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IEEE SYSTEMS JOURNAL 1
Intelligent-Reflecting-Surface-Aided Bidirectional
Full-Duplex Communication System With
Imperfect Self-Interference Cancellation and
Hardware Impairments
Tan N. Nguyen , Member, IEEE, Nguyen Nhu Thang, Ba Cao Nguyen , Tran Manh Hoang ,
and Phuong T. Tran , Senior Member, IEEE
Abstract—In this article, we combine two new technologies [full-
duplex (FD) transmission and intelligent reflecting surface (IRS)]
in a wireless communication system for investigation. Specifically,
we evaluate the performance of an IRS-aided bidirectional FD
communication system in a practical scenario where imperfect
self-interference (SI) cancellation and hardware impairments (HIs)
are taken into consideration. We successfully derive the closed-form
expressions of ergodic capacity (EC) and symbol error rate (SER)
of the IRS-aided FD-HI system over Rayleigh fading channels. We
confirm the correctness of the derived expressions via Monte-Carlo
simulations. To clarify the effects of residual SI and HIs, we com-
pare the performance of the IRS-aided FD-HI system with that of
the IRS-aided FD-ideal hardware (ID), half-duplex (HD)-HI, and
HD-ID systems. Numerical results clarify a strong impact of resid-
ual SI and HIs on the EC and SER of the IRS-aided FD-HI system.
Thus, the EC and SER of the IRS-aided FD-HI system go to the
saturated values in a high signal-to-noise regime even with a large
number of reflecting elements in the IRS. Therefore, depending on
the residual SI and HI levels as well as the requirements about the
EC and SER in practice, we can use appropriately the transmit
power of terminals and number of reflecting elements in the IRS
for enhancing the performance and saving the energy consumption
of the IRS-aided FD-HI system.
Index Terms—Ergodic capacity (EC), full-duplex (FD) com-
munications, intelligent reflecting surface (IRS), self-interference
(SI) cancellation, symbol error rate (SER).
I. INTRODUCTION
TO SATISFY the requirements such as high speed and
capacity, low latency, and ultra reliable communications
Manuscript received November18, 2021; revised February 17, 2022; accepted
April 11, 2022. (Corresponding author: Ba Cao Nguyen.)
Tan N. Nguyen is with the Communication and Signal Processing Re-
search Group, Faculty of Electrical and Electronics Engineering, Ton Duc
Thang University, Ho Chi Minh City 729000, Vietnam (e-mail: nguyennhat-
tan@tdtu.edu.vn).
Nguyen Nhu Thang, Ba Cao Nguyen, and Tran Manh Hoang are with
the Telecommunications University, Nha Trang, Khanh Hoa 650000, Viet-
nam (e-mail: nguyennhuthang@tcu.edu.vn; nguyenbacao@tcu.edu.vn; tran-
manhhoang@tcu.edu.vn).
Phuong T. Tran is with the Wireless Communications Research Group,
Faculty of Electrical and Electronics Engineering, Ton Duc Thang University,
Ho Chi Minh City 729000, Vietnam (e-mail: tranthanhphuong@tdtu.edu.vn).
Digital Object Identifier 10.1109/JSYST.2022.3167514
of the sixth generation (6G) of wireless systems, many new
technologies such as full-duplex (FD) transmission, nonorthog-
onal multiple access, millimeter wave, massive multiple-input–
multiple-output, and intelligent reflecting surface (IRS) have
been proposed and experimented [1], [2]. In these new tech-
nologies, FD transmission and IRS are two promising solutions
because they have many advantages. Ideally, FD transmission
doubles ergodic capacity (EC) in comparison with the conven-
tional half-duplex (HD) transmission. In addition, FD trans-
mission can enhance the network secrecy, the spectrum usage
flexibility, and throughput and reduce the feedback delay and
congestion [3]. Meanwhile, the IRS can improve the EC, the cov-
erage, and the reliability of the wireless systems without signal
processing [4]–[6]. Besides these advantages, compared with the
traditional relay-aided wireless systems, the IRS-aided wireless
systems have many other benefits, such as operating without
converters and amplifiers and working at any frequency [4],
[7], [8]. Consequently, the combination of FD transmission and
IRS into a wireless system is inevitable for the future wireless
networks [9]–[11].
In practice, although various self-interference (SI) cancella-
tion solutions have been proposed and deployed for FD trans-
mission; however, it is too difficult to completely remove SI
signals. Thus, residual SI will reduce the performance of the
FD wireless communication systems. As a result, the EC of the
FD wireless communication systems may be lower or higher
than that of HD ones depending on the specific values of the
residual SI [12], [13]. Fortunately, recent reports have shown
that the FD transmission can replace the HD one when the
SI cancellation solutions are deployed effectively [14], [15].
Consequently, the FD transmission can achieve a better the
performance than HD one when the quality of SI cancellation
enhances [13], [15]–[18]. Today, many efforts in both research
and experiments are still being developed to achieve a better SI
suppression and enhance the performance of the FD wireless
communication systems [19]–[21].
Recently, FD transmission are combined with the IRS tech-
nology for further enhancement of the performance of wireless
systems. In particular, the usage of larger number of reflect-
ing elements in the IRS can significantly reduce the effects
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2IEEE SYSTEMS JOURNAL
of the residual SI on the outage probability, symbol error
rate (SER), and EC of the IRS-aided FD systems [9]–[11],
[22]–[25]. Thus, to maintain the performance of the FD sys-
tems, when the residual SI power increases, the number of
reflecting elements in the IRS must be increased [10], [25].
Additionally, the end-to-end signal-to-interference-plus-noise
ratio of the IRS-aided FD systems can be characterized by
the Gamma or/and central limit theorem approximations [9].
Consequently, the outage probability, EC, and SER expressions
of the IRS-aided FD systems can be derived via the Gamma
distributions [9], [11], [23].
In recent reports, the potential of either a single IRS or multi-
IRS-aided wireless systems has been demonstrated [26]–[30].
Specifically, utilizing multi-IRS can achieve better coverage,
EC, and energy efficiency in wireless communications [26].
Moreover, different channel models such as Rayleigh, Rician,
and Nakagami-mhave been determined [27]–[30]. It was shown
that multi-IRS or/and multiuser can result in more compu-
tational complexity, especially in mathematical analysis. Im-
portantly, perfect hardware equipment is assumed in these
works.
As clearly shown in the aforementioned discussions, both
FD transmission and IRS technologies have many benefits and
can be deployed in the 6G of wireless systems. However, to
deploy them in practice, various scenarios such as enhancing
the quality of SI suppression, considering the effects of hard-
ware impairments (HIs), improving the channel estimation and
physical layer security,and proposing the optimal problems must
be considered [4], [31]–[35]. In these issues, HIs are important
problems that need to be considered. It is because HIs often
occur at the transmitters and receivers of the IRS-aided wireless
systems [34], [35]. Specifically, the HI sources include phase
noise, nonlinearities of mixers, amplifiers, and converters, etc.
Although the reasons of the HI distortion are known by the
manager and many distortion mitigating schemes have been
applied at both the transmitter and the receiver, the distortion
cannot be completely removed because some reasons belong to
the intrinsic properties of electronic components, e.g., the phase
noise and nonlinearities of low-cost oscillators, analog-to-digital
and digital-to-analog converters, mixers, and amplifiers [6],
[34]–[39]. As a result, neglecting the HIs when considering
the performance of the IRS-aided FD systems can result in
inaccurate conclusions.
Importantly, when HIs exist in the FD systems, it is hard to
apply all SI cancellation solutions effectively. It is because HIs
will result in inaccuracy in SI cancellation procedures such as
SI channel estimation errors, and analog and digital suppression
incorrectness. Moreover, higher residual SIs will cause higher
HIs because of larger input power at an FD receiver [40].
Consequently, investigating the joint effects of residual SIs
and HIs on the performance of the IRS-aided FD system is
essential. In addition, the IRS-aided FD system with HIs is
more realistic because the joint effects of these two factors
often occur in practice. These issues motivate us to investigate a
wireless system where the IRS is used to aid two FD terminals
with HIs (the IRS-aided FD-HI system in the following). By
considering the cases of residual SIs and HIs at two FD terminals,
the considered IRS-aided FD-HI system is really suitable for
practical scenarios. The main contributions of this article can be
summarized as follows.
