636 IEEE INTERNET OF THINGS JOURNAL, VOL. 5, NO.

2, APRIL 2018

Throughput Maximization and Fairness

Assurance in Data and Energy Integrated
Communication Networks
Kesi Lv, Jie Hu, Member, IEEE, Qin Yu, and Kun Yang, Senior Member, IEEE

Abstract—A typical data and energy integrated communication Conventionally, the energy supplies of user equip-
network (DEIN) conceives a conventional base station, which is ments1 (UEs) in wireless communication networks come
capable of simultaneously transmitting the data and energy to from either batteries embedded or the power grid connected.
user equipments (UEs) during the downlink (DL) transmissions
by invoking the time-division-multiple-access (TDMA) protocol However, these two energy sources have obvious limitations.
in the medium access control (MAC) layer. Several UEs oper- The limited energy stored in the batteries restricts the life
ating in this DEIN are capable of harvesting the energy from time of UEs, while the wire connected to the power grid
the DL transmissions by adopting the power splitting (PS) tech- restricts UEs’ movement. Furthermore, massive IoT devices
nique and they are also capable of exploiting the harvested are deployed in walls or under roads or in other untouch-
energy for powering their uplink (UL) data transmissions by
invoking the TDMA protocol in the MAC layer. Both of the able places. It is difficult to regularly replace their batteries,
UL sum-throughput and the UL fair-throughput of the DEIN which limit their life time. Embedding the function of energy
is maximized by deciding the duration of each time-slot dur- harvesting (EH) into UEs and seeking energy from the renew-
ing the DL/UL transmissions and by determining the optimal able sources, such as sunlight [6] and wind [7], are capable
PS factor for each UE. Both of these optimization problems are of satisfying UEs’ increasing energy demand [8]. However,
finally solved by the classic method of Lagrange multipliers in
close-form. An interesting observation shows that supporting low- energy arrivals from the renewable sources are stochastic
throughput data services during the DL transmissions does not processes, which hinders its efficient usage in supporting the
degrade the wireless energy transfer and hence does not reduce communication functions of the UEs
the throughput of the UL transmissions. Transferring energy by RF signals is more reliable and con-
Index Terms—Data and energy integrated communication trollable than renewable energy sources. Zungeru et al. [9]
network (DEIN), Internet of Things (IoT), sum-throughput/fair- has demonstrated the availability of harvesting energy from
throughput maximization. the surrounding RF signals. Varsheney [10] has provided an
information theoretical analysis for revealing the performance
limit of simultaneous wireless information and power trans-
fer (SWIPT). In order to process contaminated RF signals for
I. I NTRODUCTION
the information reception as well as to convert RF signals
UR CITIES now are in the process of transiting toward
O more smart, more automatic, and more responsive soci-
eties, which requires the integration of the modern com-
into dc for the EH, the spatial splitting [11], the power split-
ting (PS) [12], and the time switching [13] techniques have
been invoked for the SWIPT. Many efforts then have been
munication and information technology and the Internet of contributed to this prosperous subject [14]–[17]. However,
Things (IoT) [1]. The assets of smart cities contains smart most of them are merely based on the frequency-division-
transportation systems [2], smart grids [3], smart hospitals [4], multiple-access protocol, while assuming symmetric duration
smart factories [5], etc. All these realizations require the uni- of the UEs’ downlink (DL) and uplink (UL) transmissions.
versal connectivity of humans and machines. As foreseen Their optimization formulation is inapplicable, when the time-
by the industry, we will see more than 200 000 IoT devices division-multiple-access (TDMA) protocol is adopted in the
deployed in a square kilometer. medium access control (MAC) layer for supporting the infor-
Manuscript received January 31, 2017; revised June 6, 2017; accepted mation and energy transfer in the multiuser scenario, since
July 2, 2017. Date of publication July 17, 2017; date of current their methodologies failed to optimize the durations of both the
version April 10, 2018. This work was supported in part by the DL and the UL transmissions. Furthermore, wireless powered
University of Electronic Science and Technology of China under Grant
ZYGX2016KYQD103 and in part by the National Natural Science Foundation communication networks (WPCNs) relying on the TDMA pro-
of China under Grant 61601097. (Corresponding author: Jie Hu.) tocol have been investigated in [18]–[20]. In WPCNs, the pro-
K. Lv, J. Hu, and Q. Yu are with the School of Communication tocol of “harvest-then-transfer” is conceived [21]. As a result,
and Information Engineering, University of Electronic Science and
Technology of China, Chengdu 611731, China (e-mail: kslv@std.uestc.edu.cn; UEs may harvest energy from the base station (BS) during
hujie@uestc.edu.cn; yuqin@uestc.edu.cn). their DL transmissions, then the energy harvested by the UEs
K. Yang is with the School of Computer Science and Electronic
Engineering, University of Essex, Essex CO4 3SQ, U.K. (e-mail:
kunyang@essex.ac.uk). 1 The advent of IoT redefines the concept of UEs, which now includes both
Digital Object Identifier 10.1109/JIOT.2017.2727517 hand-held devices and machine-type devices.
2327-4662 c 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
LV et al.: THROUGHPUT MAXIMIZATION AND FAIRNESS ASSURANCE IN DEINs 637

(a)

Fig. 1. DL and UL transmissions of the DEIN.

