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1
Performance Analysis of Large Intelligent Surface
Aided Backscatter Communication Systems
Wenjing Zhao, Gongpu Wang, Saman Atapattu, Senior Member, IEEE,
Theodoros A. Tsiftsis, Senior Member, IEEE, and Xiaoli Ma, Fellow, IEEE
Abstract—Employing backscatter communication is a promis-
ing solution for Internet of Things (IoT). The novel large intel-
ligent surface (LIS) concept can achieve reliable communication
by establishing line-of-sight like channels. This paper thus con-
siders an LIS-aided backscatter system to support high-reliable
communications for IoT applications. In this letter, the symbol
error probability (SEP) for both intelligent and random phase
adjustments at the LIS reflectors is analytically investigated. In
particular, we calculate the SEP based on the moment generating
function approach and also provide tight SEP upper bounds
for either fully correlated or mutually independent channels.
Insightful observations of SEP outcomes reveal that having a
large number of reflective elements on the LIS has a significantly
positive impact on the SEP performance where high reliability
can be achieved in moderate signal-to-noise.
Index Terms—Backscatter communication, Internet of Things
(IoT), large intelligent surface, symbol error probability, high-
reliable communication.
I. INT ROD UC TI ON
Backscatter communication has recently emerged as a key
enabler for pervasive connectivity of low-power and low-cost
wireless devices, e.g., radio frequency identification (RFID)
technology used in various applications of the Internet of
Things (IoT) [1], [2]. In RFID systems, the reader first trans-
mits a signal to the tag which then loads its own information
to the received signal and backscatters the modulated signal
to the reader [3]. This traditional backscattering is appropriate
only for short-range communications due to round-trip path
attenuation.
To realize moderate- or long-range communications, relay-
aided [4], [5] and multi-antenna [6], [7] backscattering have
been introduced as alternative solutions. Since such techniques
This study is supported in part by Key Laboratory of Universal Wireless
Communications (BUPT), Ministry of Education, P.R.China under Grant
KFKT-2018104, in part by the Natural Science Foundation of China (NSFC)
under Grants 61571037, 61871026 and U1834210, in part by NFSC Outstand-
ing Youth under Grant 61725101, and in part by the Australian Research
Council (ARC) through the Discovery Early Career Researcher (DECRA)
Award under Grant DE160100020. (Corresponding author: Gongpu Wang)
W. Zhao and G. Wang are with Beijing Key Lab of Transportation Data
Analysis and Mining, School of Computer and Information Technology,
Beijing Jiaotong University, Beijing 100044, China (e-mail: {wenjingzhao, g-
pwang}@bjtu.edu.cn).
S. Atapattu is with the Department of Electrical and Electronic Engineer-
ing, The University of Melbourne, Parkville, VIC 3010, Australia (e-mail:
saman.atapattu@unimelb.edu.au).
T. A. Tsiftsis is with the School of Intelligent Systems Sci-
ence and Engineering, Jinan University, Zhuhai 519070, China (email:
theo tsiftsis@jnu.edu.cn).
X. Ma is with the School of Electrical and Computer Engineering,
Georgia Institute of Technology, Atlanta, GA 30332-0250 USA (e-mail:
xiaoli@gatech.edu).
include active components that consume significant energy at
digital-to-analog converter, oscillator, up-converter and power
amplifier [6], they may not be suitable for low-power appli-
cations. Moreover, relay-aided system is of high complexity
especially for full duplex scheme [5].
In the recent two years, large intelligent surface (LIS), also
called reconfigurable intelligent surface (RIS), has emerged as
an attractive solution to replace power-hungry active compo-
nents [8], [9]. Thus, it may also serve as a potential solution
to performance improvement for backscatter systems, which
is the proposition of this letter.
The LIS is an artificial smart material which consists of
a vast amount of nearly passive reflectors. Each reflector
only changes the phase of impinging signals in a software-
controlled way, but with no dedicated energy sources for signal
retransmission [10], and makes the overall communication
process controllable. Moreover, LIS can be easily embed-
ded into buildings (walls/ceilings) and other objects such as
clothes. Although the performance of LIS has been studied for
different scenarios such as data transmission [11], energy effi-
ciency of multi-user communications [9], beamforming design
[12], user assignment in distributed LIS system [13] and ultra-
reliable communication [14], [15], it has not been investigated
for backscatter communications. To fill this research gap, we
integrate the performance of backscatter technology with LIS
in terms of symbol error probability (SEP). Specifically, we
evaluate the SEP of LIS-aided intelligent and blind transmis-
sion schemes where we consider either fully correlated or mu-
tually independent channels. Numerical results show that LIS-
assisted communication with full channel state information
(CSI) outperforms the blind communication and amplify-and-
forward (AF) aided one for the entire signal-to-noise (SNR)
regime.
