Energy-efficient Optimization for IRS-assisted Wireless-powered Communication Networks

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Energy-efficient Optimization for IRS-assisted
Wireless-powered Communication Networks
Qianzhu Wang∗, Zhengnian Gao∗, Yongjun Xu∗† , and Hao Xie∗
∗School of Communication and Information Engineering, Chongqing University of Posts and
Telecommunications, Chongqing 400065, China
†Shandong Provincial Key Laboratory of Wireless Communication Technologies, Shandong University, Jinan
250100, China
Abstract—Wireless-powered communication is a promising
technique to provide convenient and perpetual energy for energy-
constrained wireless devices. However, the uplink information
transmission of wireless devices in wireless-powered commu-
nication networks relies on the harvested energy from the
downlink-energy-transfer power station (PS). To tackle this issue,
we propose a new intelligent reflecting surface (IRS)-assisted
wireless-powered network architecture, where an IRS is deployed
between a PS and multiple wireless-powered users to enhance the
efficiency of energy harvesting. The total energy efficiency (EE)
of all wireless-powered users is maximized by jointly optimizing
the energy transfer matrix of the PS, the transmission time and
power of users, and the phase shifts of the IRS. The formulated
problem is non-convex and challenging to solve. Accordingly, the
alternating optimization approach, Dinkelbach’s method, and the
variable-substitution approach are used to solve it. Simulation
results verify the effectiveness of the proposed algorithm.
Index Terms—Wireless-powered communication networks, en-
ergy efficiency, intelligent reflecting surface, resource allocation
I. INTRODUCTION
THE fifth-generation (5G) mobile communication system
has achieved large-scale connections and high-speed da-
ta transmission due to a large number of new introducing
technologies, such as ultra-dense networks, multiple-input
multiple-output systems, etc. [1]–[4]. However, massive data
communication can consume a lot of energy, which brings a
challenge for prolonging the lifetime of wireless devices with
limited battery capacities. To solve this problem, wireless-
powered communication networks (WPCNs) as a promising
solution have been proposed [5]–[7]. To be more specific, in a
WPCN, wireless devices can harvest wireless radio-frequency
energy from an energy source and then transmit the wireless
signals to the receivers [8].
In practical scenarios, the performance of WPCNs is con-
strained by the efficiency of energy transformation and trans-
mission time scheduling. Therefore, resource allocation as
an effective approach has been proposed to improve system
This research was supported by the National Natural Science Foundation of
China (61601071), in part by the Natural Science Foundation of Chongqing
(cstc2019jcyjxfkxX0002), in part by the Open Research Fund from the Shan-
dong Provincial Key Laboratory of Wireless Communication Technologies
(SDKLWCT-2019-04), in part by Entrepreneurship and Innovation Support
Program for Returned Overseas Students of Chongqing (cx2020095), in part of
the Graduate Scientific research innovation Project of Chongqing (CYS20251,
CYS20253).
Corresponding author: Yongjun Xu (xuyj@cqupt.edu.cn)
capacity and the energy efficiency (EE) of WPCNs [9], [10]. In
particular, in [9], a resource allocation algorithm was proposed
to maximize the sum rate of multiple users in a WPCN
with downlink energy transformation and uplink wireless
information transmission. The authors in [10] investigated the
maximum achievable EE of the network by jointly optimizing
the transmission time and power allocation. However, the
communication performance of the energy-constrained devices
depends on the energy harvested from a power station (PS),
while the efficiency of the energy harvesting easily suffers
from the surrounding obstacles and severe channel attenua-
tions.
Recently, intelligent reflecting surface (IRS) as a passive and
low-energy technology has been attracted great attention from
academia and industry to improve the efficiency of energy
harvesting and system performance of WPCNs. Specifically,
each element of the IRS can independently adjust the phase
shifts of the incident signal in real time, meanwhile, the
IRS can reflect the signals to the desired users in a low-
power way [12], [13]. Moreover, in [14], a resource allocation
problem with the sum-rate maximization of users was studied
for an IRS-assisted WPCN. The authors in [15] investigated
the max-min throughput-based resource allocation problem by
optimizing the transmission time and power in a cooperative
IRS-assisted WPCN. In [16], the authors considered a sum-
rate maximization problem by jointly optimizing the phase
shifts of the IRS and network resource, where the IRS can
simultaneously harvest the energy from the PS and reflect the
wireless signals to the destination.