(b)
is exploited for supporting their UL transmissions. However, in Fig. 2. Slotted DL/UL transmissions in the DEIN. (a) Structure of a single
WPCNs, the DL transmissions are dedicated to the wireless operating cycle. (b) Ui ’s operating mode during a specific cycle.
energy transfers. The simultaneous energy and data transfer
has been largely ignored. Against this background, our novel
contributions are summarized as follows. capacity. As a result, the UEs have to harvest energy from the
1) A novel DEIN is systematically established. In this DL transmissions of the BS and store the energy in the super
DEIN, the BS simultaneously transfers both of the capacitors, while simultaneously extracting their requested
information and the energy to the UEs by obeying data information from the same RF signals. The energy stored
the TDMA protocol in the MAC layer during the DL in super capacitors is then depleted for powering the UEs’
transmissions. Then the UEs initiate their UL data trans- UL transmissions. We further assume that the channel state
missions by exploiting the energy harvested during the information (CSI) is known by the BS.
DL transmission stage.
2) Relying on the tool of the convex optimization and
the classic method of the Lagrange multipliers, the A. Structure of the TDMA Aided Operating Cycle
sum-throughput maximization problem for the UL
In the DEIN studied, the UEs are fully powered by
transmissions is solved by jointly optimizing the allo-
the energy gleaned from the DL RF signals. As a result,
cation of the time slots for both of the DL and UL
their transmit power of the UL transmissions is very low.
transmissions and the diverse PS factors for all the UEs.
The TDMA protocol is then adopted for avoiding hostile
3) In order to further ensure the fairness among the UEs in
interference and collision, when multiple UEs upload their
the DEIN, the fair-throughput, which is defined as the
data to the BS. Furthermore, adopting the TDMA protocol
minimum throughput among all the UEs’ UL transmis-
for the DL transmissions is capable of orthogonally transmit-
sions, is also maximized by optimizing the allocation of
ting data to the requesters. The UEs may also flexibly switch
the time slots for both of the DL and UL transmissions
between the information decoding (ID) and EH operations in
and the diverse PS factors for all the UEs.
the time domain during the DL transmissions of the BS.
The rest of this paper is organized as follows. Our DEIN
The structure of an operating cycle having a length of T is
model is introduced in Section II, followed by the maximiza-
depicted in Fig. 2. An intact operating cycle consists of two
tion of the sum-throughput as well as the fair-throughput of
phases, namely the control phase having a duration of Tctr and
the UL transmissions in Sections III and IV, respectively.
the transmission phase having a duration of Ttra . During the
Numerical results are provided in Section V. Finally, we
control phase, the following tasks have to be completed by
conclude this paper in Section VI.
exchanging control signaling between the BS and the UEs.
1) Channel Estimation: The CSI can be acquired by the BS
II. S YSTEM M ODEL via the forward-link training together with the reverse-
We consider a typical DEIN, as portrayed in Fig. 1, for the link feedback [23]. The channel states are assumed
sake of remotely charging the UEs without violating their com- unchanged during a single operating cycle but they vary
munication demands. The DEIN consists of a single BS as well from one operating cycle to another.
as K UEs, which are denoted by the set {Ui |i = 1, . . . , K}. The 2) Resource Allocation: Given the CSI, the BS executes the
BS and the UEs all conceive a single antenna and they operate time slot allocation for both the UEs’ DL and UL trans-
on the same spectral band, which indicates that all the spa- missions and the BS also determines the signal splitting
tial resources and frequency resources are multiplexed by the strategies at the UEs for simultaneous data and energy
UEs. Moreover, the UEs in the DEIN are equipped with super reception. The BS then notifies the UEs about the time
capacitors [22]. Super capacitors may ideally store the energy slot allocation scheme and the signal splitting strategies.
that is extracted from RF signals without any energy loss. 3) Synchronization: Since all the UEs are distributed in the
However, super capacitors suffer from low energy storage coverage of the BS, they may readily be synchronized
638 IEEE INTERNET OF THINGS JOURNAL, VOL. 5, NO. 2, APRIL 2018

together by invoking the time-stamp-based synchroniza- σ 2 = σID,i

2 to denote noise power of the ID in the following
tion approach [24]. The BS may broadcast its locally problem formulation.
recorded clock information to all the UEs during the
control phase. Once the clock information is success- C. Throughput of the DL Transmissions
fully received, the UEs may adjust their local clock in
During the DL time slot tiD , the power of the RF signal
order to complete their synchronization process.
received by Ui is denoted by Precv,i = PBS hi , where PBS is
The transmission phase of a single operating cycle is divided
the transmit power of the BS.
into a range of DL time slots denoted by the set of tD =
Since only a fraction of the received signal power is
{tiD |i = 1, 2 . . . , K} and a range of UL time slots denoted
exploited by Ui for the ID, the achievable DL throughput RD
by the set of tU = {tiU |i = 1, 2 . . . , K}. Hence, we have the i
of Ui can be expressed as the following formula by exploiting
following inequality, which is expressed as:
the classic Shannon’s channel capacity equation:

