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Energy-efficient data sensing and routing in unreliable energy-harvesting wireless sensor network
Ting Lu1 • Guohua Liu1 • Shan Chang1
Published online: 31 August 2016
� Springer Science+Business Media New York 2016
Abstract Energy-harvesting wireless sensor network
(WSN) is composed of unreliable wireless channels and
resource-constrained nodes which are powered by solar
panels and solar cells. Energy-harvesting WSNs can
provide perpetual data service by harvesting energy from
surrounding environments. Due to the random character-
istics of harvested energy and unreliability of wireless
channel, energy efficiency is one of the main challenging
issues. In this paper, we are concerned with how to decide
the energy used for data sensing and transmission adap-
tively to maximize network utility, and how to route all
the collected data to the sink along energy-efficient paths
to maximize the residual battery energy of nodes. To
solve this problem, we first formulate a heuristic energy-
efficient data sensing and routing problem. Then, unlike
the most existing work that focuses on energy-efficient
data sensing and energy-efficient routing respectively,
energy-efficient data sensing and routing scheme
(EEDSRS) in unreliable energy-harvesting wireless sen-
sor network is developed. EEDSRS takes account of not
only the energy-efficient data sensing but also the energy-
efficient routing. EEDSRS is divided into three steps: (1)
an adaptive exponentially weighted moving average
algorithm to estimate link quality. (2) an distributed
energetic-sustainable data sensing rate allocation algo-
rithm to allocate the energy for data sensing and routing.
According to the allocated energy, the optimal data
sensing rate to maximize the network utility is obtained.
(3) a geographic routing with unreliable link protocol to
route all the collected data to the sink along energy-effi-
cient paths. Finally, extensive simulations to evaluate the
performance of the proposed EEDSRS are performed. The
experimental results demonstrate that the proposed
EEDSRS is very promising and efficient.
Keywords Energy-harvesting sensor network � Energy �Data sensing � Routing � Unreliable links
1 Introduction
Wireless sensor networks (WSNs) are composed of
unreliable wireless channels and resource-constrained
nodes. Energy constraint is the most important problem in
WSNs, because traditional sensor nodes are powered by
batteries with limited capacity. Limited battery capacity
allows WSNs to work only for a period of time. However,
perpetual data service is expected in WSNs. Therefore,
energy problem has restricted the further development of
WSNs [1]. In order to address this problem, heuristic
sensor nodes that have the ability to harvest energy from
surrounding environment by energy scavengers1 are
developed, and energy harvesting technologies are used in
WSNs [2–4]. Rechargeable sensor nodes harvest energy
from surrounding sources such as solar, thermal energy,
light, vibration, and wind. Harvested energy can be stored
in battery when battery level does not exceed the highest
level. The WSN composed of rechargeable sensor nodes
is called as energy-harvesting wireless sensor network
(EH-WSN).& Ting Lu
1 Donghua University, 2999 Renmin Road, Songjiang District,
Shanghai, People’s Republic of China 1 Energy scavengers provide unlimited energy to sensor node
123
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https://doi.org/10.1007/s11276-016-1360-6
Data gathering in WSNs consumes the major part of
energy [5]. Data gathering is divided into two steps: (1)
data sensing, and (2) data transmission (i.e., receiving and
transmitting packets). In order to improve energy effi-
ciency, researchers took account of residual battery energy
and energy consumption in routing protocol design.
Existing work is mainly categorized into two classes [6–8],
i.e., energy-aware routing and geographic routing.
1. Energy-aware routing Over the past few years, energy-
aware routing in traditional WSNs has received
considerable attention by researchers [9–11]. In all of
these work, routing decisions are mainly based on two
metrics: (a) energy consumption for receiving and
transmitting packets, and (b) residual battery energy of
sensor node. The former metric aims to minimize the
total energy consumption, while the latter one aims to
prolong network lifetime. With the development of
energy harvesting technologies, energy-aware routing
protocols in EH-WSN are proposed [12, 13]. Packets
are routed by rechargeable sensor nodes. Path calcu-
lation is based on the global knowledge of network,
which is not desirable in WSNs. In order to address
this problem, Lin et al. [14] proposed a distributed
algorithm. However, the distributed algorithm must
flood the whole network, which will consume more
network resource and reduce network performance
greatly. Thus, more comprehensive study in EH-WSN
is needed to design energy efficient data sensing and
routing scheme.
2. Geographic routing Geographical routing is also called
as position-based routing. The routing decision in
geographic routing is based on location information
which is obtained by location techniques [15, 16], e.g.,
global positioning system (GPS). Location information
is exchanged by neighbor nodes locally. Each node
determines the next hop for a transmitted packet
locally based on the location information of itself,
destination and its one-hop neighbors. Because most
monitoring applications in WSNs require sensor nodes
to know their location information, geographic routing
is quite applicable to WSNs. In addition, per-destina-
tion state and flooding for route establishment are not
required in geographic routing. Thus, geographic
routing has good scalability, which is promising in
WSNs. The most popular research work of geographic
routing is ‘‘greedy’’ geographic routing. ‘‘greedy’’
geographic routing aims to minimize the total number
of transmission hops by forwarding packets to the node
which is geographically close to the destination
[17, 18]. This is an efficient method if the follow
conditions are satisfied: (a) sufficient network density,
(b) accurate localization information, and (c) reliable
links. However, wireless channels are unreliable in
fact, which is not consistent with the condition (c). In
addition, ‘‘greedy’’ geographic routing does consider
the energy constraint on each node. Without consid-
ering the energy constraint will reduce its efficiency
and effectiveness [19]. Researchers proposed energy-
aware geographic routing which took account of either
residual battery energy of node or energy consumption
for receiving and delivering packets [20–24].