The existing works on the IRS-assisted WPCNs mainly
concentrated on using the IRS in WPCN and optimized
network throughput, but they neglected the balance between
transmission rate and energy consumption, namely the EE
problem. To our best knowledge, there are no open works to
address the system EE maximization problem for IRS-assisted
WPCNs.
In this paper, we propose an iteration-based resource allo-
cation algorithm for an IRS-assisted WPCN by jointly opti-
mizing the energy transfer matrix of the PS, the transmission
time and power of users, and the phase shifts of the IRS to
maximize system EE. The main contributions of this paper are
summarized as follows:
•Considering the quality of service (QoS) requirements of
users and the circuit power consumption of the whole
system, an EE-based resource allocation problem for an
IRS-assisted WPCN is formulated as a joint optimization

PS
IRS
Energy channel Information channel
Obstacle
User 1
User K
User 2
gK
g2
g1
Destination
Fig. 1. A multiuser IRS-assisted WPCN.
problem of the energy transfer matrix of the PS, the
transmission time and power of users and the phase shifts
matrix of the IRS.
•The formulated problem is non-convex due to the frac-
tional objective function and the coupled variables. To
tackle this challenging problem, we exploit the alter-
nating optimization approach, Dinkelbach’s method, and
variable substitution approaches to convert the problem
into an equivalent convex form. Also, the semidefinite
relaxation (SDR) method and the Gaussian randomization
method are used to solve it.
•Simulation results verify that our proposed algorithm has
good convergence and better EE by comparing it with the
baseline algorithms.
The rest of this paper is structured as follows. The system
model and problem formulation are presented in Section II.
In Section III, we design an EE-based maximization resource
allocation algorithm. Section IV gives the simulation results.
The paper is concluded in Section V.
II. SY ST EM MO DE L AND PROBLEM FORMULATI ON
In this paper, we consider an IRS-assisted WPCN, as shown
in Fig. 1, where the direct link from the PS to the users is
blocked by obstacles (e.g., buildings). And an IRS with N
passive reflecting elements (e.g., ∀n∈ N ={1,2,·· · , N}) is
deployed between a multi-antenna PS with Mantennas and K
wireless-powered users for assisting the energy transmission
from the PS to the users, denote K={1,2,·· · , K},∀k∈ K.
The PS provides the energy signals to the IRS. Then, the IRS
as an energy relay node provides powerful energy to the users
by changing the transmission direction of electromagnetic
waves. Furthermore, the users use the harvested energy to
transmit the wireless signals to the single-antenna destination
by a time division multiple access mode.
Meanwhile, the transmission block with the duration of T
seconds is divided into two stages, i.e., the wireless energy
transfer (WET) stage and the wireless information transmis-
sion (WIT) stage, as shown in Fig. 2. During the WET stage,
the PS transmits the energy signal to the IRS, and all users
harvest the energy from the IRS for wireless information
transmission. During the WIT stage, all users use the harvested
Ă
WET stage
T
PS IRS
IRS Users Users Destination
W
0
W
1
W
2
W
K
WIT stage
Fig. 2. Time allocation structure.
energy to transmit the wireless information to the destination.
Here, defining t0as the energy-harvesting time, and denoting
tkas the information transmission time of user k, according
to the time structure, the total time should satisfy
t0+
K
X
k=1
tk≤T(1)
A. Energy Transfer Model
During the WET stage (e.g., t0), define sE∈CM×1as the
transmit energy signal of the PS, the energy transfer matrix
W∈CM×Mcan be expressed as
W=EsEsH
E.(2)
Defining Pmax as the maximum transmit power of the PS,
the transmit power satisfies
Tr (W)≤Pmax.(3)
Denoting θn∈[0,2π)as the n-th reflecting element of
the IRS, thus, the phase shift matrix of the IRS can be
expressed as Θ= diag(v), where v= [v1, v2, ..., vN]H∆
=
[ejθ1, ejθ2, ..., ejθN]H. Then, the received signal at the user k
is expressed as
yEH
k=hH
r,kΘHsE+nk,(4)
where H∈CN×Mand hH
r,k ∈C1×Nare the channel matrix
from the PS to the IRS and from the IRS to the user k,
respectively. nk∼ CN (0, δ2
k)is the zero-mean complex white
Gaussian noise with variance δ2
kof the k-th user. Since the
receiving noise is small, it is can be neglected [16]. Thus,
based on (4), the energy harvested at the user kcan be
expressed as
EEH
k=χt0Eh|yEH
k|2i=χt0hH
r,kΘHWhH
r,kΘHH,
(5)
where the 0<χ ≤1is the energy conversion efficiency of
each user.