1) An IRS-aided FD-HI system is considered where the
effects of residual SIs and HIs are investigated. Thus,
the considered IRS-aided FD-HI system is more practical.
Importantly, the benefits of the FD transmission and the
IRS are combined in the considered system. Therefore,
the considered IRS-aided FD-HI system can satisfy the
requirements of the future wireless systems.
2) The closed-form expressions of the EC and SER of the
IRS-aided FD-HI system are derived over Rayleigh fading
channels. We observe that under the effects of residual
SIs and HIs, these expressions are more complicated than
those of the IRS-aided FD systems without HIs. Then, all
theory expressions are verified through simulation results.
3) The performance in terms of the EC and SER of the IRS-
aided FD-HI system is evaluated via different scenarios.
To prove the effects of the residual SIs and HIs on the
EC and SER of the IRS-aided FD-HI system, we compare
them with those of the IRS-aided FD-ideal hardware (ID),
HD-HI, and HD-ID systems. Specifically, under the effect
of HIs, the EC of the IRS-aided FD-HI system is signif-
icantly lower than that of the IRS-aided FD-ID system.
Meanwhile, the EC of the IRS-aided FD-HI system can
be higher or lower than that of the IRS-aided HD-ID
system. This feature depends on the certain signal-to-noise
ratio (SNR) regime and specific values of residual SIs
and HIs. On the other hand, the SER of the IRS-aided
FD-HI system is greatly higher than that of the IRS-aided
HD-ID system. In a high SNR regime, the SERs of the
IRS-aided FD-HI and HD-HI systems reach to saturated
values. Furthermore, the impacts of all system parameters
such as number of reflecting elements on the IRS, the
residual SI levels, the HI levels, and the modulation orders
on the performance of the IRS-aided FD-HI system are
fully considered.
The rest of this article is organized as follows. In Section II, we
introduce the system model where the received signals at the FD
terminals as well as the residual SI and HI signals are presented
in detail. In Section III, we mathematically calculate the EC and
SER expressions of the IRS-aided FD-HI system over Rayleigh
fading channels. In Section IV, we provide numerical results
and discussions, where the effects of various system parameters
are investigated. Finally, Section V concludes this article.
Notation: γ(., .),Γ(.), and Γ(., .)denote the lower incom-
plete gamma, gamma, and upper incomplete gamma functions,
respectively. E{.}and Var{.}denote the mean and variance
operators, respectively. F(.)and f(.)denote the cumulative
distribution function (CDF) and probability density function
(PDF), respectively. j=√−1is the imaginary unit. CN(., .)
denotes Gaussian distribution.
II. SYSTEM MODEL
Fig. 1 depicts the system and signal models of the IRS-aided
FD-HI system. In the considered system, two terminals Aand
Bexchange data via a support of the IRS. In particular, Aand
Boperate in the FD transmission mode. Thus, Aand Bcan
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NGUYEN et al.: INTELLIGENT-REFLECTING-SURFACE-AIDED BIDIRECTIONAL FULL-DUPLEX COMMUNICATION SYSTEM 3
Fig. 1. System model of the IRS-aided FD-HI system.
transmit and receive data simultaneously in the same time. Also,
Aand Bare equipped with an FD antenna.1The IRS is equipped
with Nreflecting elements. Since the distance between Aand
Bis large enough, the direct links between two terminals are
unavailable.2On the other hand, because of the FD mode, Aand
Bsuffer SIs from their output to their input. In the traditional
FD systems without the IRS, the SIs are often generated via two
paths, i.e., direct path between transmit and receive antennas and
reflect paths induced by trees, buildings, etc. Meanwhile, in the
considered IRS-aided FD-HI system, besides traditional SIs, the
reflect paths induced by the IRS (from transmit antenna to IRS
and comes back to receive antenna) will generate a strong SI
signal [9]. In other words, the IRS-aided FD-HI system maybe
suffers from more SI power than traditional FD systems without
the IRS. Let hnbe the data channel between Aand the nth
reflecting element of the IRS (n∈{1,2,...,N}). Similarly, gn
is the data channel between Band the nth reflecting element of
the IRS. ˆ
hnand ˆgnare, respectively, the SI channels from Ato
the nth reflecting element of the IRS and coming back to Aand
from Bto the nth reflecting element of the IRS and coming back
to B.˜
hAand ˜
hBare, respectively, the traditional SI channels at
Aand Bwithout the IRS. At any time slots, the received signals
at two terminals Aand Bof the IRS-aided FD-HI system are,
respectively, computed as
yA=
N
n=1
gnhnrnexp(jφn)(sB+ηt
B)
+ηr
A+˜
hA(sA+ηt
A)+˜ηr
A
+
N
n=1
ˆ
hnˆ
hnrnexp(jφn)(sA+ηt
A)+ˆηr
A+zA(1)
yB=
N
n=1
hngnrnexp(jφn)(sA+ηt
A)
+ηr
B+˜
hB(sB+ηt
B)+˜ηr
B
+
N
n=1
ˆgnˆgnrnexp(jφn)(sB+ηt
B)+ˆηr
B+zB(2)
1An FD antenna can be classified in two types, i.e., shared antenna and separate
antenna [40]. In the shared antenna configuration, only one antenna is used
for both transmitting and receiving data. Meanwhile, in the separate antenna
configuration, two separate antennas are used, one for transmitting and another
for receiving. In practical scenarios, two separate antennas are often used to
achieve better SI cancellation [41].
2The case that these links are available can be considered as our future work.
where rnand φnare, respectively, the reflected gain and ad-
justable phase induced by the nth reflecting element of the
IRS; sBand sAdenote the desired transmit signals at Band
A, respectively, with the average transmit power of PBand
PA, i.e., PB=E{|sB|2}and PA=E{|sA|2};ηt
Band ηt
Aare,
respectively, the HIs caused by the transmitters Band A;ηr
A
and ηr
Bare, respectively, the HIs caused by the receivers A
and Bcorresponding to the channels B-IRS-Aand A-IRS-B;
˜ηr
Aand ˜ηr
Bare, respectively, the HIs caused by the receivers A
and Bcorresponding to the SI channels ˜
hAand ˜
hB;ˆηr
Aand
ˆηr
Bare, respectively, the HIs caused by the receivers Aand B
corresponding to the SI channels ˆ
hnand ˆgn; and zAand zB
denote the Gaussian noises at Aand Bwith zero mean and
variance of σ2, i.e., zA∼CN(0,σ
2
A)and zB∼CN(0,σ
2
B).
Due to the features of HIs at the transmitters and
receivers [34]–[36], [42], the HIs at the transmitters
can be presented as ηt
A∼CN(0,(kt
A)2PA)and ηt
B∼
CN(0,(kt
B)2PB), where kt
Aand kt
Bdenote the levels of im-
pairments at the transmitters Aand B, respectively. Mean-
while, the HIs at the receivers depend on the channel
gains, i.e., ηr
A∼CN(0,|N
n=1 gnhnrnexp(jφn)|2(kr
A)2PB)
and ηr
B∼CN(0,|N
n=1 hngnrnexp(jφn)|2(kr
B)2PA),˜ηr
A∼
CN(0,|˜
hA|2(kr
A)2PB)and ˜ηr
B∼CN(0,|˜
hB|2(kr
B)2PA), and
ˆηr
A∼CN(0,|N
n=1 ˆ
hnˆ
hnrnexp(jφn)|2(kr
A)2PB)and ˆηr
B∼
CN(0,|N
n=1 ˆgnˆgnrnexp(jφn)|2(kr
B)2PA), where kr
Aand kr
B
denote the levels of impairments at the receivers Aand B,
respectively.