Although the aforementioned work took account of the
energy consumption for data transmission and indicated the
importance of energy consumption for data sensing, it
didn’t consider the energy consumption for data sensing in
protocol design. Research work in WSNs [25, 26] pointed
out that the energy consumed by data sensing must be
considered in protocol design to provide perpetual data
service and improve network performance.
How to allocate energy for data sensing and data
transmission according to the harvested energy is a chal-
lenging issue. Generally speaking, the more the collected
data, the better the network monitoring quality. If less
energy is used for data sensing, less data is collected which
results in poor monitoring quality. Conversely, if more
energy is used for data sensing, more data can be collected
and less energy can be used for data transmission. As a
result, not all the collected data can be transmitted to
destinations. Some important information may be lost.
Thus, the energy used for data sensing and data transmis-
sion must be allocated wisely.
In this paper, our objective is to design an energy-effi-
cient data sensing and routing scheme in unreliable EH-
WSN by jointly considering energy consumption for data
sensing and data transmission. In addition, residual battery
energy, harvested energy, limited battery capacity and link
unreliability are considered in protocol design. A com-
prehensive study on link quality estimation, adaptive data
sensing rate allocation, adaptive energy allocation and
energy-efficient routing are conducted. Our contribution is
summarized as follows. Unlike the most existing work that
focused on energy-efficient data sensing and energy-effi-
cient routing respectively, a novel energy-efficient data
sensing and routing (EEDSR) problem that takes account
of energy-efficient data sensing and routing at the
same time in unreliable EH-WSN is formulated. We
propose an energy-efficient data sensing and routing
scheme (EEDSRS) in unreliable EH-WSN, so that EH-
WSN can use the harvested energy wisely for data sensing
and routing. EEDSRS is divided into three steps: (1) an
adaptive exponentially weighted moving average algorithm
(EWMAA) to estimate link quality. (2) a distributed
energetic-sustainable data sensing rate allocation algorithm
(ESDSRAA) to allocate energy for data sensing and
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123
routing. According to the allocated energy, the optimal data
sensing rate is obtained. (3) a geographic routing with
unreliable link (GRUL) protocol to route the collected data
to destination along energy-efficient paths. Extensive
simulations based on real experimental data of harvested
energy are conducted to demonstrate the advantages of
ESDSRAA and GRUL protocol.
The remainder of this paper is organized as follows.
First, the related work is introduced in Sect. 2. Then, the
network model and problem formulation are described in
Sect. 3. EEDSRS is designed in Sect. 4 and the perfor-
mance evaluation of EEDSRS is shown in Sect. 5. Finally,
the conclusion is given in Sect. 6.
2 Related work
We divide the existing work into three parts: (1) energy-
aware routing in traditional WSN, (2) routing in EH-WSN,
and (3) geographic routing. In this section, we introduce
them in detail.
2.1 Energy-aware routing in traditional WSN
Due to energy constraint, it is required to design energy-
aware routing protocols in WSNs. During the past few
decades, energy-aware routing has been the focus of
researchers [27–31]. Energy-aware routing in traditional
WSNs can be classified into two categories: (1) reducing
energy consumption; and (2) prolonging network lifetime.
For example, Toh [27] proposed an energy-aware routing
protocol to minimize transmission energy. Their protocol
ensured that the energy consumption rate is evenly dis-
tributed among nodes. Madan and Lall [28] proposed dis-
tributed routing algorithms to maximize network lifetime.
The network lifetime in their work is defined as the time at
which the first node runs out of its battery energy. They
formulated the network lifetime problem as a linear pro-
gramming problem and designed distributed subgradient
algorithms to solve it. Similarly, Gatzianas and Georgiadis
[29] formulated the network lifetime maximization prob-
lem as a linear programming problem. They prolonged
network lifetime by routing packets to mobile sink.
Because a lot of sensor nodes may stop working due to
environmental impact and hardware failure, the definition
of network lifetime in [28] is not consistent with the actual
situation. Therefore, Karkvandi et al. [30] developed a
scheme to maximize the normalized network lifetime. Liu
et al. [31] proposed routing algorithms to balance energy
consumption among sensor nodes. The cost function in the
algorithm not only took account of the end-to-end energy
consumption but also remaining battery energy.
Although these schemes are efficient in terms of
reducing energy consumption and prolonging network
lifetime, they are difficult to be implemented in a local
algorithm. Because these work did not take account of
nodes’ capability of harvesting energy and random char-
acteristics of environmental energy, the routing schemes in
traditional WSNs cannot be used in EH-WSN directly. In
addition, these work only took account of the energy
consumption for data transmission. The energy consumed
by data sensing is not considered in protocol design, which
will result in performance degradation of these routing
schemes.
2.2 Routing in EH-WSN
Due to the random characteristics of environmental
energy, one of the challenging problems is to design
energy-efficient routing protocols according to harvested
energy. Research work [26, 32–35] focuses on routing
schemes with environmental energy supply to provide
perpetual data service. For example, Fan et al. [26]
developed a centralized algorithm and a distributed
algorithm to calculate the optimal lexicographic data
sensing rate. Liu et al. [32] proposed a distributed
algorithm, i.e., QuickFix, to allocate data sensing rate.
However, the proposed algorithm may lead to battery
outage and overflow problems. In order to solve these
problems, QuickFix with SnapIt algorithm is developed.
Chen et al. [33] proposed a distributed scheme, i.e.,
NetOnline, to maximize throughput. After that, they [34]
developed a low-complexity energy allocation and rout-
ing scheme to maximize system utility. Their
scheme doesn’t require prior knowledge of replenishment
profile. Zhang et al. [35] investigated data gathering
problem taking account of energy consumption for data
sensing and data transmission. First, they developed a
balanced energy allocation scheme (BEAS) to allocate
energy. Then, they proposed a distributed sensing rate
and routing control (DS2RC) algorithm to optimize data
gathering.