K
D   
ti + tiU ≤ Ttra . (1)   (1 − ρi )Precv,i
Ri ti , ρi = ti log2 1 +
D D D
, [bit/Hz]. (2)
i=1 σ2
The BS sends information to the requester Ui during the DL The DL throughput of (2) can also be regarded as the
time slot tiD , while Ui sends its own data to the BS during the bandwidth efficiency of the DL data transfer. Therefore, the
UL time slot tiU . Fig. 2(b) presents how Ui operates during bandwidth term of the classic Shannon’s channel capacity
a single operating cycle T. When the BS sends the data to equation is not included in (2).
another requester Uj during a specific DL time slot tjD , Ui
(i = j) may detect the RF signal emitted by the BS due to the
D. Throughput of the UL Transmissions
broadcast nature of the wireless channel. Hence, Ui is capable
of harvesting the energy from the RF signal dedicated to its The total energy harvested by Ui is the sum of the energy
peer Uj . Hence, Ui operates in the EH mode during the current harvested during the DL time slots set {tjD |j = i}, when Ui
DL time slot tjD . During its own dedicated DL time slot tiD , Ui operates in the EH mode, and the energy harvested during its
adopts the PS technique for splitting the power Precv,i of its dedicated DL time slot tiD , when Ui operates in both of the
dedicated RF signal into two portions. The power of ρi Precv,i EH and ID modes simultaneously. The total energy harvested
is relied upon for the EH, while the rest is for the ID, where by Ui can then be further expressed as
the parameter ρi is regarded as the PS factor of Ui . As a result, ⎛ ⎞
D  
Ui simultaneously operates in the EH mode and the ID mode Erecv,i t , ρi = βi Precv,i ⎝ tjD + tiD ρi ⎠ (3)
during tiD . The PS factor ρi can be adjusted by Ui in order j=i
to fulfill different energy and data requirements. For the UL
transmission, since only a single UE is allowed to transfer where βi represents the efficiency of converting the ac carried
its data during a specific time slot, Ui solely operates in the by the RF signal to the dc that can drive any electronic load.
information transfer (IT) mode during its assigned UL time Here, for simplicity, the energy conversion efficiency βi is
slot tiU . By contrast, Ui operates on the standby (St) mode assumed to be a unity.
during other UL time slots {tjU |j = i} in order to avoid any Since the energy harvested by Ui during the DL transmis-
transmission collision when the corresponding UE Uj operates sion is fully exploited for powering its own UL transmission,
in the IT mode. with the aid of (3), the achievable UL throughput RU i of Ui
can then be formulated as
B. Channel Model D U 
i t , ti , ρi
RU
The DL channel from the BS to Ui and the correspond- ⎡  ⎤
hi Precv,i t D + tD ρ
ing reversed UL channel are denoted by the complex random j=i j i i
= tiU log2 ⎣1 + ⎦, [bit/Hz] (4)
variables h̃i and g̃i , respectively, while their power gains are ti σ
U 2
denoted by hi = |h̃i |2 and gi = |g̃i |2 . For simplicity, we
assume a symmetric channel between the BS and Ui , which which can also be regarded as the bandwidth efficiency of the
indicates hi = gi . The set of channel power gains is denoted UL data transfer.
as h = {hi |i = 1, . . . , K}. Furthermore, the uncorrelated block In our model, the diverse minimum throughput requirements
fading channel models are conceived, which indicates that the of the UEs’ DL transmissions can be represented by the set
power gain of the channel remain unchanged during a sin- D = {D1 , . . . , DK }. Our ultimate objective is to maximize the
gle operating cycle T. The channel noise power is denoted throughput of the UL transmissions subject to the constraint
2 , while the noise power of the ID is denoted by σ 2 .
by σc,i ID,i that every UE’s achievable DL throughput should satisfy its
Compare to σID,i2 , the channel noise power σ 2 is negligibly
c,i minimum requirement by jointly optimizing the durations of
small and hence it has little influence on both of the practical the time slots in the DL set tD and those of the time slots in
ID and the EH [12]. As a result, the channel noise power σc,i 2 the UL set tU as well as the signal splitting strategies adopted
can be reasonably ignored in any of the formulations below. by the UEs during their dedicated DL time slots. The signal
Furthermore, the noise power of ID is assumed to be iden- splitting strategies are represented by the PS factors in the set
tical for every UE as well as the BS. For simplicity, we let ρ = {ρi |1 ≤ ρi ≤ K}. Furthermore, our model focuses on both
LV et al.: THROUGHPUT MAXIMIZATION AND FAIRNESS ASSURANCE IN DEINs 639

D 
of the sum-throughput maximization for achieving the upper-
i ti , μi ≥ Di
s.t. RD (10a)
bound of the UEs’ UL transmissions and the fair-throughput

K
D 
maximization for ensuring the UEs’ fairness during their UL ti + tiU ≤ Ttra (10b)
transmissions. i=1
0 ≤ μi ≤ tiD (10c)
III. S UM -T HROUGHPUT M AXIMIZATION 
where i = 1, . . . , K. Since f (t , μi ) = log2 [1+hi γi ( j=i tjD +
D
In this section, the sum-throughput maximization problem is μi )] is a concave function, its log-affine RU i (t , ti , μi ) is con-
D U
formulated, and then it is transformed into a convex problem, cave as well. Therefore, the objective function (10) of the
which can be solved by the classic method of the Lagrange alternative optimization problem (P2), which is the sum of a
multipliers. With the aid of (1)–(4), the sum-throughput range of concave functions, can be readily proved to be con-
maximization problem can be formulated as cave with respect to the variables tD , tU , and μ. Furthermore,
RDi (ti , μi ) in (10a) is also a concave function with these decid-
D

K
D U 
(P1): max i t , ti , ρi
RU (5) ing variables since its Hessian matrix is positive semi-definite,
tD ,tU ,ρ
i=1 while the constrains (10b) and (10c) are both affine. As a
D  result, (P2) is a convex optimization problem.
s.t. i ti , ρi ≥ Di
RD (5a)
Observe from the optimization problem (P2) that the DL

K
D  transmission requirement Di of Ui should be higher than zero
ti + tiU ≤ Ttra (5b)
and smaller than its maximum achievable DL throughput RD i ,
i=1
when Ui exploits all its received RF signal for the ID by
0 ≤ ρi ≤ 1 (5c)
completely sacrificing its EH function. The Lagrange function
where i = 1, . . . , K denotes the indices of the UEs. Since of (P2) can be then formulated as
RUi (t , ti , ρi ) of (4) and Ri (ti , ρi ) of (2) are neither convex
D U D D
   K
D U 
nor concave functions according to the definition of convexity, L tD , tU , μ, λ, ξ = RUi t , ti , μi
(P1) is thus a nonconvex problem with respect to the variables i=1
 
tD , tU , and ρ. As a result, (P1) has to be equivalently trans- 
K
D 
formed into a convex problem by introducing a new set of + λ Ttra − ti + tiU
variables μ = {μi |i = 1, ·, K} for substituting the original i=1
set of variables ρ = {ρi |i = 1, . . . , K}. The ith entry μi is 
K
 D  
expressed as + i ti , μi − Di
ξi RD (11)
i=1
μi = tiD ρi , i = 1, . . . , K. (6) where λ and ξ = {ξi |i = 1, . . . , K} are the corresponding
Accordingly, the expression of the achievable DL through- Lagrangian multipliers. Moreover, the dual function of (P2)
put RD D can be expressed as
i of Ui during its dedicated DL time slot ti can be  
reformulated as G(λ, ξ ) = supL tD , tU , μ, λ, ξ . (12)
 