The rest of the paper is organized as follows. Section II
provides the system model. Section III derives the SEP in
cases of intelligent and random adjustment for fully correlated
and mutually independent channels, respectively. Numerical
results are discussed in Section IV, and conclusions are drawn
in Section V.
Notations:∠Adenotes the phase angle of number A.
x∼ CN (µ, σ2)or N(µ, σ2)represents that xis a complex or
real Gaussian random variable with mean µand variance σ2.
E{x}and D{x}stand for the mean and variance of variable
x, respectively. ∥x∥denotes the Euclidean norm of vector x.
2
Small
Device
Reader
LIS
fm
h
bm
h
fm
g
bm
g
Fig. 1. An LIS aided backscatter communication system.
II. SY ST EM MO DE L
As illustrated in Fig. 1, we consider a backscatter com-
munication system consisting of a reader (R), a small device
such as a tag (T), a sensor or a power-limited terminal, and
an LIS where nearly passive components on the LIS only
adjust the phases of incident signals. No line-of-sight link is
available between the reader and the tag. The LIS contains
2Nreconfigurable reflectors where the mth passive element
on the LIS is denoted as Im. Further, channel gains of the links
R−In,In−T,T−Imand Im−Rare denoted and distributed
as hfn ∼ CN(0, σ2
hf ), gfn ∼ CN(0, σ2
gf ), gbm ∼ CN(0, σ2
gb)
and hbm ∼ CN (0, σ2
hb), respectively. Channels can be estimat-
ed in advance by using compressive sensing or deep learning
techniques with a few low-power active reflectors in LIS [16].
All channels are mutually independent. In the kth time period,
the signal transmitted by Ris s(k)and the modulated signal
at Tis b(k). The transmit signal power at Ris Ps. Suppose
the reflectors for the forward and backward links are placed
row by row alternately. Without loss of generality, we assume
there are two rows of reflectors with each row Nreflectors.
Also it is assumed that the closest reflectors for the forward
and backward links are nand N+nfor n∈ {1,·· · , N },
respectively. Then the received signal at Ris
y(k) =
m
n
η2hbmgbm hfngf nej(θf n +θbm )s(k)b(k) + w(k),
where n∈ {1,·· · , N },m=n+N,ηis reflection factor
inside LIS, θfn and θbm are separately adjustable phases of
the nth and mth reflectors of the LIS in the forward link (i.e.,
from Rto T) and the backward link (i.e., from Tto R), and
the additive white Gaussian noise is w(k)∼ CN(0, σ 2
w).
III. SYMBOL ERRO R PROBAB IL IT Y (SEP)
In this section, we study the SEP of M-ary phase shift
keying (M-PSK) modulation for two scenarios: A) intelligent
adjustment; and B) random adjustment. In each scenario, we
also consider two cases: 1) the forward and backward links
are fully correlated; and 2) the forward and backward links
are mutually independent. The SEP can be calculated by using
the moment generating function (MGF) based approach [14],
[15]. For M-PSK modulation, the SEP is given by [17]
PPSK
e=1
π(M−1)π
M
0
Mγ−sin2(π/M)
sin2θdθ, (1)
where Mγ(t) = E{eγt }is the MGF of γ, the SNR at R.
A. Intelligent Adjustment
In this part, full CSI is available at the LIS. Thus, LIS can
perform intelligent phase adjustment to satisfy some specific
requirements.
1) For Fully Correlated Channels: With a small distance
between reflectors for phase adjustment in two directions, the
forward and backward channels can be considered to be fully
correlated. When forward and backward channels of the same
link are fully correlated, i.e., hbm =hfn and gbm =gfn for
n∈ {1,·· · , N }and m=n+N, setting θbm =−∠hbmgbm
yields the maximum SNR at Ras
γic =η4Ps
σ2
w2N
m=N+1 |hbmgbm |4
,¯γ T 4
ic,(2)
where ¯γ,η4Ps
σ2
wand Tic ,2N
m=N+1 |hbmgbm |. According
to the central limit theorem (CLT), Tic ∼ Nµic , σ2
icfor a
sufficiently large number of elements Nat the LIS, where
µic ,E{Tic}=π
4Nσ2
hbσ2
gb and σ2
ic ,D{Tic}= (1 −
π2
16 )Nσ2
hbσ2
gb. The MGF of γic can be derived for t < 0as
Mγic (t) =
∞
q=0
µ2q
ic (−¯γt)−q
2W−q
2,1
4−(16σ4
ic¯γt)−1
23qσ4q
ic q! exp µ2
icσ−2
ic /2 + (32σ4
ic¯γt)−1(3)
where Wa,b(·)is the Whittaker function [18, eq. (9.223)]. The
proof is given in Appendix A. With the aid of (1) and (3), an
approximation for the average SEP can be calculated. Since it
is cumbersome to derive the SEP in a closed form, a numerical
integration technique should be applied. In order to further
investigate the system, setting θ=π
2leads to an upper bound
which can be derived as
PPSK
ic,up =
∞
q=0
(1 −M−1)µ2q
ic ¯γ−q
2W−q
2,1
4sin−2(π
M)
16σ4
ic ¯γ
23qσ4q
ic q! sinq(π
M) exp µ2
ic
2σ2
ic −sin−2(π
M)
32σ4
ic ¯γ.(4)
By using the same setting for the remaining cases, we will
derive the respective MGFs and upper bounds.