The aforementioned work considered time-varying
characteristics of environmental energy in protocol design.
In order to optimize data gathering, these work carefully
allocated the available energy for data sensing and trans-
mission according to the amount of harvested energy.
However, these work didn’t investigated how to route the
collected data to the sink. In addition, the unreliability of
wireless channel is not considered, which is not consistent
with the real situation [36, 37]. Without considering link
unreliability will greatly reduce the performance of these
schemes.
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123
2.3 Geographic routing
Geographic routing is a promising routing technique in
WSNs due to its good scalability. In geographic routing,
the establishment and maintenance of information for
routing path is no longer needed. Each node locally makes
routing decision based on the location information of
itself, its one hop neighbors and destination. The most
famous ‘‘greedy’’ geographic routing [38] routes packets
to the one-hop neighbor which provides the largest posi-
tive advancement to destination. Link unreliability was
not considered in ‘‘greedy’’ geographic routing. This is
not consistent with the real world. In [36], Cerpa et al.
investigated the unreliability of wireless channel and built
a model for it by statistic approach. They pointed out that
‘‘greedy’’ geographic routing has ‘‘weakest link prob-
lem’’. The neighbor nodes which are closer to destination
than current node may have ‘‘low-quality’’ links. ‘‘Low-
quality’’ links lead to a lot of packet loss and packet
retransmissions, which will consume a large amount of
energy. Recently, more studies focus on the geographic
routing problem in unreliable WSNs. For example, Seada
et al. [23] investigated the trade-off between distance and
hop count in geographic routing. In general, the longer the
transmission distance of each hop, the greater the proba-
bility that packets are lost. If routing scheme aims to
minimize the total number of hop counts by maximizing
the transmission distance per hop (as done in ‘‘greedy’’
forwarding scheme), it may consume more energy due to
retransmission. If routing scheme aims to forward packets
to close neighbors which have highly reliable links, only a
small transmission distance may be achieved by each hop
and more hop counts are needed to reach the destination,
which may also result in more energy consumption. How
to make the trade-off between hop counts and transmis-
sion distance is
challenging. Seada pointed out that the expected
packet advancement, i.e., packet reception rateðPRRÞ �advancement , is an optimal routing metric for geographic
routing in unreliable WSNs. In order to make trade-off
between distance and hop count, Lee et al. [39] proposed
a new routing metric, i.e., normalized advance (NADV).
Zamalloa et al. [40] investigated the impact of different
network parameters (e.g., channel and deployment
parameters) on the performance of different routing
strategies with respect to PRR� advancement. In order to
improve energy efficiency, Yu et al. [41] proposed a
geographic and energy aware routing (GEAR) algorithm
which routed packets to destination in energy-efficient
paths. However, their work didn’t consider the unrelia-
bility of wireless channel. Zeng et al. [24] proposed two
protocols, i.e., GREES-L and GREES-M, which took
account of not only lossy links but also random
environmental energy supply in protocol design. How-
ever, the limited capacity of rechargeable battery was not
considered. To the best of our knowledge, the aforemen-
tioned work only considered the energy consumption for
data transmission. The energy consumed by data sensing
is not considered in protocol design.
3 System model and problem formulation
3.1 Network model
We consider an EH-WSN G(V, E) with N ¼ jVj sensor
nodes (including a sink) and M ¼ jEj directional links.
Each sensor node has a unique identifier i , 1� i�N. If
sensor node i is within the transmission range of sensor
node j , there is a link ðj; iÞ 2 E, and sensor node i is called
as the neighbor node of sensor node j . Let NnbðiÞ denotethe set of neighbor nodes of sensor node i. The network is
mainly used in environmental monitoring and habitat
monitoring. All sensor nodes are equipped with the same
omni-directional antennas, solar cells and rechargeable
batteries with limited capacity Bmaxi . The harvested energy
can be stored in battery if the battery level doesn’t exceed
the highest level. We assume that the energy of sink node is
sufficient and not considered in this paper. Each sensor
node transmits information to the sink along a single path.
Let NpðiÞ be the set of sensor nodes in the path from sensor
node i to the sink. NrðiÞ denotes the set of sensor nodes
which use sensor node i as relay node. Note that i 62 NpðiÞand i 62 NrðiÞ. We assume that a time circle consists of T
time slots (T [ 0). In this paper, a time circle is 1 day and
T ¼ 24. Let Bi;t and qi;t denote the residual battery energy
and harvested energy of sensor node i at slot t , respec-
tively. Allocated energy Ai;t represents the energy allowed
to be used for sensor node i at slot t to collect and route
data, t ¼ 1; 2; . . .; T . We assume that each sensor node
knows the position of itself, its one-hop neighbors and
destination by GPS. In monitoring applications, the
assumption is reasonable because sensor nodes are required
to know position information. Sensing rate allocation and
routing decision are made slot by slot according to har-
vested energy. Sensing rate allocation starts at the begin-
ning of each slot. The network uses the media access
control (MAC) protocol that allows retransmission, e.g.,
IEEE 802.11. The acknowledgement (ACK) mechanism
retransmits the lost information, making lossy links appear
reliable to network layer. If packets are routed to where no
neighbor node is closer to destination than current node, a
‘‘communication void’’ happens. We assume that there is
no ‘‘communication void’’ which is not considered in this
paper.