  μ Since (P2) is a convex optimization problem, its optimal
solutions, {tD∗ , tU∗ , μ∗ , λ∗ , ξ ∗ }, have to satisfy the following
i
i ti , μi = ti log2 1 + γi − γi D
RD D D
(7)
ti Karush–Kuhn–Tucker (KKT) conditions:
yi
where γi = (Precv,i /σ2 ) for all i = 1, . . . , K representing ln(1 + yi ) − = λln2 (13)
the signal-to-noise-ratio (SNR) of Ui during tiD . The set of 1 + yi
 γj hj  
the UEs’ SNRs during their DL transmissions is denoted as zi
+ ξi ln(1 + γi − zi ) + = λln2 (14)
γ = {γi |i = 1, . . . , K}. The expression of the achievable UL 1 + yj 1 + ri − zi
j=i
throughput RU i of Ui during its assigned UL time slot ti can
U
γi hi γi
be further derived as = ξi
⎛  ⎞ 1 + yi 1+γi −zi
  hi γi j = i tjD + μi (15)
⎝ ⎠ (8)  
RUi t , ti , μi = ti log2 1 +
D U U
tiU 
K
λ Ttra − (tiU + tiD ) = 0 (16)
i=1
while the PS factor of Ui during its assigned DL time slot tiD  
can be expressed as ξi tiD log2 (1 + γi − zi ) − Di = 0 (17)
μi where we introduce a couple of new variables sets, denoted
ρi = D . (9) by y = {yi |i = 1, . . . , K} and z = {zi |i = 1, . . . , K}. Their ith
ti
entries can be expressed as
Therefore, the original optimization problem (P1) can be 
j=i tj + μi
D
reformulated as yi = hi γi (18)
tiU

K
D U  μi
(P2): max i t , ti , μi
RU (10) zi = γi D (19)
tD ,tU ,μ ti
i=1
640 IEEE INTERNET OF THINGS JOURNAL, VOL. 5, NO. 2, APRIL 2018

respectively, for i = 1, . . . , K. According to (14) and (15), we Algorithm 1 Iterative Algorithm for Solving (P2)
can find that λ = 0 and ξi = 0. Input: Duration of the transmission phase Ttra ; DL
Given a specific value of the Lagrange multiplier λ and throughput requirement D; channel power gains h; SNR
according to (13)–(19), the resultant optimal value tiD∗ of the in UE γ ; error tolerance δ
duration of the Ui ’s assigned DL time slot can be derived as Output: optimal allocated UL time slots tD∗ ; optimal
allocated DL time slots tU∗ ; optimal PS factors ρ ∗ ;
Di 1: Transform (P1) to (P2) by substituting μ for ρ;
tiD∗ =  . (20)
log2 1 + γi − z∗i 2: Initialize λ > 0 and iteration step length λ > 0 and
p(λ) > δ;
Furthermore, the optimal value tiU∗ of the duration of the Ui ’s 3: while |p(λ)| > δ do
assigned UL time slot can be obtained as 4: Calculate y∗ and z∗ by equations (23), (24);
 ∗
5: Calculate tD∗ , μ∗ and tU∗ by equations (20)-(21);
j=i tj + μi
D∗
ti = hi γi
U∗
. (21) 6: Update p(λ) by equation (25);
∗
yi 7: Update λ by λ = λ − p(λ)λ ;
8: end while
The optimal value of the intermediate variable μ∗i is formu- 9: Calculate ρ ∗ by equation (9);
lated as 10: return tD∗ , tU∗ , ρ ∗

z∗i tiD∗
μ∗i = . (22)
γi
IV. FAIR -T HROUGHPUT M AXIMIZATION
In (20)–(22), y∗i and z∗i are the solutions to the following In order to achieve a better sum-throughput, more resources
equations: are inclined to be allocated to the UEs having better chan-
yi nel qualities between the BS. Since the channel qualities are
ln(1 + yi ) − = λln2 (23) largely determined by the large-scale channel attenuation, such
1 + yi
as the path-loss, the UEs close to the BS may gain more
hi (1 + γi − zi )ln(1 + γi − zi ) + hi zi
 resources for harvesting energy from the BS’s DL transmission
= (1 + yi )λln2 − γj hj . (24) and for sending their own data to the BS during their UL trans-
j=i missions. As a result, the UEs relatively far away from the BS
may not be allocated sufficient resources for their own oper-
The expression on the left side of (23) increases monotonically
ations. This is regarded as the classic near-far effect, which
with respect to the variable yi , while the expression on the
yields the fairness issue among the UEs in the DEIN.
left side of (24) decreases monotonically with respect to the
In order to overcome the classic near-far effect during the
variable zi . As a result, y∗i can be calculated first by invoking
resource allocation, ensuring the fairness among the UEs’
the classic bisection method. Substituting y∗i into (24), z∗i can
UL transmissions becomes our prim objective, which yields
also be calculated by invoking the classic bisection method.
the maximization of the so-called fair-throughput. Since fair-
Given the specific value of λ, we have obtained the opti-
throughput represents the minimum throughput among all the
mal values of tU∗ , tD∗ , μ∗ , and ξ ∗ , which satisfy the equalities
UEs during their UL transmissions, we impose a constraint
of (13)–(15) and (17). Then, the subgradient descent is invoked
on the throughput of the UEs’ UL transmissions, which is
for iteratively obtaining the optimal Lagrange multiplier λ∗ .
expressed as RU i (t , ti , ρi ) ≥ R, for i = 1, . . . , K, where
D U
The subgradient of G(λ, ξ ) with respect to the Lagrange mul-
R represents the so-called fair-throughput. According to the
tiplier λ, which is denoted by p(λ), can be further expressed
system model of Section II, the fair-throughput maximization
as
problem (P3) can be formulated as