Therefore, we can aggregate the HIs at both the transmitter
and receiver as
E
N
n=1
gnhnrnexp(jφn)ηt
B+ηr
A
2
=
N
n=1
gnhnrnexp(jφn)
2[(kt
B)2+(kr
A)2]PB
=
N
n=1
gnhnrnexp(jφn)
2
E|ηBA|2(3)
E|˜
hAηt
A+˜ηr
A|2
=|˜
hA|2[(kt
A)2+(kr
A)2]PA=|˜
hA|2E|ηAA|2(4)
E
N
n=1
ˆ
hnˆ
hnrnexp(jφn)ηt
A+ˆηr
A
2
=
N
n=1
ˆ
hnˆ
hnrnexp(jφn)
2[(kt
A)2+(kr
A)2]PA
=
N
n=1
ˆ
hnˆ
hnrnexp(jφn)
2
E|ηAA|2(5)
E
N
n=1
hngnrnexp(jφn)ηt
A+ηr
B
2
=
N
n=1
hngnrnexp(jφn)
2[(kt
A)2+(kr
B)2]PA
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4IEEE SYSTEMS JOURNAL
=
N
n=1
hngnrnexp(jφn)
2
E|ηAB|2(6)
E|˜
hBηt
B+˜ηr
B|2
=|˜
hB|2[(kt
B)2+(kr
B)2]PB=|˜
hB|2|ηBB|2(7)
E
N
n=1
ˆgnˆgnrnexp(jφn)ηt
B+ˆηr
B
2
=
N
n=1
ˆgnˆgnrnexp(jφn)
2[(kt
B)2+(kr
B)2]PB
=
N
n=1
ˆgnˆgnrnexp(jφn)
2|ηBB|2(8)
where ηBA ∼CN(0,k
2
BAPB),ηAA ∼CN(0,k
2
AAPA),ηAB ∼
CN(0,k
2
ABPA), and ηBB ∼CN(0,k
2
BBPB)are, respectively,
the aggregated impairments at the transmitter Band re-
ceiver A, transmitter Aand receiver A, transmitter A
and receiver B, and transmitter Band receiver B,where
k2
BA =(kt
B)2+(kr
A)2,k2
AA =(kt
A)2+(kr
A)2,k2
AB =(kt
A)2+
(kr
B)2, and k2
BB =(kt
B)2+(kr
B)2.
Using (3)–(8), we can represent the received signals at two
terminals from (1) and (2) as
yA=
N
n=1
gnhnrnexp(jφn)(sB+ηBA)+˜
hA(sA+ηAA)
+
N
n=1
ˆ
hnˆ
hnrnexp(jφn)(sA+ηAA)+zA(9)
yB=
N
n=1
hngnrnexp(jφn)(sA+ηAB)+˜
hB(sB+ηBB)
+
N
n=1
ˆgnˆgnrnexp(jφn)(sB+ηBB)+zB.(10)
Then, Aand Bapply all SI suppression solutions to can-
cel the SI signals. Specifically, three SI suppression do-
mains, i.e., antenna cancellation, analog suppression, and dig-
ital cancellation are combined to suppress the SI power [40],
[41]. Thus, after SIC in digital domain, the SI signals, i.e.,
the terms of ˜
hA(sA+ηAA)+N
n=1 ˆ
hnˆ
hnrnexp(jφn)(sA+
ηAA)and ˜
hB(sB+ηBB)+N
n=1 ˆgnˆgnrnexp(jφn)(sB+ηBB)
in (9) and (10), respectively, become Gaussian random vari-
ables [9], [10], [13], [43], [44]. In particular, the residual SI at
Aand B(denoted by IAand IB, respectively) can be expressed
as IA∼CN(0,l
2
APA)and IB∼CN(0,l
2
BPB), where lAand
lBare the residual SI levels at Aand B, respectively.
Now, the received signals at two terminals become
yA=
N
n=1
gnhnrnexp(jφn)(sB+ηBA)+IA+zA(11)
yB=
N
n=1
hngnrnexp(jφn)(sA+ηAB)+IB+zB.(12)
From (11) and (12), the signal-to-distortion-plus-inter-
ference-and-noise ratios (SDINRs) at two terminals Aand B
(denoted by γAand γB, respectively) are given as
γA=N
n=1 gnhnrnexp(jφn)
2PB
N
n=1 gnhnrnexp(jφn)
2k2
BAPB+l2
APA+σ2
A
(13)
γB=N
n=1 hngnrnexp(jφn)
2PA
N
n=1 hngnrnexp(jφn)
2k2
ABPA+l2
BPB+σ2
B
.
(14)
Since the channels hnand gnare complex numbers, we can
represent hnand gnas
hn=anexp(−jψn)(15)
gn=bnexp(−jθn)(16)
where anand ψnare, respectively, the magnitude and phase of
hn; and bnand θnare, respectively, the magnitude and phase of
gn. In addition, according to [5], [9], [35], the reflected gain is
chosen as rn=1.
Consequently, γAand γBgiven in (13) and (14) are now
rewritten as
γA=
N
n=1 anbnexp (j(φn−ψn−θn))
2PB
N
n=1 anbnexp (j(φn−ψn−θn))
2k2
BAPB+l2
APA+σ2
A
(17)
γB=
N
n=1 anbnexp (j(φn−ψn−θn))
2PA
N
n=1 anbnexp (j(φn−ψn−θn))
2k2
ABPA+l2
BPB+σ2
B
.
(18)
As demonstrated in the literature where the IRS-aided wire-
less systems were considered, the adjustable phase φnof the
IRS can be chosen to maximize the received signal power at the
terminals [5], [9]. In the case of perfect channel state information
at two terminals, the IRS can adjust its phase as [5], [9], [45]
φn=ψn+θn.(19)
As a result, the maximum instantaneous SDINRs at Aand B
can be expressed as
γA=N
n=1 anbn2PB
N
n=1 anbn2k2
BAPB+l2
APA+σ2
A
(20)
γB=N
n=1 anbn2PA
N
n=1 anbn2k2
ABPA+l2
BPB+σ2
B
.(21)
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NGUYEN et al.: INTELLIGENT-REFLECTING-SURFACE-AIDED BIDIRECTIONAL FULL-DUPLEX COMMUNICATION SYSTEM 5
Notice that the existences of residual SIs and HIs lead to an
increase in the complexity of SDINRs at Aand Bgiven in (20)
and (21), respectively. Even ideal hardwares, these expressions
are still different to those in [5] due to the contribution of terms
l2
APAand l2
BPB. Therefore, the characteristics of EC and SER
of the considered system in this article are different to them
in [5]. In other words, the results in [5] cannot be applied for the
considered IRS-aided FD-HI system in this article.
III. PERFORMANCE ANALYSIS
A. EC Analysis
The EC of the IRS-aided FD-HI system is given as
C=E{log2(1 + γA)}+E{log2(1 + γB)}
=∞
0
log2(1 + x)fγA(x)dx +∞
0
log2(1 + x)fγB(x)dx.
(22)
Based on (22), we obtain the closed-form expression of EC
of the IRS-aided FD-HI system in the following theorem.
Theorem 1: Under the effects of residual SIs and HIs, the EC
of the IRS-aided FD-HI system is given as
C=2π
MΓNπ2
16−π2ln 2
M
m=1 1−ξ2
m
2k2
AB +1+ξm
×ΓNπ2
16 −π2,4π
16 −π2(l2
BPB+σ2
B)(1 + ξm)
k2
ABPA(1 −ξm)
(23)
where Mis the Chebyshev parameter; and ξm=cos((2m−1)π
2˜M).
Proof: From (22), we can calculate the EC as follows:
C=1
ln 2 ∞
0
1−FγA(x)
1+xdx +1
ln 2 ∞
0
1−FγB(x)
1+xdx.
(24)
As can be shown from (24), the EC of the IRS-aided FD-HI
system depends on FγA(x)and FγB(x). To reduce the length
of the obtained expressions, we assume that FγA(x)=FγB(x).
In other words, we consider the case that the IRS-aided FD-HI
system is the symmetric model. Consequently, (24) becomes
C=2
ln 2 ∞
0
1−FγB(x)
1+xdx. (25)
To calculate the EC from (25), we have to first obtain FB(x).