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3.2 Energy consumption mode
We assume that sensing, transmitting and receiving one
unit of message by sensor node i consume energy esi , etxi
and erxi , respectively. Then, the total amount of energy
consumed by sensor node i at slot t for data sensing and
data transmission is given by
etotali;t ¼ ðesi þ etxi Þ � ri;t þ ðerxi þ etxi Þ �X
j2NrðiÞrj;t; ð1Þ
where ri;t is the data sensing rate of sensor node i at slot t .
3.3 Energy harvesting model
Sudevalayam et al. [42] pointed out the amount of energy
harvested in the future is uncontrollable, but can be esti-
mated with high accuracy according to the harvesting
history. Their methods are used in this paper to estimate
qi;t. Unlike the work in [24] which uses a random process
to model the mean energy harvesting rate of sensor nodes,
we use the real experimental data obtained from the
baseline measurement system (BMS) at the National
Renewable Energy Laboratory [43]. The harvesting profile
of solar power from July to November is shown in Fig. 1.
In Fig. 1, the experimental data is based on
37 mm 9 33 mm solar cell. The data of the first day, the
second day, the third day, the fourth day and the fifth day
are the average value of July, August, September, October
and November, respectively. The average amount of har-
vested energy for the 5 days are 258.65, 302.15, 291.81,
293.6 and 208.59 mWh, respectively.
3.4 Problem definition
Given an EH-WSN G(V, E) , let UðiÞ ¼ logðri;tÞ be the
utility function of sensor node i , where ri;t is the data
sensing rate of sensor node i at slot t . The EEDSR problem
in G(V, E) is to maximize the total utility of all nodes
during a time cycle, i.e.,PN
i¼1
PTt¼1 logðri;tÞ, and route all
the collected data to the sink in energy-efficient paths.
4 Protocol and algorithm design
We propose EEDSRS to solve EEDSR problem. EEDSRS
is divided into three steps: (1) EWMAA to estimate link
quality; (2) ESDSRAA to allocate energy for data sensing
and data transmission; (3) GRUL protocol to route all the
collected data to the sink along energy-efficient paths.
Now, we introduce them as follows.
4.1 Link quality estimation
In order to estimate link quality and transmission cost,
wireless extension layer (WEL) [39] is used. WEL is a sub-
layer which is located on the top of MAC layer. The
structure of WEL is shown in Fig. 2. Link state is estimated
by WEL and MAC layer. Information for link state and
transmission is encapsulated in simple primitives which are
sent to the upper layer protocol.
In this paper, we are not interested in the deails of MAC
layer. We assume that IEEE 802.11 is used on MAC layer.
Because IEEE 802.11 retransmits the lost frames to ensure
good packet delivery ratio (PDR) on network layer, we use
frame delivery ratio (FDR) instead of PDR in this paper. In
probe engine, each sensor node periodically probes link
quality. Since probe is broadcast message, IEEE 802.11
does not acknowledge and retransmit it. ‘‘hello’’ message
are broadcasted periodically to exchange information of
neighbor node. Let FDRij denote FDR from sensor node i
to sensor node j , i; j 2 V .
Fig. 1 Average solar power
harvesting profile of
37 mm 9 33 mm solar panels
obtained by BMS from July to
November
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123
Because active probing needs to inject frames into net-
work to estimate FDR, we use the passive probing tech-
nique instead of active probing. The general framework of
passive link estimator is shown in Fig. 3. The passive link
estimator has two inputs: (1) message arrival event denoted
as M , and (2) periodic timer event denoted as T . Message
event provides infrequent input, while timer event provides
synchronous and periodic input. The estimated link quality
based on timer events are more accurate than that based on
message events. According to the minimum data rate
R provided by the protocols on higher layer, link estimator
can infer the minimum number of lost data over a period of
time and compensate accordingly.
Since the exponentially weighted moving average
(EWMA) estimator [44] is passive, simple and memory
efficient, it is used in this paper to estimate the link quality.
There are two events making sensor node j update FDRij.
One is the periodical time event T set by sensor node j , i.e.,
sensor node j updates FDRij every t seconds. The other one
is the message arrival event M that sensor node j receives a
probe message (‘‘hello’’ message) from sensor node i .
The psesudocode of the proposed EWMAA is as follows:
where dFDRij is current estimated value for FDRij, R is the
minimum data rate, numlostestimated is the estimated number of
lost frames, numlostactual is the actual number of lost frames,
MAC Layer
Wireless Extension Layer
Probe Engine Routing Protocl
MAC-specific infomation
Information from probes
Link cost query
/responseProbe
messages
Datapackets
Fig. 2 Wireless extension layer
Estimator
MessageArrival Event (M)
Timer Event (T)
Minimum Data RateConstant R
Estimation
Fig. 3 General framework of passive link estimator
Exponentially Weighted Moving Area Algorithm (EWMAA)
Description: algorithm is executed on sensor node jInput: inputting event I
Output: FDRij
FDRij = 1;numlost
estimated = [(current time − tMlast) × R];if (I is M event){
tMlast = tMcurrent;numlost
actual = seqcurrent − seqlast − 1;seqlast = seqcurrent;l = max(numlost
actual − numlostestimated, 0);
numlostestimated = 0;
FDRij = FDRij × αl+1 + (1 − α);}else if (I is T event){
l = numlostestimated;
FDRij = FDRij × αl;}
616 Wireless Netw (2018) 24:611–625
123
seqcurrent is the sequence number of current frame which is
received successfully, seqlast is the sequence number of last
frame which is received successfully, l is the number of
lost frames compensated into estimator, tMlast is the time
stamp of last M event, tMcurrent is the time stamp of the
current M event, ½�� is an integral function (i.e., ½x� � x. For
example, ½2:3� ¼ 2, ½�2:3� ¼ �3Þ, and a (0\a\1) is a
tuning parameter. If the input event isM event, the message
must be received successfully, and EWMAA sets
tMlast ¼ tMcurrent.