2) For Independent Channels: We consider mutually in-
dependent channels which can be achieved with reasonable
separation between reflectors. Setting θbm =−∠hbmgbm and
θfn =−∠hfn gfn yields the maximum SNR at Ras
γii = ¯γ2N
m=N+1
N
n=1 |hbmgbm hfngf n|2
,¯γ T 2
ii ,(5)
where Tii ,2N
m=N+1 N
n=1 |hbmgbm hfngf n|. For large
N, we also have Tii ∼ CN(µii , σ2
ii)where µii =
π2
16 N2σ2
hbσ2
gbσ2
hf σ2
gf and σ2
ii =N2+π2
8N2(N−1) +
π4
256 N2(N−1)2−π4
256 N4σ2
hbσ2
gbσ2
hf σ2
gf . The MGF of γii
can be derived for t < 0as
Mγii (t) = exp µ2
ii¯γt(1 −2σ2
ii¯γt)−1(1 −2σ2
ii¯γt)−1
2.(6)
The proof is given in Appendix B. While the SEP can be
calculated numerically by using (1) and (6), its upper bound
can be obtained as
PPSK
ii,up =
(M−1) exp −µ2
ii ¯γsin2(π
M)
1+2σ2
ii ¯γsin2(π
M)
M1+2σ2
ii¯γsin2(π
M)
.(7)
3
B. Random Adjustment
We assume CSI is unavailable at the LIS in this part. Thus,
the LIS may not be able to adjust the phases optimally for the
maximum receive SNR.
1) For Fully Correlated Channels: In this case, the SNR
at Rcan be derived as
γbc =¯γ
2N
m=N+1
hbmgbm ejθbm
4
,¯γ∥Tbc∥4,(8)
where Tbc ,2N
m=N+1 hbmgbm ejθbm . For large N, we have
Tbc ∼ CN0, σ2
bcwhere σ2
bc =N σ2
hbσ2
gb. The MGF of γbc
can be derived for t < 0as
Mγbc (t) = −π
σ4
bc ¯γt exp −1
4σ4
bc ¯γt Q1
−2σ4
bc ¯γt ,(9)
where Q(z)is the Gaussian Q-function [18]. The proof is
given in Appendix C. While the exact average SEP can be
calculated numerically by using (1) and (9), its upper bound
can be obtained as
PPSK
bc,up =(1 −M−1)√πcbc exp (cbc/4) Qcbc /2,(10)
where cbc =σ−4
bc ¯γ−1sin−2(π/M).
2) For Independent Channels: In this case, the SNR at R
can be derived as
γbi = ¯γ
2N
m=N+1
hbmgbm ejθbm
N
n=1
hfngf nej θfn
2
,¯γ∥TbibTbif ∥2,(11)
where Tbib ,2N
m=N+1 hbmgbm ejθbm and Tbif ,
N
n=1 hfngf nej θfn . For large N, we have Tbib ∼
CN0, σ2
biband Tbif ∼ CN0, σ 2
bif , where σ2
bib =Nσ2
hbσ2
gb
and σ2
bif =Nσ2
hf σ2
gf . The MGF of γbi can be derived for
t < 0as
Mγbi (t) = 1
−σ2
bi¯γt exp −1
2σ2
bi¯γt W−1
2,0−1
σ2
bi¯γt (12)
where σ2
bi =σ2
bibσ2
bif . The proof is given in Appendix D.
While the exact average SEP can be calculated numerically
by using (1) and (12), its upper bound can be obtained as
PPSK
bi,up =(1 −M−1)√cbi exp (cbi/2) W−1/2,0(cbi ),(13)
where cbi =σ−2
bi ¯γ−1sin−2(π/M).