K
D  (P3): max R (26)
p(λ) = Ttra − ti + tiU . (25) tD ,tU ,μ
i=1 D 
i ti , μi ≥ Di
s.t. RD (26a)
With the aid of (25), we can iteratively obtain the opti- D U 
i t , ti , μi ≥ R
RU (26b)
mal Lagrange multiplier λ∗ . We update λ by the formula
0 ≤ μi ≤ tiD (26c)
λ(n) = λ(n−1) −p(λ(n−1) )λ in each iteration, where n denotes
the nth iteration and λ represents the step length of each K

iteration. Substituting λ(n) into (20)–(24), we may obtain the (tiD + tiU ) ≤ Ttra (26d)
i=1
corresponding values of tiD and tiU and hence derive the spe-
cific value of p(λ(n) ). The iteration continues until we find where μi = tiD ρi for all i = 1, . . . , K is adopted for
the optimal λ∗ , which makes |p(λ∗ )| smaller than the specific ensuring the concavity of both the achievable DL through-
error tolerance δ. Finally, the PS factors set ρ ∗ can be calcu- put RD i (ti , μi ) of Ui during its DL time slot ti and the
D D

lated by invoking (9). The procedure for iteratively solving the achievable UL throughput Ri (t , ti , μi ) during its UL time
U D U

alternative optimization problem (P2) is detailed in the pseudo slot tiU , which have been proved in Section III. As a result,
code of Algorithm 1. the fair-throughput maximization problem (P3) can be readily
LV et al.: THROUGHPUT MAXIMIZATION AND FAIRNESS ASSURANCE IN DEINs 641

proved to be a convex optimization problem. Note that the Algorithm 2 Iterative Algorithm for Solving (P4)
achievable DL throughput RD i (ti , μi ) is an increasing func-
D Input: duration of the transmission phase Ttra ; DL through-
D
tion with respect to ti , while the achievable UL throughput put requirement D; channel power gains h; SNR in UE
RUi (t , ti , μi ) is also an increasing function with respect to
D U γ ; error tolerance δλ and δR
ti and tiU . Therefore, the fair-throughput R increases when
D Output: optimal allocated UL time slots tD∗ ; optimal allo-

t = K i=1 ti + ti increases. As a result, we may iteratively
D U cated DL time slots tU∗ ; optimal PS factors ρ ∗ ; optimal
solve the following convex optimization problem (P4) in order fair-throughput R∗
to maximize the fair-throughput R: 1: Initialize Rmin = 0 and Rmax (large enough) and t∗ = 0;
2: while |Ttra − t∗ | > δR do

K
D  3: Let R = 0.5(Rmax + Rmin );
(P4): min ti + tiU (27)
tD ,tU ,μ 4: Initialize λi > 0 and λ > 0 and p(λ) (let |p(λ)| > δλ );
i=1
D  5: while |p(λ)| > δλ do
s.t. i ti , μi ≥ Di
RD (27a) 6: Calculate y∗ and z∗ by equations (30) and (31);
D U 
i t , ti , μi ≥
RU R (27b) 7: Calculate tD∗ , tU∗ μ∗ by equations (20)-(21);
0 ≤ μi ≤ tiD (27c) 8: Calculate p(λ) = {p(λi )|i = 1, · · · , K} by equation
(32);
where i = 1, . . . , K. The Lagrange function of (P4) is further 9: Update λ by λ = λ − p(λ)λ ;
expressed as 10: end while 
11: Calculate t∗ = K i=1 ti + ti ;
D∗ U∗
  K
∗
if |Ttra − t | > δR then
L tD , tU , μ, λ, ξ = (tiD + tiU ) 12:
i=1 13: if t∗ > Ttra then
14: Let Rmax = R;

K
 
+ ξi Di − RD else
i (ti , μi )
D 15:
i=1 16: Let Rmin = R;

K 17: end if
 
+ λi R − RU
i (t , ti , μi )
D U
(28) 18: end if
i=1 19: end while
20: Calculate ρ ∗ by equation (9);
where λ = {λi |i = 1, . . . , K} and ξ = {ξi |i = 1, . . . , K} are
21: return tD∗ , tU∗ , ρ ∗ ,R∗
the corresponding Lagrangian multipliers. The dual function
of (P4) then can be expressed as
 