Each sensor node i estimates FDRji by EWMAA. The
measured FDRs of node i are included in probes. Each
neighbor node j of sensor node i obtains the FDRji from
probes sent by sensor node i .
4.2 ESDSRAA
We formulate the ESDSRA problem as a combinatorial
optimization problem which aims to minimize the objec-
tive function shown in Eq. (2).
maxri;t
XN
i¼1
XT
t¼1
UðiÞ: ð2Þ
subject to
Ai;t �Bi;t þ qi;t; 8i; 8t; ð3Þ
Ai;t � etotali;t ; 8i; 8t; ð4Þ
XT
t¼1
Ai;t �Bi;1 þXT
t¼1
qi;t; 8i; ð5Þ
Bi;t þ qi;t � Ai;t �Bmaxi ; 8i; 8t: ð6Þ
Equations (3) and (4) ensure that the allocated energy for
sensor node i at slot t cannot be greater than current
available energy and smaller than the total amount of
energy consumed by node i at slot t . Equation (5) ensures
that the total amount of allocated energy at all slots of
sensor node i cannot be greater than the total amount of
available energy. Bi;1 in Eq. (5) represents the initial bat-
tery energy of sensor node i . Equations (3), (4) and (5)
guarantee the energy sustainability of the network, i.e.,
each sensor node cannot run out its energy and stop
working. Equation (6) ensures that the battery level of
sensor node i will not exceed the highest level, i.e., all the
harvested energy can be stored in battery and sensor node i
will not miss the opportunity to recharge. Because the
objective function ( i.e.,PN
i¼1
PTt¼1 UðiÞ ¼
PNi¼1PT
t¼1 logðri;tÞ ) is strictly concave, it can achieve the pro-
portional fairness of sensing rate [45]. If sensing rate is
determined, the energy used for data sensing and trans-
mission can be determined.
In order to solve ESDSRA problem, ESDSRAA is pro-
posed. First, ESDSRAA allocates the energy allowed to be
used by sensor node i at slot t , i.e., Ai;t. Then, ESDSRAA
decides the optimal sensing rate ri;t according to Ai;t. Some
research work [32] demonstrated that the optimal energy
allocation scheme is qi;t ¼ 1T
PTt¼1 qi;t, if the battery capacity
of sensor node i is large enough to store all the harvested
energy at time slot t . However, qi;t is not the optimal allo-
cation scheme since battery capacity is limited. Let
Ai;t ¼ ð1� biÞ � qi;t þ bi � qi;t; ð7Þ
where 0� bi � 1 is a tuning parameter. The proposed
ESDSRAA is as follows:
Energetic-Sustainable Data Sensing Rate Allocation Algorithm(ESDSRAA)
Step 1. Compute the average energy harvesting rate ρi,t of sensor node i,i = 1, 2, . . . , N, t = 1, 2, . . . , T .
Step 2. Compute βi using tuning parameter allocation algorithm (TPAA),i = 1, 2, . . . , N .
Step 3. Compute Ai,t using Eq.(7), i = 1, 2, . . . , N, t = 1, 2, . . . , T .Step 4. Compute ri,t based on Ai,t using sensing rate allocation algorithm (SRAA).
Wireless Netw (2018) 24:611–625 617
123
The TPAA used in ESDSRAA is as follows:
Tuning Parameter Allocation Algorithm (TPAA)
for (each sensor node i, i = 1, 2, . . . , N){
ρi,t = 1T
Tt=1 ρi,t;
βi = 0.5;}for (each sensor node i, i = 1, 2, . . . , N){
for (each slot t, t = 1, 2, . . . , T ){
Ai,t = max(0, min(Bi,t + ρi,t, (1 − βi)ρi,t + βiρi,t));oi,t = Bi,t + ρi,t − Ai,t − Bmax
i ;Bi,t+1 = min(Bi,t + ρi,t − Ai,t, B
maxi );
compute βi = max(0,min(1, βi +max{ oi,t
ρi,t, t = 1, 2, . . . , T}));
until one of the two conditions stated as follows is satisfied:(1) max{oi,t, t = 1, 2, . . . , T} = 0;(2) max{oi,t, t = 1, 2, . . . , T} < 0 while βi = 0;end compute
}}return βi, i = 1, 2, . . . , N
In TPAA, if the battery level of sensor node i at slot t
doesn’t exceed the highest level, oi;t � 0 (8i, 8t). Thus,maxfoi;tqi;t
; t ¼ 1; . . .; Tg� 0.
1. If oi;t\0 (8i), we know that maxfoi;tqi;t; t ¼ 1; . . .; Tg
\0. The negative value of maxfoi;tqi;t; t ¼ 1; . . .; Tg will
lead to bi ¼ 0 eventually. Therefore, when bi ¼ 0,
TPAA stops running and finds the desirable bi.2. If oi;t ¼ 0 (8i), we know that maxfoi;tqi;t
; t ¼ 1; . . .; Tg¼ 0. There is no change on bi for each iteration. TPAA
stops running and finds the desirable bi.3. If there are some oi;t ¼ 0 and some oi;t\0 (8i), we
know that maxfoi;tqi;t; t ¼ 1; . . .; Tg ¼ 0. This situation is
similar to situation (2).