From the definition of the CDF, we have
FγB(x)=Pr {γB<x}.(26)
Replacing γBgiven in (21) into (26), we have
FγB(x)
=Pr ⎧
⎪
⎨
⎪
⎩
N
n=1 anbn2PA
N
n=1 anbn2k2
ABPA+l2
BPB+σ2
B
<x
⎫
⎪
⎬
⎪
⎭
=Pr ⎧
⎨
⎩N
n=1
anbn2
PA(1 −k2
ABx)<(l2
BPB+σ2
B)x⎫
⎬
⎭
.
(27)
It is obvious from (27) that there are two cases occurring in this
expression, i.e., 1−k2
ABx≤0and 1−k2
ABx>0. In the case
that 1−k2
ABx≤0or x≥1/k2
AB,wehaveFγB(x)=1because
the probability in (27) is always true. In the case that 1−k2
ABx>
0or x<1/k2
AB, the probability in (27) can be calculated as
Pr ⎧
⎨
⎩N
n=1
anbn2
PA(1 −k2
ABx)<(l2
BPB+σ2
B)x⎫
⎬
⎭
=Pr Y2<(l2
BPB+σ2
B)x
PA(1 −k2
ABx)
=Pr Y<
(l2
BPB+σ2
B)x
PA(1 −k2
ABx)(28)
where Y=N
n=1 anbn=N
n=1 Xnand Xn=anbn. Based
on [46, Sec. 2.2], the PDF of Ycan be given as
fY(x)= xΘ
ΨΘ+1Γ(Θ+1) exp −x
Ψ(29)
where
Θ=[E{Y}]2
Var {Y}−1,Ψ= Var {Y}
E{Y}.(30)
Due to the independence of anand bn, the mean and variance
of Xn=anbnare, respectively, given by [4]
E{Xn}=π
4,Var {Xn}=16 −π2
16 .(31)
Using the central limit theorem, the mean and
variance of Yare, respectively, obtained as E{Y}=
NE{Xn}and Var{Y}=NVa r {Xn}[4], [47], [48].
Consequently, we have
Θ= Nπ2
16 −π2−1,Ψ=16 −π2
4π.(32)
Then, we compute the CDF of Yas
FY(y)=Pr{Y<y}=y
0
fY(x)dx
=1
ΨΘ+1Γ(Θ+1) y
0
xΘexp −x
Ψdx. (33)
Using [49, eq. (3.351.1)], the aforementioned equation be-
comes
FY(y)=γΘ+1,1
Ψy
Γ(Θ + 1) .(34)
Replacing Θand Ψgiven in (32) into (34) combining with
the feature Γ(a, x)+γ(a, x)=Γ(a),wehave
FY(y)=1−1
ΓNπ2
16−π2ΓNπ2
16 −π2,4π
16 −π2y.(35)
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6IEEE SYSTEMS JOURNAL
Based on (35), the probability in (28) is expressed as
Pr Y<
(l2
BPB+σ2
B)x
PA(1 −k2
ABx)=FY(l2
BPB+σ2
B)x
PA(1 −k2
ABx)
=1−1
ΓNπ2
16−π2ΓNπ2
16 −π2,4π
16 −π2(l2
BPB+σ2
B)x
PA(1 −k2
ABx).
(36)
Combining the aforementioned two cases, we obtain the CDF
of γBof the IRS-aided FD-HI system as
FγB(x)=
⎧
⎪
⎨
⎪
⎩
1−1
ΓNπ2
16−π2ΓNπ2
16−π2,4π
16−π2(l2
BPB+σ2
B)x
PA(1−k2
ABx),x<1/k2
AB
1,x≥1/k2
AB.
(37)
As can be seen from (37), the joint effects of residual
SIs and HIs lead to a remarkable increase in the computa-
tion complexity of the IRS-aided FD-HI system. Particularly,
due to the existence of PA(1 −k2
ABx)in the denominator of
(l2
BPB+σ2
B)x/(PA(1 −k2
ABx)) in the incomplete Gamma
function, it is a challenge to derive EC and SER expressions.
Thus, most of previous works assumed perfect hardware equip-
ment in the IRS-aided wireless systems.
Substituting FγB(x)from (37) into (25), the EC is now
computed as
C=2
ln 2 1/k2
AB
0
1
(1 + x)Γ Nπ2
16−π2
×ΓNπ2
16 −π2,4π
16 −π2(l2
BPB+σ2
B)x
PA(1 −k2
ABx)dx
=2
ΓNπ2
16−π2ln 2
×1/k2
AB
0
1
(1 + x)Γ
×Nπ2
16 −π2,4π
16 −π2(l2
BPB+σ2
B)x
PA(1 −k2
ABx)dx. (38)
Using [50, eq. (25.4.30)], the integral in (38) is solved as
1/k2
AB
0
1
(1 + x)ΓNπ2
16 −π2,4π
16 −π2(l2
BPB+σ2
B)x
PA(1 −k2
ABx)dx
=π
2˜Mk2
AB
M
m=1 1−ξ2
m
1
1+1+ξm
2k2
AB
×ΓNπ2
16 −π2,4π
16 −π2
!
!
!
"
(l2
BPB+σ2
B)1+ξm
2k2
AB
PA1−k2
AB 1+ξm
2k2
AB .(39)
Substituting (39) into (38) and applying some mathematical
transforms, we obtain the EC of the IRS-aided FD-HI system as
in (23) in Theorem 1. The proof is complete.
B. SER Analysis
The SER at terminal B(SER of the IRS-aided FD-HI system
in the following) can be computed as
SER =αE{Q(βγB)}=α
√2π∞
0
FγBt2
βexp t2
2dt
(40)
where Q(x)= 1
√2π#∞
xe−t2/2dt is the Gaussian function; α
and βare constants calculated through the certain modulation
types, i.e., α=1,β =2 and α=2,β =1 corresponding to
binary phase-shift keying (BPSK) and 4-quadrature amplitude
modulation (4-QAM), respectively [51]. The values of αand β
corresponding to all modulation types are given in [51, Table
6.1].
Setting x=t2
b, (40) can be represented as
SER =α√β
2√2π∞
0
FγB(x)
√xexp −βx
2dx. (41)
Based on (41), the SER of the IRS-aided FD-HI system is
given in the following theorem.
Theorem 2: The SER of the IRS-aided FD-HI system with
residual SI and HIs is given as
SER =α√β
2√2π$%2π
β−π
MΓNπ2
16−π2
M
i=1 1−ξm
2k2
AB
×exp −β(1 + ξm)
4k2
AB
×ΓNπ2
16 −π2,4π
16 −π2(l2
BPB+σ2
B)(1 + ξm)
k2
ABPA(1 −ξm)&.
(42)
Proof: Replacing FγB(x)from (37) into (41), the SER is now
computed as
SER =α√β
2√2π1/k2
AB
0
1
√xexp −βx
2
×$1−1
ΓNπ2
16−π2Γ
×Nπ2
16 −π2,4π
16 −π2(l2
BPB+σ2
B)x
PA(1 −k2
ABx)&dx
+∞
1/k2
AB
1
√xexp −βx
2dx.(43)
Then, we reorganize (43) as
SER =α√β
2√2π$∞
0
1
√xexp −βx
2dx
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NGUYEN et al.: INTELLIGENT-REFLECTING-SURFACE-AIDED BIDIRECTIONAL FULL-DUPLEX COMMUNICATION SYSTEM 7
−1
ΓNπ2
16−π21/k2
AB
0
1
√xexp −βx
2
×ΓNπ2
16 −π2,4π
16 −π2(l2
BPB+σ2
B)x
PA(1 −k2
ABx)dx&.
(44)
Applying [49, eq. (3.361.2)], we have
∞
0
1
√xexp −βx
2dx =%2π
β.(45)
Applying [50, eq. (25.4.30)], we can solve the second integral
in (44) as
1/k2
AB
0
1
√xexp −βx
2Γ
×Nπ2
16 −π2,4π
16 −π2(l2
BPB+σ2
B)x
PA(1 −k2
ABx)dx
=π
2˜Mk2
AB
M
m=1 1−ξ2
mexp −β(1 + ξm)
4k2
AB 1
1+ξm
2k2
AB
×ΓNπ2
16 −π2,4π
16 −π2
!