Remark 1: We approximate the SNR at Ras a Gaussian
random variable by assuming large N. Since the SNR is a
positive value, its behavior may not be fully described by a
Gaussian random variable which may have negative values.
This reason causes the gap between theoretical and simulation
results in Section IV.
Remark 2: For M-ary quadrature amplitude modulation
(M-QAM), the SEP expression is given in [17, eq. (9.21)].
Given the MGFs in Section III for different scenarios/cases,
we can calculate the average SEP numerically, and can also
derive upper bounds analytically. Due to space limitation, we
do not provide further details.
10 15 20 25 30 35 40 45
SNR
10-5
10-4
10-3
10-2
10-1
100
SEP
Simulation
(intelligent
for correlated)
Approximation
((3) for intelligent)
Upper Bound
((4) for intelligent)
Simulation
(random
for correlated)
Approximation
((9) for random)
Upper Bound
((10) for random)
Simulation
(backscatter)
Simulation
(AF relay)
N=40 N=30
N=30,40
Fig. 2. The average SEP of 8-PSK vs SNR for fully correlated channels.
10 15 20 25 30 35 40 45
SNR
10-5
10-4
10-3
10-2
10-1
100
SEP
Simulation (intelligent
for independent)
Approximation
((6) for intelligent)
Upper Bound
((7) for intelligent)
Simulation (random
for independent)
Approximation
((12) for random)
Upper Bound
((13) for random)
Simulation
(backscatter)
Simulation
(AF relay)
N=40
N=30
N=30,40
Fig. 3. The average SEP of 8-PSK vs SNR for independent channels.
IV. SIMULATION RESULTS
In this section, simulation results are provided to verify the
accuracy of the analytical results, and to discuss the perfor-
mance of LIS. All channels are subject to small scale fading
and large scale fading. We suppose the variance of small scale
fading is one [20], and path loss and distance parameters for
large scale fading are 2 and 6.32 m, respectively. The noise
variance is set as σ2
w= 1. All figures show the average SEP
vs SNR. All theoretical approximation values are calculated
numerically by using (1) and corresponding MGFs. All the-
oretical upper-bound values are calculated by using closed-
form analytical expressions in Section III. Comparisons to AF
relay and traditional backscatter [3] aided communication are
provided in Fig. 2 and Fig. 3. It can be found that LIS-aided
backscatter with intelligent adjustment far outperforms AF
relay assisted one. However, relay-aided systems have better
SEP performance than LIS-based ones in the case of no CSI.
As seen, traditional backscatter behaves worst.
All figures show that theoretical approximations approx-
imates to simulations (exact). However, approximations be-
come loose for small N, e.g., N= 30, at moderate and high
SNRs due to the reason mentioned in Remark 1. Over the
entire simulated SNR region, upper bounds follow the similar
4
0 5 10 15 20 25 30
SNR
10-5
10-4
10-3
10-2
10-1
100
SEP
Simulation (intelligent for correlated)
Approximation ((3) for intelligent)
Simulation (random for correlated)
Approximation ((9) for random)
Simulation (intelligent for independent)
Approximation ((6) for intelligent)
Simulation (random for independent)
Approximation ((12) for random)
M=4
M=4
M=2
M=2
Fig. 4. The average SEP vs SNR when N= 30.
performance trend as approximations. For example, as intel-
ligent transmission with N= 40 in Fig. 2, the gap between
simulation and approximation is 1.2 dB and the gap between
approximation and upper-bound is 1.25 dB at 10−5SEP. This
confirms that our analytical expressions are accurate enough
to highlight the performance trend of the LIS. Moreover, we
achieve a significant SEP improvement by using intelligent
adjustment. As shown in Fig. 2 for N= 40, the gain achieved
by intelligent adjustment over random adjustment and relay-
aided one is more than 25 dB at 10−2SEP. In general, as we
expected, the SEP reduces when i) SNR increases (all figures);
ii) Nincreases (Figs. 2 and 3); and iii) Mdecreases (Fig. 4).
For example, as intelligent transmission in Fig. 2, the proposed
system LIS achieves around 5.8 dB gain at 10−5SEP when
Nincreases from 30 to 40. Fig. 4 also shows that the system
has lower SEP under independent channels than the correlated
ones.
V. CONCLUSION
One LIS-based backscatter system was proposed, and its
SEP performance was analyzed. Specifically, we studied both
intelligent and blind transmissions via the LIS for fully corre-
lated and mutually independent channels. For each scenario,
we first derived the SNR at the reader, then modeled its
statistic as a Gaussian random variable by assuming a large
number of reflected elements on the LIS, and finally obtained
the corresponding MGF. This MGF helps us to calculate an
approximation for the average SEP of M-PSK modulation.