From above analysis, it is obvious that the two termination
conditions in TPAA ensure Eq. (6). In TPAA, Ai;t ¼maxð0; minðBi;t þ qi;t; ð1� biÞ � qi;t þ bi � qi;tÞÞ ensures
Eq. (3), i.e., Ai;t �Bi;t þ qi;t. From Eq. (3), we can deduce
that
XT
t¼1
Ai;t �XT
t¼1
ðBi;t þ qi;tÞ; 8i 2 N: ð8Þ
Since
XT
t¼1
ðBi;t þ qi;tÞ ¼XT
t¼1
Bi;t þXT
t¼1
qi;t �Bi;1 þXT
t¼1
qi;t: ð9Þ
We can get thatPT
t¼1 Ai;t �Bi;1 þPT
t¼1 qi;t; 8i. Therefore,Eq. (5) is satisfied.
When the allocated energy for each sensor node at each
slot is obtained by TPAA, the ESDSRA problem can be
simplified as follows:
maxri;t
XN
i¼1
XT
t¼1
logðri;tÞ; ð10Þ
subject to
Ai;t � etotali;t ; 8i; 8t: ð11Þ
In order to design a distributed algorithm, the theory of
dual decomposition [46] is used. The Lagrangian of the
problem described in Eq. (10) is defined as
Lðai;tÞ ¼maxri;t
XN
i¼1
XT
t¼1
logðri;tÞ�
þ ai;tðAi;t � ðesi þ etxi Þ � ri;t
� ðetxi þ erxi Þ �X
j2NrðiÞrj;tÞ
):
ð12Þ
where ai;t � 0 is the Lagrangian multiplier of sensor node i
at slot t with respect to the constraint shown in Eq. (11).
The dual problem shown in Eq. (10) can be written as
follows:
minai;t
Lðai;tÞ: ð13Þ
618 Wireless Netw (2018) 24:611–625
123
Then, sub-gradient method updates Lagrangian multiplier
ai;t iteratively as follows:
ai;tðmþ 1Þ ¼maxð0; ai;tðmÞ � cðAi;t � ðeri þ etxi Þ � ri;t� ðerxi þ etxi Þ
X
j2NrðiÞrj;tÞÞ;
ð14Þ
where m is the iteration number, and c[ 0 is a constant step
size. For a given sensor node i , Eq. (12) can be written as
Lðai;tÞ ¼maxri;t
XN
i¼1
ðlogðri;tÞ þ ai;t � Ai;t � ai;t � ri;t � ðesi þ etxi Þ
� ri;tX
j2NrðiÞaj;t � ðetxi þ erxi ÞÞg:
ð15Þ
Because logðri;tÞ is a strictly concave function, there is a
unique maximizer ri;tðaÞ for all a . When ai;t(i ¼ 1; 2; . . .;N) are scalars, the maximum sensing data rate
can be obtained by Kuhn–Tucker theorem [47] as follows:
r�i;t ¼ maxri;t
X
i
flogðri;tÞ þ ai;t � Ai;t � ai;t � ri;t � ðesi þ etxi Þ
� ri;t �X
j2NrðiÞaj;t � ðerxj þ etxj Þg
¼ maxð0;minðU0�1 � ðvni;t þ vmi;tÞÞÞ;ð16Þ
where
vni;t ¼ai;tðesi þ etxi Þ; ð17Þ
vmi;t ¼X
j2NrðiÞai;tðerxi þ etxi Þ: ð18Þ
Note that U0�1 is the inverse of U0.The distributed SRAA used in ESDSRAA to allocate
optimal sensing rate is as follows:
4.3 GRUL protocol
In GRUL, each sensor node maintains the information of
its one-hop neighbor nodes, e.g., residual battery energy,
sensing rate, energy harvesting rate, location, and link
quality (e.g., FDR). If sensor node i wants to transmit a
message to the sink D , GRUL tries to balance the geo-
graphical advancement per hop and the available energy on
the neighbor nodes of sensor node i .
Because wireless channel is unreliable, the actual
advancing distance (AAD) of a packet transmission at slot t
from sensor node i to sensor node j should consider
FDRijðtÞ and FDRjiðtÞ [48]. Thus, we define the
AAD(i, j, D, t) from sensor node i to sensor node j towards
the direction of destination D as follows:
AADði; j;D; tÞ ¼ progressði; j;D; tÞ � FDRijðtÞ � FDRjiðtÞ;ð19Þ
where D is the destination node, progress(i, j, D, t) is the
progress distance at slot t from sensor node i to sensor node
j towards the direction of destination node D . FDRijðtÞ �FDRjiðtÞ is the inverse of the expected transmission count
(ETC) defined in [49]. The physical meaning of
AAD(i, j, D, t) is the expected progress distance at slot t
towards the destination D per frame transmission. To
illustrate Eq. (19), an example is given in Fig. 4. The
progress(1, 2, 3, 9) is the distance between sensor node 1
and the projection 20 of sensor node 2 . The projection 20 ison the line connecting nodes 1 and 3. progressð1; 2; 3; 9Þ¼ distð1; 20Þ ¼ 5. Thus, AADð1; 2; 3; 9Þ ¼ progressð1; 2;3; 9Þ � FDR12ð9Þ � FDR21ð9Þ ¼ 5� 0:7� 0:3 ¼ 1:05:
Obviously, the total amount of available energy AE(j, t)
on sensor node j at slot t which is allowed to be used for
delivering messages can be computed by
AEðj; tÞ ¼ Bj;t þ qj;t � esj � rj;t; ð20Þ
Sensing Rate Allocation Algorithm (SRAA)
Input: Ai,t, i = 1, 2, . . . , N, t = 1, 2, . . . , TOutput: ri,t, i = 1, 2, . . . , N, t = 1, 2, . . . , T
for (each sensor node i, i = 1, 2, . . . , N){
for (each slot t, t = 1, 2, . . . , T ){
Step 1. sensor node i updates Lagrangian multiplier ai,t locally by Eq. (14).Step 2. sensor node i sends its ai,t to sensor node j, j ∈ Nr(i), collects
and forwards aj,t, j ∈ Np(i).Step 3. sensor node i computes its vn
i,t and vmi,t by Eqs. (17) and (18).