!
!
"
(l2
BPB+σ2
B)1+ξm
2k2
AB
PA1−k2
AB 1+ξm
2k2
AB
=π
M
M
m=1 1−ξm
2k2
AB
exp −β(1 + ξm)
4k2
AB
×ΓNπ2
16 −π2,4π
16 −π2(l2
BPB+σ2
B)(1 + ξm)
k2
ABPA(1 −ξm).(46)
Replacing (45) and (46) into (44), we obtain the SER of the
IRS-aided FD-HI system as in (42) in Theorem 2. The proof is
thus complete.
C. Asymptotic SDINR
As shown in (23) and (42), they are cumbersome. Thus, it is
difficult to gain any direct insights into the system behaviors.
However, approximate forms of (23) and (42) cause great errors
due to consisting of Gamma and incomplete Gamma functions.
Therefore, we determine SDINRs at Aand Bin high SNR
regime instead of approximations (23) and (42). In particular,
let E{an}=E{bn}=1,PA=PB=P,σ2
A=σ2
B=σ2, and
SNR =P/σ2,wehave
lim
SNR→∞ γA= lim
SNR→∞ N
n=1 anbn2P/σ2
N
n=1 anbn2k2
BAP/σ2+l2
AP/σ2+1
= lim
SNR→∞ N
n=1 anbn2SNR
N
n=1 anbn2k2
BASNR +l2
ASNR +1
=N2
N2k2
BA +l2
A
(47)
lim
SNR→∞ γB= lim
SNR→∞ N
n=1 anbn2P/σ2
N
n=1 anbn2k2
ABP/σ2+l2
BP/σ2+1
= lim
SNR→∞ N
n=1 anbn2SNR
N
n=1 anbn2k2
ABSNR +l2
BSNR +1
=N2
N2k2
AB +l2
B
.(48)
As shown in (47) and (48), γAand γBat Aand Bof the
IRS-aided HI-FD system in a high SNR regime depend on N
(the number of reflecting elements), k2
AB and k2
BA (the aggregated
HI levels), and l2
Aand l2
B(the residual SI levels). For a certain
system, N,k2
AB,k2
BA,l2
A, and l2
Bare constants. Thus, in a high
SNR regime, γAand γBare constants leading to the EC and
SER of the IRS-aided HI-FD system are also constants.
IV. NUMERICAL RESULTS AND DISCUSSIONS
In this section, the effects of all system parameters on the
EC and SER of the IRS-aided FD-HI system are investigated.
Monte-Carlo simulations are used to confirm the correctness
of the derived expressions. Additionally, the ECs and SERs
of the IRS-aided FD-ideal hardware (ID), HD-HI, and HD-ID
systems are also provided for comparison. In all investigated
scenarios, the system parameters are set as follows:3the transmit
power of two terminals Aand Bare PA=PB=P; the power
noises at two receivers Aand Bare σ2
A=σ2
B=σ2;theHI
levels at the transmitters and receivers are (kt
A)2=(kr
B)2=
(kt
B)2=(kr
B)2=k2; the residual SI levels at two receivers A
and Bare l2
A=l2
B=l2; and the average SNR is computed as
SNR =P/σ2.
Fig. 2 illustrates the EC of the IRS-aided FD-HI system in
comparison with that of the IRS-aided FD-ID, HD-HI, and
HD-ID systems for N=20reflecting elements, k2=0.01, and
l2=0.1. We use (23) in Theorem 1 to obtain the theory curve
of the EC of the IRS-aided FD-HI system. It is clear from Fig. 2
that for the investigated parameters, the EC of the IRS-aided
FD-ID system is the best, while the EC of the IRS-aided HD-HI
system is the worst. In addition, although the EC of the IRS-aided
FD-HI system is always higher than that of the IRS-aided HD-HI
system, however, it may be higher or lower than that of the
IRS-aided HD-ID system. This feature depends on the certain
SNR range. Specifically, the EC of the IRS-aided FD-HI system
is higher for SNR <10 dB and lower for SNR >10 dB than
EC of the IRS-aided HD-ID system. As a result, the usage of
the FD transmission mode can greatly enhance the capacity of
the IRS-aided wireless systems in comparison with the con-
ventional HD transmission mode. Particularly, the ECs of the
IRS-aided FD-ID, FD-HI, HD-ID, and HD-HI systems are, re-
spectively, 15.5, 10.8, 7.9, and 5.4 bits per channel use (bpcu) at
3Similar to recent reports [4], [6], [9], [34], the distances between transmitter
and IRS, and IRS and receiver are normalized in our simulation scenarios. How-
ever, we also note that the IRS position has a great impact on the performance
of IRS-aided wireless systems in practice [7].
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8IEEE SYSTEMS JOURNAL
Fig. 2. EC of the IRS-aided HI-FD system in comparison with that of the
IRS-aided FD-ID, HD-HI, and HD-ID systems for N=20reflecting elements,
k2=0.01,andl2=0.1.
Fig. 3. EC of the IRS-aided FD-HI system for different values of residual SIs,
N=20,andk2=0.001.
SNR =0 dB. In other words, due to the effects of HIs, the EC
of the IRS-aided FD system reduces by 4.7 bpcu (from 15.5
with ID hardwares to 10.8 with HIs). Similarly, the EC of the
IRS-aided HD system reduces by 2.5 bpcu (from 7.9 with ID
hardwares to 5.4 with HIs). On the other hand, the effect of
the HIs is stronger in the higher SNR regime. It is because the
EC of the IRS-aided FD-HI system is significantly lower than
that of the IRS-aided HD-ID system in the high SNR regime,
especially when SNR =30dB. Moreover, the saturation ceiling
of the EC of the IRS-aided FD-HI system is perfectly accurate
with analysis expressions given in (47) and (48).
Fig. 3 investigates the effects of the residual SIs on the EC of
the IRS-aided FD-HI system for l2=0,0.1,0.2,0.3,0.4. Since
the HI level in Fig. 3 is smaller than that in Fig. 2, the ECs of
the IRS-aided FD-HI and HD-HI systems in Fig. 3 are higher
than those in Fig. 2. As shown in Fig. 3, higher residual SIs
lead to lower ECs of the IRS-aided FD-HI and FD-ID systems,
especially for the IRS-aided FD-ID system. Note that in the case
Fig. 4. Effects of HI levels on the ECs of the IRS-aided FD-HI system for
N=20and l2=0.1.
of l2=0(perfect SI cancellation), the ECs of the FD-HI and
FD-ID systems are double in comparison with the ECs of HD-HI
and HD-ID systems, respectively. In addition, the effect of HIs in
the low SNR regime (SNR <−5dB) is very slight. It is because
the ECs of FD-HI and FD-ID systems are similar, and the ECs of
HD-HI and HD-ID systems are also similar in this SNR range.
However, for higher SNR such as SNR >0dB, the differences
between the ECs of HI and ID systems are significant. On the
other hand, when l2increases from 0 to 0.4, the ECs of the
FD-HI and FD-ID systems greatly reduce. Specifically, for SNR
=10dB, the ECs of the IRS-aided FD-ID system are 22.4, 20.4,
19.3, 18.4, and 17.8 corresponding to l2=0,0.1,0.2,0.3, and
0.4, respectively. Meanwhile, they are 17.4, 16.9, 16.5, 16.1,
and 15.9 for the IRS-aided FD-HI system. In other words, when
residual SIs increase, the ECs of the IRS-aided FD-ID system
decrease faster than those of the IRS-aided FD-HI system.
Fig. 4 considers the effects of HI levels on the ECs of the
IRS-aided FD-HI system for k2=10
−4,10−3,10−2, and 10−1.
