “Mitigating NLD for wireless
networks: Effect of nonlinear power amplifiers on future wireless com-
munication networks,” IEEE Microw. Mag., vol. 18, no. 5, pp. 73–90,
Jun. 2017.
[25] E. Balti and M. Guizani, “Impact of non-linear high-power amplifiers on
cooperative relaying systems,” IEEE Trans. Commun., vol. 65, no. 10,
pp. 4163–4175, Jul. 2017.
[26] N. Kumar, S. Sharma, and V. Bhatia, “Performance analysis of OFDM-
based nonlinear AF multiple-relay systems,” IEEE Wireless Commun.
Lett., vol. 6, no. 1, pp. 122–125, Dec. 2016.
[27] D.E. Simmons and J. P. Coon, “Two-way OFDM-based nonlinear amplify-
and-forward relay systems,” IEEE Trans. Veh. Technol., vol. 65, no. 5,
pp. 3808–3812, May 2016.
[28] P. K. Singya, N. Kumar, and V. Bhatia, “Performance analysis of op-
portunistic two-way 3P-ANC multi-relay system with imperfect CSI and
NLPA,” in Proc. IEEE Glob. Commun. Conf., Dec. 2018, pp. 206–212.
[29] S. Parvez, D. Kumar, and V. Bhatia, “On performance of SWIPT enabled
two-way relay system with non-linear power amplifier,” in Proc. IEEE
Nat. Conf. Commun., Apr. 2020, pp. 1–6.
[30] M. Abdelaziz and T. A. Gulliver, “Triangular constellations for adap-
tive modulation,” IEEE Trans. Commun., vol. 66, no. 2, pp. 756–766,
Feb. 2018.
[31] P. K. Singya, P. Shaik, N. Kumar, V. Bhatia, and M.-S. Alouini, “A
survey on higher-order QAM constellations: Technical challenges, re-
cent advances, and future trends,” IEEE Open J. Commun. Soc.,vol.2,
pp. 617–655, Mar. 2021.
[32] D. Dixit and P. Sahu, “Performance analysis of rectangular QAM with
SC receiver over Nakagami-mfading channels,” IEEE Commun. Lett.,
vol. 18, no. 7, pp. 1262–1265, Jul. 2014.
[33] X.-C. Zhang, H. Yu, and G. Wei, “Exact symbol error probability of cross-
QAM in AWGN and fading channels,” EURASIP J. Wireless Commun.
Netw., vol. 2010, pp. 1–1, Dec. 2010.
[34] P. K. Singya, N. Kumar, V. Bhatia, and M. Alouini, “On the performance
analysis of higher order QAM schemes over mixed RF/FSO systems,”
IEEE Trans. Veh. Technol., vol. 69, no. 7, pp. 7366–7378, Jul. 2020.
[35] N. Kumar, P. K. Singya, and V. Bhatia, “ASER analysis of hexagonal and
rectangular QAM schemes in multiple-relay networks,” IEEE Trans. Veh.
Technol., vol. 67, no. 2, pp. 1815–1819, Feb. 2018.
[36] P. K. Singya, N. Kumar, and V. Bhatia, “Impact of imperfect CSI on
ASER of hexagonal and rectangular QAM for AF relaying network,” IEEE
Commun. Lett., vol. 22, no. 2, pp. 428–431, Feb. 2018.
[37] L. Rugini, “Symbol error probability of hexagonal QAM,” IEEE Commun.
Lett., vol. 20, no. 8, pp. 1523–1526, Aug. 2016.
[38] P. K. Singya, N. Kumar, V. Bhatia, and M.-S. Alouini, “On performance
of hexagonal, cross, and rectangular QAM for multi-relay systems,” IEEE
Access, vol. 7, pp. 60 602–60 616, May. 2019.
[39] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products,
8th ed., New York, NY, USA: Academic Press, 2014.
[40] E. Boshkovska, D. W. K. Ng, N. Zlatanov, and R. Schober, “Prac-
tical non-linear energy harvesting model and resource allocation for
SWIPT systems,” IEEE Commun. Lett., vol. 19, no. 12, pp. 2082–2085,
Dec. 2015.
[41] Y. Zeng, B. Clerckx, and R. Zhang, “Communications and signals design
for wireless power transmission,” IEEE Trans. Commun., vol. 65, no. 5,
pp. 2264–2290, May 2017.
[42] Y. Gu and S. Aïssa, “RF-based energy harvesting in decode-and-forward
relaying systems: Ergodic and outage capacities,” IEEE Trans. Wireless
Commun., vol. 14, no. 11, pp. 6425–6434, Jul. 2015.
[43] C. Nguyen, N. X. Tran, T. D. Tran, N. X. Pham, and D. T. Le, “Impact
of hardware impairments on the outage probability and ergodic capacity
of one-way and two-way full-duplex relay systems,” IEEE Trans. Veh.
Technol., vol. 69, no. 8, pp. 8555–8567, Aug. 2020.
[44] The wolfram function site. [Online]. Available: http://functions.wolfram.
com/
[45] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions
With Formulas, Graphs, and Mathematical Tables, 9th ed. New York, NY,
USA: Dover, 1970.
[46] E. Soleimani-Nasab, M. Matthaiou, and M. Ardebilipour, “Multi-relay
MIMO systems with OSTBC over Nakagami-mfading channels,” IEEE
Trans. Veh. Technol., vol. 62, no. 8, pp. 3721–3736, Oct. 2013.
Authorized licensed use limited to: Indian Institute of Technology Indore. Downloaded on October 16,2021 at 16:40:38 UTC from IEEE Xplore. Restrictions apply.