Then, we introduced an upper bound for the average SEP
which closely follows the LIS performance. It was shown
that the proposed LIS transmission scheme can achieve high-
reliable (low SEP) backscatter communications at moderate
SNR with a large number of reflective elements. Moreover,
LIS scheme with smart phase adjustment outperforms relay
one. Therefore, this can be a promising candidate for future
communication in IoT and RFID applications.
APP EN DI X A
Define z,T2
ic. For sufficiently large number N, the random
variable zfollows a noncentral chi-squared distribution, and
its probability density function (PDF) is [19]
fz(z) =0.5(2πσ2
icz)−0.5exp −0.5σ−2
ic (z+µ2
ic)(A.1)
exp µicσ−2
ic √z+ exp −µic σ−2
ic √z.
Then, we can obtain the MGF Mγic (t)as
Mγic (t)(a)
=
∞
q=0
µ2q
ic (−¯γt)−q
2−1
4D−q−1
22−3
2σ−2(−¯γt)−1
2
25
2q+3
4σ4q+1
ic q! exp µ2
ic
2σ2
ic +1
32σ4
ic ¯γt
(b)
=
∞
q=0
µ2q
ic (−¯γt)−q
2W−q
2,1
4−σ−4
ic (16¯γt)−1
23qσ4q
ic q! exp µ2
ic
2σ2
ic +1
32σ4
ic ¯γt ,
where (a) results by using the definition of the MGF, then
applying the infinite series expansion of exponential terms, and
finally solving the integration with the aid of [18, eq. (3.462)]
where Dp(z)is a parabolic cylinder function; and (b) follows
by using the identities Dp(z) = 21
4+p
2W1
4+p
2,−1
4(z2
2)z−1
2and
Wλ,−µ(z) = Wλ,µ(z).
APPENDIX B
Define z,T2
ii . For sufficiently large number N, the PDF
of zin this case is also similar to (A.1) but by replacing µic
and σ2
ic with µii and σ2
ii, respectively. Then, the MGF Mγii(t)
can be derived as
Mγii (t) =
exp −µ2
ii
2σ2
ii
2πσ2
ii
∞
q=0
µ2q
ii
σ4q
ii (2q)! ∞
0
e¯γzt−z
2σ2
ii zq−1
2dz
(a)
= exp −µ2
ii
2σ2
ii ∞
q=0
µ2q
ii (0.5σ−2
ii −¯γt)−q−1
2
(2σ2
ii)2q+1
2q!,
where (a) follows from [18, eq. (3.371)]. By using the identity
exp(x) = ∞
q=0 xq
q!for (a), we can derive (6).
APPENDIX C
Define z,∥Tbc∥2where zis an exponentially distributed
random variable with PDF
fz(z) = σ−2
bc exp(−zσ−2
bc ).(C.1)
Then the MGF Mγic (t)can be derived as
Mγiu (t) = ∞
0
σ−2
bc exp ¯γz2t−zσ−2
bc dz
(a)
=−πσ−4
bc (¯γt)−1exp −(4σ4
bc ¯γt)−1Q(−2σ4
bc ¯γt)−1
2,
where (a) follows with the aid of [18, eq. (3.322.2)] and then
by using the identity Φ(z) = 1 −2Q(√2z). Here Φ(z)is
probability integral function.
APPENDIX D
Define zb,∥Tbib∥2,zf,∥Tbif ∥2and z,zbzf. The
PDFs of zband zffollow (C.1). Since two random variables
zband zfare independent, the PDF fz(z)is the convolution
5
of two PDFs fzb(z)and fzf(x). Therefore, we have: fz(z) =
∞
0fzb(zb)fzf(z
zb)dzbwhich can be derived as
fz(z)(a)
=∞
0
σ−2
bibσ−2
bif x−1exp −zb−zσ−2
bibσ−2
bif x−1dx
(b)
=2σ−2
bibσ−2
bif K02zσ−2
bibσ−2
bif ,
where (a) follows by substituting x=zbσ−2
bib; and (b) follows
from [18, eq. (3.471.12)] where Kα(x)is the modified Bessel
function of the second kind. Then the MGF Mγib (t)can be
derived as
Mγbi (t) = ∞
0
2σ−2
bibσ−2
bif exp ¯γztK02zσ−2
bibσ−2
bif dz
(a)
= (−cbit)−1/2exp −2−1c−1
bi t−1W−1
2,0−c−1
bi t−1,
where (a) follows by [18, eq. (6.643.3)], and cbi =σ2
bibσ2
bif ¯γ.
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