Step 4. sensor node i computes its sensing data rate ri,t by Eq. (16).}
}return ri,t, i = 1, 2, . . . , N, t = 1, 2, . . . , T
Wireless Netw (2018) 24:611–625 619
123
where esj � rj;t is the amount of energy on node j used for
data sensing.
In GRUL protocol, in order to route a packet to desti-
nation D , routing decision on node i at slot t is based on the
transmission cost cost(i, j, D, t) of link (i, j) ,
costði; j;D; tÞ ¼ 1
l �NAADði; j;D; tÞ þ ð1� lÞ �NAEði; j; tÞ ;
j 2 NnbðiÞ;ð21Þ
where 0�l�1 is a regulate weight. NAAD(i, j, D, t) is the
normalized advancing distance from sensor node i to its
one-hop neighbor node j towards the direction of destina-
tion D ,
NAADði; j;D; tÞ ¼ AADði; j;D; tÞmaxfAADði; k;D; tÞ; k 2 NnbðiÞg
:
ð22Þ
NAE(i, j, t) is the normalized available energy,
NAEðj; tÞ ¼ AEðj; tÞmaxfAEðk; tÞ; k 2 NnbðiÞg
: ð23Þ
Minimizing the cost shown in Eq. (21) is equivalent to
maximizing the denominator, which is a linear combina-
tion of two parts. The first part is NAAD(i, j, D, t) .
NAAD(i, j, D, t) represents how much the normalized
progress a packet can make on unreliable link (i, j) at
slot t towards the destination D . Maximizing
NAAD(i, j, D, t) can reduce the number of hop counts from
source to destination, which reduces the energy consump-
tion (when the transmission power is fixed). The second
part NAE(i, j, t) describes the normalized available energy
of sensor node j at slot t which is allowed to be used for
delivering packets. From Eqs. (20) and (23), we can see
that NAE(i, j, t) is a combination of harvested energy,
residual battery energy and energy consumption for sensing
data. Minimizing Eq. (21) can balance the importance of
progress per packet transmission (related to energy con-
sumption and delay) and residual energy (related to load
balancing and network lifetime).
In Eq. (21), if l ¼ 1, GRUL is equivalent to geographic
routing as in [39], which only took account of unreliability
of wireless channel. If l ¼ 0, GRUL is equivalent to
traditional energy aware routing based on residual energy
and energy consumption (as in [31]).
We assume that there is no communication voids. Thus,
there is at least one neighbor node j of sensor node i sat-
isfying AADði; j;D; tÞ[ 0. In this paper, we follows [24],
i.e., we only consider the neighbor node j 2 NnbðiÞ with
FDRijðtÞ[ 0:2 and FDRjiðtÞ[ 0:2 as the candidate next
hop of sensor node i . Small FDR will make a large number
of retransmissions, which will increase not only the energy
consumption but also the inference to other nodes.
5 Performance evaluation
In this section, simulation results are provided to demon-
strate the performance of the proposed ESDSRAA and
GRUL over existing algorithms, the corresponding residual
energy based protocol and ‘‘greedy’’ routing protocol of
GRUL. All the results are obtained by Matlab and Glo-
MoSim library [50]. GloMoSim library is a scalable sim-
ulation environment for wireless networks.
5.1 Simulation setting
The simulation studies involve random networks with 196
stationary nodes which are uniformly distributed in
250 9 250 m2 square region. All sensor nodes have the
same transmission power. Ground reflection (Two-Ray)
path loss model and Ricean fading model [51] for signal
propagation are used to simulate the unrealiable wireless
channel. The reception decision of a packet is based on the
signal-to-noise ratio (SNR) threshold. If the SNR at the
receiver is larger than the pre-defined constant, the packet
is received successfully. Otherwise, the packet is lost or
received with error. The maximum transmission range is
35 m. a in EWMAA is set to 0.9 . IEEE 802.11 is used as
the protocol on MAC layer. The battery capacity Bmaxi of all
nodes are 304 mWh. The initial battery energy Bi;1 of all
nodes are 150 mWh. We adopt the energy consumption
parameters where etxi ¼ 63mW, erxi ¼ 69mW and esi ¼5:4mW (when transmission power is 0 dBm , transmit data
rate is 250 kbps ). We set l in Eq. (21) to 0.5. In our
protocol, ‘‘hello’’ message broadcasts periodically every
50s to exchange neighbor nodes’ information and probe
link quality.
5.2 Results for ESDSRAA
Figure 5 shows the results of energy allocation for a ran-
domly selected sensor node using ESDSRAA, QuickFix
and QuickFix with SnapIt. From Fig. 5, we can see that the
Fig. 4 Example of AAD(i, j, D)
620 Wireless Netw (2018) 24:611–625
123
values of allocated energy computed by QuickFix and
QuickFix with SnapIt are 0 at some time slots, which
means that the sensor node runs out its energy at these time
slots. However, energy allocation computed by ESDSRAA
does not have this problem. Furthermore, the minimal
values of allocated energy computed by ESDSRAA are
very stable, while the values of allocated energy computed
by the other two algorithms are changed with energy har-
vesting rate. This demontrates the advantage of ESDSRAA
in terms of energy allocation.
Figure 6 shows the battery level of the selected sensor
node. If the sensor node uses QuickFix or QuickFix with
SnapIt, the battery level of the sensor node can reach the
highest battery level or the lowest battery level at some
time slots, which means that the sensor node will miss the
opportunity to recharge its battery or run out of energy. If
the sensor node uses ESDSRAA, the battery level of the
sensor node cannot reach the highest battery level and
lowest battery level, which demonstrates that ESDSRAA
can take full advantage of the opportunity to recharge and
avoid running out of battery energy.