With small values of k2, i.e., k2=10
−4and 10−3, the ECs of the
IRS-aided FD-HI and HD-HI systems increase when the SNR
increases and reach the ceiling values at SNR =20dB. However,
for higher values of k2, i.e., k2=10
−2and 10−1, the ECs of
the IRS-aided FD-HI and HD-HI systems increase slowly and
reach the ceiling values soon at SNR =5dB. As a result, when
HIs are large enough, a higher SNR cannot increase the ECs
of the IRS-aided FD-HI and HD-HI systems, especially in the
case that k2=10
−1. Thus, depending on the HI levels measured
in practical devices, we can use suitable transmit power of the
terminals for saving the energy consumption and reaching the
maximal capacity.
Fig. 5 illustrates the advantages of using the IRS for sup-
porting FD-HI and FD-ID systems, where number of reflecting
elements in the IRS varies, i.e., N=5,10,20,30, and 40. It is
obvious from Fig. 5 that increasing Nsignificantly enhances the
ECs of the IRS-aided FD-HI and FD-ID systems. Specifically,
in the case that small N, i.e., N=5and N=10, the ECs of the
IRS-aided FD-HI and FD-ID systems are similar. In other words,
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NGUYEN et al.: INTELLIGENT-REFLECTING-SURFACE-AIDED BIDIRECTIONAL FULL-DUPLEX COMMUNICATION SYSTEM 9
Fig. 5. ECs of the IRS-aided FD-HI and FD-ID systems for different values
of number of reflecting elements Nfor k2=10
−4and l2=0.1.
Fig. 6. SER of the IRS-aided FD-HI system versus the average SNR for two
modulation types, N=5,k2=0.01,andl2=0.01.
with small N, the impact of HIs on the ECs of the IRS-aided
FD-HI system is very small. However, for higher N, that impact
is significant, especially in a high SNR regime. Particularly, at
SNR =10 dB, the ECs of the IRS-aided FD-HI and FD-ID
systems are, respectively, 19.9 and 20.4 bpcu for N=20, 21.6
and 22.8 bpcu for N=30, and 22.6 and 24.5 bpcu for N=40.
Consequently, when the number of reflecting elements in the
IRS increases from 20 to 30, the ECs of the IRS-aided FD-HI
and FD-ID systems increase by 1.7 and 2.4 bpcu, respectively.
Additionally, the increasing in the ECs of the IRS-aided FD-HI
and FD-ID systems when Nincreases from 5 to 10 or 10 to 20
is higher than that when Nincreases from 20 to 30 or from 30 to
40. That means that the ECs of the IRS-aided FD-HI and FD-ID
systems are not the linear functions of the N.
Fig. 6 investigates the SER of the IRS-aided FD-HI system
in comparison with that of the IRS-aided FD-ID, HD-HI, and
HD-ID systems for two modulation types, i.e., 8-QAM (α=
4−√2,β =3/7) and 16-QAM (α=3,β =1/5). We use N=
5,k2=0.01, and l2=0.01. The theory curves in Fig. 6 are
obtained by using (42) in Theorem 2. Since the FD systems are
affected by residual SIs, the SER of the IRS-aided FD-ID system
Fig. 7. Impact of the number of reflecting elements Non the SER of the
IRS-aided FD-HI system using 16-QAM for SNR =5dB,k2=0.005,and
l2=0.5.
is greatly higher than that of the HD-ID system, especially in
the case of 16-QAM. However, under the effects of HIs, the
SER of the IRS-aided FD-HI and HD-HI systems are nearly
similar, especially in the case of 16-QAM. Furthermore, the
SER of the IRS-aided HD-ID system avoids the error floor for
both modulation types. Meanwhile, the SERs of the IRS-aided
FD-ID, FD-HI, and HD-HI systems reach the error floor in a
high SNR regime, especially in the case of 16-QAM. In other
words, the effects of HIs and/or residual SI are stronger for higher
modulation orders.
Finally, the impact of the number of reflecting elements N
on the SER of the IRS-aided FD-HI system using 16-QAM is
considered in Fig. 7. It is clear that when Nincreases, the SERs
of the IRS-aided FD-HI, FD-ID, HD-HI, and HD-ID systems
decrease. Specifically, the SERs of the IRS-aided FD-ID and
HD-ID systems decrease quickly when Nincreases from 1
to 20. Also, the SERs reach 10−6when N=14and N=19
corresponding to the IRS-aided HD-ID and FD-ID systems.
Meanwhile, the SERs of the IRS-aided FD-HI and HD-HI
systems decrease quickly when Nincreases from 1 to 20 and
decrease slowly when Nincreases from 20 to 30. Then, the
SERs of the IRS-aided FD-HI and HD-HI systems are saturated
when N≥60. On the other hand, when N<40, the SERs of the
IRS-aided FD-HI and HD-HI systems are significantly different.
However, they are similar when N≥60. In other words, when
Nis large enough, the effect of residual SIs on the SER of
the IRS-aided FD-HI system is trivial. This result is reasonable
because (47) and (48) reach to 1/k2
BA and 1/k2
AB, respectively,
when Nis large enough. As a result, the usage of the IRS
with larger number of reflecting elements can greatly reduce
the impact of residual SIs caused by FD transmission mode.
V. CONCLUSION
In this article, we considered a practical scenario of the
IRS-aided wireless systems where imperfect self-interference
cancellation and transceiver hardwares in FD terminals are in-
vestigated. We successfully derived the closed-form expressions
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10 IEEE SYSTEMS JOURNAL
of the EC and SER of the IRS-aided FD-HI system. Then, we
compared the performance in terms of EC and SER of the
IRS-aided FD-HI system with that of the IRS-aided FD-ID,
HD-HI, and HD-ID systems to clearly indicate the effects of
residual SIs and HIs. Numerical results obviously show that
the effects of residual SIs and HIs on the performance of the
IRS-aided FD-HI system are significant. Specifically, the EC of
the IRS-aided FD-HI system can be higher or lower than that
of the IRS-aided HD-ID system. This feature depends on the
specific values of the residual SIs and HIs, and the average SNR
range. Meanwhile, the SER of the IRS-aided FD-HI system is
greatly higher than that of the IRS-aided HD-ID system. These
results demonstrated a strong joint effect of the residual SIs
and HIs on the performance of the IRS-aided FD-HI system.
Additionally, the impacts of residual SIs and HIs are stronger
in high SNR regime and high modulation orders. These impacts
lead the EC and SER of the IRS-aided FD-HI system to reach the
saturated values in a high SNR regime. Thus, when the residual
SIs and HIs exist in the IRS-aided FD systems, we should use
appropriate number of reflecting elements to reach the targets
EC and SER for satisfying the practical requirements. Moreover,
we can utilize multi-IRS and exploit transmitter–receiver direct
links to significantly enhance the performance of the IRS-aided
FD-HI system. Also, proposing algorithms and methods to
reduce residual SIs and HIs is essential before deploying the
IRS-aided FD-HI system in practice. We leave them for our
future work.
REFERENCES
[1] M. H. Alsharif, A. H. Kelechi, M. A. M. Albreem, S. A. Chaudhry, M.
S. Zia, and S. Kim, “Sixth generation (6G) wireless networks: Vision,
research activities, challenges and potential solutions,” Symmetry, vol. 12,
no. 4, pp. 676–699, 2020.
[2] P. Yang, Y. Xiao, M. Xiao, and S. Li, “6G wireless communications:
Vision and potential techniques,” IEEE Netw., vol. 33, no. 4, pp. 70–75,
Jul./Aug. 2019.
[3] A. H. Gazestani, S. A. Ghorashi, B. Mousavinasab, and M. Shikh-Bahaei,
“A survey on implementation and applications of full duplex wireless
communications,” Phys. Commun., vol. 34, pp. 121–134, 2019.
[4] E. Basar, M. D. Renzo, J. de Rosny, M. Debbah, M. Alouini, and R. Zhang,
“Wireless communications through reconfigurable intelligent surfaces,”
IEEE Access, vol. 7, pp. 116753–116773, 2019.
[5] A. A. Boulogeorgos and A. Alexiou, “Performance analysis of reconfig-
urable intelligent surface-assisted wireless systems and comparison with
relaying,” IEEE Access, vol. 8, pp. 94463–94483, 2020.