B. Information Transmission Model
During the WIT stage, the user ktransmits its information
to the destination in tk. Defining skas the symbol of the user
k, and satisfies Eh|sk|2i= 1, the transmission signal of the
user kcan be expressed as
xk=√pksk,(6)

where pkis transmit power of the user kand satisfies the
following energy constraint
pktk+pC
k(t0+tk)≤EEH
k,(7)
where pC
kis the circuit power consumption of user k. The
received signal of the destination is defined as yD
ki.e.,
yD
k=gkxk+nD,(8)
where gkdenotes the channel coefficient from the user kto the
destination. nD∼ CN(0,δ2
0)is the zero-mean complex white
Gaussian noise with variance δ2
0at the destination. Motivated
by the work in [16], the achievable throughput of user kis
Rk=tklog21 + pk|gk|2
δ2
0.(9)
Denoting the t= [t1, t2, ..., tK]Tand p= [p1, p2, ..., pK]T
as the time allocation vector and transit power vector of the
users, respectively. Based on (9), the sum throughput of all
users is defined as R, is given by
R(t,p) =
K
X
k=1
Rk=
K
X
k=1
tklog21 + pk|gk|2
δ2
0.(10)
C. Energy Consumption Model
Defining the circuit power consumption of the PS and the
destination as PC
PS and PC
D, respectively. Meanwhile, denote
the circuit power consumption of the IRS as PC
IRS =Nu,
where uis the circuit power consumption of each element
[17].
During the WET stage, the overall energy consumption of
the considered system is
QWET (W, t0,Θ) = t0PC
PS +PC
IRS+
K
X
k=1
t0pC
k
+t0Tr (W)−
K
X
k=1
χt0hH
r,kΘHWhH
r,kΘHH
(11)
During the WIT stage, the energy consumption is
QWIT (t,p) =
K
X
k=1
tkpk+
K
X
k=1
tkpC
k+
K
X
k=1
tkPC
D(12)
Based on (11) and (12), the total energy consumption of the
whole system is
Qtotal (W, t0,t,p,Θ) = QWET (W, t0,Θ) + QWIT (t,p)
=t0PC
PS +PC
IRS+
K
X
k=1
(t0+tk)pC
k+t0Tr (W)
−
K
X
k=1
χt0hH
r,kΘHWhH
r,kΘHH+
K
X
k=1
tkPC
D
+
K
X
k=1
tkpk.
(13)
D. Problem Formulation
In this subsection, a resource allocation problem with the
system EE maximization is formulated as follows
max
W,t0,t,p,Θ
R(t,p)
Qtotal (W, t0,t,p,Θ)
s.t. C1:pktk+pC
k(t0+tk)≤EEH
k,
C2:t0+
K
X
k=1
tk≤T, t0≥0, tk≥0,
C3:tklog21 + pk|gk|2
δ2
0≥Rmin
k,
C4: Tr (W)≤Pmax,
C5:|Θn,n|= 1,∀n,
(14)
where Rmin
kdenotes the individual QoS constraint of the k-th
user. C1ensures that the energy consumption of user kdoes
not exceed the harvested energy EEH
k.C2denotes the total
time constraint. C3is the minimum throughput constraint of
the users. C4limits the maximum transmit power of the PS. C5
is the phase shift constraint. Problem (14) is non-convex due to
the fractional objective function and the coupled optimization
variables.
III. ENERGY-EFFIC IE NT RESOURCE AL LO CATI ON
ALGORITHM
In this section, the alternating optimization technique [18],
Dinkelbach’s method [19], and variable substitution approach-
es are used to solve problem (14).