Figure 7 shows the total sensing rates of all nodes for
each day. From Fig. 7, we can see that the total sensing rate
of ESDSRAA is the largest one expect for the first day.
This is because sensor nodes use the initial battery energy
irrespective of the harvested energy in the first day.
Obviously, the larger the total amount of sensing rate, the
better the network monitoring quality. Figure 7 demon-
strates that ESDSRAA achieves the best network moni-
toring quality among the three algorithms.
The network utility of each day is shown in Table 1. It
can be seen that ESDSRAA has the largest network utility
expect for the first day. This is because sensor nodes can
use the initial battery energy irrespective of the harvested
energy in the first day. The network utility of QuickFix and
QuickFix with SnapIt is negative infinity in the third, fourth
and fifth days, because the sensing rate of some sensor
nodes is 0 in these days.
Fig. 5 Energy allocation of a
sensor node
Fig. 6 Battery level states
Wireless Netw (2018) 24:611–625 621
123
5.3 Results for GRUL
In order to evaluate the energy efficiency of GRUL pro-
tocol, two metrics are defined as follows:
• Average residual energy This metric calculates the
average residual battery energy of all sensor nodes at
each time slot. It represents the energy efficiency of
routing protocol, when the same number of packets are
transmitted in the network. The more the average
residual battery energy is, the better the energy
efficiency of the protocol is. A better routing protocol
in EH-WSN should provide more residual energy when
the same amount of packets are transmitted in the
network.
• Standard deviation of residual energy This metric
evaluates the standard deviation of residual energy.
This metric indicates how the energy consumption is
distributed among sensor nodes. The small the value of
this metric is, the better the performance of the routing
protocol is in balancing energy consumption.
Figures 8 and 9 show the simulation results. In the two
figures, ‘‘Greedy’’ denotes the geographic routing without
Fig. 7 Total sensing rate of all
nodes for each day
Table 1 Network utility of
each dayAlgorithm Network utility
First day Second day Third day Fourth day Fifth day
QuickFix 3769 4386 �1 �1 �1QuickFix with SnapIt 3886 3985 �1 �1 �1ESDSRAA 3849 4567 4041 4130 3762
Fig. 8 Average residual energy
of all sensor nodes
622 Wireless Netw (2018) 24:611–625
123
energy awareness. ‘‘Greedy’’ protocol only takes account
of the unreliability of wireless channel, which is the
extreme situation of ESDSRAA by setting l ¼ 1 in
Eq. (21). ‘‘Energy aware’’ denotes the energy aware routing
protocol which considers energy consumption and residual
energy of each node. ‘‘energy aware’’ is the extreme situ-
ation of ESDSRAA by setting l ¼ 0 in Eq. (21).
From Figs. 8 and 9, we can see that ESDSRAA is more
energy efficient than ‘‘energy aware’’ routing and
‘‘Greedy’’ routing in terms of having more average residual
energy and smaller standard deviation of residual energy.
This is because ESDSRAA routing takes into account not
only the harvested energy but also the nodes’ residual
energy. In addition, the unreliability of wireless channel is
considered in ESDSRAA, which reduces energy con-
sumption. From Figs. 7 and 8, we can see that ‘‘Greedy’’
routing has the lowest average residual energy and the
largest standard deviation of residual energy. ‘‘Greedy’’
routing has the worst performance on energy efficiency,
because it considers neither the harvested environmental
energy nor residual battery energy in routing decision.
6 Conclusion and future work
In this paper, we have studied the energy-efficient data
sensing and routing problem in unreliable energy-harvest-
ing wireless sensor network (EH-WSN). We proposed an
energy-efficient data sensing and routing
scheme (EEDSRS), so that EH-WSN can use the harvested
energy wisely for data sensing and transmission according
to current available energy to maximize network utility and
route all the collected data to the sink along energy-effi-
cient paths. EEDSRS is divided into three steps: (1)
adaptive exponentially weighted moving average algorithm
(EWMAA) to estimate link quality. (2) distributed ener-
getic-sustainable data sensing rate allocation algorithm
(ESDSRAA) to allocate energy for data sensing and
transmission. According to the allocated energy, the opti-
mal data sensing rate is obtained. (3) geographic routing
with unreliable link (GRUL) protocol to route all the col-
lected data to the destination along energy-efficient paths.
We performed extensive simulations to demonstrate the
efficiency of our protocol by comparing with existing
work, the corresponding energy aware routing protocol and
‘‘Greedy’’ routing protocol of GRUL. Our future work will
focus on investigating the theoretical analysis of our pro-
tocol and the impact of inaccurate solar power harvesting
profile on data sensing and routing in EH-WSN.
Acknowledgments The authors would like to thank the reviewers
and the editors for their valuable suggestions and comments that
helped improve the paper.
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simulation of Ricean fading within a packet simulator. In Pro-
ceedings of IEEE-VTS Fall VTC.
Ting Lu Received the Ph.D.
degree in School of Electronic
Information and Electrical
Engineering, Shanghai Jiaotong
University, China in 2013. Her
research interests includes
resource management, cross-
layer optimization, and dis-
tributed algorithm design in
wireless networks.
Guohua Liu has been a full
professor at Donghua Univer-
sity. His current interests
include wireless networks and
internet of things.
Shan Chang Received the
Ph.D. degree in School of
Electronic Information and
Electrical Engineering, Xian
Jiaotong University, China in
2012. Her research interests
includes participatory sensing,
privacy preservation, data trust-
worthiness and data accuracy in
wireless networks.
Wireless Netw (2018) 24:611–625 625
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