[6] E. Björnson, Ö. Özdogan, and E. G. Larsson, “Intelligent reflecting surface
versus decode-and-forward: How large surfaces are needed to beat relay-
ing?,” IEEE Wireless Commun. Lett., vol. 9, no. 2, pp. 244–248, Feb. 2020.
[7] I. Yildirim, A. Uyrus, and E. Basar, “Modeling and analysis of reconfig-
urable intelligent surfaces for indoor and outdoor applications in future
wireless networks,” IEEE Trans. Commun., vol. 69, no. 2, pp. 1290–1301,
Feb. 2021.
[8] H. Yu, H. D. Tuan, A. A. Nasir, T. Q. Duong, and H. V. Poor, “Joint design
of reconfigurable intelligent surfaces and transmit beamforming under
proper and improper Gaussian signaling,” IEEE J. Sel. Areas Commun.,
vol. 38, no. 11, pp. 2589–2603, Nov. 2020.
[9] S. Atapattu, R. Fan, P. Dharmawansa, G. Wang, J. S. Evans, and T. A.
Tsiftsis, “Reconfigurable intelligent surface assisted two-way communi-
cations: Performance analysis and optimization,” IEEE Trans. Commun.,
vol. 68, no. 10, pp. 6552–6567, Oct. 2020.
[10] P. K. Sharma and P. Garg, “Intelligent reflecting surfaces to achieve the
full-duplex wireless communication,” IEEE Commun. Lett., vol. 25, no. 2,
pp. 622–626, Feb. 2021.
[11] B. C. Nguyen et al., “Cooperative communications for improving the per-
formance of bidirectional full-duplex system with multiple reconfigurable
intelligent surfaces,” IEEE Access, vol. 9, pp. 134733–134742, 2021.
[12] S. Narayanan, H. Ahmadi, and M. F. Flanagan, “On the performance of
spatial modulation MIMO for full-duplex relay networks,” IEEE Trans.
Wireless Commun., vol. 16, no. 6, pp. 3727–3746, Jun. 2017.
[13] B. C. Nguyen, X. N. Tran, D. T. Tran, X. N. Pham, and L. T. Dung, “Impact
of hardware impairments on the outage probability and ergodic capacity
of one-way and two-way full-duplex relaying systems,” IEEE Trans. Veh.
Technol., vol. 69, no. 8, pp. 8555–8567, Aug. 2020.
[14] L. Irio and R. Oliveira, “Distribution of the residual self-interference power
in in-band full-duplex wireless systems,” IEEE Access, vol. 7, pp. 57516–
57526, 2019.
[15] A. Koç, I. Altunbas, and E. Basar, “Two-way full-duplex spatial modula-
tion systems with wireless powered AF relaying,” IEEE Wireless Commun.
Lett., vol. 7, no. 3, pp. 444–447, Jun. 2018.
[16] T. M. Hoang, B. C. Nguyen, N. N. Thang, M. Tran, and P. T. Tran, “Perfor-
mance and optimal analysis of time-switching energy harvesting protocol
for MIMO full-duplex decode-and-forward wireless relay networks with
various transmitter and receiver diversity techniques,” J. Franklin Inst.,
vol. 357, no. 17, pp. 13205–13230, 2020.
[17] N. Nguyen, H. Q. Ngo, T. Q. Duong, H. D. Tuan, and D. B. da Costa,
“Full-duplex cyber-weapon with massive arrays,” IEEE Trans. Commun.,
vol. 65, no. 12, pp. 5544–5558, Dec. 2017.
[18] T. N. Nguyen, M. Tran, T.-L. Nguyen, and M. Voznak, “Adaptive relaying
protocol for decode and forward full-duplex system over rician fading
channel: System performance analysis,” China Commun., vol. 16, no. 3,
pp. 92–102, 2019.
[19] Z. Zhang, Y. Liu, F. Luo, and X. Wang, “On cancellation capability of
full-duplex RF self-interference cancellation schemes,” Mobile Inf. Syst.,
vol. 2019, pp. 5627178-1–5627178-7, 2019.
[20] V. Tapio, M. Sonkki, and M. J. Juntti, “Self-interference cancelation in
the presence of non-linear power amplifier and receiver IQ imbalance,”
EURASIP J. Wireless Commun. Netw., vol. 2020, no. 1, pp. 127–148, 2020.
[21] D. Korpi, L. Anttila, T. Riihonen, and M. Valkama, “Digital self-
interference cancellation for low-cost full-duplex radio devices,” in Full-
Duplex Communications for Future Wireless Networks, H. Alves, T.
Riihonen, and H. A. Suraweera, Eds. Berlin, Germany: Springer, 2020,
pp. 61–98.
[22] Z. Yang et al., “Optimal control for full-duplex communications with
reconfigurable intelligent surface,” in Proc. IEEE Int. Conf. Commun.,
2021, pp. 1–6.
[23] B. C. Nguyen, T. M. Hoang, L. T. Dung, and T. Kim, “On performance
of two-way full-duplex communication system with reconfigurable intel-
ligent surface,” IEEE Access, vol. 9, pp. 81274–81285, 2021.
[24] J. Ye, A. Kammoun, and M. Alouini, “Spatially-distributed RISs vs relay-
assisted systems: A fair comparison,” IEEE Open J. Commun. Soc.,vol.2,
pp. 799–817, 2021.
[25] Z. Peng, Z. Zhang, C. Pan, L. Li, and A. L. Swindlehurst, “Multiuser
full-duplex two-way communications via intelligent reflecting surface,”
IEEE Trans. Signal Process., vol. 69, pp. 837–851, 2021.
[26] T. Shafique, H. Tabassum, and E. Hossain, “Stochastic geometry analysis
of IRS-assisted downlink cellular networks,” IEEE Trans. Commun., 2022,
vol. 70, no. 2, pp. 1442–1456, Feb. 2022.
[27] H. Ibrahim, H. Tabassum, and U. T. Nguyen, “Exact coverage analysis of
intelligent reflecting surfaces with Nakagami-m channels,” IEEE Trans.
Veh. Technol., vol. 70, no. 1, pp. 1072–1076, Jan. 2021.
[28] X. Lu, E. Hossain, T. Shafique, S. Feng, H. Jiang, and D. Niyato, “In-
telligent reflecting surface enabled covert communications in wireless
networks,” IEEE Netw., vol. 34, no. 5, pp. 148–155, Sep./Oct. 2020.
[29] L. Yang, Y. Yang, D. B. da Costa, and I. Trigui, “Outage probability
and capacity scaling law of multiple RIS-aided networks,” IEEE Wireless
Commun. Lett., vol. 10, no. 2, pp. 256–260, Feb. 2021.
[30] A. M. Salhab and M. H. Samuh, “Accurate performance analysis of
reconfigurable intelligent surfaces over Rician fading channels,” IEEE
Wireless Commun. Lett., vol. 10, no. 5, pp. 1051–1055, May 2021.
[31] B. Di, H. Zhang, L. Song, Y. Li, Z. Han, and H. V. Poor, “Hybrid
beamforming for reconfigurable intelligent surface based multi-user com-
munications: Achievable rates with limited discrete phase shifts,” IEEE J.
Sel. Areas Commun., vol. 38, no. 8, pp. 1809–1822, Aug. 2020.
[32] M. A. ElMossallamy, H. Zhang, L. Song, K. G. Seddik, Z. Han, and G.
Y. Li, “Reconfigurable intelligent surfaces for wireless communications:
Principles, challenges, and opportunities,” IEEE Trans. Cogn. Commun.
Netw., vol. 6, no. 3, pp. 990–1002, Sep. 2020.
Authorized licensed use limited to: Chungbuk National Univ. Downloaded on May 01,2022 at 00:16:00 UTC from IEEE Xplore. Restrictions apply.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
NGUYEN et al.: INTELLIGENT-REFLECTING-SURFACE-AIDED BIDIRECTIONAL FULL-DUPLEX COMMUNICATION SYSTEM 11
[33] S. Lin, B. Zheng, G. C. Alexandropoulos, M. Wen, M. D. Renzo, and F.
Chen, “Reconfigurable intelligent surfaces with reflection pattern mod-
ulation: Beamforming design and performance analysis,” IEEE Trans.