G(λ, ξ ) = infL tD , tU , μ, λ, ξ . (29) iteration, where n denotes the nth iteration and λ rep-
Similar to the method invoked for solving the sum- resents the step length of the iteration. The iteration for
throughput maximization problem (P2), the KKT conditions obtaining the optimal Lagrange multiplier set λ∗ termi-
are also exploited for solving the fair-throughput maximiza- nates until the subgradient of the dual function G(λ, ξ )
tion problem (P4). Hence, given a range of specific values satisfies the condition of |p(λ∗ )| ≤ δλ , where δλ repre-
for the multiplier set λ = {λi |i = 1, . . . , K}, the optimal value sents the absolute error tolerance of the Lagrange multiplier
of the duration of the DL time slot tiD∗ , that of the duration set λ.
of the UL time slot tiU∗ and that of the intermediate variable We reduce the fair-throughput R after obtaining the opti-
μ∗i can still be expressed by (20)–(22). Furthermore, y∗i and mal result t∗ by solving the alternative optimization problem
z∗i can be obtained by solving the following equations: (P4), if the optimal result t∗ is higher than the duration Ttra
of the transmission phase, say t∗ > Ttra . By contrast, if
ln(1 + yi ) −
yi
=
ln2
(30) the optimal result t∗ is lower than the duration Ttra of the
1 + yi λi transmission phase, say t∗ < Ttra , we have to increase the fair-
(1 + γi − zi )ln(1 + γi − zi ) + zi  throughput R. This iteration process terminates until we have
1 + yi j=i λj γj hj |Ttra − t∗ | < δR , which yields the maximum fair-throughput
= ln2 − . (31) R∗ . Here, δR represents the error tolerance. The iterative algo-
λi hi λi hi
rithm of solving the alternative optimization problem (P4) is
Relying on the monotonous properties of the expressions on
tailored in Algorithm 2.
the left side of the equalities of (30) and (31), we can read-
ily obtain the solutions of y∗i and z∗i by invoking the classic
bisection method. The subgradient of G(λ, ξ ) with respect to V. N UMERICAL R ESULT
λ, which is denoted by p(λ) = {p(λi )|i = 1, . . . , K}, can be In this section, the numerical results of the maximum sum-
further expressed as throughput obtained by solving the optimization problem (P1)
  and those of the maximum fair-throughput obtained by solving
p(λi ) = tiU∗ log2 1 + y∗i − R (32)
the optimization problem (P3) are compared with each other
for all i = 1, . . . , K. We iteratively update the Lagrange in a typical DEIN consisting of a BS and several UEs. Without
multiplier set λ by λ(n) = λ(n−1) − p(λ)λ in each loss of generality, the additive-white-Gaussian-noise channel
642 IEEE INTERNET OF THINGS JOURNAL, VOL. 5, NO. 2, APRIL 2018

Fig. 3. Individual throughput of the UEs’ UL transmission. Fig. 4. PS strategies of the UEs during their DL transmissions.

as well as the path loss are conceived. Therefore, the DL and

UL channel power gains are modeled by hi = gi = 10−3 Yi−α ,
for all i = 1, . . . , K, where Yi represents the distance between
the BS and Ui . The exponent is set to be α = 2 for repre-
senting the short-range free-space path loss model. A 30 dB
signal power attenuation in average is assumed at a reference
distance of 1 m for this channel model. The noise power of the
information decoder is set to be −50 dBm, while the channel
noise is ignored.
We first compare the UE’s individual UL through-
put obtained by solving the sum-throughput maximization
problem (P1) to that obtained by solving the fair-throughput
maximization problem (P4). The transmit power PBS is set Fig. 5. Throughput of the UL transmission versus the transmit power of
to be 30 dBm. We have K = 5 UEs in total in the DEIN. the BS.
The distances from the UEs to the BS are {Y1 = 4, Y2 = 5,
Y3 = 5.5, Y4 = 9, Y5 = 10} m, while the minimum require-
ments of the UEs’ DL throughput are {D1 = 0.5, D2 = all converted to the energy, which is exploited for supporting
0.4, D3 = 0.8, D4 = 0.3, D5 = 0.2} bit/Hz. The duration of their UL transmissions. As a result, U1 and U2 are capable
the transmission phase is Ttra = 1 s. of achieving higher UL transmission throughput. By contrast,
As illustrated in Fig. 3, the UEs within the proximity of the since U4 and U5 are far away from the BS, they have to exploit
BS, such as U1 and U2 , are capable of transferring more data all their received signals for the ID. As a result, they do not
during their UL transmissions than the UEs far away from the harvest sufficient energy for supporting their UL transmissions.
BS, such as U4 and U5 , if we aim for maximizing the sum- Hence, they suffer from very low UL transmission throughput.
throughput of the UEs’ UL transmission. In order to achieve Note that when the fair-throughput maximization is invoked
this objective, more time is assigned to the UEs having better in our resource allocation and strategy selection schemes, all
channel qualities, which results in the substantial unfairness the UEs choose moderate PS strategies in order to achieve the
among the UEs. As a result, in order to attain a fair resource fairness of their UL transmissions.
allocation scheme, the maximization of the fair-throughput We further plot both of the sum-throughput and the fair-
is studied in order to ensure the fairness among the UEs throughput against the transmit power PBS of the BS in
by suffering somewhat degradation of the sum-throughput. Fig. 5, where we adopt the same parameter setting as those
We can observe from Fig. 3 that in order to maximize the for obtaining the numerical results of Fig. 3. Observe from
fair-throughput, the actual UL throughput of different UEs Fig. 5 that when the transmit power PBS of the BS increases,
are soundly fair by distributing more time to UEs having both of the sum-throughput obtained by solving the opti-
worse channel qualities for the sake of overcoming the adverse mization problem (P1) and the fair-throughput obtained by
near-far effect. solving the optimization problem (P4) increase. Furthermore,
Furthermore, we plot the PS strategy for these five UEs the sum-throughput is more sensitive to the increase of PBS
during their DL transmissions in Fig. 4. We first focus on than the fair-throughput. Without considering the fairness
the sum-throughput maximization. Since U1 and U2 are very among the UEs, the UL throughputs of the UEs near the
close to the BS, they only exploit a very small fraction of BS may be significantly increased by increasing the trans-
their received signal for the ID so as to satisfy their DL mit power of PBS . However, the UL throughputs of the UEs
throughput requirement. The rest of their received signal is far away from the BS may be improved little due to the
LV et al.: THROUGHPUT MAXIMIZATION AND FAIRNESS ASSURANCE IN DEINs 643