A. Optimize W, t0,t,punder the fixed Θ
For a given phase shift Θ, the channels from the PS to the
IRS and from the IRS to the user kcan be equivalently written
as Gk=hH
r,kΘH. Substituting (5) into (14), We can obtain
the following optimization problem
max
W,t0,t,p
R(t,p)
Qtotal (W, t0,t,p)
s.t. C2−C4,
˜
C1:pktk+pC
k(t0+tk)≤χt0GkWGH
k,
(15)
Since the objective function is a nonlinear form, it’s difficult
to solve it directly. Based on Dinkelbach’s method [19], a
fractional expression can be transformed into a non-fractional
form. Then, define ηas the optimal system EE, we have an
equivalent problem, i.e.,
η∗= max
W,t0,t,p
R(t,p)
Qtotal (W, t0,t,p).(16)
Based on (16), there exists an equivalent problem i.e.,
max
W,t0,t,pR(t,p)−η∗Qtotal (W, t0,t,p)= 0.(17)
The optimal EE can be obtained under the optimal variables
(W∗, t∗
0,t∗,p∗). Based on (17), problem (15) can be rewritten
as
max
W,t0,t,pR(t,p)−ηQtotal (W, t0,t,p)
s.t. ˜
C1, C2−C4.
(18)

Although problem (18) is more tractable than the original
problem (15), it is still a non-convex optimization problem
due to the coupled variables in the objective function and
the constraints. To resolve the non-convex problem, define
the auxiliary variables ¯
W=t0W,e= [e1, e2, ..., eK]T,
ek=pktk, problem (18) can be written as
max
¯
W,t0,t,e
K
X
k=1
tklog21 + ek|gk|2
tkδ2
0−η t0PC
PS
+PC
IRS+
K
X
k=1
(t0+tk)pC
k+
K
X
k=1
tkPC
D+
K
X
k=1
ek+ Tr ¯
W−
K
X
k=1
χGk¯
WGH
k!
s.t. ¯
C1:ek+pC
k(t0+tk)≤χGk¯
WGH
k,
¯
C2:t0+
K
X
k=1
tk≤T, t0≥0, tk≥0,
¯
C3:tklog21 + ek|gk|2
tkδ2
0≥Rmin
k,
¯
C4: Tr ¯
W≤t0Pmax.
(19)
Problem (19) is a standard convex optimization problem,
which can be solved directly by using CVX tools [20].
B. Optimize the phase shift Θunder the fixed (W, t0,t,p)
For fixed the (W, t0,t,p), the optimization problem of the
phase shifts Θcan be formulated as
max
Θ
K
X
k=1
χt0hH
r,kΘHWhH
r,kΘHH
s.t. C1:pktk+pC
k(t0+tk)≤EEH
k,
C5:|Θn,n|= 1,∀n.
(20)
Define Φk= diag hH
r,kH, then hH
r,kΘH =
vHdiag hH
r,kH=vHΦk. Thus, problem (20) can be
rewritten as
max
v
K
X
k=1
χt0vHΦkWΦH
kv
s.t. ˆ
C1:pktk+pC
k(t0+tk)≤χt0vHΦkWΦH
kv,
ˆ
C5:|vn|2= 1,∀n.
(21)
However, problem (21) is still a non-convex problem, since
ˆ
C5is a non-convex quadratic equality constraint. Because of
vHΦkWΦH
kv= Tr ΦkWΦH
kvvH, denote V=vvH,
which satisfies Rank (V)=1and V0[16]. However, the
rank-one constraint is non-convex, the SDR method is used to
relax this constraint. As a result, problem (21) is relaxed as
max
V
K
X
k=1
χt0Tr ΦkWΦH
kV
s.t. :¯
C1:pktk+pc
k(t0+tk)≤χt0Tr ΦkWΦH
kV,
¯
C5:Vn,n = 1,∀n, V0.
(22)
(0,0)
(2,2)
PS
(-8,2)
0
0
(1,0) (3,0) (4,0)
Destination
(60,0)
IRS
y
x
Obstacle
Users
(
3
0
dPI=10 m
H
g4
Fig. 3. The simulated network model.