Wireless Commun., vol. 20, no. 2, pp. 741–754, Feb. 2021.
[34] M. H. N. Shaikh, V.A. Bohara, A. Srivastava, and G. Ghatak, “Performance
analysis of intelligent reflecting surface-assisted wireless system with non-
ideal transceiver,” IEEE Open J. Commun. Soc., vol. 2, pp. 671–686, 2021.
[35] A. Hemanth, K. Umamaheswari, A. C. Pogaku, D. Do, and B. M. Lee,
“Outage performance analysis of reconfigurable intelligent surfaces-aided
NOMA under presence of hardware impairment,” IEEE Access,vol.8,
pp. 212156–212165, 2020.
[36] E. Björnson, M. Matthaiou, and M. Debbah, “A new look at dual-hop
relaying: Performance limits with hardware impairments,” IEEE Trans.
Commun., vol. 61, no. 11, pp. 4512–4525, Nov. 2013.
[37] A. K. Papazafeiropoulos, S. K. Sharma, T. Ratnarajah, and S. Chatzinotas,
“Impact of residual additive transceiverhardware impairments on rayleigh-
product MIMO channels with linear receivers: Exact and asymptotic
analyses,” IEEE Trans. Commun., vol. 66, no. 1, pp. 105–118, Jan. 2018.
[38] T. Schenk, RF Imperfections in High-Rate Wireless Systems: Impact and
Digital Compensation. Berlin, Germany: Springer, 2008.
[39] H. Holma and A. Toskala, LTE for UMTS.: Evolution to LTE-Advanced.
Hoboken, NJ, USA: Wiley, 2011.
[40] A. Sabharwal, P. Schniter, D. Guo, D. W. Bliss, S. Rangarajan, and R.
Wichman, “In-band full-duplex wireless: Challenges and opportunities,”
IEEE J. Sel. Areas Commun., vol. 32, no. 9, pp. 1637–1652, Sep. 2014.
[41] E. Ahmed and A. M. Eltawil, “All-digital self-interference cancella-
tion technique for full-duplex systems,” IEEE Trans. Wireless Commun.,
vol. 14, no. 7, pp. 3519–3532, Jul. 2015.
[42] E. Björnson, J. Hoydis, M. Kountouris, and M. Debbah, “Massive MIMO
systems with non-ideal hardware: Energy efficiency, estimation, and ca-
pacity limits,” IEEE Trans. Inf. Theory, vol. 60, no. 11, pp. 7112–7139,
Nov. 2014.
[43] C. Li, Z. Chen, Y. Wang, Y. Yao, and B. Xia, “Outage analysis of the
full-duplex decode-and-forward two-way relay system,” IEEE Trans. Veh.
Technol., vol. 66, no. 5, pp. 4073–4086, May 2017.
[44] C. Li, B. Xia, S. Shao, Z. Chen, and Y. Tang, “Multi-user scheduling of
the full-duplex enabled two-way relay systems,” IEEE Trans. Wireless
Commun., vol. 16, no. 2, pp. 1094–1106, Feb. 2017.
[45] D. Kudathanthirige, D. Gunasinghe, and G. Amarasuriya, “Performance
analysis of intelligent reflective surfaces for wireless communication,” in
Proc. IEEE Int. Conf. Commun., 2020, pp. 1–6.
[46] S. Primak, V. Kontorovich, and V. Lyandres, Stochastic Methods and
Their Applications to Communications: Stochastic Differential Equations
Approach. Hoboken, NJ, USA: Wiley, 2005.
[47] M. K. Elhattab, M. A. Arfaoui, C. Assi, and A. Ghrayeb, “Reconfigurable
intelligent surface assisted coordinated multipoint in downlink NOMA
networks,” IEEE Commun. Lett., vol. 25, no. 2, pp. 632–636, Feb. 2021.
[48] T. C. W. Schenk, E. R. Fledderus, and P. F. M. Smulders, “Performance
analysis of zero-if MIMO OFDM transceivers with IQ imbalance,” J.
Commun., vol. 2, no. 7, pp. 9–19, 2007.
[49] A. Jeffrey and D. Zwillinger, Table of Integrals, Series, and Products.New
York, NY, USA: Academic, 2007.
[50] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions
With Formulas, Graphs, and Mathematical Tables,vol.9.NewYork,NY,
USA: Dover, 1972.
[51] A. Goldsmith, Wireless Communications. New York, NY, USA: Cam-
bridge Univ. Press, 2005.
Tan N . N g u y e n (Member, IEEE) was born in Nha
Trang City, Vietnam, in 1986. He received the B.S.
and M.S. degrees in electronics and telecommuni-
cations engineering, in 2008 and 2012, respectively,
from the Ho Chi Minh University of Natural Sciences,
a member university of the Vietnam National Univer-
sity,Ho Chi Minh City, Vietnam, and the Ph.D. degree
in computer science, communication technology and
applied mathematics, in 2019, from the VSB Techni-
cal University of Ostrava, Ostrava, Czech Republic,
where he is currently working toward the Ph.D. degree
in electrical engineering.
In 2013, he joined the Faculty of Electrical and Electronics Engineering, Ton
Duc Thang University, Ho Chi Minh City, and has been working as a Lecturer
since then. His major research interests include cooperative communications,
cognitive radio, and physical layer security.
Nguyen Nhu Thang received the B.S., M.S., and
Ph.D. degrees in electrical engineering from Le Quy
Don Technical University, Hanoi, Vietnam, in 1991,
1997, and 2017, respectively.
He currently works as a Lecturer with Telecommu-
nications University, Nha Trang, Khanh Hoa, Viet-
nam. His main research interests include antenna,
wireless communication, and cooperative communi-
cation.
Ba Cao Nguyen received the B.S. degree in electri-
cal engineering from Telecommunication University,
Nha Trang, Khanh Hoa, Vietnam, in 2006, the M.S.
degree in electrical engineering from the Posts and
Telecommunications Institute of Technology, Ho Chi
Minh City, Vietnam, in 2011, and the Ph.D. degree
in electrical engineering from Le Quy Don Technical
University, Hanoi, Vietnam in 2020.
From November 2019 to April 2021, he worked
as a Lecturer with Telecommunications University.
He has been with Chungbuk National University as a
Postdoctoral Research Fellow since May 2021 and also with Telecommunica-
tions University as a Lecturer. His research interests include energy harvesting,
full-duplex, spatial modulation, nonorthogonal multiple access, multiple-input
multiple-output, reconfigurable intelligent surface, and cooperative communi-
cation.
Tran Manh Hoang received the B.S. degree in
communication command from Telecommunications
University, Ministry of Defense, Nha Trang, Khanh
Hoa, Vietnam, in 2002, the B.Eng. degreein electrical
engineering from Le Quy Don Technical University,
Ha Noi, Vietnam, in 2006, the M.Eng. degree in
electronics engineering from Posts and Telecommu-
nications, Institute of Technology, Ho Chi Minh City,
Vietnam, in 2013, and the Ph.D. degree in electrical
engineering from Le Quy Don Technical University,
Hanoi, Vietnam, in 2020.
He has been with Chungbuk National University as a visiting Professor and
also with Telecommunications University as a Lecturer. His research interests
include energy harvesting, nonorthogonal multiple access, and signal processing
for wireless cooperative communications.
Phuong T. Tran (Senior Member, IEEE) was born in
Ho Chi Minh City, Vietnam, in 1979. He received the
B.Eng. and M.Eng. degrees in electrical engineering
from the Ho Chi Minh University of Technology, Ho
Chi Minh City, in 2002 and 2005, respectively, and
the M.S. degree in mathematics and Ph.D. degree
in electrical and computer engineering from Purdue
University, West Lafayette, IN, USA, in 2013.
In 2007, he became a Vietnam Education Founda-
tion Fellow with Purdue University. In 2013, he joined
the Faculty of Electrical and Electronics Engineering,
Ton Duc Thang University, Ho Chi Minh City, where he has been the Vice Dean
with Faculty since October 2014. His main research interests include the area
of wireless communications and network information theory.
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