arXiv:2109.11509v1 [eess.SP] 23 Sep 2021
SUBMITTED TO IEEE 1
Integration of Backscatter Communication with Multi-cell NOMA:
A Spectra l Efficiency Optimization under Imp erfect SIC
Wali Ullah Khan, Eva Lagunas, Asad Ma hmood, Symeon Chatzinotas, and Bj¨orn Ottersten
Abstract—Non-orthogonal multiple access (NOMA) is expected
to provide h igh spectral efficiency (SE) and massive connectivity
in futu re wireless networks. On the other side, backscatter
communications (BC) is an emerging technology towards battery-
free transmission in future wireless networks by leveraging
ambient radio frequency (RF) waves that enable communications
among wireless devices. This paper proposes a new optimization
framework to maximize the SE of the NOMA-BC network. In
particular, we simultaneously optimize the transmit power of
the base station and reflection coefficient of the backscatter
device in each cell under the assumption of imp erfect decoding
of successive interference cancellation. The SE optimization
problem is coupled on multiple variables which makes it very
difficult to solve. Thus, we ap ply a decomposition method
and KKT conditions to get an efficient solution. Simulation
results demonstrate the superiority of th e proposed NOMA-BC
framework over the benchmark NOMA without BC f ramework.
Index Terms—Backscatter communication, non-orthogonal
multiple access, imperfect successive interference cancellation.
I. IN TRODUCTION
N
EXT-GENERATION wireless tec hnolog ies a re expected
to improve conn e ction density, latency, energy consump-
tion, and data reliability [1]. Non-orthogonal multiple access
(NOMA) using power multiplexing is one of the emerging
technologies to support a h uge number of wireless devices
while providing high data rates an d low transmission delay
[2]. In NOMA, multiple users can access the same spectr um
and time resources for transmission using different power
levels. In addition to th at, bac kscatter communication s (BC)
has emerged as a promising technology to use the ambient
signals of TV, WiFi, and cellular for the data transmission
between wireless devices [3]. Exploiting the ambient energy
harvesting technique , BC a llows the wireless device to transmit
data towards surroun ding users by reflecting an d modulating
radio frequen cy [4]. The integratio n of BC with NOMA can
further boost the performanc e of the system.
The coexistence of BC with NOMA networks has recently
been investigated [5]–[8]. For example, Khan et al. [5] h ave
optimized the transmit power of the base station (BS) and
reflection c oefficient (RC) of the backscatter device (BD)
to maximize the spectral e fficiency (SE) of the NOMA -BC
system under imperfect SIC detection. In a nother study, Yang
et al. [6] have optimized the time and RC of BD to improve
the minimum throughput of the NOMA-BC system. The work
of Chen et al. [7] have optimized the transmit power of the BS
and RC of BD to m aximize the ergodic capacity of the system.
Moreover, the authors of [8] have optimized the transmit power
of the BS and RC of BD to maximize the energy efficiency
Authors are with the Interdisciplinary Center for Security, Relia-
bility and Trust (SnT), University of Luxembourg, 1855 Luxembourg
City, Luxembourg (Emails: {waliullah.khan, eva.lagunas, asad.mahmood,
symeon.chatzinotas,bjorn.ottersten}@uni.lu).
of the system. Of late, Khan et al. [9] have optimized the
transmit power of the BS and roadside units to ma ximize the
SE of the veh ic ular network.
The above literature considers single-cell scenarios. Besides
that, most of the works [6]–[8] assume perfect SIC detection
which is impractical. To the best of our knowledge, the prob-
lem of resource allo cation for a multi-cell NOMA-BC network
that simultaneously optimizes the transmit power of BS and
reflection coefficient of BD under imperfect SIC detectio n has
not yet been investigated. To fill th is g ap, this paper proposes
a new optimization framework to maximize the SE of the
system while ensuring the minimum data rate of ea ch user. In
particular, we formulate the ma ximization of the SE subject to
various practical constraints. Dual theory and KKT conditions
are exploited to obtain the closed-form suboptimal solution,
where dual variables are iteratively upda ted. Numerical results
confirm the benefits of the proposed NOMA-BC framework
over th e conventional NOMA framework.
II. SYSTEM MODEL AND PROBLEM FORMULATION
We consider a downlink multi-cell NOMA-BC network,
where each BS reuse the same spectrum resources to en-
hance the spectral efficiency. We denote the set of cells as
C = {C
j
|j = 1, 2, 3, . . . , J}. We consider that C
j
serves
two cellular users (U
n
and U
m
) at a given time using NOMA
protocol [10]. If th e transmit power of C
j
is P
j
and the power
allocation coefficient of U
n
and U
m
is denoted as ϕ
n,j
and
ϕ
m,j
. The n the superimposed signa l that C
j
sends to U
n
and
U
m
can be expressed as x
j
=
p
P
j
ϕ
n,j
x
n,j
+
p
P
j
ϕ
m,j
x
m,j
.
Meanwhile, a BD (denoted as D
i
) also receives x
j
from C
j
,
modulate and r eflect a signal e(t) towards U
n
and U
m
with
a power of β
i
, wh ere E[|e(t)|
2
] = 1. Note that E[.] denotes
the expectation operation. Let model the channel from C
j
to
U
n
and U
m
as h
n,j
=
¯
h
n,j
d
−δ/2
n,j
and h
m,j
=
¯
h
m,j
d
−δ/2
m,j
.
Where
¯
h
ι,j
∼ CN(0, 1), ι ∈ {n, m} denotes the coefficient
of Rayleigh fading, d
ι,j
is the distance between C
j
and U
ι
and δ represents the pathloss exponent. This work assumes
the perfect channel state information, thus, the signals that U
n
and U
m
receive from C
j
can be written as
y
n,j
=
p
h
n,j
x
j
+
q
β
i,j
g
j
n,i
(h
i,j
x
j
)e(t)
+
J
X
j
′
=1,j
′
6=j
q
P
j
′
h
j
n,j
′
x
j
′
+
n,j
, (1)
y
m,j
=
p
h
m,j
x
j
+
q
β
i,j
g
j
m,i
(h
j
m,i
x
j
)e(t)
+
J
X
j
′
=1,j
′
6=j
q
P
j
′
h
j
m,j
′
x
j
′
+
m,j
, (2)
where the first segment in (1) and (2) is the r eceived signal
from C
j
, the second segment is the reflected signal from D
i
,
the third segment represents the in te r-cell interference, and the
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