VI. C ONCLUSION
This paper has studied a novel DEIN model, where the BS
simultaneously transmit the data and energy during the DL
transmissions and the UEs harvest the energy from the DL
signals for powering their own UL transmissions. In order
to avoid any collision and interference, a TDMA protocol is
adopted in the MAC layer for both the DL and UL trans-
missions. At a UE’s end, the received RF signal is split in
the power domain. One portion of the signal is for the ID,
while the other is for the EH. Relying on the classic con-
vex optimization theory, both of the sum-throughput and the
fair-throughput are maximized by optimizing both of the time
slots allocation and the PS factors. Iterative algorithms are
Fig. 6. Throughput of the UL transmission versus the minimum throughput proposed for numerically solving the throughput maximiza-
requirement in the DL transmission. tion problems. Furthermore, our numerical results demonstrate
the advantage of our DEIN over the WPCN and the WIT
systems.
signal propagation of long distances. Hence, the substantial
increase of the sum-throughput is mainly contributed by the
UEs near the BS. Since the fair-throughput mainly depends R EFERENCES
on the UEs having worse channel qualities, it may not be
improved a lot by increasing the transmit power PBS of [1] W. Ejaz, M. Naeem, A. Shahid, A. Anpalagan, and M. Jo, “Efficient
energy management for the Internet of Things in smart cities,” IEEE
the BS. Commun. Mag., vol. 55, no. 1, pp. 84–91, Jan. 2017.
We plot both of the sum-throughput and the fair-throughput [2] F. Zhu, Z. Li, S. Chen, and G. Xiong, “Parallel transportation man-
of the UL transmission against the minimum throughput agement and control system and its applications in building smart
cities,” IEEE Trans. Intell. Transp. Syst., vol. 17, no. 6, pp. 1576–1585,
requirement of the DL transmission in Fig. 6. For simplicity, Jun. 2016.
we set the minimum DL throughput requirement identical for [3] A. Boustani, A. Maiti, S. Y. Jazi, M. Jadliwala, and V. Namboodiri,
all the UEs. Note that if the minimum DL throughput require- “Seer grid: Privacy and utility implications of two-level load prediction
ment falls to zero, our DEIN becomes a typical WPCN. In in smart grids,” IEEE Trans. Parallel Distrib. Syst., vol. 28, no. 2,
pp. 546–557, Feb. 2017.
the WPCN, the DL transmission of the BS does not carry [4] X. Chen, L. Wang, J. Ding, and N. Thomas, “Patient flow scheduling
any requested data. The DL signal is only for transferring the and capacity planning in a smart hospital environment,” IEEE Access,
energy to the UEs. Observe from Fig. 6 that as we increase vol. 4, pp. 135–148, 2016.
[5] P. Xu, H. Mei, L. Ren, and W. Chen, “ViDX: Visual diagnostics of
the minimum DL throughput requirement, both of the sum- assembly line performance in smart factories,” IEEE Trans. Vis. Comput.
throughput and fair-throughput of the UL transmission are Graph., vol. 23, no. 1, pp. 291–300, Jan. 2017.
reduced. We also have an interesting observation that when the [6] M. Hassanalieragh, T. Soyata, A. Nadeau, and G. Sharma, “Ur-SolarCap:
An open source intelligent auto-wakeup solar energy harvesting system
minimum DL throughput requirement is lower than 0.3 bit/Hz, for supercapacitor-based energy buffering,” IEEE Access, vol. 4,
it has little influence on both of the sum-throughput and the pp. 542–557, 2016.
fair-throughput of the UL transmission. The observation indi- [7] D. Porcarelli et al., “Adaptive rectifier driven by power intake predictors
cates that our DEIN can efficiently support the low-rate DL for wind energy harvesting sensor networks,” IEEE J. Emerg. Sel. Topics
Power Electron., vol. 3, no. 2, pp. 471–482, Jun. 2015.
transmission, such as the signaling exchange, while fulfill- [8] S. Ulukus et al., “Energy harvesting wireless communications: A review
ing the wireless charging tasks, without any significant loss of recent advances,” IEEE J. Sel. Areas Commun., vol. 33, no. 3,
of the UEs’ UL transmissions. As the minimum through- pp. 360–381, Mar. 2015.
[9] A. M. Zungeru, L.-M. Ang, S. R. S. Prabaharan, and K. P. Seng,
put requirement of the DL transmission continually increases, “Radio frequency energy harvesting and management for wireless sensor
both of the sum-throughput and the fair-throughput gradually networks,” in Green Mobile Devices and Networks: Energy Optimization
become zero. This is because a large portion of the received and Scavenging Techniques. Boca Raton, FL, USA: CRC Press, 2012,
pp. 341–368.
RF signal of the DL transmission is fully exploited for the
[10] L. R. Varshney, “Transporting information and energy simultaneously,”
information decoder in order to satisfy the harsh DL through- in Proc. IEEE Int. Symp. Inf. Theory, Toronto, ON, Canada, Jul. 2008,
put requirement and hence the UEs cannot harvest sufficient pp. 1612–1616.
energy for supporting their own UL transmissions. As shown [11] B. Koo and D. Park, “Interference alignment and wireless energy transfer
via antenna selection,” IEEE Commun. Lett., vol. 18, no. 4, pp. 548–551,
in Fig. 6, the UL throughput reduces to zero, when the min- Apr. 2014.
imum DL throughput requirement increases to 1.57 (bit/Hz). [12] L. Liu, R. Zhang, and K.-C. Chua, “Wireless information and power
At this moment, the UEs completely sacrifice the function transfer: A dynamic power splitting approach,” IEEE Trans. Commun.,
vol. 61, no. 9, pp. 3990–4001, Sep. 2013.
of the EH in order to achieve the minimum DL throughput
[13] Y. Dong, M. J. Hossain, and J. Cheng, “Joint power control
requirements, which makes our DEIN model a conventional and time switching for SWIPT systems with heterogeneous QoS
wireless IT (WIT) system. If the DL throughput requirement requirements,” IEEE Commun. Lett., vol. 20, no. 2, pp. 328–331,
is higher than 1.57 (bit/Hz), this requirement is beyond the Feb. 2016.
[14] P. Grover and A. Sahai, “Shannon meets Tesla: Wireless information
transmission capability of the DEIN in the current parameter and power transfer,” in Proc. IEEE Int. Symp. Inf. Theory, Austin, TX,
settings. USA, Jun. 2010, pp. 2363–2367.
644 IEEE INTERNET OF THINGS JOURNAL, VOL. 5, NO. 2, APRIL 2018