Problem (22) is a standard convex semidefinite program
(SDP), it can be solved by using convex optimization tools
[20]. However, the optimal solution of (22) may not satisfy a
rank-one solution, i.e., Rank (V)6= 1. Therefore, the Gaussian
randomization method [18] is further employed to solve it.
Define ¯
Vas the optimal solution of the problem (22), we can
obtain the singular value decomposition (SVD) ¯
V=UΛUH,
where U= [u1,u2, ..., uN]and Λ= diag (σ1, σ2, ..., σN)are
the unitary matrix and the diagonal matrix [14], respective-
ly. Then, the sub-optimal solution of problem (21) can be
constructed as ¯
v=UΛ1/2r, where r∼ CN (0,IN)is a
random vector. The maximum objective function of problem
(21) can be obtained by finding the best r∗. Then, we can
obtain ¯
v∗=UΛ1/2r∗. Since ¯
v∗is the sub-optimal solution
of the problem (21), we have v∗= exp jarg h¯
v∗
¯
v∗
Ni1:N
As a result, the optimal phase shift matrix of the IRS is given
by Θ∗= diag (v∗).
IV. SIMULATION RESULTS
In this section, simulation results are provided to evaluate
the effectiveness of the proposed algorithm. The simulated
network model is illustrated in Fig. 3. The coordinates of the
PS, the IRS and the destination as (−8,2),(2,2), and (60,0),
respectively. The path-loss model is Γ (d)=Γ0(d/d0)−α,
where Γ0=−10 dB denotes the path-loss factor at d0= 1
m, dis the distance between one transmitter and one receiver,
and αis the path-loss exponent [16]. The path-loss exponents
of the links from the PS and to the IRS and from the
IRS and to the users are set as αPI = 2 and αIU = 2,
respectively. In addition, the path-loss exponent from the users
to the destination is defined as αUD = 3. Other simulation
parameters are given as follows: χ= 0.8,pC
k= 0.005 W,
u= 0.0015 W, PC
PS = 0.05 W, PC
D= 0.05 W, T = 1 s,
M= 6,N= 30,K= 4,Rmin
k= 0.5bits, δ2
0=−80 dBm
and Pmax = 25 dBm.
Fig. 4 shows that the total EE of users versus the number
of iterations. It is observed that the proposed algorithm can
reach convergence quickly even if the number of the reflecting
elements (e.g., N) of the IRS or antennas (e.g., M) at the
PS is very large. Thus, the proposed algorithm has good
convergence. In addition, it can be seen that the total EE
is improved with the increase of N. The reason is that the
more reflecting elements can reflect more energy signals to
the users and increase the harvested energy. Moreover, the

1 2 3 4 5 6 7 8 9 10
Number of iterations
50
60
70
80
90
100
110
120
The total EE of users (bits/Joule)
Fig. 4. The convergence of the proposed algorithm.
345678910
The number of users K
40
50
60
70
80
90
100
110
120
The total EE of users (bits/Joule)
The total EE-based algorithm with random phase shifts
The proposed algorithm
The throughput-based maximization algorithm
Fig. 5. System EE versus the number of users.
increasing antennas of the PS can improve the system EE.
Because a lot of transmission antennas can concentrate energy
beam transmission and reduce energy loss during wireless
signal propagation.
In order to further demonstrate the superiority of our pro-
posed algorithm, we compare the proposed algorithm with the
baseline algorithms: the total EE-based algorithm with random
phase shifts, the throughput-based maximization algorithm.
Fig. 5 depicts the total EE versus the number of users
under different algorithms. From the figure, as the increasing
number of users (e.g., K), the total EE under three different
algorithms is increased. The reason is that as the number of
users increases, more energy is harvested. In addition, the total
EE of the proposed algorithm is much larger than that of the
baseline algorithms.
V. CONCLUSION
In this paper, we proposed a resource allocation algorithm
for maximizing the system EE in an IRS-assisted WPCN by
jointly optimizing the energy transmit matrix of the PS, the
transmit time and power of the users, and the phase shifts
of the IRS. The formulated problem was non-convex. The
alternating approach, Dinkelbach’s method, and the variable-
substitution approach were used to convert it into an equivalent
convex form. The simulation results had shown that the
proposed algorithm had good convergence and could achieve
better system EE by comparing it with the baseline algorithms.
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