[15] K. Huang and E. Larsson, “Simultaneous information and power transfer Jie Hu (S’11–M’16) received the B.Eng. and
for broadband wireless systems,” IEEE Trans. Signal Process., vol. 61, M.Sc. degrees from the Beijing University of Posts
no. 23, pp. 5972–5986, Dec. 2013. and Telecommunications, Beijing, China, in 2008
[16] X. Zhou, R. Zhang, and C. K. Ho, “Wireless information and and 2011, respectively, and the Ph.D. degree from
power transfer in multiuser OFDM systems,” in Proc. IEEE Glob. the Faculty of Physical Sciences and Engineering,
Commun. Conf. (GLOBECOM), Atlanta, GA, USA, Dec. 2013, University of Southampton, Southampton, U.K., in
pp. 4092–4097. 2015.
[17] R. Zhang and C. K. Ho, “MIMO broadcasting for simultaneous wire- Since 2016, he has been with the School
less information and power transfer,” IEEE Trans. Wireless Commun., of Communication and Information Engineering,
vol. 12, no. 5, pp. 1989–2001, May 2013. University of Electronic Science and Technology of
[18] H. Ju and R. Zhang, “Throughput maximization in wire- China, Chengdu, China, as a Lecturer. His research
less powered communication networks,” in Proc. IEEE Glob. is funded by the National Natural Science Foundation of China. He is also
Commun. Conf. (GLOBECOM), Atlanta, GA, USA, Dec. 2013, in great partnership with industry such as Huawei, Shenzhen, China, and
pp. 4086–4091. ZTE, Shenzhen. His current interests include wireless communication and
[19] Y. L. Che, L. Duan, and R. Zhang, “Spatial throughput maximiza- networking, such as cognitive radio and cognitive networks, mobile social
tion of wireless powered communication networks,” IEEE J. Sel. Areas networks, data and energy integrated communication networks, and commu-
Commun., vol. 33, no. 8, pp. 1534–1548, Aug. 2015. nication and computation convergence.
[20] H. Ju and R. Zhang, “Optimal resource allocation in full-duplex wireless- Dr. Hu has acted been a member of the Technical Program Committee for
powered communication network,” IEEE Trans. Commun., vol. 62, several prestigious international conferences including Globecom 2016/2017,
no. 10, pp. 3528–3540, Oct. 2014. ICC 2017.
[21] S. Bi, Y. Zeng, and R. Zhang, “Wireless powered communication
networks: An overview,” IEEE Wireless Commun., vol. 23, no. 2,
Qin Yu received the B.S. degree in communica-
pp. 10–18, Apr. 2016. [Online]. Available: http://ieeexplore.ieee.org/
tion engineering from the Chongqing University of
document/7462480/
Posts and Telecommunications, Chongqing, China,
[22] O. Ozel, K. Shahzad, and S. Ulukus, “Optimal energy allocation for
in 1996, and the M.S. and Ph.D. degrees in com-
energy harvesting transmitters with hybrid energy storage and process-
munication and information engineering from the
ing cost,” IEEE Trans. Signal Process., vol. 62, no. 12, pp. 3232–3245,
University of Electronic Science and Technology of
Jun. 2014.
China (UESTC), Chengdu, China, in 2002 and 2006,
[23] J. Park and B. Clerckx, “Joint wireless information and energy
respectively.
transfer with reduced feedback in MIMO interference channels,”
She joined the School of Communication and
IEEE J. Sel. Areas Commun., vol. 33, no. 8, pp. 1563–1577,
Information Engineering, UESTC, in 2007, where
Aug. 2015.
she conducted post-doctoral research in information
[24] W. Sun, E. G. Ström, F. Brännström, and M. R. Gholami, “Random
security with Prof. Z. Qin from 2007 to 2009. Her current research interests
broadcast based distributed consensus clock synchronization for
include wireless networks and information security.
mobile networks,” IEEE Trans. Wireless Commun., vol. 14, no. 6,
pp. 3378–3389, Jun. 2015.
Kun Yang (M’00–SM’07) received the B.Sc.
and M.Sc. degrees from the Computer Science
Department, Jilin University, Changchun, China,
and the Ph.D. degree from the Department of
Electronic and Electrical Engineering, University
College London (UCL), London, U.K.
He was involved with several European Union
research projects with UCL for several years. He
is currently a Chair Professor with the School
of Computer Science and Electronic Engineering,
Kesi Lv received the B.S. degree from the University
University of Essex, Essex, U.K., leading the
of Electronic Science and Technology of China,
Network Convergence Laboratory. He is also an Affiliated Professor with
Chengdu, China, in 2016, where he is currently pur-
the University of Electronic Science and Technology of China, Chengdu,
suing the master’s degree.
China. He manages research projects funded by various sources such as
His current research interests include data and
EPSRC, Swindon, U.K., EU FP7/H2020, and industries. He has authored
energy integrated communication networks and con-
or co-authored over 100 journal papers. His current research interests include
vex optimization.
wireless networks, future Internet technology and network virtualization, and
mobile cloud computing and networking.
Dr. Yang serves on the Editorial Boards of both IEEE and non-IEEE
journals. He has been a fellow of the IET since 2009.